Transcendental Analytic

B 74 Transcendental Doctrine of Elements Second Part Transcendental Logic

Introduction The Idea of a Transcendental Logic

I. On logic in general

Our cognition arises from two fundamental sources of the mind. The first is the reception of representations (the receptivity of impressions); the second is the faculty of cognizing an object through these representations (the spontaneity of concepts). Through the first an object is given to us; through the second it is thought in relation to that representation (as a mere determination of the mind). Intuition and concepts thus constitute the elements of all our cognition, so that neither concepts without an intuition in some way corresponding to them, nor intuition without concepts, can yield a cognition. Both are either pure or empirical: empirical when sensation (which presupposes the actual presence of the object) is contained in them; pure when no sensation is mixed into the representation. Sensation can be called the matter of sensible cognition.

B 75 Hence pure intuition contains solely the form under which something is intuited, and a pure concept solely the form of thinking an object in general. Pure intuitions or concepts alone are possible a priori; empirical ones only a posteriori.

If we call the receptivity of our mind to receive representations insofar as it is affected in some way sensibility, then the faculty of producing representations itself, or the spontaneity of cognition, is the understanding. Our nature is so constituted that intuition can never be other than sensible, that is, it contains only the way we are affected by objects. The faculty of thinking the object of sensible intuition, by contrast, is the understanding. Neither of these properties is to be preferred to the other. Without sensibility no object would be given to us, and without understanding none would be thought. Thoughts without content are empty; intuitions without concepts are blind. It is therefore just as necessary to make our concepts sensible, that is, to add their object in intuition, as to make our intuitions intelligible, that is, to bring them under concepts. Nor can these two faculties or capacities exchange their functions. The understanding can intuit nothing, and the senses can think nothing. Only through their union can cognition arise.

B 76 But we must not on that account mix their contributions; rather, we have strong grounds for carefully separating and distinguishing each from the other. We therefore distinguish the science of the rules of sensibility in general, aesthetic, from the science of the rules of the understanding in general, logic.

Logic can in turn be undertaken with a twofold aim: either as the logic of the general use of the understanding, or of its particular use. The first contains the absolutely necessary rules of thinking, without which no use of the understanding occurs at all; it therefore concerns the understanding without regard to the difference of objects toward which it may be directed. The logic of the particular use of the understanding contains the rules for thinking correctly about a certain kind of object. The former can be called elementary logic, the latter the organon of this or that science. The latter is usually placed before the sciences in the schools as a propaedeutic, although in the course of human reason it is the last thing reached, attained only when the science has long been complete and needs only the finishing touch for its correction and perfection. For one must already know the objects to a fairly high degree.

B 77 One needs this if one wishes to state the rule for bringing about a science of them.

General logic is either pure or applied logic. In the former we abstract from all empirical conditions under which our understanding is exercised: for example, from the influence of the senses, the play of imagination, the laws of memory, the power of habit, inclination, and so on; hence also from the sources of prejudices, indeed from all causes in general from which certain cognitions may arise in us or be foisted upon us. For these concern the understanding merely under certain circumstances of its application, and experience is required to know them. A general but pure logic therefore deals solely with a priori principles and is a canon of the understanding and reason, but only with regard to the formal aspect of their use, whatever the content may be, empirical or transcendental. General logic is called applied, however, when it is directed to the rules for using the understanding under the subjective empirical conditions psychology teaches us. It therefore has empirical principles, although it is general insofar as it concerns the use of the understanding without distinction of objects. For that reason it is not a canon of the understanding in general.

B 78 Nor is it an organon of particular sciences, but solely a cathartic for ordinary understanding.

In general logic, therefore, the part that is to constitute the pure doctrine of reason must be entirely separated from the part constituting applied (though still general) logic. The former alone is properly science, though brief and dry, as the scholarly presentation of an elementary doctrine of the understanding requires. In this, then, logicians must always keep two rules in view.

1 As general logic it abstracts from all content of the understanding’s cognition and from the difference of its objects, and deals with nothing but the mere form of thinking.

2 As pure logic it has no empirical principles, and thus draws nothing (as people have sometimes persuaded themselves) from psychology. Psychology therefore has no influence at all on the canon of the understanding. It is a demonstrated doctrine, and everything in it must be certain entirely a priori.

What I call applied logic—contrary to the usual meaning of the term, according to which it is supposed to contain certain exercises for which pure logic gives the rule—is a representation of the understanding and the rules of its necessary use in concreto: namely, under the contingent conditions of the subject that can hinder or promote this use and that are all given only empirically.

B 79 It treats of attention, its hindrances and consequences, the origin of error, the states of doubt, scruple, conviction, and so on. General and pure logic stands to it as pure morality, which contains merely the necessary moral laws of a free will in general, stands to the doctrine of virtue proper. The latter considers these laws under the hindrances of feelings, inclinations, and passions to which human beings are more or less subject, and can never yield a true and demonstrated science, because it requires empirical and psychological principles just as that applied logic does.

II. On transcendental logic

As we have shown, general logic abstracts from all content of cognition, that is, from every relation of cognition to the object, and considers only the logical form in the relation of cognitions to one another, that is, the form of thinking in general. But since there are pure as well as empirical intuitions, as transcendental aesthetic demonstrates, a distinction might also be found between pure and empirical thinking of objects.

B 80 In that case there would be a logic in which one did not abstract from all content of cognition. For a logic containing merely the rules of the pure thinking of an object would exclude all cognitions of empirical content. It would also concern the origin of our cognitions of objects insofar as that origin cannot be ascribed to the objects. General logic, by contrast, has nothing to do with this origin of cognition. Rather, it considers representations, whether originally a priori in ourselves or merely given empirically, only according to the laws under which the understanding uses them in relation to one another when it thinks. It thus treats only of the form of understanding that can be imparted to representations, wherever else they may have originated.

Here I make an observation that extends its influence over all the following considerations and must be kept firmly in view: not every a priori cognition must be called transcendental, but only that through which we cognize that, and how, certain representations (intuitions or concepts) are applied or are possible solely a priori. That is, “transcendental” concerns the possibility of cognition or its use a priori.

B 81 Hence neither space nor any a priori geometrical determination of it is a transcendental representation. Rather, only the cognition that these representations are not of empirical origin at all, and the possibility of how they can nevertheless relate a priori to objects of experience, can be called transcendental. Likewise, the use of space concerning objects in general would also be transcendental; but if it is restricted solely to objects of the senses, it is called empirical. The distinction between the transcendental and the empirical therefore belongs only to the critique of cognitions and does not concern their relation to their object.

In the expectation, then, that there may perhaps be concepts that relate a priori to objects, not as pure or sensible intuitions but merely as acts of pure thinking, and that are thus concepts of neither empirical nor aesthetic origin, we form in advance the idea of a science of the cognition of pure understanding and reason through which we think objects wholly a priori. A science that determined the origin, scope, and objective validity of such cognitions would have to be called transcendental logic. For it deals only with the laws of understanding and reason.

B 82 It does so solely insofar as it is related a priori to objects, and not, like general logic, to empirical as well as pure cognitions of reason without distinction.

III. On the division of general logic into analytic and dialectic

The old and famous question with which people imagined they could drive logicians into a corner, seeking to force them either to be caught in a wretched evasion or to confess their ignorance and thus the vanity of their entire art, is this: What is truth? The nominal explanation of truth, namely that it is the agreement of cognition with its object, is granted and presupposed here. But what is demanded is to know the universal and secure criterion of the truth of every cognition.

It is already a great and necessary proof of prudence or insight to know what one ought reasonably to ask. For if the question is in itself absurd and calls for needless answers, then, besides shaming the person who raises it, it sometimes has the further disadvantage of leading an unwary listener into absurd answers.

B 83 It then presents the ridiculous spectacle that one person (as the ancients said) milks a male goat while the other holds a sieve beneath it.

If truth consists in the agreement of a cognition with its object, this object must thereby be distinguished from others. For a cognition is false if it does not agree with the object to which it is referred, even if it contains something that could well hold of other objects. Now a universal criterion of truth would be one valid for all cognitions without distinction of their objects. But it is clear that, since in such a criterion we abstract from all content of cognition (its relation to its object), while truth concerns precisely this content, it is quite impossible and absurd to ask for a mark of the truth of this content of cognitions. Hence a sufficient and yet at the same time universal mark of truth cannot possibly be given. Since we have already called the content of a cognition its matter, we must say: no universal mark of the truth of cognition as regards its matter can be demanded, because this is self-contradictory.

But concerning cognition as regards its mere form, setting all content aside, it is equally clear that a logic, insofar as it sets out the universal and necessary rules of the understanding, must present criteria of truth in these very rules.

B 84 For whatever contradicts them is false, because the understanding then conflicts with its universal rules of thinking and hence with itself. Yet these criteria concern only the form of truth, that is, of thinking in general, and are to that extent entirely correct but not sufficient. For although a cognition may conform completely to logical form, that is, not contradict itself, it can nevertheless still contradict the object. Thus the merely logical criterion of truth, namely the agreement of a cognition with the universal and formal laws of understanding and reason, is indeed the conditio sine qua non, hence the negative condition, of all truth. But logic can go no further, and no touchstone of logic can discover an error concerning not the form but the content.

General logic now resolves the entire formal business of understanding and reason into its elements and presents them as principles of all logical assessment of our cognition. This part of logic can therefore be called analytic, and for that very reason is the at least negative touchstone of truth. For we must first test and appraise all cognition as to its form by these rules, before investigating it as to its content to determine whether it contains positive truth with regard to the object.

B 85 But since the mere form of cognition, however much it may agree with logical laws, is far from sufficient to establish material (objective) truth for cognition, no one can venture to judge objects and assert anything about them merely by means of logic without first having acquired well-grounded information about them outside logic. Only then may one attempt their use and connection in a connected whole according to logical laws, or, better still, merely test them by those laws. Nevertheless, there is something so seductive in possessing an art so plausible as that of giving all our cognitions the form of the understanding, even though we may still be very empty and poor as to their content, that general logic, which is merely a canon for judging, has been used as if it were an organon for the actual production of objective assertions, or at least for the illusion of such production, and has thereby in fact been misused. General logic as a supposed organon is called dialectic.

However various the senses in which the ancients used this name for a science or art, its actual use allows us to infer securely that for them it was nothing other than the logic of illusion.

B 86 It was a sophistical art of giving one’s ignorance, indeed even one’s deliberate deceptions, the veneer of truth by imitating the method of thoroughness prescribed by logic in general and using its topics to embellish every empty pretense. Now we may note as a secure and useful warning that general logic, considered as an organon, is always a logic of illusion, that is, dialectical. For it teaches us nothing at all about the content of cognition, but only the formal conditions of agreement with the understanding, which are otherwise entirely indifferent to the objects. The demand to use it as an instrument, an organon, for expanding and enlarging our cognitions, at least in pretense, must therefore amount to nothing but chatter: asserting anything one pleases with some show of plausibility, or disputing it at will.

Such instruction is in no way consistent with the dignity of philosophy. For this reason the name “dialectic” has instead been included in logic as a critique of dialectical illusion, and that is how we wish it to be understood here as well.

B 87 IV. On the division of transcendental logic into transcendental analytic and dialectic

In a transcendental logic we isolate the understanding (just as above, in transcendental aesthetic, we isolated sensibility) and select from our cognition merely that part of thinking that has its origin solely in the understanding. But the use of this pure cognition rests on the condition that objects are given to us in intuition to which it can be applied. For without intuition all our cognition lacks objects and then remains entirely empty. The part of transcendental logic that sets out the elements of pure cognition of the understanding and the principles without which no object can be thought at all is therefore transcendental analytic, and at the same time a logic of truth. For no cognition can contradict it without at the same time losing all content, that is, every relation to any object, and hence all truth. But it is very tempting and seductive to employ these pure cognitions and principles of the understanding alone, even beyond the boundaries of experience. Yet it is experience alone that can supply us with the matter (the objects).

B 88 It is to this matter that those pure concepts of the understanding can be applied. The understanding thus runs the risk of making a material use of the merely formal principles of the pure understanding through empty rationalizing, and of judging indiscriminately about objects that are not given to us and perhaps cannot be given in any way at all. Since transcendental analytic should properly be only a canon for assessing the empirical use of the understanding, it is misused when we allow it to count as the organon of a general and unrestricted use, and venture with the pure understanding alone to judge, assert, and decide synthetically about objects in general. The use of the pure understanding would then be dialectical. The second part of transcendental logic must therefore be a critique of this dialectical illusion and is called transcendental dialectic—not as an art of dogmatically producing such illusion (an unfortunately very common art of various kinds of metaphysical trickery), but as a critique of understanding and reason with regard to their hyperphysical use. Its aim is to expose the false illusion of their groundless presumptions and reduce their claims to discovery and enlargement, which they imagine they can achieve merely through transcendental principles, to the mere assessment of the pure understanding and its protection against sophistical deception.

B 89 Transcendental Logic First Division Transcendental Analytic

This analytic is the analysis of our entire a priori cognition into the elements of pure cognition of the understanding. The following points matter here: 1. That the concepts are pure and not empirical concepts. 2. That they belong not to intuition and sensibility but to thinking and understanding. 3. That they are elementary concepts and are clearly distinguished from those derived from them or composed of them. 4. That their table is complete and they entirely fill the whole field of the pure understanding. Now this completeness of a science cannot reliably be assumed on an estimate of an aggregate brought about merely through trial. It is therefore possible only through an idea of the whole of the understanding’s a priori cognition and through the division, determined by that idea, of the concepts constituting it; hence only through their connection in a system. The pure understanding separates itself completely not only from everything empirical, but even from all sensibility. It is therefore a unity subsisting on its own, sufficient to itself, and incapable of being enlarged by any additions from outside.

B 90 Hence the sum total of its cognition will constitute a system to be comprehended and determined under one idea, whose completeness and articulation can at the same time provide a touchstone of the correctness and genuineness of all the elements of cognition that fit into it. This entire part of transcendental logic consists of two books, one containing the concepts, the other the principles of the pure understanding.

Transcendental Analytic First Book The Analytic of Concepts

By the analytic of concepts I understand not their analysis, or the usual procedure in philosophical investigations of analyzing the content of the concepts that present themselves and bringing them to distinctness. I mean, rather, the as yet little-attempted analysis of the faculty of understanding itself, in order to investigate the possibility of a priori concepts by seeking them in the understanding alone as their birthplace and analyzing its pure use in general.

B 91 For this is the distinctive business of a transcendental philosophy; the rest is the logical treatment of concepts in philosophy in general. We will therefore trace pure concepts back to their first seeds and predispositions in the human understanding, where they lie prepared until, on the occasion of experience, they are finally developed and, freed by that same understanding from the empirical conditions attaching to them, presented in their purity.

The Analytic of Concepts First Chapter On the Guiding Thread for Discovering All Pure Concepts of the Understanding

When a cognitive faculty is brought into play, various concepts emerge on its different occasions of activity, making this faculty known. They can be collected in a more or less exhaustive list, according to whether they have been observed for a longer time or with greater acuteness. By this as it were mechanical procedure, it can never be determined with certainty when the investigation will be complete. Nor do concepts found only as occasion offers reveal themselves in any order or systematic unity.

B 92 In the end they are merely paired according to similarities and arranged in series according to the magnitude of their content, from the simple to the more composite. These series are produced in a manner that is indeed methodical in a certain way, but anything but systematic.

Transcendental philosophy has the advantage, but also the obligation, of seeking its concepts according to a principle, because they arise pure and unmixed from the understanding as an absolute unity and must therefore themselves be connected with one another according to a concept or idea. Such a connection, however, supplies a rule by which the place of each pure concept of the understanding, and the completeness of all of them together, can be determined a priori. Otherwise all this would depend on discretion or chance.

The Transcendental Guiding Thread for Discovering All Pure Concepts of the Understanding First Section On the Logical Use of the Understanding in General

Above, the understanding was explained only negatively, as a nonsensible faculty of cognition. Now, independently of sensibility, we cannot partake in any intuition. The understanding is therefore not a faculty of intuition.

B 93 But apart from intuition there is no other way of cognizing than through concepts. Hence the cognition of every understanding, at least of the human understanding, is cognition through concepts, not intuitive but discursive. All intuitions, as sensible, rest on affections; concepts, therefore, on functions. By function, however, I understand the unity of the act of ordering different representations under a common one. Concepts are thus grounded on the spontaneity of thinking, just as sensible intuitions are grounded on the receptivity of impressions. Now the understanding can make no other use of these concepts than to judge by means of them. Since no representation except intuition relates immediately to the object, a concept is never referred immediately to an object, but to some other representation of it, whether this is an intuition or itself already a concept. Judgment is therefore the mediate cognition of an object, hence the representation of a representation of it. In every judgment there is a concept that holds of many representations and, among these many, comprehends a given representation, which is then referred immediately to the object. Thus, for example, in the judgment “All bodies are alterable,” the concept of the divisible relates to various other concepts; but among these it is here referred especially to the concept of body, and this to certain appearances we encounter.

B 94 These objects are therefore represented mediately through the concept of divisibility. All judgments are accordingly functions of unity among our representations: instead of an immediate representation, a higher one, comprehending this and several others under itself, is used to cognize the object, and many possible cognitions are thereby drawn together into one. But we can reduce all acts of the understanding to judgments, so that the understanding in general can be represented as a faculty of judging. For, according to the above, it is a faculty of thinking. Thinking is cognition through concepts. Concepts, however, as predicates of possible judgments, relate to some representation of an as yet undetermined object. Thus the concept of body signifies something, for example metal, that can be cognized through that concept. It is therefore a concept only because other representations are contained under it, through which it can relate to objects. It is thus the predicate of a possible judgment, for example, “Every metal is a body.” The functions of the understanding can therefore all be found if the functions of unity in judgments can be presented completely. The following section will show that this can quite well be accomplished.

B 95 The Guiding Thread for Discovering All Pure Concepts of the Understanding Second Section

§ 9 On the logical function of the understanding in judgments

If we abstract from all content of a judgment in general and attend only to the mere form of understanding in it, we find that the function of thinking in it can be brought under four headings, each containing three moments under itself. They may conveniently be presented in the following table.

1 Quantity of judgments: universal, particular, singular

2 Quality: affirmative, negative, infinite

3 Relation: categorical, hypothetical, disjunctive

4 Modality: problematic, assertoric, apodictic

B 96 Since this division seems in some, though not essential, respects to depart from the customary technique of logicians, the following safeguards against possible misunderstanding will not be unnecessary.

1 Logicians rightly say that in using judgments in inferences of reason we can treat singular judgments like universal ones. For precisely because they have no extension at all, their predicate cannot be referred merely to some of what is contained under the concept of the subject while being excluded from the rest. It therefore holds of that concept without exception, just as if the concept were a generally valid one with an extension to whose entire range of meaning the predicate applied. If, by contrast, we compare a singular judgment with a generally valid one merely as cognition, as regards magnitude, it stands to the latter as unity to infinity and is thus in itself essentially different from it. Hence, if I appraise a singular judgment (judicium singulare) not merely according to its inner validity but also as cognition in general, according to its magnitude in comparison with other cognitions, it is certainly distinct from generally valid judgments (judicia communia) and deserves a special place in a complete table of the moments of thinking in general.

B 97 Admittedly, it does not deserve one in a logic restricted merely to the use of judgments in relation to one another.

2 Likewise, in a transcendental logic infinite judgments must still be distinguished from affirmative ones, although in general logic they are rightly counted among the latter and form no separate member of the division. For general logic abstracts from all content of the predicate, even when it is negative, and considers only whether it is ascribed to the subject or opposed to it. Transcendental logic, however, also considers the judgment according to the worth or content of this logical affirmation by means of a merely negative predicate, and the gain it provides with regard to cognition as a whole. Had I said of the soul that it is not mortal, I would at least have warded off an error through a negative judgment. Now, through the proposition “The soul is nonmortal,” I have actually affirmed something as regards logical form, by placing the soul within the unlimited extension of beings that do not die. Since the mortal comprises one part of the entire extension of possible beings and the undying the other, my proposition says nothing more than that the soul is one of the infinite multitude of things left over when I remove everything mortal. But this limits the infinite sphere of everything possible only to the extent that the mortal is separated from it.

B 98 The soul is thereby placed in the remaining extension of its space. Despite this exclusion, however, this space still remains infinite, and further parts of it can be removed without the concept of the soul thereby growing in the least or being affirmatively determined. These judgments, infinite as regards logical extension, are thus actually merely limiting as regards the content of cognition in general. To that extent they must not be passed over in the transcendental table of all moments of thinking in judgments, because the function of the understanding exercised here may be important in the field of its pure a priori cognition.

3 All relations of thinking in judgments are those a) of the predicate to the subject, b) of the ground to the consequence, c) of the divided cognition and the collected members of the division to one another. In the first kind of judgment only two concepts are considered in relation to one another; in the second, two judgments; in the third, several judgments. The hypothetical proposition “If there is perfect justice, then the persistently wicked person is punished” contains, properly speaking, the relation of two propositions: “There is perfect justice,” and “The persistently wicked person is punished.” Whether both propositions are true in themselves remains undecided here. Only the consequence is thought through this judgment.

B 99 Finally, the disjunctive judgment contains a relation of two or more propositions to one another, not a relation of consequence but of logical opposition, insofar as the sphere of one excludes that of the other, yet at the same time of community, insofar as together they fill the sphere of the cognition proper. It is thus a relation of the parts of the sphere of a cognition, where the sphere of each part complements that of the other to make up the whole sum of the divided cognition. For example: “The world exists either through blind chance, or through inner necessity, or through an external cause.” Each of these propositions occupies a part of the sphere of possible cognition concerning the existence of a world in general; all together occupy the entire sphere. To remove the cognition from one of these spheres means to place it in one of the others; conversely, to place it in one sphere means to remove it from the others. Thus in a disjunctive judgment there is a certain community of cognitions, consisting in their mutually excluding one another, yet thereby determining the true cognition as a whole, since taken together they constitute the entire content of one single given cognition. And this alone is what I find necessary to note here for the sake of what follows.

4 The modality of judgments is a quite special function of them.

B 100 It is distinguished by contributing nothing to the content of the judgment—for apart from quantity, quality, and relation there is nothing further that constitutes a judgment’s content—but concerning only the value of the copula in relation to thinking in general. Problematic judgments are those in which affirmation or negation is assumed as merely possible (at one’s discretion). Assertoric judgments are those in which it is regarded as actual (true). Apodictic judgments are those in which it is regarded as necessary*. Thus the two judgments whose relation constitutes the hypothetical judgment (antecedens and consequens), and likewise those whose interaction constitutes the disjunctive judgment (members of the division), are all merely problematic. In the example above, the proposition “There is perfect justice” is not asserted assertorically, but is thought only as an optional judgment that someone might possibly adopt; only the consequence is assertoric. Hence such judgments may also be manifestly false and yet, taken problematically, be conditions of cognizing truth. Thus the judgment “The world exists through blind chance” has only problematic significance in the disjunctive judgment: namely, that someone might adopt this proposition for a moment.

B 101 Yet it serves to find the true proposition, just as marking the false path among all those one can take serves to find the right one. A problematic proposition is therefore one expressing only logical possibility, which is not objective: that is, a free choice to let such a proposition count, a merely discretionary admission of it into the understanding. An assertoric proposition speaks of logical actuality or truth, as for instance in a hypothetical inference of reason the antecedens occurs problematically in the major premise and assertorically in the minor, and it indicates that the proposition is already combined with the understanding according to its laws. The apodictic proposition thinks the assertoric one as determined through these laws of the understanding itself, and hence as asserting a priori, and in this way expresses logical necessity. Since everything here is incorporated into the understanding by degrees, so that one first judges something problematically, then perhaps also accepts it assertorically as true, and finally asserts it as inseparably combined with the understanding, that is, as necessary and apodictic, these three functions of modality can also be called so many moments of thinking in general.

* As if thinking in the first case were a function of the understanding, in the second of the power of judgment, and in the third of reason. This observation awaits its clarification only in what follows.

B 102 The Guiding Thread for Discovering All Pure Concepts of the Understanding Third Section

§ 10 On the pure concepts of the understanding, or categories

As has already been said several times, general logic abstracts from all content of cognition and expects representations to be given to it from elsewhere, wherever they may come from, in order first to transform them into concepts, which proceeds analytically. Transcendental logic, by contrast, has lying before it an a priori manifold of sensibility, offered to it by transcendental aesthetic, to provide material for the pure concepts of the understanding. Without this it would have no content at all and would thus be entirely empty. Now space and time contain a manifold of pure a priori intuition, yet they belong to the conditions of our mind’s receptivity under which alone it can receive representations of objects, and which must therefore also always affect the concept of these objects. But the spontaneity of our thinking requires that this manifold first be gone through, taken up, and combined in a certain way in order to make a cognition of it. This act I call synthesis.

B 103 By synthesis in the most general sense, however, I understand the act of adding different representations to one another and comprehending their manifoldness in one cognition. Such a synthesis is pure if the manifold is given not empirically but a priori, as is the manifold in space and time. Before any analysis of our representations, these must first be given, and no concepts can arise analytically as regards their content. But the synthesis of a manifold, whether given empirically or a priori, first produces a cognition that may initially still be crude and confused, and thus requires analysis. Yet synthesis is what properly gathers the elements into cognitions and unites them into a certain content. It is therefore the first thing to which we must attend if we wish to judge the first origin of our cognition.

Synthesis in general is, as we will see later, the mere effect of imagination, a blind though indispensable function of the soul, without which we would have no cognition at all, but of which we are seldom even conscious. Yet bringing this synthesis to concepts is a function belonging to the understanding, through which it first supplies us with cognition in the proper sense.

B 104 Pure synthesis, represented generally, now yields the pure concept of the understanding. By this synthesis, however, I understand one resting on a ground of a priori synthetic unity. Thus our counting (it is especially noticeable with larger numbers) is a synthesis according to concepts, because it proceeds according to a common ground of unity (for example the decimal system). Under this concept, therefore, unity in the synthesis of the manifold becomes necessary.

Different representations are brought analytically under one concept (a business treated by general logic). But transcendental logic teaches how to bring not the representations but the pure synthesis of representations to concepts. The first thing that must be given to us for the a priori cognition of all objects is the manifold of pure intuition. The synthesis of this manifold through imagination is the second, but does not yet yield cognition. The concepts that give unity to this pure synthesis, and consist solely in the representation of this necessary synthetic unity, provide the third element for the cognition of an object encountered, and rest on the understanding.

The same function gives unity to the different representations in a judgment.

B 105 It also gives unity to the mere synthesis of different representations in an intuition. This unity, expressed generally, is called the pure concept of the understanding. Thus the same understanding, through the very same acts by which it brought about the logical form of a judgment in concepts by means of analytic unity, also introduces a transcendental content into its representations by means of the synthetic unity of the manifold in intuition in general. For this reason they are called pure concepts of the understanding, which relate a priori to objects, something general logic cannot accomplish.

In this way there arise exactly as many pure concepts of the understanding relating a priori to objects of intuition in general as there were logical functions in all possible judgments in the preceding table. For the understanding is completely exhausted by those functions, and its capacity is thereby measured in full. Following Aristotle, we will call these concepts categories, since our purpose is originally the same as his, although in its execution it departs very far from his.

B 106 Table of Categories

1 Of Quantity: unity, plurality, totality.

2 Of Quality: reality, negation, limitation.

3 Of Relation: of inherence and subsistence (substantia et accidens); of causality and dependence (cause and effect); of community (interaction between agent and patient).

4 Of Modality: possibility—impossibility, existence—nonbeing, necessity—contingency.

This, then, is the list of all originally pure concepts of synthesis that the understanding contains a priori within itself, and for whose sake alone it is a pure understanding. For through them alone can it understand something in the manifold of intuition, that is, think an object of it. This division is generated systematically from a common principle, namely the faculty of judging, which is the same as the faculty of thinking. It has not arisen rhapsodically from a haphazard search for pure concepts.

B 107 Of the completeness of such concepts we can never be certain, since it is inferred only through induction—not to mention that by this latter method we never understand why precisely these concepts, and not others, reside in the pure understanding. Aristotle’s plan to seek out these fundamental concepts was worthy of an acute thinker. But since he had no principle, he gathered them as he happened upon them, and at first collected ten, which he called categories (predicaments). Later he believed he had discovered five more, which he added under the name of postpredicaments. Yet his table still remained deficient. Moreover, some modi of pure sensibility are found among them (quando, ubi, situs, likewise prius, simul), and also an empirical one (motus), which do not belong at all in this register of the understanding’s ancestry. Or else derived concepts are counted among the original concepts (actio, passio), while some of the latter are entirely missing.

For the sake of these latter concepts, it must also be noted that the categories, as the true fundamental concepts of the pure understanding, also have their equally pure derived concepts, which can by no means be passed over in a complete system of transcendental philosophy. In a merely critical essay, however, I can be content with simply mentioning them.

B 108 Let me call these pure but derived concepts of the understanding the predicables of the pure understanding (in contrast to the predicaments). Once we have the original and primitive concepts, the derived and subordinate ones can easily be added, and the family tree of the pure understanding can be fully drawn. Since my concern here is not the completeness of the system but only of the principles for a system, I reserve this completion for another undertaking. But this aim can be largely attained by taking the ontological textbooks in hand and subordinating, for example, to the category of causality the predicables of force, action, and passion; to that of community those of presence and resistance; and to the predicaments of modality those of coming to be, passing away, alteration, and so on. The categories, combined with the modi of pure sensibility or with one another, yield a great multitude of derived a priori concepts. To note these and, if possible, list them completely would be a useful and not unpleasant effort, but one dispensable here.

In this treatise I deliberately refrain from defining these categories, although I may well be in possession of their definitions. Later I will analyze these concepts to the degree sufficient for the doctrine of method I am developing.

B 109 In a system of pure reason one could rightly demand their definitions of me; but here they would only distract us from the main point of the investigation by provoking doubts and attacks that can quite well be referred to another undertaking without detracting from the essential purpose. Meanwhile, the little I have said about them makes it clearly evident that a complete dictionary, with all the requisite explanations, is not only possible but easy to produce. The compartments are already there; they need only be filled, and a systematic topic such as the present one makes it difficult to miss the place to which each concept properly belongs, while at the same time making it easy to notice any place still empty.

§ 11

Interesting reflections can be made on this table of categories that might perhaps have significant consequences for the scientific form of all rational cognitions. For it is already self-evident that this table is extraordinarily useful, indeed indispensable, in the theoretical part of philosophy for drawing up the complete plan of a whole science insofar as it rests on a priori concepts, and dividing it mathematically according to determinate principles. This is clear from the fact that the table contains all the elementary concepts of the understanding completely.

B 110 It contains, indeed, even the form of a system of them in the human understanding, and consequently gives directions for all the moments of a proposed speculative science, even for their order. I have also given an example of this elsewhere*. Here are some of these observations.

* Metaphysical Foundations of Natural Science.

The first is that this table, which contains four classes of concepts of the understanding, can first be divided into two divisions. The first is directed to objects of intuition, pure as well as empirical; the second to the existence of these objects, either in relation to one another or to the understanding.

I would call the first class that of the mathematical categories, the second that of the dynamical categories. The first class, as we see, has no correlates; these are encountered only in the second class. This difference must surely have a ground in the nature of the understanding.

2nd observation. Each class everywhere has the same number of categories, namely three. This too invites reflection, since otherwise all a priori division through concepts must be a dichotomy. In addition, the third category everywhere arises from the combination of the second with the first in its class.

B 111 Thus totality is nothing other than plurality considered as unity; limitation nothing other than reality combined with negation; community is the causality of a substance in determining another reciprocally; finally, necessity is nothing other than existence given through possibility itself. But we must by no means think that the third category is therefore merely a derived concept and not a fundamental concept of the pure understanding. For combining the first and second to produce the third concept requires a special act of the understanding not identical with the act exercised in the first and second. Thus the concept of a number (which belongs to the category of totality) is not always possible wherever the concepts of multitude and unity are present (for example in the representation of the infinite). Nor, from my combining the concept of a cause and that of a substance, is influence immediately understood: that is, how one substance can become the cause of something in another substance. It is evident from this that a special act of the understanding is required for it; and so with the others.

3rd observation. In the case of a single category, namely that of community, which is found under the third heading, the agreement is not as obvious as in the others.

B 112 This is the agreement with the corresponding form of a disjunctive judgment in the table of logical functions.

To assure ourselves of this agreement, we must note that in all disjunctive judgments the sphere (the multitude of everything contained under the judgment) is represented as a whole divided into parts (the subordinate concepts). Since one cannot be contained under another, they are thought as coordinated with, not subordinated to, one another, so that they determine one another not one-sidedly, as in a series, but reciprocally, as in an aggregate: if one member of the division is posited, all the others are excluded, and conversely.

Now a similar connection is thought in a whole of things, where one is not subordinated as effect to another as the cause of its existence, but is at the same time reciprocally coordinated as cause with regard to the determination of the others. This occurs, for example, in a body whose parts mutually attract and also resist one another. This is an entirely different kind of connection from that encountered in the mere relation of cause to effect, of ground to consequence, in which the consequence does not in turn reciprocally determine the ground, and therefore does not form a whole with it, as the creator of the world does not with the world.

B 113 The understanding observes the same procedure when it represents the sphere of a divided concept as when it thinks a thing as divisible. Just as the members of the division in the first case exclude one another and yet are combined in one sphere, so it represents the parts of the thing in the latter case as each having existence, as substances, independently of the others, yet as combined in one whole.

§ 12

In the transcendental philosophy of the ancients, however, there is yet another chapter containing pure concepts of the understanding that, though not counted among the categories, were nevertheless supposed by them to hold as a priori concepts of objects. In that case they would increase the number of categories, which cannot be. These are set forth in the proposition so renowned among the scholastics: quodlibet ens est unum, verum, bonum. Although the use of this principle proved very meager in its consequences, yielding nothing but tautological propositions, so that even in modern times it is usually included in metaphysics almost only for honor’s sake, a thought that has survived so long, however empty it may seem, always deserves an investigation of its origin. It warrants the conjecture that it has its ground in some rule of the understanding that has merely, as often happens, been misinterpreted.

B 114 These supposedly transcendental predicates of things are nothing other than logical requirements and criteria of all cognition of things in general, and take the categories of quantity—unity, plurality, and totality—as its foundation. But while these categories should properly have been taken materially, as belonging to the possibility of things themselves, they were in fact used only in a formal sense, as belonging to the logical requirement concerning every cognition; yet these criteria of thinking were incautiously made into properties of things in themselves. In every cognition of an object there is, first, unity of the concept, which may be called qualitative unity insofar as by it we think only the unity of the gathering together of the manifold of cognitions, such as the unity of the theme in a play, a speech, or a fable. Second, truth with regard to consequences. The more true consequences follow from a given concept, the more marks there are of its objective reality. This could be called the qualitative plurality of marks belonging to a concept as a common ground (not to be thought in it as a magnitude). Finally, third, perfection, which consists in this plurality’s leading back, conversely, to the unity of the concept and agreeing completely with this concept and no other. This can be called qualitative completeness (totality).

B 115 From this it is evident that these logical criteria of the possibility of cognition in general here transform the three categories of magnitude, in which the unity in the generation of the quantum must be assumed throughout to be homogeneous, solely with regard to the connection even of heterogeneous elements of cognition in one consciousness through the quality of a cognition as principle. Thus the criterion of the possibility of a concept (not of its object) is the definition, in which the unity of the concept, the truth of everything that may be derived immediately from it, and finally the completeness of what has been drawn from it together constitute what is required to restore the whole concept. Likewise, the criterion of a hypothesis is the intelligibility of the assumed explanatory ground, or its unity (without an auxiliary hypothesis); the truth (agreement among themselves and with experience) of the consequences to be derived from it; and finally the completeness of the explanatory ground for them. These consequences point back to nothing more or less than was assumed in the hypothesis, and analytically supply again a posteriori what was thought synthetically a priori, agreeing with it.—Thus the concepts of unity, truth, and perfection do not supplement the transcendental table of categories as if it were deficient.

B 116 Rather, with the relation of these concepts to objects entirely set aside, the procedure with them is merely brought under general logical rules of the agreement of cognition with itself.

Transcendental Analytic Second Chapter On the Deduction of the Pure Concepts of the Understanding

First Section

§ 13 On the principles of a transcendental deduction in general

When jurists speak of entitlements and presumptions, they distinguish in a legal dispute the question of what is lawful (quid juris) from the question concerning the fact (quid facti). In demanding proof of both, they call the first proof, which is to establish the entitlement or legal claim, the deduction. We employ a multitude of empirical concepts without anyone’s objection and consider ourselves entitled, even without a deduction, to ascribe a sense and an imagined meaning to them, because experience is always at hand to prove their objective reality.

B 117 Yet there are also usurped concepts, such as luck and fate, which circulate with almost universal indulgence but are occasionally challenged by the question quid juris. We then find ourselves in no small difficulty over their deduction, since we can cite no clear legal ground, either from experience or from reason, that would make the entitlement to their use evident.

Among the many concepts that constitute the very mixed fabric of human cognition, however, some are also destined for a pure a priori use (wholly independent of all experience), and their entitlement always requires a deduction. For proofs from experience are not sufficient to establish the lawfulness of such a use, yet we must know how these concepts can relate to objects that they do not obtain from any experience. I therefore call the explanation of how concepts can relate a priori to objects their transcendental deduction. I distinguish it from an empirical deduction, which shows how a concept has been acquired through experience and reflection on it, and therefore concerns not its lawfulness but the fact through which its possession arose.

B 118 We already have two kinds of concepts, of entirely different sorts, that nevertheless agree in both relating wholly a priori to objects: the concepts of space and time as forms of sensibility, and the categories as concepts of the understanding. To attempt an empirical deduction of them would be wholly wasted labor. For the distinctive feature of their nature lies precisely in their relating to their objects without having borrowed anything from experience for the representation of those objects. If, then, a deduction of them is necessary, it must always be transcendental.

Nevertheless, for these concepts as for all cognition, we can seek in experience, if not the principle of their possibility, at least the occasional causes of their generation. The impressions of the senses then provide the first occasion for unfolding our entire cognitive power with regard to them and bringing about experience, which contains two very dissimilar elements: a matter for cognition from the senses, and a certain form for ordering it from the inner source of pure intuiting and thinking. These are first brought into activity on the occasion of the former and produce concepts. Such a tracing of the first efforts of our cognitive power has undoubtedly its great use.

B 119 Its aim is to rise from individual perceptions to general concepts, and we owe the first opening of this path to the celebrated Locke. But a deduction of pure a priori concepts is never achieved by it, for such a deduction does not lie on this path at all. As regards their future use, which is to be entirely independent of experience, these concepts must be able to show a birth certificate quite different from that of descent from experiences. This attempted physiological derivation, which cannot properly be called a deduction at all because it concerns a quaestionem facti, I will therefore call the explanation of the possession of a pure cognition. It is thus clear that there can be only a transcendental deduction of these concepts, and by no means an empirical one, and that with regard to pure a priori concepts the latter are nothing but futile attempts, occupying only someone who has not understood the wholly distinctive nature of these cognitions.

But although the only possible kind of deduction of pure a priori cognition is conceded to be the transcendental one, this does not yet make it evident that such a deduction is indispensably necessary. Above, by means of a transcendental deduction, we traced the concepts of space and time to their sources and explained and determined their objective a priori validity.

B 120 Nevertheless, geometry advances securely through entirely a priori cognitions without needing to request from philosophy a certificate attesting the pure and lawful descent of its fundamental concept of space. But in this science the use of the concept also concerns only the outer sensible world, of whose intuition space is the pure form. In this world all geometrical cognition, because it is grounded on a priori intuition, has immediate evidence, and the objects are given a priori in intuition, as regards their form, through cognition itself. With the pure concepts of the understanding, by contrast, there begins an indispensable need to seek a transcendental deduction not only of these concepts themselves but also of space. For these concepts speak of objects not through predicates of intuition and sensibility but through predicates of pure a priori thinking, and thus relate universally to objects without any conditions of sensibility. Since they are not grounded on experience, they also cannot exhibit in a priori intuition an object on which to ground their synthesis before all experience. They therefore not only arouse suspicion concerning the objective validity and limits of their use, but also make that concept of space ambiguous, through their inclination to use it beyond the conditions of sensible intuition.

B 121 For this reason a transcendental deduction of space was also necessary above. The reader must therefore be convinced of the indispensable necessity of such a transcendental deduction before taking a single step in the field of pure reason. Otherwise he proceeds blindly and, after wandering about in many directions, must return to the ignorance from which he started. But he must also clearly grasp the unavoidable difficulty in advance, so as not to complain of obscurity where the matter itself is deeply veiled, or grow weary too soon of clearing away the obstacles. For the issue is either to abandon entirely all claims to insights of pure reason in its favorite field, namely beyond the boundaries of all possible experience, or to bring this critical investigation to completion.

Above, with the concepts of space and time, we were able with little effort to make comprehensible how these, as a priori cognitions, must nevertheless necessarily relate to objects and make synthetic cognition of them possible independently of all experience. For since only by means of such pure forms of sensibility can an object appear to us, that is, be an object of empirical intuition.

B 122 Space and time are therefore pure intuitions containing a priori the condition of the possibility of objects as appearances, and the synthesis in them has objective validity.

The categories of the understanding, by contrast, do not at all represent to us the conditions under which objects are given in intuition. Objects can therefore certainly appear to us without necessarily having to relate to functions of the understanding, so that the understanding would contain their conditions a priori. Here, then, a difficulty emerges that we did not encounter in the field of sensibility: how subjective conditions of thinking should have objective validity, that is, provide conditions of the possibility of all cognition of objects. For appearances can certainly be given in intuition without functions of the understanding. I take, for example, the concept of cause, which signifies a particular kind of synthesis in which, upon something A, something entirely different B is posited according to a rule. It is not clear a priori why appearances should contain anything of this kind. Experiences cannot be cited as proof, for the objective validity of this concept must be capable of being demonstrated a priori. It is therefore doubtful a priori whether such a concept may not be entirely empty and encounter no object anywhere among appearances.

B 123 For that objects of sensible intuition must conform to the formal conditions of sensibility lying a priori in the mind is clear, because otherwise they would not be objects for us. But that they must also, in addition, conform to the conditions the understanding needs for the synthetic insight of thinking is an inference not so easy to grasp. For appearances might conceivably be so constituted that the understanding found them wholly out of keeping with the conditions of its unity, and everything lay in such confusion that, for example, in the succession of appearances nothing presented itself that supplied a rule of synthesis and thus corresponded to the concept of cause and effect. This concept would then be entirely empty, null, and without meaning. Appearances would nevertheless offer objects to our intuition, for intuition in no way requires the functions of thinking.

If someone thought to escape the labor of these investigations by saying that experience continually offers examples of such regularity in appearances as provide sufficient occasion to abstract the concept of cause from them, and thereby at the same time to confirm the objective validity of such a concept, he would fail to notice that the concept of cause cannot arise in this way at all. Rather, it must either be grounded wholly a priori in the understanding or be abandoned entirely as a mere figment of the brain.

B 124 For this concept absolutely requires that something A be such that something else B follows from it necessarily and according to an absolutely universal rule. Appearances certainly supply cases from which a rule is possible according to which something usually happens, but never that the outcome is necessary. Hence the synthesis of cause and effect carries a dignity that cannot be expressed empirically at all: namely, that the effect is not merely added to the cause but posited through it and follows from it. Nor is the strict universality of the rule a property of empirical rules, which through induction can acquire no more than comparative universality, that is, widespread applicability. But the use of pure concepts of the understanding would change entirely if we wished to treat them merely as empirical products.

§ 14 Transition to the transcendental deduction of the categories

There are only two possible cases in which synthetic representation and its objects can coincide, necessarily relate to one another, and as it were meet one another. Either the object alone makes the representation possible, or the representation alone makes the object possible.

B 125 In the first case this relation is only empirical, and the representation is never possible a priori. This is the case with appearances as regards what belongs in them to sensation. In the second case, however, since representation in itself does not produce its object as to its existence—for its causality by means of the will is not at issue here at all—representation is nevertheless then a priori determining with regard to the object if through it alone it is possible to cognize something as an object. There are, however, two conditions under which alone cognition of an object is possible: first, intuition, through which it is given, but only as appearance; second, concept, through which an object corresponding to this intuition is thought. It is clear from the above that the first condition, namely that under which alone objects can be intuited, in fact lies a priori in the mind at the foundation of objects as regards their form. All appearances therefore necessarily agree with this formal condition of sensibility, because only through it can they appear, that is, be empirically intuited and given. The question now is whether a priori concepts also precede as conditions under which alone something, though not intuited, is nevertheless thought as an object in general.

B 126 For then all empirical cognition of objects necessarily conforms to such concepts, because without presupposing them nothing is possible as an object of experience. But all experience contains, besides the intuition of the senses through which something is given, a concept of an object that is given in intuition, or appears. Accordingly, concepts of objects in general will underlie all cognition through experience as a priori conditions. Consequently, the objective validity of the categories as a priori concepts will rest on the fact that through them alone experience is possible as regards the form of thinking. For then they necessarily and a priori relate to objects of experience, because only by their means can any object of experience be thought at all.

The transcendental deduction of all a priori concepts thus has a principle toward which the entire inquiry must be directed: that these concepts must be cognized as a priori conditions of the possibility of experiences, whether of the intuition encountered in experience or of thinking. Concepts that provide the objective ground of the possibility of experience are necessary for that very reason. But unfolding the experience in which they are encountered is not their deduction but their illustration, because in that case they would still be merely contingent.

B 127 Without this original relation to possible experience, in which all objects of cognition occur, their relation to any object could not be comprehended at all.

Lacking this consideration, and finding pure concepts of the understanding in experience, the celebrated Locke also derived them from experience; yet he proceeded so inconsistently that he ventured with them on attempts at cognitions extending far beyond every boundary of experience. David Hume recognized that, to do the latter, these concepts would necessarily have to originate a priori. But he could not explain at all how it was possible that the understanding must think concepts that are not in themselves combined in the understanding as nevertheless necessarily combined in the object. Nor did it occur to him that perhaps the understanding could itself, through these concepts, be the author of the experience in which its objects are encountered. Driven by necessity, he therefore derived them from experience: namely, from a subjective necessity arising through repeated association in experience, which is finally mistaken for an objective one, that is, from habit. But afterward he proceeded very consistently in declaring it impossible to go beyond the boundary of experience with these concepts and the principles they occasion.

B 128 The empirical derivation that both hit upon, however, cannot be reconciled with the actuality of the scientific a priori cognitions we possess, namely pure mathematics and general natural science, and is thus refuted by the fact.

The first of these two celebrated men opened the door wide to fanaticism, because once reason has entitlements on its side, it can no longer be kept within limits by indefinite commendations of moderation. The second surrendered himself entirely to skepticism, once he believed he had discovered so universal a deception of our cognitive faculty, taken for reason. We are now about to attempt whether human reason can be brought safely between these two reefs, assigned determinate boundaries, and yet have the whole field of its purposeful activity kept open for it.

Beforehand I wish only to supply the explanation of the categories. They are concepts of an object in general through which its intuition is regarded as determined with respect to one of the logical functions for judging. Thus the function of the categorical judgment was that of the relation of the subject to the predicate, for example, “All bodies are divisible.” But with regard to the merely logical use of the understanding, the matter remained undetermined.

B 129 It was left open which of the two concepts one wished to give the function of subject and which that of predicate. For one can also say, “Some divisible thing is a body.” Through the category of substance, however, if I bring the concept of a body under it, it is determined that its empirical intuition in experience must always be regarded only as subject, never as mere predicate; and so with all the other categories.

The Deduction of the Pure Concepts of the Understanding Second Section Transcendental Deduction of the Pure Concepts of the Understanding

§ 15 On the possibility of combination in general

The manifold of representations can be given in an intuition that is merely sensible, that is, nothing but receptivity; and the form of this intuition can lie a priori in our faculty of representation without being anything other than the way the subject is affected. But the combination (conjunctio) of a manifold in general can never come to us through the senses, and thus cannot already be contained in the pure form of sensible intuition.

B 130 For it is an act of the spontaneity of the power of representation; and since this, as distinguished from sensibility, must be called understanding, all combination is an act of the understanding, whether we become conscious of it or not, whether it is a combination of the manifold of intuition or of various concepts, and, in the former case, of sensible or nonsensible intuition. We would give this act the general name synthesis, to make clear at the same time that we can represent nothing as combined in the object without having previously combined it ourselves; and that among all representations, combination is the only one that cannot be given through objects but can only be carried out by the subject itself, because it is an act of its self-activity. We readily become aware here that this act must originally be one and equally valid for all combination, and that dissolution, analysis, which seems to be its opposite, nevertheless always presupposes it. For where the understanding has not previously combined anything, it cannot dissolve anything either, since only through it could anything have been given as combined to the power of representation.

But besides the concept of the manifold and of its synthesis, the concept of combination also carries with it that of the manifold’s unity. Combination is the representation of the synthetic unity of the manifold*.

B 131 The representation of this unity therefore cannot arise from combination; rather, by being added to the representation of the manifold, it first makes the concept of combination possible. This unity, which precedes a priori all concepts of combination, is not the category of unity (§ 10). For all categories are grounded on logical functions in judgments, but in these combination, and hence unity of given concepts, is already thought. The category therefore already presupposes combination. We must consequently seek this unity (as qualitative, § 12) still higher: namely, in what itself contains the ground of the unity of different concepts in judgments, and hence of the possibility of the understanding, even in its logical use.

* Whether the representations themselves are identical, and one can therefore be thought analytically through the other, is not considered here. Insofar as the manifold is at issue, consciousness of the one must still always be distinguished from consciousness of the other, and only the synthesis of this (possible) consciousness concerns us here.

§ 16 On the original synthetic unity of apperception

The “I think” must be able to accompany all my representations.

B 132 For otherwise something would be represented in me that could not be thought at all, which amounts to saying that the representation would either be impossible or at least be nothing for me. The representation that can be given before all thinking is called intuition. Thus all the manifold of intuition has a necessary relation to the “I think” in the same subject in which this manifold is encountered. But this representation is an act of spontaneity, that is, it cannot be regarded as belonging to sensibility. I call it pure apperception, to distinguish it from empirical apperception, or also original apperception. For it is the self-consciousness that, in producing the representation “I think,” which must be able to accompany all the others and is one and the same in all consciousness, cannot itself be accompanied by any further representation. I also call its unity the transcendental unity of self-consciousness, to indicate the possibility of a priori cognition from it. For the manifold representations given in a certain intuition would not all be my representations unless they all belonged to one self-consciousness. That is, as my representations, even if I am not conscious of them as such, they must nevertheless necessarily conform to the condition under which alone they can stand together in a universal self-consciousness, since otherwise they would not all belong to me.

B 133 Much can be inferred from this original combination.

Namely, this thoroughgoing identity of the apperception of a manifold given in intuition contains a synthesis of representations and is possible only through the consciousness of this synthesis. For the empirical consciousness accompanying different representations is in itself dispersed and without relation to the identity of the subject. This relation therefore does not yet arise through my accompanying each representation with consciousness, but through my adding one representation to another and being conscious of their synthesis. Thus only because I can combine a manifold of given representations in one consciousness is it possible for me to represent to myself the identity of consciousness in these representations themselves. That is, the analytic unity of apperception is possible only on the presupposition of some synthetic unity*.

B 134 The thought “These representations given in intuition all belong to me” accordingly means the same as “I unite them in one self-consciousness, or can at least unite them in it.” Although this thought is not itself yet the consciousness of the synthesis of representations, it nevertheless presupposes the possibility of that synthesis. That is, only because I can comprehend their manifold in one consciousness do I call them all my representations; otherwise I would have as multicolored and diverse a self as I have representations of which I am conscious. The synthetic unity of the manifold of intuitions, as given a priori, is therefore the ground of the identity of apperception itself, which precedes a priori all my determinate thinking. Combination, however, does not lie in objects and cannot be borrowed from them through perception and thereby first taken up into the understanding.

B 135 It is solely an operation of the understanding, which is itself nothing more than the faculty of combining a priori and bringing the manifold of given representations under the unity of apperception. This principle is the supreme one in the whole of human cognition.

* The analytic unity of consciousness attaches to all common concepts as such. For example, if I think red in general, I thereby represent a constitution that (as a mark) can be encountered in something or combined with other representations. Thus only by virtue of a previously thought possible synthetic unity can I represent analytic unity to myself. A representation that is to be thought as common to different representations is regarded as belonging to ones that also have something different in themselves besides it. Consequently, it must first be thought in synthetic unity with other representations, even if these are only possible, before I can think in it the analytic unity of consciousness that makes it a conceptus communis. And so the synthetic unity of apperception is the highest point to which we must attach every use of the understanding, even the whole of logic and, after it, transcendental philosophy. Indeed, this faculty is the understanding itself.

Now this principle of the necessary unity of apperception is itself indeed identical, hence an analytic proposition; yet it declares a synthesis of the manifold given in an intuition to be necessary, without which that thoroughgoing identity of self-consciousness cannot be thought. For through the I, as a simple representation, no manifold is given. It can be given only in intuition, which is distinct from the I, and thought through combination in one consciousness. An understanding in which all the manifold were given at the same time through self-consciousness would intuit; ours can only think and must seek intuition in the senses. I am therefore conscious of the identical self with regard to the manifold of representations given to me in an intuition, because I call them all my representations, which make up one. But this amounts to my being conscious a priori of a necessary synthesis of them, called the original synthetic unity of apperception.

B 136 All representations given to me stand under it, but they must also be brought under it through a synthesis.

§ 17 The principle of the synthetic unity of apperception is the supreme principle of every use of the understanding

According to transcendental aesthetic, the supreme principle of the possibility of all intuition in relation to sensibility was that all its manifold stands under the formal conditions of space and time. The supreme principle of this same possibility in relation to the understanding is that all the manifold of intuition stands under conditions of the original synthetic unity of apperception*. All manifold representations of intuition stand under the first principle insofar as they are given to us; under the second insofar as they must be capable of being combined in one consciousness.

B 137 For without this nothing can be thought or cognized through them, because the given representations would not have the act of apperception, “I think,” in common and would thus not be comprehended in one self-consciousness.

* Space and time, and all their parts, are intuitions, hence singular representations together with the manifold they contain within themselves (see the Transcendental Aesthetic), and hence not mere concepts. In them we encounter not the same consciousness as contained in many representations, but many representations as contained in one, and consciousness of them; thus they are encountered as composite, and consequently the unity of consciousness is encountered as synthetic, yet original. This singularity of theirs is important in application (see § 25).

Understanding, generally speaking, is the faculty of cognitions. These consist in the determinate relation of given representations to an object. An object, however, is that in whose concept the manifold of a given intuition is united. But all unification of representations requires unity of consciousness in their synthesis. Consequently, the unity of consciousness alone constitutes the relation of representations to an object, hence their objective validity, and consequently their becoming cognitions; and on it, therefore, even the possibility of the understanding rests.

The first pure cognition of the understanding, then, on which its entire remaining use is grounded, and which is at the same time wholly independent of all conditions of sensible intuition, is the principle of the original synthetic unity of apperception. Thus the mere form of outer sensible intuition, space, is not yet cognition at all; it gives only the manifold of intuition a priori for a possible cognition.

B 138 But to cognize anything in space, for example a line, I must draw it, and thus synthetically bring about a determinate combination of the given manifold, so that the unity of this act is at the same time the unity of consciousness (in the concept of a line), and only thereby is an object (a determinate space) cognized. The synthetic unity of consciousness is therefore an objective condition of all cognition, not merely a condition I myself need in order to cognize an object, but one under which every intuition must stand in order to become an object for me. For in any other way, and without this synthesis, the manifold would not unite in one consciousness.

This latter proposition, as stated, is itself analytic, although it makes synthetic unity the condition of all thinking. For it says nothing more than that all my representations in any given intuition must stand under the condition under which alone I can count them, as my representations, as belonging to the identical self, and can thus comprehend them, as synthetically combined in one apperception, through the general expression “I think.”

But this principle is not a principle for every possible understanding in general, only for one through whose pure apperception in the representation “I am” no manifold is yet given at all.

B 139 An understanding through whose self-consciousness the manifold of intuition were given at the same time—an understanding through whose representation the objects of that representation would at the same time exist—would not require a special act of synthesis of the manifold into the unity of consciousness, as the human understanding, which merely thinks and does not intuit, requires. Yet for the human understanding it is unavoidably the first principle, so that it cannot form even the least concept of another possible understanding, whether one that itself intuited or one that, though having a sensible intuition as its foundation, had one of a kind different from intuition in space and time.

§ 18 What the objective unity of self-consciousness is

The transcendental unity of apperception is that through which all the manifold given in an intuition is united in a concept of the object. It is therefore called objective and must be distinguished from the subjective unity of consciousness, which is a determination of inner sense through which that manifold of intuition is empirically given for such a combination. Whether I can be empirically conscious of the manifold as simultaneous or as successive depends on circumstances or empirical conditions.

B 140 Hence the empirical unity of consciousness through the association of representations itself concerns an appearance and is entirely contingent. By contrast, the pure form of intuition in time, merely as intuition in general containing a given manifold, stands under the original unity of consciousness solely through the necessary relation of the manifold of intuition to the one “I think”; thus through the pure synthesis of the understanding, which underlies the empirical synthesis a priori. That unity alone is objectively valid. The empirical unity of apperception, which we are not considering here and which is also derived only from the former under given conditions in concreto, has merely subjective validity. One person combines the representation of a certain word with one thing, another with another thing; and the unity of consciousness in what is empirical is not necessary and universally valid with regard to what is given.

§ 19 The logical form of all judgments consists in the objective unity of apperception of the concepts contained in them

I have never been able to satisfy myself with the explanation logicians give of a judgment in general: it is, as they say, the representation of a relation between two concepts.

B 141 Without quarreling with them here over the defect in this explanation—that at most it fits only categorical, not hypothetical and disjunctive judgments, since these latter contain not a relation of concepts but of judgments themselves—although many troublesome consequences have grown out of this oversight in logic,* I note only that what this relation consists in is not determined here.

* The extensive doctrine of the four syllogistic figures concerns only categorical inferences of reason. Although it is nothing more than an art of slipping immediate inferences (consequentiae immediatiae) under the premises of a pure inference of reason to create the illusion of more kinds of inference than that of the first figure, it would not thereby alone have enjoyed any particular success had it not managed to establish the exclusive authority of categorical judgments as those to which all others must be reducible. This, however, is false according to § 9.

But if I examine more closely the relation of given cognitions in every judgment, and distinguish it, as belonging to the understanding, from the relation according to laws of reproductive imagination, which has only subjective validity, I find that a judgment is nothing other than the way of bringing given cognitions to the objective unity of apperception.

B 142 This is what the relational word “is” in judgments aims at: distinguishing the objective unity of given representations from their subjective unity. For it designates their relation to original apperception and its necessary unity, even if the judgment itself is empirical and hence contingent, for example, “Bodies are heavy.” By this I do not mean that these representations necessarily belong together in empirical intuition, but that they belong together by virtue of the necessary unity of apperception in the synthesis of intuitions: that is, according to principles of the objective determination of all representations insofar as cognition can arise from them. These principles are all derived from the principle of the transcendental unity of apperception. Only in this way does this relation become a judgment, that is, a relation that is objectively valid and sufficiently distinct from a relation of the very same representations in which there would be merely subjective validity, for example according to laws of association. According to the latter I could say only, “When I carry a body, I feel a pressure of weight,” but not, “It, the body, is heavy.” The latter means that these two representations are combined in the object, that is, regardless of the state of the subject, and not merely together in perception, however often it may be repeated.

B 143 § 20 All sensible intuitions stand under the categories, as conditions under which alone their manifold can come together in one consciousness

The manifold given in a sensible intuition necessarily falls under the original synthetic unity of apperception, because through this alone the unity of intuition is possible (§ 17). But the act of the understanding through which the manifold of given representations, whether intuitions or concepts, is brought under one apperception in general is the logical function of judgments (§ 19). Thus all the manifold, insofar as it is given in one empirical intuition, is determined with regard to one of the logical functions of judging, namely that through which it is brought to one consciousness in general. But the categories are nothing other than precisely these functions of judging insofar as the manifold of a given intuition is determined with regard to them (§ 13). Therefore the manifold in a given intuition also necessarily stands under categories.

B 144 § 21 Observation

A manifold contained in an intuition that I call mine is represented through the synthesis of the understanding as belonging to the necessary unity of self-consciousness, and this occurs through the category*. The category thus indicates that the empirical consciousness of a given manifold of one intuition stands under a pure a priori self-consciousness, just as empirical intuition stands under a pure sensible intuition, which likewise occurs a priori.—In the above proposition, then, a beginning has been made toward a deduction of the pure concepts of the understanding. In this deduction, since the categories arise in the understanding alone independently of sensibility, I must still abstract from the way the manifold is given for an empirical intuition, to attend only to the unity added to intuition through the category by the understanding. Later (§ 26) the way empirical intuition is given in sensibility will be taken as the basis.

B 145 It will then be shown that its unity is none other than that which, according to the preceding § 20, the category prescribes to the manifold of a given intuition in general. Only then, through explaining its a priori validity with regard to all objects of our senses, will the aim of the deduction be fully attained.

* The ground of proof rests on the represented unity of intuition through which an object is given. This unity always includes a synthesis of the manifold given for an intuition, and already contains the relation of this manifold to the unity of apperception.

But there is one point from which I could not abstract in the above proof: namely, that the manifold for intuition must be given before the synthesis of the understanding and independently of it; how it is given, however, remains undetermined here. For if I wished to think an understanding that itself intuited, such as a divine understanding that did not represent given objects but through whose representation the objects themselves were at the same time given or produced, the categories would have no meaning at all with regard to such cognition. They are only rules for an understanding whose entire capacity consists in thinking: that is, in the act of bringing the synthesis of the manifold given to it from elsewhere in intuition to the unity of apperception. Such an understanding therefore cognizes nothing at all on its own, but merely combines and orders the material for cognition, the intuition that must be given to it through the object. Yet no further ground can be given for this peculiarity of our understanding.

B 146 It brings about a priori unity of apperception only by means of the categories, and only through precisely this kind and number of them. Nor can any ground be given for why we have precisely these and no other functions of judging, or why time and space are the only forms of our possible intuition.

§ 22 The category has no other use for the cognition of things than its application to objects of experience

To think an object and to cognize an object are therefore not the same. Cognition requires two elements: first, the concept through which an object in general is thought (the category); and second, the intuition through which it is given. For if an intuition corresponding to the concept could not be given at all, the concept would be a thought as regards form, but without any object, and through it no cognition of any thing would be possible. For, so far as I knew, there would be and could be nothing to which my thought could be applied. Now all intuition possible for us is sensible (Aesthetic). Hence, for us, thinking an object in general through a pure concept of the understanding can become cognition only insofar as this concept is related to objects of the senses.

B 147 Sensible intuition is either pure intuition (space and time) or empirical intuition of what is immediately represented as actual in space and time through sensation. By determining the former, we can obtain a priori cognitions of objects (in mathematics), but only as regards their form, as appearances. Whether there can be things that must be intuited in this form still remains undecided. Consequently, all mathematical concepts are not in themselves cognitions, except insofar as we presuppose that there are things that can be presented to us only in conformity with the form of that pure sensible intuition. But things in space and time are given only insofar as they are perceptions (representations accompanied by sensation), hence through empirical representation. Consequently, pure concepts of the understanding, even when applied to a priori intuitions (as in mathematics), yield cognition only insofar as these intuitions, and hence also the concepts of the understanding through them, can be applied to empirical intuitions. Consequently, the categories, even by means of intuition, supply us with no cognition of things except through their possible application to empirical intuition: that is, they serve only for the possibility of empirical cognition. This, however, is called experience. Consequently, the categories have no other use for the cognition of things.

B 148 Their use extends only so far as these are taken as objects of possible experience.

§ 23

The above proposition is of the greatest importance, for it determines the boundaries of the use of pure concepts of the understanding with regard to objects, just as transcendental aesthetic determined the boundaries of the use of the pure form of our sensible intuition. Space and time, as conditions of the possibility of how objects can be given to us, hold no further than for objects of the senses, hence only of experience. Beyond these boundaries they represent nothing at all, for they are only in the senses and have no actuality outside them. Pure concepts of the understanding are free from this restriction and extend to objects of intuition in general, whether the intuition is like ours or not, provided only that it is sensible and not intellectual. But this further extension of concepts beyond our sensible intuition is of no help to us. For they are then empty concepts of objects, about which we cannot judge through them whether the objects are even possible or not: mere forms of thought without objective reality. For we have no intuition at hand to which the synthetic unity of apperception, which alone they contain, could be applied, so that they could thereby determine an object.

B 149 Our sensible and empirical intuition alone can give them sense and meaning.

If, then, an object of nonsensible intuition is assumed as given, we can certainly represent it through all the predicates already contained in the presupposition that nothing belonging to sensible intuition applies to it: that it is not extended or in space; that its duration is not time; that no alteration (succession of determinations in time) is encountered in it; and so on. But it is no proper cognition if I merely indicate how the intuition of the object is not constituted, without being able to say what is contained in it. For then I have not represented the possibility of an object for my pure concept of the understanding at all, since I could give no intuition corresponding to it, but could only say that ours does not apply to it. The chief point here, however, is that not even a single category could be applied to such a something: for example, the concept of a substance, that is, of something that could exist as subject but never as mere predicate. I do not know at all whether there could be any thing corresponding to this determination of thought unless empirical intuition supplied me with the case of its application. But more of this later.

B 150 § 24 On the application of the categories to objects of the senses in general

Pure concepts of the understanding relate, through the understanding alone, to objects of intuition in general, leaving it undetermined whether this is our intuition or some other, though still sensible, intuition. But for that very reason they are mere forms of thought through which no determinate object is yet cognized. The synthesis or combination of the manifold in them related merely to the unity of apperception and was thereby the ground of the possibility of a priori cognition insofar as it rests on the understanding, and hence was not only transcendental but also purely intellectual. But since a certain form of sensible intuition lies a priori at the foundation in us, resting on the receptivity of the capacity for representation (sensibility), the understanding, as spontaneity, can determine inner sense through the manifold of given representations in accordance with the synthetic unity of apperception. It can thus think a priori the synthetic unity of apperception of the manifold of sensible intuition as the condition under which all objects of our (human) intuition must necessarily stand. In this way the categories, as mere forms of thought, acquire objective reality.

B 151 This means application to objects that can be given to us in intuition, but only as appearances; for only of these are we capable of a priori intuition.

This synthesis of the manifold of sensible intuition, which is possible and necessary a priori, can be called figurative (synthesis speciosa), as distinguished from the synthesis that was thought in the mere category with regard to the manifold of an intuition in general and is called combination of the understanding (synthesis intellectualis). Both are transcendental, not merely because they themselves proceed a priori, but also because they ground the possibility of other a priori cognition.

But figurative synthesis, when it relates solely to the original synthetic unity of apperception, that is, this transcendental unity thought in the categories, must be called the transcendental synthesis of imagination, as distinguished from merely intellectual combination. Imagination is the faculty of representing an object in intuition even without its presence. Now, since all our intuition is sensible, imagination belongs to sensibility because of the subjective condition under which alone it can give the concepts of the understanding a corresponding intuition.

B 152 Yet insofar as its synthesis is an exercise of spontaneity, which is determining and not, like sense, merely determinable, and can thus determine sense a priori as regards its form in accordance with the unity of apperception, imagination is to that extent a faculty of determining sensibility a priori. Its synthesis of intuitions, in conformity with the categories, must be the transcendental synthesis of imagination. This is an effect of the understanding on sensibility and its first application, at the same time the ground of all the others, to objects of the intuition possible for us. As figurative, it is distinguished from intellectual synthesis, without any imagination, through the understanding alone. Insofar as imagination is spontaneity, I also sometimes call it productive imagination, thereby distinguishing it from reproductive imagination, whose synthesis is subject solely to empirical laws, namely those of association. The latter therefore contributes nothing to explaining the possibility of a priori cognition, and for that reason belongs not to transcendental philosophy but to psychology.

* * *

Here is the place to make intelligible the paradox that must have struck everyone in the exposition of the form of inner sense (§ 6).

B 153 The paradox is how this sense presents even ourselves to consciousness only as we appear to ourselves, not as we are in ourselves, because we intuit ourselves only as we are inwardly affected. This seems contradictory, since we would have to stand in a passive relation to ourselves. Hence in systems of psychology it is usual to prefer identifying inner sense with the faculty of apperception, which we carefully distinguish.

What determines inner sense is the understanding and its original faculty of combining the manifold of intuition, that is, of bringing it under one apperception (on which even its own possibility rests). Now in us human beings the understanding is not itself a faculty of intuitions, and even if these were given in sensibility, it cannot take them into itself so as to combine, as it were, the manifold of its own intuition. Its synthesis, considered on its own, is therefore nothing other than the unity of the act of which it is conscious as such even without sensibility, but through which it is itself capable of inwardly determining sensibility with regard to the manifold that may be given to it according to the form of sensibility’s intuition. Under the name of a transcendental synthesis of imagination, then, it exercises on the passive subject whose faculty it is that act of which we rightly say that inner sense is affected by it.

B 154 Apperception and its synthetic unity are so far from being identical with inner sense that the former, as the source of all combination, relates to the manifold of intuitions in general under the name of the categories, and to objects in general before all sensible intuition. Inner sense, by contrast, contains the mere form of intuition, but without combination of the manifold in it, hence no determinate intuition at all. Such intuition is possible only through consciousness of the determination of inner sense by the transcendental act of imagination (the synthetic influence of the understanding on inner sense), which I have called figurative synthesis.

We also perceive this in ourselves at all times. We cannot think a line without drawing it in thought, think a circle without describing it, or represent the three dimensions of space without setting three lines perpendicular to one another from the same point. We cannot even represent time without, in drawing a straight line (that is to be the outwardly figurative representation of time), attending merely to the act of synthesizing the manifold through which we successively determine inner sense, and thus to the succession of this determination in it.

B 155 Motion as an act of the subject (not as a determination of an object)*, and hence the synthesis of the manifold in space, first produces even the concept of succession, if we abstract from space and attend merely to the act through which we determine inner sense in conformity with its form. Thus the understanding does not find such a combination of the manifold already in inner sense, but produces it by affecting that sense. But how the I that thinks is distinct from the I that intuits itself, in that I can at least represent another way of intuiting as possible, and yet is identical with this latter I as the same subject; how I can therefore say, “I, as intelligence and thinking subject, cognize myself as a thought object, insofar as I am also given to myself in intuition, only as I appear to myself, like other phenomena, not as I am before the understanding”—this involves neither more nor less difficulty than how I can be an object to myself at all, indeed an object of intuition and inner perceptions.

B 156 That this must nevertheless actually be so can be clearly demonstrated, if space is admitted to be a mere pure form of the appearances of outer senses, from the following. We cannot represent time, which is no object of outer intuition at all, in any other way than under the image of a line insofar as we draw it; without this manner of presentation we could not cognize the unity of its dimension at all. Likewise, we must always derive the determination of temporal length, or even of positions in time, for all inner perceptions from what outer things present to us as changeable. Consequently, we must order the determinations of inner sense as appearances in time in precisely the same way as we order those of outer senses in space. Hence, if we concede of the latter that through them we cognize objects only insofar as we are outwardly affected, we must also grant of inner sense that through it we intuit ourselves only as we are inwardly affected by ourselves: that is, as regards inner intuition, we cognize our own subject only as appearance, not as it is in itself∗∗.

* Motion of an object in space does not belong to a pure science, and hence not to geometry, because that something is movable cannot be cognized a priori, but only through experience. But motion as the describing of a space is a pure act of the successive synthesis of the manifold in outer intuition in general through productive imagination, and belongs not only to geometry but even to transcendental philosophy.

∗∗ I do not see how one can find so many difficulties in inner sense’s being affected by ourselves. Every act of attention can give us an example. In it the understanding always determines inner sense, in conformity with the combination it thinks, to an inner intuition corresponding to the manifold in the synthesis of the understanding. Everyone can perceive in himself how greatly the mind is ordinarily affected by this.

§ 25

B 157 By contrast, in the transcendental synthesis of the manifold of representations in general, and hence in the original synthetic unity of apperception, I am conscious of myself not as I appear to myself, nor as I am in myself, but only that I am. This representation is a thinking, not an intuiting. Now cognition of ourselves requires, besides the act of thinking that brings the manifold of every possible intuition to the unity of apperception, a determinate kind of intuition through which this manifold is given.

B 158 My own existence is therefore indeed not appearance (much less mere illusion), but the determination of my existence* can occur only in conformity with the form of inner sense, according to the particular way the manifold I combine is given in inner intuition. Accordingly, I have no cognition of myself as I am, but merely as I appear to myself. Consciousness of oneself is thus far from being a cognition of oneself, despite all the categories that constitute the thinking of an object in general through combination of the manifold in one apperception. Just as, to cognize an object distinct from me, I still need, besides the thinking of an object in general (in the category), an intuition through which I determine that general concept, so, to cognize myself, I need, besides consciousness or my thinking myself, an intuition of the manifold in me through which I determine this thought. I exist as an intelligence conscious solely of its faculty of combination, but, with regard to the manifold it is to combine, subject to a limiting condition it calls inner sense.

B 159 This intelligence can make that combination intuitable only according to relations of time, which lie entirely outside the proper concepts of the understanding. Hence it can cognize even itself only as, with regard to an intuition that cannot be intellectual and given through the understanding itself, it merely appears to itself, not as it would cognize itself if its intuition were intellectual.

* The “I think” expresses the act of determining my existence. Existence is therefore already given through it, but the way I am to determine it, that is, posit in myself the manifold belonging to it, is not yet thereby given. This requires self-intuition, which has an a priori given form, time, as its foundation; this form is sensible and belongs to the receptivity of what is determinable. Now if I do not have another self-intuition that gives what determines in me, of whose spontaneity alone I am conscious, before the act of determining, just as time gives what is determinable, then I cannot determine my existence as that of a self-active being. Rather, I represent only the spontaneity of my thinking, that is, of determining, and my existence always remains determinable only sensibly, that is, as the existence of an appearance. Yet this spontaneity makes me call myself an intelligence.

§ 26 Transcendental deduction of the universally possible use in experience of the pure concepts of the understanding

In the metaphysical deduction the a priori origin of the categories in general was demonstrated through their complete coincidence with the universal logical functions of thinking; in the transcendental deduction their possibility as a priori cognitions of objects of an intuition in general was presented (§§ 20, 21). We must now explain the possibility of cognizing a priori, through categories, whatever objects may ever come before our senses, not as regards the form of their intuition but according to the laws of their combination; thus, as it were, of prescribing laws to nature and even making nature possible.

B 160 For without this fitness of the categories it would not be evident how everything that may ever come before our senses must stand under laws that arise a priori from the understanding alone.

First I note that by the synthesis of apprehension I understand the composition of the manifold in an empirical intuition through which perception, that is, empirical consciousness of it (as appearance), becomes possible.

In the representations of space and time we have a priori forms of outer as well as inner sensible intuition, and the synthesis of apprehension of the manifold of appearance must always conform to these, because it can itself occur only according to this form. But space and time are represented a priori not merely as forms of sensible intuition, but as intuitions themselves (containing a manifold), hence with the determination of the unity of this manifold in them (see the Transcendental Aesthetic)*.

B 161 Thus even unity of the synthesis of the manifold, outside us or within us, and hence also a combination to which everything to be represented determinately in space or time must conform, is already given a priori together with (not in) these intuitions, as a condition of the synthesis of all apprehension. But this synthetic unity can be none other than the unity of the combination of the manifold of a given intuition in general in an original consciousness, in conformity with the categories, only applied to our sensible intuition. Consequently, all synthesis through which even perception becomes possible stands under the categories. And since experience is cognition through connected perceptions, the categories are conditions of the possibility of experience, and thus also hold a priori of all objects of experience.

* Space represented as an object, as is actually required in geometry, contains more than the mere form of intuition: namely, the comprehension of the manifold given according to the form of sensibility in one intuitive representation. Thus the form of intuition gives merely the manifold, but formal intuition gives unity of the representation. In the Aesthetic I counted this unity merely as belonging to sensibility, only to point out that it precedes all concepts, although it presupposes a synthesis not belonging to the senses, through which, however, all concepts of space and time first become possible. For since through this synthesis, as the understanding determines sensibility, space or time are first given as intuitions, the unity of this intuition belongs a priori to space and time, not to the concept of the understanding (§ 24).

* * *

B 162 Thus, for example, when I make the empirical intuition of a house into a perception by apprehending its manifold, the necessary unity of space and of outer sensible intuition in general lies at the foundation for me, and I as it were trace its shape in conformity with this synthetic unity of the manifold in space. But this very same synthetic unity, if I abstract from the form of space, has its seat in the understanding and is the category of the synthesis of the homogeneous in an intuition in general: that is, the category of magnitude, to which that synthesis of apprehension, that is, perception, must therefore wholly conform*.

* In this way it is proved that the synthesis of apprehension, which is empirical, must necessarily conform to the synthesis of apperception, which is intellectual and contained entirely a priori in the category. It is one and the same spontaneity that introduces combination into the manifold of intuition, there under the name of imagination, here under that of understanding.

When (in another example) I perceive the freezing of water, I apprehend two states (fluidity and solidity) as standing in a temporal relation to one another.

B 163 But in the time that I place at the foundation of the appearance as inner intuition, I necessarily represent synthetic unity of the manifold, without which that relation could not be given as determined in one intuition with regard to temporal succession. Now this synthetic unity, as the a priori condition under which I combine the manifold of an intuition in general, is, if I abstract from the constant form of my inner intuition, time, the category of cause. Through this category, when I apply it to my sensibility, I determine everything that happens in time in general as regards its relation. Thus apprehension in such an event, and hence the event itself as regards possible perception, stands under the concept of the relation of effects and causes, and so in all other cases.

* * *

Categories are concepts that prescribe laws a priori to appearances, hence to nature as the sum total of all appearances (natura materialiter spectata). Now, since the categories are not derived from nature and do not conform to it as their model, for otherwise they would be merely empirical, the question is how we can comprehend that nature must conform to them: that is, how they can determine a priori the combination of the manifold of nature without drawing it from nature. Here is the solution to this riddle.

B 164 Now it is no more surprising that the laws of appearances in nature must agree with the understanding and its a priori form, that is, its faculty of combining the manifold in general, than that appearances themselves must agree with the form of sensible intuition a priori. For laws exist in appearances no more than appearances exist in themselves: laws exist only relative to the subject in which appearances inhere, insofar as it has understanding, just as appearances exist only relative to that same being insofar as it has senses. Things in themselves would necessarily possess their conformity to law even apart from an understanding that cognizes them. But appearances are only representations of things that exist uncognized as regards what they may be in themselves. As mere representations, however, they stand under no law of connection except the one prescribed by the connecting faculty. Now what connects the manifold of sensible intuition is imagination, which depends on the understanding as regards the unity of its intellectual synthesis and on sensibility as regards the manifoldness of apprehension. Since all possible perception depends on the synthesis of apprehension, and this empirical synthesis itself depends on the transcendental synthesis and hence on the categories, all possible perceptions, and thus everything that can ever reach empirical consciousness, that is, all appearances of nature, must stand under the categories as regards their combination.

B 165 Nature, considered merely as nature in general, depends on these as the original ground of its necessary conformity to law (as natura formaliter spectata). But the pure faculty of understanding does not suffice to prescribe a priori laws to appearances through mere categories beyond those laws on which a nature in general rests, as conformity to law of appearances in space and time. Particular laws, because they concern empirically determined appearances, cannot be fully derived from those laws, although they all stand under them. Experience must be added in order to know these particular laws at all. But concerning experience in general, and what can be cognized as an object of it, those a priori laws alone provide instruction.

§ 27 The result of this deduction of the concepts of the understanding

We cannot think an object except through categories; we cannot cognize a thought object except through intuitions corresponding to those concepts. Now all our intuitions are sensible, and this cognition, insofar as its object is given, is empirical. But empirical cognition is experience.

B 166 Consequently, no a priori cognition is possible for us except solely of objects of possible experience*.

* To prevent anyone from taking premature offense at the feared harmful consequences of this proposition, I will merely recall that in thinking the categories are not limited by the conditions of our sensible intuition, but have an unbounded field. Only cognizing what we think, determining the object, requires intuition. Where intuition is lacking, the thought of the object can nevertheless still have its true and useful consequences for the subject’s use of reason. But this use, since it is not always directed to determining the object, hence to cognition, but also to determining the subject and its willing, cannot yet be set out here.

But this cognition, restricted solely to objects of experience, is not on that account all borrowed from experience. Rather, both pure intuitions and pure concepts of the understanding are elements of cognition found in us a priori. Now there are only two ways in which a necessary agreement of experience with the concepts of its objects can be thought: either experience makes these concepts possible, or these concepts make experience possible.

B 167 The first does not hold with regard to the categories (nor to pure sensible intuition), for they are a priori concepts and hence independent of experience; asserting an empirical origin would be a kind of generatio aequivoca. Consequently, only the second remains, as it were a system of the epigenesis of pure reason: namely, that the categories contain, on the side of the understanding, the grounds of the possibility of all experience in general. How they make experience possible, however, and what principles of its possibility they supply in their application to appearances, will be taught more fully by the following chapter on the transcendental use of the power of judgment.

If someone wished to propose a middle way between the two sole ways just named—namely, that the categories were neither self-thought first a priori principles of our cognition nor drawn from experience, but subjective predispositions for thinking implanted in us together with our existence, arranged by our author so that their use agreed precisely with the laws of nature according to which experience proceeds, a kind of preformation system of pure reason—then, apart from the fact that under such a hypothesis no end can be seen to how far one might carry the assumption of predetermined predispositions for future judgments, the following would be decisive against this middle way.

B 168 In such a case the categories would lack the necessity that belongs essentially to their concept. For example, the concept of cause, which asserts the necessity of an outcome under a presupposed condition, would be false if it rested only on an arbitrary subjective necessity implanted in us to combine certain empirical representations according to such a rule of relation. I could not say, “The effect is combined with the cause in the object, that is, necessarily,” but only, “I am so constituted that I cannot think this representation as connected in any other way.” This is precisely what the skeptic most desires. For then all our insight, through the supposed objective validity of our judgments, is nothing but sheer illusion; and there would also be no shortage of people who would not admit to this subjective necessity, which must be felt, in themselves. At least one could not dispute with anyone over what rests merely on the way his subject is organized.

Brief account of this deduction

It is the presentation of the pure concepts of the understanding, and with them of all theoretical a priori cognition, as principles of the possibility of experience. Experience, in turn, is presented as the determination of appearances in space and time in general.

B 169 And this determination, finally, is presented from the principle of the original synthetic unity of apperception, as the form of the understanding in relation to space and time as original forms of sensibility.

* * *

Only up to this point do I consider division into numbered sections necessary, because we have been dealing with elementary concepts. Now that we wish to present their use, the exposition may proceed in a continuous connection without such division.

Transcendental Analytic Second Book

The Analytic of Principles

General logic is built on a plan that coincides precisely with the division of the higher cognitive faculties. These are understanding, power of judgment, and reason. In its analytic, that doctrine therefore treats of concepts, judgments, and inferences, precisely in accordance with the functions and order of those powers of the mind comprehended under the broad name of understanding in general.

B 170 Since this merely formal logic abstracts from all content of cognition, whether pure or empirical, and concerns itself solely with the form of thinking, discursive cognition, in general, it can also include in its analytic part the canon for reason. Reason’s form has its secure prescription, which can be understood a priori through mere analysis of the acts of reason into their moments, without considering the particular nature of the cognition used in them.

Transcendental logic, being restricted to a determinate content, namely solely that of pure a priori cognitions, cannot follow general logic in this division. For it becomes apparent that the transcendental use of reason is not objectively valid at all, and hence does not belong to the logic of truth, the analytic, but as a logic of illusion requires a separate part of the scholarly doctrinal structure under the name of transcendental dialectic.

Understanding and power of judgment accordingly have their canon of objectively valid, hence true, use in transcendental logic, and thus belong to its analytic part. But reason is wholly dialectical in its attempts to establish anything a priori about objects and to enlarge cognition beyond the boundaries of possible experience.

B 171 Its illusory assertions do not fit at all into a canon such as the analytic is to contain.

The analytic of principles will therefore be solely a canon for the power of judgment, teaching it to apply to appearances the concepts of the understanding that contain the condition for a priori rules. For this reason, in taking the proper principles of the understanding as my theme, I will employ the name “doctrine of the power of judgment,” which designates this business more precisely.

Introduction On the Transcendental Power of Judgment in General

If understanding in general is explained as the faculty of rules, then the power of judgment is the faculty of subsuming under rules, that is, of distinguishing whether something stands under a given rule (casus datae legis), or not. General logic contains no precepts for the power of judgment and cannot contain any. For since it abstracts from all content of cognition, nothing remains for it but one business.

B 172 That business is to unfold analytically the mere form of cognition in concepts, judgments, and inferences, and thereby to establish formal rules for every use of the understanding. If it now wished to show generally how one should subsume under these rules, that is, distinguish whether something stands under them or not, this could happen only through another rule. But precisely because it is a rule, this would in turn require instruction for the power of judgment. It thus becomes apparent that, although the understanding is capable of being instructed and equipped through rules, the power of judgment is a special talent that cannot be taught at all, but only practiced. Hence it is also the distinctive element of so-called native wit, whose lack no schooling can make good. For although a school can supply a limited understanding with an abundance of rules borrowed from another’s insight, and as it were graft them onto it, the capacity to use them correctly must nevertheless belong to the pupil himself; and without such a natural gift, no rule prescribed to him for this purpose is safe from misuse*.

B 173 Thus a physician, a judge, or a statesman may have many excellent pathological, legal, or political rules in his head, to the point of being a thorough teacher of them himself, and yet easily go wrong in applying them. This may be either because he lacks natural power of judgment, though not understanding, and can indeed grasp the universal in abstracto but cannot distinguish whether a case in concreto falls under it, or because he has not been sufficiently trained for this judgment through examples and actual business. This is also the one great benefit of examples: they sharpen the power of judgment. For as regards the correctness and precision of the understanding’s insight, examples ordinarily impair it somewhat instead, because they only rarely fulfill the condition of the rule adequately (as casus in terminis). Moreover, they often weaken the effort of the understanding to grasp rules in general, independently of the particular circumstances of experience, as regards their sufficiency, and thus in the end accustom us to using them more as formulas than as principles.

B 174 Examples are therefore the wheeled walking frame of the power of judgment, which anyone lacking its natural talent can never do without.

* Lack of power of judgment is properly what is called stupidity, and there is no remedy at all for such a defect. A dull or limited mind, lacking nothing but the proper degree of understanding and its own concepts, can be very well equipped through learning, even to the point of erudition. But since it then usually also lacks that (the secunda Petri), it is not unusual to encounter very learned men who, in using their science, frequently reveal that never-remediable deficiency.

But although general logic can give the power of judgment no precepts, the situation with transcendental logic is quite different. Indeed, the latter seems to have as its proper business the correction and securing of the power of judgment in the use of the pure understanding through determinate rules. For philosophy seems unnecessary, or rather ill placed, as a doctrine for enlarging the understanding in the field of pure a priori cognitions, since after all previous attempts little or no ground has been gained by it. But as a critique, to prevent the missteps of the power of judgment (lapsus judicii) in using the few pure concepts of the understanding we possess, philosophy is called upon with all its acuteness and art of examination, although its benefit is then merely negative.

Transcendental philosophy, however, has this peculiarity: besides the rule, or rather the universal condition for rules, given in the pure concept of the understanding, it can at the same time indicate a priori the case to which they are to be applied.

B 175 The reason for its advantage in this respect over all other instructive sciences, apart from mathematics, lies precisely in its treating of concepts that are to relate a priori to their objects. Their objective validity therefore cannot be demonstrated a posteriori, for that would leave their distinctive dignity entirely untouched. Rather, it must at the same time set out, in general but sufficient marks, the conditions under which objects can be given in agreement with those concepts; otherwise they would have no content at all and would thus be mere logical forms, not pure concepts of the understanding.

This transcendental doctrine of the power of judgment will now contain two chapters: the first treating of the sensible condition under which alone pure concepts of the understanding can be used, that is, the schematism of the pure understanding; the second, of the synthetic judgments that flow a priori from pure concepts of the understanding under these conditions and underlie all other a priori cognitions, that is, the principles of the pure understanding.

B 176 Transcendental Doctrine of the Power of Judgment (or Analytic of Principles) First Chapter On the Schematism of the Pure Concepts of the Understanding

In every subsumption of an object under a concept, the representation of the former must be homogeneous with the latter: that is, the concept must contain what is represented in the object to be subsumed under it. For this is precisely what the expression means: an object is contained under a concept. Thus the empirical concept of a plate is homogeneous with the pure geometrical concept of a circle, in that the roundness thought in the former can be intuited in the latter.

But pure concepts of the understanding, compared with empirical, indeed with sensible intuitions in general, are entirely heterogeneous and can never be encountered in any intuition. How, then, is the subsumption of the latter under the former, and hence the application of the category to appearances, possible, since no one will say that a category, for example causality, can also be intuited through the senses and is contained in appearance?

B 177 This very natural and important question is properly the reason that makes a transcendental doctrine of the power of judgment necessary: namely, to show how pure concepts of the understanding can possibly be applied to appearances in general. In all other sciences, where the concepts through which the object is thought generally are not so different and heterogeneous from those that represent it in concreto as it is given, no special exposition concerning the application of the former to the latter is necessary.

Now it is clear that there must be a third thing that must be homogeneous on the one hand with the category and on the other with the appearance, making possible the application of the former to the latter. This mediating representation must be pure (without anything empirical) and yet intellectual on the one hand and sensible on the other. Such a representation is the transcendental schema.

The concept of the understanding contains pure synthetic unity of the manifold in general. Time, as the formal condition of the manifold of inner sense, hence of the connection of all representations, contains an a priori manifold in pure intuition. Now a transcendental determination of time is homogeneous with the category (which constitutes its unity) insofar as it is universal and rests on an a priori rule.

B 178 But it is, on the other hand, homogeneous with appearance insofar as time is contained in every empirical representation of the manifold. Hence an application of the category to appearances will be possible by means of the transcendental determination of time, which, as the schema of the concepts of the understanding, mediates the subsumption of appearances under the category.

After what has been shown in the deduction of the categories, I hope no one will hesitate to decide the question whether these pure concepts of the understanding have merely an empirical use or also a transcendental one: that is, whether they relate a priori to appearances solely as conditions of a possible experience, or whether, as conditions of the possibility of things in general, they can be extended to objects in themselves (without any restriction to our sensibility). For there we saw that concepts are entirely impossible and cannot have any meaning unless an object is given either to them themselves or at least to the elements of which they consist; hence they cannot relate to things in themselves (without regard to whether and how these may be given to us) at all. Further, we saw that the only way objects are given to us is the modification of our sensibility.

B 179 Finally, pure a priori concepts, besides the function of the understanding in the category, must also contain a priori formal conditions of sensibility (specifically of inner sense), containing the universal condition under which alone the category can be applied to any object. We will call this formal and pure condition of sensibility, to which the concept of the understanding is restricted in its use, the schema of this concept of the understanding, and the understanding’s procedure with these schemata the schematism of the pure understanding.

In itself the schema is always only a product of imagination. But since the synthesis of imagination aims not at any singular intuition but solely at unity in the determination of sensibility, the schema must nevertheless be distinguished from the image. Thus, if I place five points in a row,..... this is an image of the number five. But if I merely think a number in general, which may be five or a hundred, this thinking is more the representation of a method for representing a multitude, for example a thousand, in an image according to a certain concept than it is this image itself, which in the latter case I could hardly survey and compare with the concept.

B 180 This representation of a general procedure of imagination for providing a concept with its image I call the schema for that concept.

In fact, our pure sensible concepts are grounded not on images of objects but on schemata. No image of a triangle would ever be adequate to the concept of a triangle in general. For it would not attain the universality of the concept, which makes it hold for all triangles, right-angled or oblique-angled, and so on, but would always be restricted to only part of this sphere. The schema of the triangle can exist nowhere but in thought, and signifies a rule of the synthesis of imagination with regard to pure shapes in space. Still less does an object of experience or an image of it ever attain the empirical concept. Rather, the latter always relates immediately to the schema of imagination as a rule for determining our intuition according to a certain general concept. The concept of a dog signifies a rule according to which my imagination can trace the shape of a four-footed animal in general, without being restricted to any one particular shape offered to me by experience, or to any possible image I can present in concreto. This schematism of our understanding with regard to appearances and their mere form is a hidden art in the depths of the human soul. Its true operations we are hardly ever likely to succeed in divining from nature.

B 181 Nor are we likely ever to lay them unveiled before our eyes. We can say only this much: the image is a product of the empirical faculty of productive imagination; the schema of sensible concepts, such as figures in space, is a product and, as it were, a monogram of pure a priori imagination, through which and according to which images first become possible. Yet these images must always be connected with the concept only by means of the schema they designate, and in themselves do not fully coincide with it. By contrast, the schema of a pure concept of the understanding is something that cannot be brought into any image at all. Rather, it is only the pure synthesis according to a rule of unity by concepts in general, which the category expresses. It is a transcendental product of imagination concerning the determination of inner sense in general according to the conditions of its form (time) with regard to all representations insofar as these are to be connected a priori in one concept in conformity with the unity of apperception.

Rather than linger over a dry and tedious analysis of what is required for transcendental schemata of pure concepts of the understanding in general, let us instead present them in the order of the categories and in connection with them.

B 182 The pure image of all magnitudes (quantorum) before outer sense is space; that of all objects of the senses in general, however, is time. But the pure schema of magnitude (quantitatis), as a concept of the understanding is number, a representation comprehending the successive addition of one to one (homogeneous ones). Thus number is nothing other than the unity of the synthesis of the manifold of a homogeneous intuition in general, through my generating time itself in the apprehension of the intuition.

Reality, in the pure concept of the understanding, is what corresponds to a sensation in general; hence that whose concept in itself indicates a being (in time). Negation is that whose concept represents a nonbeing (in time). The opposition of the two thus occurs in the difference of the same time as either filled or empty time. Since time is only the form of intuition, hence of objects as appearances, what corresponds in these to sensation is the transcendental matter of all objects as things in themselves (thinghood, reality). Now every sensation has a degree or magnitude through which it can fill the same time, that is, inner sense with regard to the same representation of an object, more or less, until it ceases in nothing (= 0 = negatio).

B 183 Hence there is a relation and connection, or rather a transition, from reality to negation that represents every reality as a quantum. The schema of a reality, as the quantity of something insofar as it fills time, is precisely this continuous and uniform generation of it in time, as we descend in time from a sensation having a certain degree to its disappearance, or gradually ascend from negation to its magnitude.

The schema of substance is the persistence of the real in time, that is, its representation as a substratum of empirical time-determination in general, which therefore remains while everything else changes. (Time does not elapse; rather, the existence of what is mutable elapses in it. To time, therefore, which is itself unchanging and enduring, there corresponds in appearance what is unchanging in existence, that is, substance. Only by reference to substance can the succession and simultaneity of appearances be determined in time.)

The schema of the cause and of the causality of a thing in general is the real upon which, whenever it is posited at will, something else always follows. It thus consists in the succession of the manifold insofar as this is subject to a rule.

The schema of community (interaction), or of the reciprocal causality of substances with regard to their accidents, is simultaneity.

B 184 This simultaneity is that of the determinations of the one with those of the other, according to a universal rule.

The schema of possibility is the agreement of the synthesis of different representations with the conditions of time in general (for example, since opposites cannot be in one thing simultaneously but only successively), hence the determination of the representation of a thing at some time.

The schema of actuality is existence at a determinate time.

The schema of necessity is the existence of an object at all times.

From all this we now see what the schema of each category contains and represents: that of magnitude, the generation (synthesis) of time itself in the successive apprehension of an object; the schema of quality, the synthesis of sensation (perception) with the representation of time, or the filling of time; that of relation, the relation of perceptions to one another at all times (that is, according to a rule of time-determination); and finally the schema of modality and its categories, time itself as the correlate of the determination of an object as to whether and how it belongs to time. The schemata are therefore nothing but a priori determinations of time according to rules. These concern, in the order of the categories, the time-series and the content of time.

B 185 They concern also the order of time, and finally the sum total of time with regard to all possible objects.

It is now evident from this that the schematism of the understanding through the transcendental synthesis of imagination amounts to nothing other than the unity of all the manifold of intuition in inner sense, and thus indirectly to the unity of apperception as the function corresponding to inner sense (a receptivity). Thus the schemata of the pure concepts of the understanding are the true and sole conditions for providing these concepts with a relation to objects, and hence with meaning. The categories are therefore ultimately capable of no use other than a possible empirical use. For they serve merely to subject appearances to universal rules of synthesis through grounds of an a priori necessary unity (owing to the necessary unification of all consciousness in one original apperception), and thereby make them fit for thoroughgoing connection in one experience.

But all our cognitions lie within the whole of all possible experience, and transcendental truth, which precedes all empirical truth and makes it possible, consists in the universal relation to that experience.

Yet it is also evident: the schemata of sensibility first realize the categories.

B 186 They nevertheless also restrict them, that is, limit them to conditions lying outside the understanding, namely in sensibility. Hence the schema is properly only the phenomenon, or the sensible concept of an object in agreement with the category. (Numerus est quantitas phaenomenon, sensatio realitas phaenomenon, constans et perdurabile rerum substantia phaenomenon—aeternitas, necessitas, phaenomena and so on.) If we now leave out a restricting condition, we seem to amplify the concept previously limited. Thus the categories in their pure meaning, without any conditions of sensibility, should hold of things in general as they are, whereas their schemata represent them only as they appear; the categories would thus have a meaning independent of all schemata and extending much further. In fact, even after all sensible conditions have been removed, pure concepts of the understanding certainly retain a meaning, but only a logical one, that of the mere unity of representations. Yet no object is given to these, and hence no meaning that could yield a concept of the object. Thus, for example, if the sensible determination of persistence were omitted, substance would signify nothing more than a something that can be thought as subject (without being a predicate of something else). Now I can make nothing of this representation.

B 187 For it does not indicate at all what determinations the thing that is to count as such a first subject has. Thus without schemata the categories are only functions of the understanding for concepts, but represent no object. This meaning comes to them from sensibility, which realizes the understanding while at the same time restricting it.

Transcendental Doctrine of the Power of Judgment (or Analytic of Principles) Second Chapter

System of All Principles of the Pure Understanding

In the preceding chapter we considered the transcendental power of judgment only in terms of the general conditions under which it is entitled to use the pure concepts of the understanding for synthetic judgments. Our task now is to present, in systematic combination, the judgments that the understanding actually produces a priori under this critical caution. For this our table of categories must undoubtedly give us the natural and secure guidance. For it is precisely these whose relation to possible experience must constitute all pure a priori cognition of the understanding.

B 188 And their relation to sensibility in general will, for that very reason, set out all the transcendental principles governing the use of the understanding, completely and in a single system.

A priori principles bear this name not merely because they contain the grounds of other judgments, but also because they are not themselves grounded in higher and more general cognitions. Yet this property does not always exempt them from proof. For although the principle could not be proved any further objectively, and rather underlies all cognition of its object, this does not prevent a proof from being possible, and indeed necessary, from the subjective sources of the possibility of cognition of an object in general. Otherwise the proposition would still lie under the gravest suspicion of being a merely surreptitious assertion.

Second, we will confine ourselves to those principles that relate to the categories. The principles of transcendental aesthetic, according to which space and time are the conditions of the possibility of all things as appearances, and likewise the restriction on these principles—namely, that they cannot be applied to things in themselves—thus fall outside our demarcated field of inquiry. Mathematical principles likewise form no part of this system, because they are drawn only from intuition, not from the pure concept of the understanding.

B 189 Yet their possibility, since they are nevertheless synthetic a priori judgments, must necessarily find a place here: not to prove their correctness and apodictic certainty, which they do not need, but only to make the possibility of such evident a priori cognitions intelligible and to deduce it.

We must, however, also discuss the principle of analytic judgments, in contrast to the synthetic judgments with which we are properly concerned. For precisely this contrast frees the theory of the latter from all misunderstanding and clearly displays their distinctive nature.

The System of the Principles of Pure Understanding First Section On the Supreme Principle of All Analytic Judgments

Whatever the content of our cognition, and however it may relate to its object, the universal, though merely negative, condition of all our judgments in general is that they must not contradict themselves. Otherwise these judgments are nothing in themselves, even without regard to the object.

B 190 Yet even if our judgment contains no contradiction, it may still combine concepts in a way that the object does not warrant, or without our being given any ground, either a priori or a posteriori, that would justify such a judgment. Thus a judgment, despite being free from all internal contradiction, may still be either false or groundless.

The proposition that no thing can have a predicate that contradicts it is called the principle of contradiction. It is a universal, though merely negative, criterion of all truth, but it belongs to logic alone, because it holds of cognitions merely as cognitions in general, regardless of their content, and declares that contradiction utterly destroys and nullifies them.

Yet it can also be put to a positive use, that is, not merely to banish falsehood and error insofar as they rest on contradiction, but also to recognize truth. For if a judgment is analytic, whether negative or affirmative, its truth must always be sufficiently recognizable by the principle of contradiction. For of whatever already lies as a concept in the cognition of the object and is thought there, the opposite is always correctly denied, while the concept itself must necessarily be affirmed of it.

B 191 The reason is that the contrary of the concept would contradict the object.

We must therefore recognize the principle of contradiction as the universal and wholly sufficient principle of all analytic cognition; but its authority and usefulness as a sufficient criterion of truth extend no further. That no cognition can conflict with it without destroying itself certainly makes this principle a conditio sine qua non, but not the determining ground of the truth of our cognition. Since we are properly concerned only with the synthetic part of our cognition, we will always take care never to violate this inviolable principle, but can never expect it to shed any light on the truth of cognition of this kind.

There is, however, a formulation of this famous principle, devoid of all content and merely formal though it is, that contains a synthesis carelessly and quite unnecessarily mixed into it. It runs: it is impossible for something both to be and not to be at the same time. Apart from the superfluous addition of apodictic certainty through the word “impossible”—a certainty that must surely follow of itself from the proposition—the proposition is affected by the condition of time.

B 192 It says, as it were: a thing = A that is something = B cannot at the same time be non-B; but it can perfectly well be both B and non-B in succession. For example, a person who is young cannot at the same time be old; but that same person can very well be young at one time and not young, that is, old, at another. As a merely logical principle, however, the principle of contradiction must not restrict its pronouncements to temporal relations. Such a formulation therefore runs directly counter to its purpose. The misunderstanding arises solely because one first separates a predicate of a thing from the concept of that thing, and then connects its opposite with this predicate. This never produces a contradiction with the subject, but only with its predicate, which has been synthetically combined with the subject, and even then only if the first and second predicates are posited at the same time. If I say that a person who is unlearned is not learned, the condition “at the same time” must be included, since someone unlearned at one time may very well be learned at another. But if I say that no unlearned person is learned, the proposition is analytic, because the mark of being unlearned now helps constitute the concept of the subject. The negative proposition then follows immediately from the principle of contradiction, without any need to add the condition “at the same time.”

B 193 This is also why I altered its formulation above, so that it clearly expresses the nature of an analytic proposition.

The System of the Principles of Pure Understanding Second Section On the Supreme Principle of All Synthetic Judgments

Explaining the possibility of synthetic judgments is a task with which general logic has nothing to do; it must not even know its name. In a transcendental logic, however, this is the most important business of all, and indeed its only business when the question concerns the possibility of synthetic a priori judgments, together with the conditions and extent of their validity. For once it has completed this task, it can fully accomplish its purpose: determining the scope and boundaries of pure understanding.

In an analytic judgment I remain within the given concept in order to determine something about it. If the judgment is affirmative, I ascribe to this concept only what was already thought in it; if negative, I merely exclude its contrary from it. In synthetic judgments, however, I must go beyond the given concept to consider something quite different from what was thought in it as standing in a relation to it.

B 194 This relation is therefore never one of either identity or contradiction, and neither truth nor error can be discerned in the judgment itself.

Granted, then, that one must go beyond a given concept to compare it synthetically with another, a third thing is needed in which alone the synthesis of two concepts can arise. But what is this third thing, the medium of all synthetic judgments? It is only a sum total in which all our representations are contained: inner sense, and its a priori form, time. The synthesis of representations rests on imagination, but their synthetic unity, which is required for judgment, rests on the unity of apperception. Here, then, we must seek the possibility of synthetic judgments and, since all three contain sources of a priori representations, also the possibility of pure synthetic judgments. Indeed, on these grounds such judgments will even be necessary if there is to be cognition of objects that rests solely on the synthesis of representations.

If a cognition is to have objective reality—that is, to relate to an object and have meaning and significance in it—the object must be capable of being given in some way. Without this, concepts are empty: through them one has, to be sure, thought.

B 195 In fact, however, one has cognized nothing through this thinking, but merely played with representations. To give an object, if this is not meant merely indirectly but as presenting it immediately in intuition, is nothing other than to relate its representation to experience, whether actual or at least possible. Even space and time, however pure these concepts are of everything empirical, and however certain it is that they are represented entirely a priori in the mind, would lack objective validity, meaning, and significance unless their necessary use for the objects of experience were demonstrated. Indeed, their representation is a mere schema that always relates to the reproductive imagination, which calls up the objects of experience, without which they would have no significance. The same holds for all concepts without exception.

The possibility of experience, then, is what gives all our a priori cognitions objective reality. Now experience rests on the synthetic unity of appearances, that is, on a synthesis according to concepts of the object of appearances in general. Without this it would not even be cognition, but a rhapsody of perceptions that would fit together in no context according to rules of a thoroughly connected possible consciousness, and hence not in the transcendental and necessary unity of apperception either.

B 196 Experience therefore has a priori principles of its form as its foundation: universal rules of unity in the synthesis of appearances. Their objective reality as necessary conditions can always be shown in experience, indeed in its very possibility. Outside this relation, however, synthetic a priori propositions are altogether impossible, since they have no third thing, namely a pure object, in which the synthetic unity of their concepts could demonstrate objective reality.

Thus, although we cognize a great deal a priori in synthetic judgments about space in general, or about the figures that productive imagination draws in it, and actually need no experience whatever for this, such cognition would still be nothing but an occupation with a mere fantasy if space were not to be regarded as the condition of the appearances that constitute the material of outer experience. Those pure synthetic judgments therefore relate, though only indirectly, to possible experience, or rather to its very possibility, and ground the objective validity of their synthesis on this alone.

Since experience, as empirical synthesis, is thus, in its possibility, the only kind of cognition that gives reality to every other synthesis, this other synthesis, as a priori cognition, has truth only in one way.

B 197 Truth, that is agreement with the object, belongs to it solely because it contains nothing beyond what is necessary for the synthetic unity of experience in general.

The supreme principle of all synthetic judgments is therefore this: every object is subject to the necessary conditions of the synthetic unity of the manifold of intuition in a possible experience.

Synthetic a priori judgments are possible in this way: we relate the formal conditions of a priori intuition, the synthesis of imagination, and its necessary unity in a transcendental apperception to a possible empirical cognition in general, and say that the conditions of the possibility of experience in general are at the same time conditions of the possibility of the objects of experience, and for that reason have objective validity in a synthetic a priori judgment.

The System of the Principles of Pure Understanding Third Section Systematic Presentation of All Its Synthetic Principles

That there are principles anywhere at all is due solely to pure understanding.

B 198 It is not only the faculty of rules concerning what happens, but itself the source of principles according to which everything that can ever appear to us as an object necessarily stands under rules, for without such rules appearances could never yield cognition of an object corresponding to them. Even laws of nature, when regarded as fundamental laws of the empirical use of understanding, carry with them an expression of necessity, and hence at least the presumption of a determination from grounds valid a priori and before all experience. But all laws of nature without exception stand under higher principles of the understanding, since they merely apply these to particular cases of appearance. These principles alone, then, provide the concept that contains the condition and, as it were, the exponent of a rule in general; experience supplies the case that falls under the rule.

There can properly be no danger of taking merely empirical principles for principles of pure understanding, or the reverse. The necessity according to concepts that distinguishes the latter, and whose absence is readily perceived in every empirical proposition, however universally it may hold, can easily prevent this confusion. But there are pure a priori principles that I would nevertheless not attribute specifically to pure understanding, because they are drawn not from pure concepts.

B 199 They are drawn instead from pure intuitions, though through the understanding; and understanding is the faculty of concepts. Mathematics has principles of this kind. Yet their application to experience, and hence their objective validity, indeed the possibility of such synthetic a priori cognition—its deduction—always rests on pure understanding.

I will therefore not count the principles of mathematics among my principles, but rather those on which their possibility and objective validity are grounded a priori, and which must accordingly be regarded as the principle of those principles, proceeding from concepts to intuition and not from intuition to concepts.

In applying the pure concepts of the understanding to possible experience, the use of their synthesis is either mathematical or dynamical: it concerns in part merely the intuition, and in part the existence, of an appearance in general. The a priori conditions of intuition are absolutely necessary with respect to a possible experience; those of the existence of the objects of a possible empirical intuition are in themselves only contingent. Hence the principles of mathematical use will read as unconditionally necessary, that is, apodictic. Those of dynamical use will indeed also bear the character of a priori necessity, but only under the condition of empirical thinking in an experience, and thus only mediately and indirectly.

B 200 Consequently they will not contain the immediate self-evidence peculiar to the former, though this does not impair their certainty as universally related to experience. This will be easier to assess, however, at the conclusion of this system of principles.

The table of categories gives us an entirely natural guide to the table of principles, since these are nothing other than rules for the objective use of the categories. All the principles of pure understanding are accordingly:

1 Axioms of intuition

2 Anticipations of perception

3 Analogies of experience

4 Postulates of empirical thinking in general

I have chosen these names carefully, so that differences in the self-evidence and application of these principles should not pass unnoticed. It will soon become clear, however, how matters stand.

B 201 With respect both to self-evidence and to the a priori determination of appearances according to the categories of magnitude and quality (if one attends merely to the form of the latter), their principles differ markedly from the other two. The former admit of intuitive certainty, the latter of merely discursive certainty, though both admit of complete certainty; I will therefore call the former mathematical and the latter dynamical principles*.

B 202 But it should be carefully noted that here I have in view neither the principles of mathematics in the one case nor the principles of general (physical) dynamics in the other, but only those of pure understanding in relation to inner sense, without distinction among the representations given in it, through which all those principles acquire their possibility. I name them, then, more with regard to their application than to their content, and now turn to consider them in the same order in which the table presents them.

* Every combination (conjunctio) is either composition (compositio) or connection (nexus). The former is the synthesis of a manifold whose elements do not necessarily belong together: for example, the two triangles into which a square is divided by its diagonal do not in themselves necessarily belong together. Such is the synthesis of the homogeneous in everything that can be considered mathematically. This synthesis can in turn be divided into aggregation and coalition, the former directed toward extensive and the latter toward intensive magnitudes. The second combination (nexus) is the synthesis of a manifold insofar as its elements necessarily belong together, as an accident belongs to a substance, or an effect to its cause. Thus, though heterogeneous, they are nevertheless represented as combined a priori. I call this combination, which is not arbitrary, dynamical because it concerns the combination of the existence of the manifold. This can in turn be divided into the physical combination of appearances with one another and their metaphysical combination a priori in the faculty of cognition.

1 Axioms of Intuition

Their principle is: all intuitions are extensive magnitudes.

Proof

In their form, all appearances contain an intuition in space and time that underlies them all a priori. They can therefore be apprehended—that is, taken up into empirical consciousness—only through the synthesis of the manifold by which the representations of a determinate space or time are generated: through the composition of the homogeneous and the consciousness of the synthetic unity of this homogeneous manifold.

B 203 Now the consciousness of the homogeneous manifold in intuition in general, insofar as it first makes the representation of an object possible, is the concept of a magnitude (quanti). Thus even the perception of an object as appearance is possible only through the same synthetic unity of the manifold of given sensible intuition through which the unity of the composition of the homogeneous manifold is thought in the concept of a magnitude. That is, appearances are all magnitudes, and indeed extensive magnitudes, because as intuitions in space or time they must be represented through the same synthesis by which space and time in general are determined.

I call a magnitude extensive when the representation of its parts makes the representation of the whole possible, and therefore necessarily precedes it. I cannot represent a line, however small, without drawing it in thought: without generating all its parts successively from a point and thereby first tracing this intuition. The same holds for any time, however small. In it I think only the successive advance from one instant to another, through all the parts of time and their addition, until a determinate magnitude of time is finally generated. The mere intuition in all appearances is either space or time.

B 204 Every appearance as intuition is therefore an extensive magnitude, because it can be cognized in apprehension only through successive synthesis, from part to part. All appearances are accordingly already intuited as aggregates—a multitude of previously given parts. This is not the case with every kind of magnitude, but only with those represented and apprehended by us extensively as such.

On this successive synthesis of productive imagination in generating figures rests the mathematics of extension, geometry, with its axioms. These express the a priori conditions of sensible intuition under which alone the schema of a pure concept of outer appearance can come about: for example, between two points only one straight line is possible; two straight lines enclose no space, and so on. These are the axioms that properly concern only magnitudes (quanta) as such.

As for magnitude (quantitas)—that is, the answer to the question how large something is—there are, strictly speaking, no axioms concerning it, although several such propositions are synthetic and immediately certain (indemonstrabilia). For the propositions that equals added to equals, or subtracted from them, give equals are analytic. In them I am immediately conscious of the identity of one generation of magnitude with the other.

B 205 Axioms, however, are supposed to be synthetic a priori propositions. By contrast, the evident propositions concerning numerical relations are indeed synthetic, but are not universal like those of geometry, and for precisely that reason are not axioms either; they may instead be called numerical formulas. That 7+5=12 is not an analytic proposition. For neither in the representation of 7, nor of 5, nor in the representation of their composition do I think the number 12. Whether I ought to think it in adding the two is not at issue here, since in an analytic proposition the question is only whether I actually think the predicate in the representation of the subject. But although this proposition is synthetic, it is still only a singular proposition. Insofar as we attend here merely to the synthesis of the homogeneous, the units, the synthesis can take place in only one way, although the subsequent use of these numbers is universal. If I say that a triangle can be drawn with three lines, any two of which together are greater than the third, I have here the mere function of productive imagination, which can draw the lines larger or smaller and bring them together at all kinds of arbitrarily chosen angles. By contrast, the number 7 is possible in only one way, as is the number 12 generated through the synthesis of the former with 5.

B 206 Such propositions must therefore be called not axioms, since otherwise there would be infinitely many, but numerical formulas.

This transcendental principle of the mathematics of appearances greatly extends our a priori cognition. For it alone makes pure mathematics, in all its precision, applicable to objects of experience. Without this principle that applicability might not be so evident in itself, and has indeed occasioned many objections. Appearances are not things in themselves. Empirical intuition is possible only through pure intuition, of space and time; hence what geometry says of the latter also holds incontestably of the former. And the evasions, as if objects of the senses need not conform to the rules of construction in space (for example the infinite divisibility of lines or angles), must fall away. For this denies objective validity to space and, with it, to all mathematics, leaving us no longer knowing why or how far mathematics may be applied to appearances. The synthesis of spaces and times, as the essential form of all intuition, is what also makes possible the apprehension of appearance, hence every outer experience, and consequently all cognition of its objects. What mathematics proves concerning that synthesis in its pure use necessarily holds of this cognition as well.

B 207 All objections to this are merely the quibbles of a misguided reason, which mistakenly intends to free the objects of the senses from the formal condition of our sensibility and represents them, though they are mere appearances, as objects in themselves given to the understanding. In that case, of course, nothing at all could be synthetically cognized of them a priori, not even through pure concepts of space; and the science that determines these concepts, geometry, would itself be impossible.

2 Anticipations of Perception

Their principle is: in all appearances the real, which is an object of sensation, has intensive magnitude, that is, a degree.

Proof

Perception is empirical consciousness, that is, a consciousness in which sensation is also present. Appearances, as objects of perception, are not pure, merely formal intuitions like space and time, which in themselves cannot be perceived at all. Besides intuition, therefore, they contain the materials for an object in general, through which something existing in space or time is represented: the real of sensation. This is a merely subjective representation, of which one can become conscious only that the subject is affected, and which one relates to an object in general.

B 208 Now a gradual change from empirical to pure consciousness is possible, in which its real element entirely vanishes and there remains a merely formal a priori consciousness of the manifold in space and time. Hence a synthesis generating the magnitude of a sensation is also possible, from its beginning, pure intuition = 0, up to any chosen magnitude of it. Since sensation in itself is not an objective representation at all, and neither the intuition of space nor that of time is found in it, it will indeed have no extensive magnitude. Yet it will have a magnitude—through its apprehension, in which empirical consciousness can grow in a certain time from nothing = 0 to its given measure—and thus an intensive magnitude. Correspondingly, all objects of perception, insofar as perception contains sensation, must be assigned intensive magnitude, that is, a degree of influence on sense.

Any cognition through which I can cognize and determine a priori what belongs to empirical cognition may be called an anticipation. This is undoubtedly the sense in which Epicurus used his expression προληψις. But there is something in appearances that is never cognized a priori, and that therefore also constitutes the actual distinction between the empirical and cognition a priori.

B 209 This is sensation, as the matter of perception; and it follows that sensation is precisely what cannot be anticipated at all. By contrast, we could call the pure determinations in space and time, with respect both to figure and to magnitude, anticipations of appearances, since they represent a priori whatever may be given a posteriori in experience. Suppose, however, that there were nevertheless something in every sensation, as sensation in general, that could be cognized a priori without any particular sensation being given. This would deserve to be called an anticipation in an exceptional sense, since it seems strange to forestall experience in precisely what concerns its matter, which can be drawn only from experience. And this is in fact the case here.

Apprehension merely through sensation fills only an instant, if, that is, I leave aside the succession of many sensations. As something in appearance whose apprehension is not a successive synthesis proceeding from parts to the whole representation, it therefore has no extensive magnitude. The absence of sensation in that same instant would represent it as empty, hence = 0. Now what corresponds to sensation in empirical intuition is reality (realitas phaenomenon); what corresponds to its absence is negation = 0.

B 210 Every sensation, however, admits of diminution, so that it can decrease and gradually disappear. Hence between reality in appearance and negation there is a continuous connection of many possible intermediate sensations, whose difference from one another is always smaller than the difference between the given sensation and zero, or complete negation. That is, the real in appearance always has a magnitude, which is not, however, found in apprehension, since apprehension through mere sensation takes place in an instant, not through the successive synthesis of many sensations, and thus does not proceed from parts to whole. It therefore has a magnitude, but not an extensive one.

Now I call a magnitude intensive when it is apprehended only as a unity, and when multiplicity in it can be represented only through approximation to negation = 0. Thus every reality in appearance has intensive magnitude, that is, a degree. If this reality is regarded as a cause, whether of sensation or of another reality in appearance, for example a change, the degree of reality as cause is called a moment, for example the moment of gravity. This is because the degree designates only that magnitude whose apprehension is not successive but instantaneous. I mention this here only in passing, however, since for now I am not yet concerned with causality.

B 211 Every sensation, then, and hence every reality in appearance, however small, has a degree, that is, an intensive magnitude that can always be further diminished. Between reality and negation there is a continuous connection of possible realities and possible smaller perceptions. Every color, red for example, has a degree that, however small, is never the smallest; and the same holds everywhere for heat, the moment of gravity, and so on.

The property of magnitudes by which no part of them is the smallest possible—no part is simple—is called their continuity. Space and time are quanta continua, because no part of them can be given without enclosing it between boundaries, points and instants, and thus only in such a way that this part is itself again a space or a time. Space therefore consists only of spaces, time of times. Points and instants are only boundaries, mere positions marking their limitation. Positions, however, always presuppose the intuitions they are to limit or determine; neither space nor time can be composed of mere positions as constituents that could be given before space or time. Such magnitudes may also be called flowing, because the synthesis of productive imagination in generating them is an advance in time.

B 212 The continuity of time is commonly designated in particular by the expression of flowing (elapsing).

All appearances in general are accordingly continuous magnitudes: extensive magnitudes in their intuition, and intensive magnitudes in their mere perception, sensation and hence reality. If the synthesis of the manifold of appearance is interrupted, the result is an aggregate of many appearances, not properly an appearance as a quantum. It is generated not by the mere continuation of a productive synthesis of a certain kind, but by the repetition of a synthesis that keeps coming to an end. If I call 13 thalers a quantum of money, I name it correctly insofar as I mean by it the content of one mark of fine silver. This is certainly a continuous magnitude, in which no part is the smallest, but every part could constitute a coin that would always contain material for still smaller ones. But if by that designation I mean 13 round thalers as so many coins, whatever their silver content may be, it is improper to call this a quantum of thalers; I must call it an aggregate, that is, a number of coins. Since unity must nevertheless underlie every number, appearance as unity is a quantum, and as such is always a continuum.

Now all appearances, considered both extensively and intensively, are continuous magnitudes.

B 213 The proposition that all change too—the transition of a thing from one state to another—is continuous could therefore readily be proved here with mathematical self-evidence, were it not that the causality of a change in general lies altogether outside the boundaries of a transcendental philosophy and presupposes empirical principles. For the understanding gives us no a priori disclosure at all of the possibility of a cause that alters the state of things, that is, determines them to the opposite of a given state. This is not merely because it has no insight into that possibility, since such insight is lacking in several a priori cognitions, but because alterability concerns only certain determinations of appearances that experience alone can teach, whereas their cause is to be found in the unalterable. Here, however, we have nothing available to use but the pure fundamental concepts of all possible experience, among which there must be nothing empirical whatever. We therefore cannot anticipate general natural science, which is built on certain basic experiences, without violating the unity of the system.

Nevertheless, we do not lack evidence of the great influence our principle has in anticipating perceptions, and even in compensating for their absence far enough to bar every false inference that might be drawn from it.

B 214 If all reality in perception has a degree, between which and negation there lies an infinite succession of ever smaller degrees, while every sense must nevertheless have a determinate degree of receptivity to sensations, then no perception, and hence no experience, is possible that could prove a complete absence of everything real in appearance, either directly or indirectly, by whatever roundabout inference. That is, no proof of empty space or empty time can ever be drawn from experience. For, first, the complete absence of the real in sensible intuition cannot itself be perceived; second, it cannot be inferred from any single appearance or from the difference in the degree of its reality, nor may it ever be assumed to explain that appearance. For even if the entire intuition of a determinate space or time is real throughout, that is, no part of it is empty, there must nevertheless be infinitely different degrees with which space or time is filled, because every reality has its degree, which can decrease by infinite stages to nothing (the void) while the extensive magnitude of the appearance remains unchanged; and the intensive magnitude in different appearances can be smaller or larger even though the extensive magnitude of the intuition is equal.

B 215 Let us give an example. Nearly all natural philosophers, on perceiving a great difference in the quantity of matter of different kinds within equal volumes—partly through the moment of gravity or weight, partly through the moment of resistance to other moving matter—unanimously conclude that this volume, the extensive magnitude of appearance, must be empty in all matter, though to different extents. Yet who among these investigators of nature, mostly mathematicians and mechanists, would ever have considered that they base this inference solely on a metaphysical presupposition, the very thing they claim so emphatically to avoid? They assume that the real in space—I will not call it impenetrability or weight here, since these are empirical concepts—is everywhere of one and the same kind, and can differ only in extensive magnitude, that is, in amount. Against this presupposition, for which they could have no ground in experience and which is therefore merely metaphysical, I set a transcendental proof. It is not intended to explain the difference in the filling of spaces, but it entirely removes the supposed necessity of that presupposition: that the difference in question can be explained only by assuming empty spaces. It has the merit of at least freeing the understanding to think this diversity in another way as well.

B 216 It may do so should the explanation of nature make some hypothesis necessary for the purpose. For we see here that, although equal spaces may be completely filled by different kinds of matter, so that neither contains a point where its matter is not present, everything real of the same quality nevertheless has its degree, of resistance or of weight. This can become infinitely smaller without any diminution of extensive magnitude or amount, before passing into the void and disappearing. Thus an expansion filling a space, heat for example, and likewise every other reality in appearance, can decrease infinitely in its degrees without leaving the smallest part of that space empty in the least, and can nevertheless fill the space with these smaller degrees just as well as another appearance does with greater ones. My purpose here is by no means to assert that this is actually how matters stand with the diversity of matter in its specific gravity. It is only to show, from a principle of pure understanding, that the nature of our perceptions makes such an explanation possible; and that it is a mistake to assume that the real in appearance is equal in degree and differs only in aggregation and its extensive magnitude, and even to claim this, supposedly, through an a priori principle of the understanding.

B 217 Yet this anticipation of perception always has something striking about it for an investigator accustomed to transcendental inquiry and made cautious by it. It raises some concern that the understanding should advance such a synthetic proposition as that concerning the degree of everything real in appearances, and hence the possibility of an internal difference in sensation itself when we abstract from its empirical quality. It is therefore still a question not unworthy of solution: how can the understanding here pronounce synthetically on appearances a priori, and anticipate them even in what is properly and merely empirical, namely in what concerns sensation?

The quality of sensation is always merely empirical and cannot be represented a priori at all, as with colors, taste, and so on. But the real that corresponds to sensations in general, in contrast to negation = 0, represents only something whose concept in itself contains being, and signifies nothing but synthesis in an empirical consciousness in general. In inner sense, namely, empirical consciousness can be raised from 0 to any greater degree, so that the very same extensive magnitude of intuition, for example an illuminated surface, arouses as much sensation as an aggregate of many other, less illuminated surfaces together.

B 218 We can therefore abstract entirely from the extensive magnitude of appearance and still represent in the mere sensation of an instant a synthesis of uniform increase from 0 to the given empirical consciousness. All sensations as such are therefore indeed given only a posteriori, but their property of having a degree can be cognized a priori. It is remarkable that in magnitudes in general we can cognize a priori only a single quality, continuity; while in all quality, the real of appearances, we can cognize a priori nothing beyond its intensive quantity, namely that it has a degree. Everything else is left to experience.

3 Analogies of Experience

Their principle is: experience is possible only through the representation of a necessary connection of perceptions.

Proof

Experience is an empirical cognition, that is, a cognition that determines an object through perceptions. It is therefore a synthesis of perceptions that is not itself contained in perception, but contains the synthetic unity of their manifold in one consciousness. This unity constitutes the essential element of a cognition of objects of the senses, that is, of experience, not merely of the intuition or sensation of the senses.

B 219 Now in experience perceptions, to be sure, come together only contingently, so that no necessity of their connection is or can be evident from the perceptions themselves. For apprehension is only an assembling of the manifold of empirical intuition; it contains no representation of the necessity of the combined existence in space and time of the appearances it assembles. But since experience is a cognition of objects through perceptions, and must therefore represent in it the relation in the existence of the manifold, not as it is assembled in time but as it objectively is in time, and since time itself cannot be perceived, the existence of objects in time can be determined only through their combination in time in general, and thus only through concepts connected a priori. Since these always carry necessity with them as well, experience is possible only through a representation of the necessary connection of perceptions.

The three modi of time are persistence, succession, and simultaneity. Hence three rules of all temporal relations of appearances, according to which the existence of each can be determined with respect to the unity of all time, will precede all experience and first make it possible.

B 220 The general principle of all three analogies rests on the necessary unity of apperception with respect to all possible empirical consciousness, perception, at every time. Consequently, since that unity underlies it a priori, the principle rests on the synthetic unity of all appearances according to their relation in time. For original apperception relates to inner sense (the sum total of all representations), and indeed relates a priori to its form: the relation of the manifold empirical consciousness in time. Now in original apperception all this manifold is to be united in its temporal relations. This is what its transcendental unity declares a priori, the unity under which everything must stand that is to belong to my cognition—my single cognition—and thus become an object for me. This a priori determined synthetic unity in the temporal relation of all perceptions is therefore the law that all empirical determinations of time must stand under rules of general determination of time. The analogies of experience, which we are now to discuss, must be rules of this kind.

These principles have the peculiarity that they consider not appearances and the synthesis of their empirical intuition, but only their existence and their relation to one another with respect to that existence.

B 221 Now the manner in which something is apprehended in appearance can be determined a priori in such a way that the rule of its synthesis can at the same time supply this intuition a priori in any given empirical instance, that is, produce it from the rule. But the existence of appearances cannot be cognized a priori. And even if we could arrive by this route at an inference to some existence, we could still not cognize it determinately, that is, anticipate what distinguishes its empirical intuition from others.

The previous two principles, which I called mathematical because they authorize the application of mathematics to appearances, concerned appearances as to their mere possibility. They taught how appearances could be generated, both in their intuition and in the real of their perception, according to rules of a mathematical synthesis. Hence numerical magnitudes, and with them the determination of appearance as magnitude, can be used in both cases. Thus, for example, I will be able to compose the degree of the sensations of sunlight from some 200,000 illuminations by the moon, and give it determinately a priori, that is, construct it. We can therefore call those first principles constitutive.

Matters must be quite different with those principles that are to bring the existence of appearances under a priori rules. For existence cannot be constructed.

B 222 They will therefore concern only the relation of existence and can supply none but merely regulative principles. Here, then, neither axioms nor anticipations are in question. Rather, if a perception is given to us in a temporal relation to other, though indeterminate, perceptions, we cannot say a priori what other perception, or how great a perception, is involved, but only how, in this modo of time, it is necessarily combined in existence with the given perception. In philosophy analogies mean something very different from what they represent in mathematics. In mathematics they are formulas expressing the equality of two quantitative relations, and are always constitutive: if two terms of the proportion are given, the third is thereby also given, that is, can be constructed. In philosophy, however, analogy is not the equality of two quantitative but of two qualitative relations. From three given terms I can cognize and supply a priori only the relation to a fourth, not this fourth term itself. Yet I do have a rule for seeking it in experience and a mark by which to find it there. An analogy of experience will therefore be only a rule according to which unity of experience is to arise from perceptions (not as perception itself arises, as empirical intuition in general). As a principle concerning objects of appearances it will hold not constitutively, but merely regulatively.

B 223 The very same will also hold of the postulates of empirical thinking in general, which together concern the synthesis of mere intuition, the form of appearance; of perception, its matter; and of experience, the relation of these perceptions. They too are only regulative principles and differ from the mathematical principles, which are constitutive, not in certainty, which is established a priori in both, but in the kind of self-evidence, that is, in its intuitive character, and hence also in demonstration.

What was noted concerning all synthetic principles, and must be especially stressed here, is this: these analogies have their sole meaning and validity as principles not of the transcendental but merely of the empirical use of understanding, and can therefore be proved only as such. Consequently appearances must be subsumed not under the categories outright, but only under their schemata. For if the objects to which these principles are to relate were things in themselves, it would be quite impossible to cognize anything of them synthetically a priori. But they are nothing but appearances, whose complete cognition, to which all a priori principles must ultimately lead, is simply possible experience. Consequently these principles can aim at nothing beyond the conditions of the unity of empirical cognition in the synthesis of appearances.

B 224 This unity is thought only in the schema of the pure concept of the understanding; the category contains the function of its unity as a synthesis in general, unrestricted by any sensible condition. Through these principles, then, we will be entitled to put appearances together only by analogy with the logical and universal unity of concepts. In the principle itself we will therefore indeed employ the category; but in carrying it out, in applying it to appearances, we will put its schema in its place as the key to its use—or rather place the schema alongside the category as a restrictive condition, under the name of a formula of the category.

A. First Analogy

Principle of the Persistence of Substance

In all change of appearances substance persists, and its quantity in nature is neither increased nor diminished.

Proof

All appearances are in time. In time alone, as substrate, as the persistent form of inner intuition, can both simultaneity and succession be represented.

B 225 Thus the time in which all change of appearances is to be thought remains and does not change, because it is that in which succession or simultaneity can be represented only as its determinations. Now time by itself cannot be perceived. Consequently there must be found in the objects of perception, that is, in appearances, the substrate that represents time in general, and in relation to which all change or simultaneity can be perceived in apprehension through the relation of appearances to it. But the substrate of everything real, of everything belonging to the existence of things, is substance; in it everything belonging to existence can be thought only as a determination. Consequently the persistent, in relation to which alone all temporal relations of appearances can be determined, is substance in appearance: its real element, which as the substrate of all change always remains the same. Since substance therefore cannot change in its existence, its quantity in nature can neither be increased nor diminished.

Our apprehension of the manifold of appearance is always successive, and thus always changing. Through it alone, therefore, we can never determine whether this manifold, as an object of experience, is simultaneous or successive, unless something underlies it that always is: something lasting and persistent.

B 226 All change and simultaneity are merely so many ways (modi of time) in which this persistent exists. Thus temporal relations are possible only in the persistent, since simultaneity and succession are the only relations in time. That is, the persistent is the substrate of the empirical representation of time itself, in which alone all determination of time is possible. Persistence expresses time in general as the constant correlate of all existence of appearances, of all change and all concomitance. For change does not affect time itself, but only appearances in time, just as simultaneity is not a modus of time itself, in which no parts are simultaneous but all are successive. If one tried to ascribe a succession to time itself, one would have to think yet another time in which this succession was possible. Through the persistent alone, existence in different successive parts of the temporal series acquires a magnitude called duration. For in mere succession alone existence is always disappearing and beginning, and never has the least magnitude. Without this persistent element there is therefore no temporal relation. Now time in itself cannot be perceived; hence this persistent element in appearances is the substrate of all determination of time, and consequently also the condition of the possibility of all synthetic unity of perceptions, that is, of experience.

B 227 In this persistent element all existence and all change in time can be regarded only as a modus of the existence of what remains and persists. Thus in all appearances the persistent is the object itself, that is, substance (phaenomenon); everything that changes or can change belongs only to the way in which this substance or these substances exist, and hence to their determinations.

I find that at all times not only philosophers but even common understanding have presupposed this persistence as a substrate of all change in appearances, and will always accept it as unquestionable. The philosopher merely expresses the matter somewhat more precisely, saying: through all alterations in the world substance remains, and only accidents change. Yet nowhere do I find even an attempt to prove this thoroughly synthetic proposition. Indeed, it rarely even stands, as it ought, at the head of the pure laws of nature that hold entirely a priori. In fact, the proposition that substance persists is tautological. For this persistence alone is why we apply the category of substance to appearance; what should have been proved is that in all appearances there is something persistent, of which the changeable is nothing but a determination of its existence. But such a proof can never be conducted dogmatically, that is, from concepts, since it concerns a synthetic a priori proposition.

B 228 And no one ever considered that propositions of this kind are valid only in relation to possible experience, and hence can be proved only through a deduction of the possibility of experience. It is therefore no wonder that this proposition has indeed been made the basis of all experience, because its necessity for empirical cognition is felt, but has never been proved.

A philosopher was asked, “How much does smoke weigh?” He replied, “Subtract the weight of the remaining ash from the weight of the wood that was burned, and you have the weight of the smoke.” He thus presupposed as incontestable that even in fire matter, substance, does not perish, but only undergoes an alteration of form. Likewise the proposition “Nothing comes from nothing” was only another consequence of the principle of persistence, or rather of the perpetual existence of the actual subject in appearances. For if what we wish to call substance in appearance is to be the actual substrate of all determination of time, then all existence in past as well as future time must be determinable in it alone. We can therefore give an appearance the name of substance only because we presuppose its existence at all times. This is not even well expressed by the word “persistence.”

B 229 That word points more toward future time. Yet the inner necessity of persisting is inseparably combined with the necessity of always having been, and the expression may therefore stand. Gigni de nihilo nihil, in nihilum nil posse reverti were two propositions the ancients inseparably connected. They are now sometimes separated through misunderstanding, because people imagine they concern things in themselves, and that the first might conflict with the world’s dependence on a supreme cause, even as to its substance. This concern is unnecessary, since we are speaking here only of appearances in the field of experience. Their unity would never be possible if we allowed new things, as substances, to arise. For then what alone can represent the unity of time would disappear: the identity of the substrate in which alone all change has thoroughgoing unity. This persistence, however, is still nothing more than the way we represent to ourselves the existence of things in appearance.

The determinations of a substance, which are nothing other than particular ways in which it exists, are called accidents. They are always real, because they concern the existence of substance; negations are only determinations expressing the nonbeing of something in the substance.

B 230 If one assigns a distinct existence to this real element in substance, for example to motion as an accident of matter, this existence is called inherence, in distinction from the existence of substance, which is called subsistence. But this gives rise to many misinterpretations, and it is more precise and correct to designate the accident only through the way in which the existence of a substance is positively determined. Yet under the conditions governing the logical use of our understanding, it is unavoidable that we should, as it were, separate what can change in the existence of a substance while the substance remains, and consider it in relation to what properly persists and underlies it. Hence this category too stands under the heading of relations, more as their condition than as itself containing a relation.

This persistence also grounds the correction of the concept of alteration. Arising and perishing are not alterations of what arises or perishes. Alteration is one way of existing that succeeds another way of existing of the very same object. Hence everything that undergoes alteration remains, and only its state changes. Since this change therefore concerns only determinations that can cease or begin, we may say, in an expression that seems somewhat paradoxical: only the persistent (substance) is altered.

B 231 The changeable undergoes no alteration, but a change, as some determinations cease and others begin.

Alteration can therefore be perceived only in substances. Arising or perishing outright, without merely concerning a determination of the persistent, can be no possible perception at all. For precisely this persistent element makes possible the representation of a transition from one state to another, and from nonbeing to being; these can therefore be empirically cognized only as changing determinations of what remains. Suppose something begins to be outright: you must have a point in time at which it was not. But to what will you attach this point, if not to something already there? For an empty time preceding it is no object of perception. If, however, you connect this arising with things that existed before and continue up to what arises, then the latter was only a determination of the former as the persistent. The same holds for perishing, since it presupposes the empirical representation of a time when an appearance no longer is.

Substances in appearance are the substrates of all determinations of time. The arising of some and the perishing of others would abolish the sole condition of the empirical unity of time itself.

B 232 Appearances would then relate to two different times in which existence flowed side by side, which is absurd. For there is only one time, in which all different times must be posited not simultaneously but successively.

Persistence is therefore a necessary condition under which alone appearances, as things or objects, are determinable in a possible experience. What the empirical criterion of this necessary persistence, and with it of the substantiality of appearances, may be, we will have occasion to discuss as needed in what follows.

B. Second Analogy

Principle of Temporal Succession According to the Law of Causality

All alterations occur according to the law of the connection of cause and effect.

Proof

(The preceding principle has shown that all appearances in temporal succession are merely alterations: a successive being and nonbeing of the determinations of a substance that persists. Consequently the being of substance itself following its nonbeing, or its nonbeing following its existence, does not occur.

B 233 In other words, the arising or perishing of substance itself does not take place. That principle could also have been expressed as follows: all change, succession, of appearances is only alteration. For the arising or perishing of substance is not an alteration of it, since the concept of alteration presupposes the very same subject as existing with two opposed determinations, and hence as persisting.—After this preliminary reminder, the proof follows.)

I perceive that appearances follow one another: that a state of things exists at one time whose opposite existed in the preceding state. Thus I am actually connecting two perceptions in time. Now connection is not the work of mere sense and intuition, but here the product of a synthetic faculty of imagination that determines inner sense with regard to temporal relations. Yet imagination can combine the two states in question in two ways, letting either one precede the other in time. For time cannot be perceived in itself, nor can what precedes and what follows in the object be determined, as it were empirically, in relation to it. I am therefore conscious only that my imagination posits one before and the other afterward, not that in the object one state precedes the other.

B 234 In other words, mere perception leaves the objective relation of successive appearances undetermined. For this relation to be cognized as determined, the relation between the two states must be thought in such a way that it necessarily determines which must be posited before and which after, and not the reverse. But a concept carrying with it a necessity of synthetic unity can only be a pure concept of the understanding, not one lying in perception. Here it is the concept of the relation of cause and effect, in which the former determines the latter in time as its consequence, not as something that could merely precede in imagination, or perhaps not be perceived at all. Thus only by subjecting the succession of appearances, and hence all alteration, to the law of causality is experience itself, that is, empirical cognition of them, possible. Consequently they themselves, as objects of experience, are possible only according to this same law.

The apprehension of the manifold of appearance is always successive. The representations of the parts follow one another. Whether they also follow one another in the object is a second point of reflection, not contained in the first. Now everything, and even every representation insofar as we are conscious of it, can indeed be called an object.

B 235 But what this word is to mean in the case of appearances, not insofar as they themselves are objects as representations, but insofar as they merely designate an object, requires deeper investigation. Insofar as they are merely representations and at the same time objects of consciousness, they are not at all distinct from apprehension, that is, from being taken up into the synthesis of imagination. We must therefore say that the manifold of appearances is always generated successively in the mind. If appearances were things in themselves, no one could infer from the succession of representations of their manifold how that manifold is combined in the object. For we are concerned only with our representations; how things may be in themselves, without regard to the representations through which they affect us, lies entirely beyond our sphere of cognition. Now although appearances are not things in themselves, they are nevertheless the only things that can be given to us for cognition. I must therefore indicate what combination in time belongs to the manifold in appearances themselves, while its representation in apprehension is always successive. For example, the apprehension of the manifold in the appearance of a house standing before me is successive. The question is whether the manifold of this house is itself also successive within it, which certainly no one will concede.

B 236 Yet as soon as I raise my concepts of an object to transcendental significance, the house is no thing in itself at all, but only an appearance, a representation whose transcendental object is unknown. What, then, do I mean by asking how the manifold may be combined in the appearance itself, which is after all nothing in itself? Here what lies in successive apprehension is regarded as representation, while the appearance given to me, although nothing more than a sum total of these representations, is regarded as their object, with which my concept drawn from the representations of apprehension is to agree. We soon see that, since truth is the agreement of cognition with the object, the question here can concern only the formal conditions of empirical truth. In contrast with the representations of apprehension, appearance can be represented as their object, distinct from them, only if it stands under a rule that distinguishes it from every other apprehension and makes a manner of combining the manifold necessary. That in appearance which contains the condition of this necessary rule of apprehension is the object.

Let us now proceed with our task. That something happens—that something, or a state, comes to be that was not before—cannot be empirically perceived unless an appearance precedes it that does not contain this state.

B 237 For an actuality following an empty time, and hence an arising preceded by no state of things, can no more be apprehended than empty time itself. Every apprehension of an event is therefore a perception following another. But since this holds of every synthesis of apprehension, as I showed above with the appearance of a house, it does not yet distinguish this apprehension from others. Yet I also note that, if in an appearance containing an occurrence I call the preceding state of perception A and the succeeding one B, then B can only follow A in apprehension, whereas perception A cannot follow B but can only precede it. For example, I see a ship drifting downstream. My perception of its position farther downstream follows my perception of its position farther upstream, and it is impossible that, in apprehending this appearance, the ship should be perceived first downstream and afterward upstream. Here, then, the order in the succession of perceptions in apprehension is determined, and apprehension is bound to it. In the previous example of a house, my perceptions in apprehension could begin at its top and end at the ground, but could also begin below and end above.

B 238 Likewise I could apprehend the manifold of empirical intuition from right or left. In the series of these perceptions, then, there was no determinate order making it necessary where I had to begin in apprehension in order to combine the manifold empirically. But this rule is always found in the perception of what happens, and makes necessary the order of the successive perceptions in the apprehension of this appearance.

In our case, then, I must derive the subjective succession of apprehension from the objective succession of appearances, because otherwise the former is entirely undetermined and distinguishes no appearance from another. It alone proves nothing about the connection of the manifold in the object, since it is entirely arbitrary. The objective succession will therefore consist in the order of the manifold of appearance according to which the apprehension of one thing, what happens, follows that of another, what precedes, according to a rule. Only in this way can I be entitled to say of the appearance itself, and not merely of my apprehension, that a succession is found in it. This means that I cannot conduct the apprehension otherwise than in precisely this succession.

According to such a rule, therefore, what precedes an event in general must contain the condition of a rule.

B 239 According to this rule the event always and necessarily follows. Conversely, however, I cannot go backward from the event and determine through apprehension what precedes it. For no appearance goes back from the succeeding point in time to the preceding one, though it does relate to some preceding point; from a given time, by contrast, the advance to the determinate succeeding time is necessary. Hence, since there is after all something that follows, I must necessarily relate it to something else in general that precedes it and on which it follows according to a rule, that is, necessarily. The event, as the conditioned, thus reliably points to some condition, while this condition determines the event.

Suppose that nothing preceded an event on which it had to follow according to a rule. All succession of perception would then lie solely in apprehension and be merely subjective, without thereby objectively determining which of the perceptions must properly be preceding and which succeeding. We would thus have only a play of representations relating to no object at all: through our perception no appearance would be distinguished from any other in its temporal relation. For succession in apprehending is everywhere the same, and there would thus be nothing in appearance that determines it so as to make a particular succession objectively necessary.

B 240 I would therefore not say that two states follow one another in the appearance, but only that one apprehension follows another. This is merely subjective and determines no object, and hence cannot count as cognition of any object, not even in appearance.

Whenever we experience that something happens, then, we always presuppose that something precedes it on which it follows according to a rule. Without this I would not say of the object that it follows, because mere succession in my apprehension, unless determined through a rule in relation to something preceding, warrants no succession in the object. Thus it is always with reference to a rule according to which appearances in their succession, that is, as they happen, are determined by the preceding state that I make my subjective synthesis of apprehension objective. Only under this presupposition alone is even the experience of something happening possible.

Admittedly, this seems to contradict all the observations ever made about the course of our use of understanding. According to these, only by perceiving and comparing the corresponding successions of many events after preceding appearances have we been led to discover a rule.

B 241 By this rule certain events always follow certain appearances, and we were thereby first prompted to form the concept of cause. On this footing the concept would be merely empirical, and the rule it supplies, that everything that happens has a cause, would be just as contingent as experience itself. Its universality and necessity would then be merely invented and have no true universal validity, since they would rest not on a priori grounds but only on induction. The situation here, however, is the same as with other pure a priori representations, such as space and time, which we can extract from experience as clear concepts only because we had put them into experience, and thereby first brought experience about through them. Certainly the logical clarity of this representation of a rule determining the series of events, as a concept of cause, is possible only once we have made use of it in experience. Yet reference to this rule, as the condition of the synthetic unity of appearances in time, was the ground of experience itself, and thus preceded it a priori.

What matters, then, is to show by an example that even in experience we never ascribe succession to the object—the succession of an event in which something happens that was not before—and distinguish it from the subjective succession of our apprehension, except where a rule underlies it.

B 242 This rule compels us to observe this order of perceptions rather than another; indeed, this compulsion is precisely what first makes the representation of a succession in the object possible.

We have representations within us, of which we can also become conscious. But however extensive, exact, or precise this consciousness may be, they still remain only representations: inner determinations of our mind in this or that temporal relation. How, then, do we come to posit an object for these representations, or, beyond their subjective reality as modifications, to ascribe to them some further objective reality, I do not know what kind? Objective significance cannot consist in a relation to another representation, of what one wished to call the object; otherwise the question arises again: how does this representation in turn go beyond itself and acquire objective significance in addition to the subjective significance proper to it as a determination of the state of mind? If we investigate what new character relation to an object gives our representations, and what standing they thereby acquire, we find that it does nothing more than make their combination necessary in a certain way and subject them to a rule.

B 243 Conversely, objective significance is conferred on them only because a certain order in the temporal relation of our representations is necessary.

In the synthesis of appearances the manifold of representations is always successive. This does not represent any object at all, since this succession, common to all apprehensions, distinguishes nothing from anything else. But as soon as I perceive, or presuppose, that in this succession there is a relation to the preceding state from which the representation follows according to a rule, something is represented as an event, as something that happens. That is, I cognize an object that I must place at a certain determinate position in time, a position that cannot be assigned to it otherwise in view of the preceding state. Thus when I perceive that something happens, this representation contains, first, that something precedes it, because it is precisely in relation to this that the appearance acquires its temporal relation: existing after a preceding time in which it was not. But it can acquire its determinate position in time within this relation only by something being presupposed in the preceding state on which it always follows, that is, follows according to a rule. From this it follows, first, that I cannot reverse the series and place what happens before that on which it follows; second, that when the preceding state is posited, this determinate event follows inevitably and necessarily.

B 244 In this way an order arises among our representations in which the present, insofar as it has come to be, points to some preceding state as a correlate, though still undetermined, of this given occurrence. This correlate, however, relates determinately to the occurrence as its consequence, and necessarily connects it with itself in the temporal series.

Now if it is a necessary law of our sensibility, and hence a formal condition of all perceptions, that preceding time necessarily determines succeeding time, since I can reach the latter only through the former, then it is also an indispensable law of the empirical representation of the temporal series that appearances of past time determine every existence in the time that follows. These later appearances, as events, take place only insofar as the former determine their existence in time, that is, establish it according to a rule. For only in appearances can we empirically cognize this continuity in the connection of times.

Understanding belongs to all experience and its possibility. Its first contribution is not to make the representation of objects distinct, but to make the representation of an object in general possible.

B 245 It does this by transferring temporal order to appearances and their existence, assigning to each as a consequence a position in time determined a priori with respect to preceding appearances. Without this, appearance would not agree with time itself, which determines the position of all its parts a priori. This determination of position cannot be borrowed from the relation of appearances to absolute time, since absolute time is no object of perception. Rather, appearances must conversely determine one another’s positions in time itself and make them necessary in the temporal order. That is, what follows or happens must follow according to a universal rule upon what was contained in the preceding state. The result is a series of appearances that, through the understanding, produces and makes necessary in the series of possible perceptions precisely the same order and continuous connection as is found a priori in the form of inner intuition, time, in which all perceptions must have their positions.

That something happens is thus a perception belonging to a possible experience. This experience becomes actual when I regard the appearance as determined in its position in time, and hence as an object that can always be found according to a rule in the connection of perceptions.

B 246 But this rule for determining something according to temporal succession is that what precedes must contain the condition under which the event always, that is, necessarily, follows. The principle of sufficient reason is therefore the ground of possible experience: of the objective cognition of appearances with respect to their relation in temporal succession.

The proof of this proposition rests solely on the following considerations. All empirical cognition involves a synthesis of the manifold through imagination, which is always successive: its representations always follow one another. But in imagination this succession is not at all determined as to its order, as to what must precede and what follow; the series of successive representations can be taken backward just as well as forward. If, however, this synthesis is a synthesis of apprehension, of the manifold of a given appearance, then the order is determined in the object. More precisely, there is in it an order of successive synthesis that determines an object, according to which something must necessarily precede and, when this is posited, the other must necessarily follow. If, therefore, my perception is to contain cognition of an event, of something actually happening, it must be an empirical judgment in which the succession is thought as determined: as presupposing another appearance in time upon which it follows necessarily, or according to a rule.

B 247 Otherwise, if I posited the preceding appearance and the event did not necessarily follow it, I would have to regard it as merely a subjective play of my imaginings; and if I nevertheless represented something objective by it, I would call it a mere dream. Thus the relation of appearances as possible perceptions, according to which what follows, what happens, is necessarily determined in its existence and according to a rule in time by something preceding it—the relation of cause to effect—is the condition of the objective validity of our empirical judgments concerning the series of perceptions, hence of their empirical truth, and thus of experience. The principle of the causal relation in the succession of appearances therefore also holds for all objects of experience under the conditions of succession, because it is itself the ground of the possibility of such experience.

But a difficulty still arises here that must be removed. In our formulation the principle of causal connection among appearances is restricted to their succession. Yet its use shows that it also applies to their concomitance, and that cause and effect can be simultaneous. For example, there is warmth in a room that is not found in the open air.

B 248 I look for the cause and find a heated stove. Now this, as cause, is simultaneous with its effect, the warmth of the room. Here, then, there is no temporal succession between cause and effect; they are simultaneous, and yet the law holds. Most efficient causes in nature are simultaneous with their effects, and the temporal succession of the latter is occasioned only by the cause’s inability to produce its entire effect in an instant. But at the instant when the effect first arises it is always simultaneous with the causality of its cause, since if that causality had ceased an instant earlier, the effect would not have arisen at all. Here we must carefully note that the issue concerns the order of time, not its passage. The relation remains even if no time has elapsed. The time between the causality of the cause and its immediate effect may vanish, so that they are simultaneous, but the relation of one to the other still always remains determinable in time. If I regard a ball resting on a stuffed cushion and pressing a hollow into it as a cause, it is simultaneous with its effect. Yet I still distinguish the two through the temporal relation of their dynamical connection. For when I place the ball on the cushion, the hollow follows its previously smooth shape.

B 249 But if the cushion has a hollow (I do not know from where), a lead ball does not follow upon it.

Thus temporal succession is indeed the sole empirical criterion of an effect in relation to the causality of the cause that precedes it. The glass is the cause of the water’s rising above its horizontal surface, although both appearances are simultaneous. For as soon as I draw water with the glass from a larger vessel, something follows: its horizontal level there changes into the concave one it assumes in the glass.

This causality leads to the concept of action, this to the concept of force, and thereby to the concept of substance. Since I do not wish to mix my critical undertaking, which concerns solely the sources of synthetic a priori cognition, with analyses concerned merely with clarifying concepts, not extending them, I leave their detailed discussion to a future system of pure reason. Such analysis, however, is already found abundantly in the familiar textbooks of this kind. But I cannot leave untouched the empirical criterion of a substance insofar as it seems to reveal itself not through the persistence of appearance, but better and more easily through action.

B 250 Where there is action, and hence activity and force, there is also substance; in substance alone must we seek the seat of this fertile source of appearances. That is very well said. But if one must explain what one understands by substance, while avoiding a vicious circle, the answer is not so easy. How is one to infer straight from action the persistence of what acts, which is after all so essential and distinctive a mark of substance (phaenomenon)? After what we have said, however, solving the question presents no such difficulty, although on the usual method of proceeding merely analytically with one’s concepts it would be quite insoluble. Action already signifies the relation of the subject of causality to the effect. Since every effect consists in what happens, and thus in the changeable that marks time in succession, its ultimate subject is the persistent, as the substrate of everything changing, that is, substance. For according to the principle of causality, actions are always the first ground of all change in appearances, and thus cannot lie in a subject that itself changes, since otherwise other actions and another subject determining this change would be required. By virtue of this, action, as a sufficient empirical criterion, proves substantiality.

B 251 There is no need for me first to seek its persistence by comparing perceptions; nor could this be done by that route with the completeness required by the scope and strict universal validity of the concept. For that the primary subject of the causality of all arising and perishing cannot itself arise and perish in the field of appearances is a secure inference. It leads to empirical necessity and persistence in existence, and hence to the concept of a substance as appearance.

When something happens, its mere arising, without regard to what arises, is already in itself an object of investigation. The transition from the nonbeing of a state into that state, even supposing the state contained no quality in appearance, already requires investigation on its own. As was shown under A, this arising concerns not substance, which does not arise, but its state. It is therefore merely alteration, not origination from nothing. If this origination is regarded as the effect of an external cause, it is called creation. Creation cannot be admitted as an event among appearances, since its mere possibility would abolish the unity of experience. Yet things might be considered not as phenomena but as things in themselves.

B 252 As objects of mere understanding they could then, although they are substances, nevertheless be regarded as dependent for their existence on an external cause. This, however, would entail quite different meanings of words and would not apply to appearances as possible objects of experience.

How anything can be altered at all—how it is possible for a state at one point in time to be followed by an opposite state at another—we have not the least a priori concept. This requires acquaintance with actual forces, which can be given only empirically: for example, moving forces, or, what amounts to the same thing, certain successive appearances, as motions, that indicate such forces. But the form of every alteration, the condition under which alone it can occur as the arising of another state (whatever its content, that is, the state that is altered, may be), and hence the succession of states itself (what has happened), can nevertheless be considered a priori according to the law of causality and the conditions of time*.

* Note carefully that I am speaking not of a change in certain relations in general, but of an alteration of state. Thus when a body moves uniformly, it does not alter its state of motion at all; it does so, however, when its motion increases or decreases.

B 253 When a substance passes from a state a into another b, the point in time of the second differs from and follows that of the first state. Likewise the second state, as reality in appearance, differs from the first, in which this reality was not, as b differs from zero. That is, even if state b differed from state a only in magnitude, the alteration is an arising of b−a, which was not in the preceding state, and with respect to which that state is = 0.

The question, then, is how a thing passes from one state = a into another = b. Between two instants there is always a time, and between two states at those instants there is always a difference that has a magnitude, since all parts of appearances are always magnitudes in turn. Thus every transition from one state to another occurs in a time contained between two instants, the first determining the state the thing leaves, the second the state it reaches. Both, then, are boundaries of the time of an alteration, and hence of the intermediate state between the two states, and as such belong to the entire alteration. Now every alteration has a cause that manifests its causality throughout the time in which the alteration takes place.

B 254 This cause therefore produces its alteration not suddenly, all at once or in an instant, but in a time, so that as the time increases from the initial instant a to its completion in b, the magnitude of reality, b−a, is also generated through all the smaller degrees contained between the first and the last. All alteration is therefore possible only through a continuous action of causality, which, insofar as it is uniform, is called a moment. Alteration does not consist of these moments, but is generated through them as their effect.

This, then, is the law of the continuity of all alteration. Its ground is that neither time nor appearance in time consists of smallest parts, and yet in its alteration the state of the thing passes through all these parts, as elements, to its second state. No difference in the real in appearance is the smallest, just as no difference in the magnitude of times is the smallest. Thus the new state of reality grows from the first, in which this reality was not, through all its infinitely many degrees, whose differences from one another are all smaller than the difference between 0 and a.

What use this proposition may have in investigating nature does not concern us here. But how such a proposition, which seems so greatly to extend our cognition of nature, is possible entirely a priori very much requires our examination, even though direct observation proves it actual and correct.

B 255 One might therefore think oneself excused from asking how it was possible. For there are so many unfounded pretensions to extending our cognition through pure reason that it must be adopted as a general principle to be thoroughly distrustful in this regard, and to believe or accept nothing of the kind, even on the clearest dogmatic proof, without documents that can supply a sound deduction.

Every increase in empirical cognition and every advance of perception is nothing but an extension of the determination of inner sense, an advance in time, whatever the objects may be, whether appearances or pure intuitions. This advance in time determines everything and is itself determined by nothing further; that is, its parts are given only in time and through the synthesis of time, not before it. Accordingly every transition in perception to something following in time is a determination of time through the generation of this perception. Since time, always and in all its parts, is a magnitude, this is the generation of a perception as a magnitude through all degrees, none of which is the smallest, from zero up to its determinate degree. This makes clear the possibility of cognizing a law of alterations a priori as to their form.

B 256 We anticipate only our own apprehension, whose formal condition, since it is present in us before any given appearance, must certainly be capable of being cognized a priori.

Thus, just as time contains the sensible a priori condition of the possibility of a continuous advance from what exists to what follows, so understanding, through the unity of apperception, is the a priori condition of the possibility of continuously determining all positions for appearances in this time through the series of causes and effects. The causes inevitably entail the existence of their effects, and thereby make the empirical cognition of temporal relations valid for every time, universally, and hence objectively.

C. Third Analogy

Principle of Simultaneity According to the Law of Interaction, or Community

All substances, insofar as they can be perceived in space as simultaneous, are in thoroughgoing interaction.

Proof

Things are simultaneous when in empirical intuition the perception of one can follow the perception of the other.

B 257 It can do so reciprocally (which, as was shown with the second principle, cannot happen in the temporal succession of appearances). Thus I can direct my perception first to the moon and afterward to the earth, or conversely first to the earth and then to the moon. Because the perceptions of these objects can follow one another reciprocally, I say they exist simultaneously. Now simultaneity is the existence of the manifold at the same time. But time itself cannot be perceived, so as to infer from things being posited in the same time that their perceptions can follow one another reciprocally. The synthesis of imagination in apprehension would therefore merely indicate each of these perceptions as present in the subject when the other is not, and conversely. It would not indicate that the objects are simultaneous: that when one is, the other is also at the same time, and that this is necessary if the perceptions are to follow one another reciprocally. Consequently a concept of the understanding concerning the reciprocal succession of the determinations of these things existing simultaneously outside one another is required, in order to say that the reciprocal succession of perceptions is grounded in the object, and thereby to represent simultaneity as objective.

B 258 Now the relation of substances in which one contains determinations whose ground is contained in the other is the relation of influence; and when each reciprocally contains the ground of determinations in the other, it is the relation of community or interaction. Thus the simultaneity of substances in space can be cognized in experience only on the presupposition of their interaction with one another. This is therefore also the condition of the possibility of the things themselves as objects of experience.

Things are simultaneous insofar as they exist in one and the same time. But how do we recognize that they are in one and the same time? When the order in the synthesis of apprehension of this manifold is indifferent, that is, when it can proceed from A through B, C, D to E, or conversely from E to A. For if they were successive in time, in the order beginning with A and ending with E, it would be impossible to begin apprehension in perception with E and proceed backward to A, because A belongs to past time and can therefore no longer be an object of apprehension.

Suppose now that in a manifold of substances as appearances each were completely isolated: none acted on another or reciprocally received influences from it.

B 259 I say that their simultaneity would be no object of a possible perception, and the existence of one could lead by no route of empirical synthesis to the existence of another. For if you imagine them separated by a completely empty space, perception advancing in time from one to another would indeed determine the existence of the latter through a subsequent perception, but could not distinguish whether the appearance objectively followed the first or was instead simultaneous with it.

There must therefore be something besides mere existence through which A determines B’s position in time, and conversely B determines A’s. Only under this condition can the substances in question be empirically represented as existing simultaneously. Now only what is the cause of another thing or its determinations determines that thing’s position in time. Thus every substance, since it can be a consequence only in respect of its determinations, must contain both the causality of certain determinations in the other and the effects of the other’s causality within itself. That is, they must stand in dynamical community, directly or indirectly, if simultaneity is to be cognized in any possible experience. But everything without which experience of objects would itself be impossible is necessary with respect to objects of experience.

B 260 Thus all substances in appearance, insofar as they are simultaneous, must necessarily stand in a thoroughgoing community of interaction with one another.

The word “community” in our language is ambiguous: it can mean either communio or commercium. We use it here in the latter sense, as a dynamical community, without which even spatial community (communio spatii) could never be empirically cognized. It is easy to observe in our experiences that only continuous influences throughout space can guide our sense from one object to another; that the light playing between our eye and the heavenly bodies can bring about an indirect community between us and them, thereby proving their simultaneity; that we can make no empirical change of place (perceive this change) unless matter everywhere makes the perception of our position possible; and that matter can show its simultaneity, and thereby its coexistence even with the most distant objects, though only indirectly, solely through its reciprocal influence. Without community every perception of an appearance in space is cut off from every other, and the chain of empirical representations, that is, experience, would begin entirely afresh with a new object.

B 261 The previous one would not be in the least connected with it, nor could it stand in any temporal relation to it. I do not intend by this to refute empty space at all; it may well exist where perceptions do not reach and hence no empirical cognition of simultaneity takes place. But it is then no object at all for any of our possible experience.

The following may serve to clarify this. In our mind all appearances, as contained in a possible experience, must stand in a community (communio) of apperception. Insofar as objects are to be represented as connected in simultaneous existence, they must reciprocally determine their positions in one time and thereby constitute a whole. If this subjective community is to rest on an objective ground, or be related to appearances as substances, the perception of one must, as ground, make the perception of another possible, and conversely, so that the succession that is always present in perceptions as apprehensions is not ascribed to the objects, but these can be represented as existing simultaneously. This, however, is a reciprocal influence, a real community (commercium) of substances, without which the empirical relation of simultaneity could not occur in experience.

B 262 Through this commercium appearances, insofar as they stand outside one another yet in connection, constitute a composite (compositum reale), and such composita become possible in many ways. The three dynamical relations from which all others arise are therefore those of inherence, consequence, and composition.

* * *

These, then, are the three analogies of experience. They are nothing other than principles for determining the existence of appearances in time according to all three of its modi: the relation to time itself as a magnitude (the magnitude of existence, that is, duration); the relation in time as a series (one after another); and finally the relation in it as a sum total of all existence (at the same time). This unity of temporal determination is thoroughly dynamical. That is, time is not regarded as that in which experience immediately determines a position for each existence, which is impossible because absolute time is no object of perception with which appearances could be compared. Rather, the rule of understanding, through which alone the existence of appearances can acquire synthetic unity according to temporal relations, determines for each its position in time, and does so a priori and validly for each and every time.

B 263 By nature in the empirical sense we understand the connection of appearances in their existence according to necessary rules, that is, laws. Thus there are certain laws, indeed a priori laws, that first make a nature possible. Empirical laws can occur and be discovered only through experience, and in accordance with those original laws through which experience itself first becomes possible. Our analogies therefore properly present the unity of nature in the connection of all appearances under certain exponents. These express nothing but the relation of time, insofar as it contains all existence, to the unity of apperception, which can occur only in synthesis according to rules. Together, then, they say that all appearances lie in one nature, and must lie in it, because without this a priori unity no unity of experience, and hence no determination of objects in it, would be possible.

A remark must be made, however, about the method of proof we have employed for these transcendental laws of nature and its distinctive character. It must also be very important as a prescription for every other attempt to prove propositions that are both intellectual and synthetic a priori. Suppose we had wished to prove these analogies dogmatically, that is, from concepts.

B 264 We should then have had to prove that everything existing is found only in what persists; that every event presupposes something in the preceding state on which it follows according to a rule; and finally that in the simultaneous manifold the states are simultaneous in relation to one another according to a rule (stand in community). All our effort would have been utterly in vain. For from one object and its existence one cannot arrive at the existence of another, or at its way of existing, through mere concepts of these things, however one analyzes them. What, then, remained to us? The possibility of experience, as a cognition in which all objects must ultimately be capable of being given to us if their representation is to have objective reality for us. In this third thing, whose essential form consists in the synthetic unity of the apperception of all appearances, we found a priori conditions of the thoroughgoing and necessary temporal determination of all existence in appearance, without which even empirical determination of time would be impossible. We found rules of a priori synthetic unity through which we could anticipate experience. The lack of this method, and the delusion of wishing to prove dogmatically synthetic propositions recommended as principles by the experiential use of understanding, explain why proof of the principle of sufficient reason has been attempted so often, yet always in vain.

B 265 No one thought of the other two analogies, though they were always tacitly employed*, because the guiding thread of the categories was missing. This alone can discover and expose every gap in the understanding, in concepts as well as principles.

* The unity of the world as a whole, in which all appearances are to be connected, is plainly a mere consequence of the tacitly accepted principle of the community of all simultaneous substances. For if they were isolated, they would not constitute a whole as its parts; and if their connection, the interaction of the manifold, were not already necessary on account of simultaneity, one could not infer that real relation from this merely ideal one. We have shown in the appropriate place, however, that community is properly the ground of the possibility of an empirical cognition of coexistence, and that one therefore actually infers backward only from this cognition to community as its condition.

4 The Postulates of Empirical Thinking in General

1 What agrees with the formal conditions of experience (as to intuition and concepts) is possible.

2 B 266 What is connected with the material conditions of experience (of sensation) is actual.

3 That whose connection with the actual is determined according to universal conditions of experience is (exists) necessarily.

Elucidation

The categories of modality have the peculiarity that, as determinations of the object, they do not in the least enlarge the concept to which they are added as predicates, but express only its relation to the faculty of cognition. Even when the concept of a thing is already entirely complete, I can still ask of this object whether it is merely possible or also actual, or, if actual, whether it is also necessary. No further determinations are thereby thought in the object itself. The question is only how it, together with all its determinations, relates to the understanding and its empirical use, to the empirical power of judgment, and to reason in its application to experience.

For this very reason the principles of modality are nothing further than explanations of the concepts of possibility, actuality, and necessity in their empirical use. At the same time they restrict all categories to merely empirical use, without admitting or permitting their transcendental use.

B 267 For if these categories are not to have a merely logical meaning, analytically expressing the form of thinking, but are to concern things and their possibility, actuality, or necessity, they must relate to possible experience and its synthetic unity, in which alone objects of cognition are given.

The postulate of the possibility of things therefore requires that their concept agree with the formal conditions of an experience in general. These conditions, the objective form of experience in general, contain all the synthesis required for cognition of objects. A concept containing a synthesis must be regarded as empty, and relates to no object, if this synthesis does not belong to experience. It may belong to experience either as borrowed from it, in which case the concept is called empirical, or as a synthesis on which experience in general, its form, rests as an a priori condition. In the latter case it is a pure concept that nevertheless belongs to experience, because its object can be found only there. For where would one obtain the mark of the possibility of an object thought through a synthetic a priori concept, if not from the synthesis constituting the form of empirical cognition of objects?

B 268 That such a concept must contain no contradiction is indeed a necessary logical condition, but is far from sufficient for the concept’s objective reality, that is, the possibility of an object such as the concept thinks. Thus there is no contradiction in the concept of a figure enclosed by two straight lines, for the concepts of two straight lines and their meeting contain no negation of a figure. Rather, the impossibility rests not on the concept in itself but on its construction in space, on the conditions of space and its determination. These in turn have their objective reality, that is, they relate to possible things, because they contain a priori the form of experience in general.

Let us now display the extensive use and influence of this postulate of possibility. If I represent a thing that persists, so that everything changing belongs merely to its state, I can never cognize from such a concept alone that such a thing is possible. Or I represent something as so constituted that, when it is posited, something else always and inevitably follows. This may certainly be thought without contradiction; but whether such a property, as causality, is to be found in any possible thing cannot thereby be judged.

B 269 Finally, I can represent different things, substances, so constituted that the state of one entails a consequence in the state of the other, and reciprocally. But whether such a relation can belong to any things cannot at all be gathered from these concepts, which contain a merely arbitrary synthesis. Only because these concepts express a priori the relations of perceptions in every experience do we cognize their objective reality, that is, their transcendental truth. We do so independently of experience, certainly, but not independently of all relation to the form of an experience in general and to the synthetic unity in which alone objects can be empirically cognized.

But if one wished to fashion entirely new concepts of substances, forces, and interactions from the material perception offers us, without borrowing from experience itself an example of their connection, one would fall into sheer fantasies whose possibility has no distinguishing mark whatever. For here one neither accepts experience as teacher nor borrows these concepts from it. Unlike the categories, such invented concepts cannot acquire the mark of their possibility a priori as conditions on which all experience depends, but only a posteriori as concepts given through experience itself.

B 270 Their possibility must be cognized either a posteriori and empirically or not at all. A substance persistently present in space yet not filling it, like the intermediate entity between matter and thinking beings that some have wished to introduce; a special fundamental power of our mind to intuit the future in advance, not merely infer it; or finally a faculty of the mind for sharing thoughts with other people, however distant they may be: these are concepts whose possibility is entirely groundless. It cannot be grounded on experience and its known laws, and without them it is an arbitrary combination of thoughts that, though containing no contradiction, can claim no objective reality, and hence no possibility of an object such as one intends to think here. As for reality, it is surely self-evidently forbidden to think it in concreto without enlisting experience, because it can concern only sensation as the matter of experience, not the form of relation with which one might perhaps play in inventions.

But I pass over everything whose possibility can be gathered only from actuality in experience, and consider here only the possibility of things through a priori concepts.

B 271 Of these I continue to maintain that they can never establish possibility by themselves alone, but always only as formal and objective conditions of an experience in general.

It does indeed seem as though the possibility of a triangle could be cognized from its concept in itself, which is certainly independent of experience. For we can in fact give it an object entirely a priori, that is, construct it. But since this is only the form of an object, it would still remain merely a product of imagination whose object’s possibility remained doubtful. Something more is required: that such a figure be thought solely under conditions on which all objects of experience rest. That space is an a priori formal condition of outer experiences, and that the very same formative synthesis through which we construct a triangle in imagination is entirely identical with the synthesis we exercise in apprehending an appearance in order to form an experiential concept of it: this alone connects with that concept the representation of the possibility of such a thing. Likewise the possibility of continuous magnitudes, indeed of magnitudes in general, since their concepts are all synthetic, becomes clear not from the concepts themselves, but only from them as formal conditions for determining objects in experience in general.

B 272 And where else would we seek objects corresponding to concepts, if not in experience, through which alone objects are given to us? We can indeed cognize and characterize the possibility of things without first supplying experience itself, merely in relation to the formal conditions under which something in experience is determined as an object in general, and thus entirely a priori—but still only in relation to experience and within its boundaries.

The postulate for cognizing the actuality of things requires perception, and hence sensation of which one is conscious. It does not require immediate perception of the very object whose existence is to be cognized, but does require that object’s connection with some actual perception according to the analogies of experience, which set out all real connection in an experience in general.

In the mere concept of a thing no mark of its existence can be found. For however complete it may be, so that nothing whatever is lacking for thinking a thing with all its inner determinations, existence has nothing at all to do with any of this. It concerns only the question whether such a thing is given to us, so that its perception could, if need be, precede its concept.

B 273 For the concept’s preceding perception signifies its mere possibility; perception, however, which supplies the material for the concept, is the sole mark of actuality. Yet we can also cognize a thing’s existence before perceiving it, and thus comparatively a priori, provided it is connected with some perceptions according to the principles of their empirical connection, the analogies. For then the thing’s existence is still connected with our perceptions in a possible experience, and by following those analogies we can arrive from our actual perception at the thing in the series of possible perceptions. Thus we cognize the existence of a magnetic matter penetrating all bodies from the perception of attracted iron filings, although the constitution of our organs makes immediate perception of this matter impossible for us. For according to the laws of sensibility and the context of our perceptions, we would in general also encounter an immediate empirical intuition of it in an experience if our senses were finer. Their coarseness does not affect the form of possible experience in general. Thus our cognition of the existence of things extends as far as perception and what follows from it according to empirical laws.

B 274 If we do not begin with experience, or do not proceed according to laws of the empirical connection of appearances, we boast in vain of wishing to guess or investigate the existence of anything. Idealism, however, raises a powerful objection to these rules for proving existence indirectly, and this is the proper place for its refutation.

Refutation of Idealism

Idealism—I mean material idealism—is the theory that declares the existence of objects in space outside us either merely doubtful and unprovable, or false and impossible. The former is the problematic idealism of Descartes, who declares only one empirical assertion (assertio), namely “I am,” indubitable. The second is the dogmatic idealism of Berkeley, who declares space, together with all the things to which it is attached as an inseparable condition, something impossible in itself, and therefore declares things in space to be mere imaginings. Dogmatic idealism is unavoidable if space is regarded as a property that is to belong to things in themselves; for then it, together with everything for which it serves as a condition, is a nonentity. We have, however, removed the ground of this idealism in the transcendental aesthetic.

B 275 Problematic idealism asserts nothing on this matter, but merely alleges our inability to prove an existence other than our own through immediate experience. It is reasonable and accords with a thorough philosophical cast of mind: to allow no decisive judgment before a sufficient proof has been found. The proof demanded must therefore show that we have experience, not merely imagination, of outer things. This can hardly be accomplished otherwise than by proving that even our inner experience, which Descartes regards as indubitable, is possible only on the presupposition of outer experience.

Theorem

The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.

Proof

I am conscious of my existence as determined in time. All determination of time presupposes something persistent in perception. But this persistent something cannot be something in me, because my existence in time can be determined in the first place only through this persistent something 1). Thus the perception of this persistent something is possible only through a thing outside me, not through the mere representation of a thing outside me. Consequently the determination of my existence in time is possible only through the existence of actual things that I perceive outside me.

B 276 Now consciousness in time is necessarily combined with consciousness of the possibility of this determination of time. Thus it is also necessarily combined with the existence of things outside me as the condition of the determination of time. That is, consciousness of my own existence is at the same time an immediate consciousness of the existence of other things outside me.

1 According to Kant’s preface to this second edition, the sentence is to be altered as follows: “But this persistent something cannot be an intuition in me. For all the determining grounds of my existence that can be found in me are representations, and as such themselves require something persistent distinct from them, in relation to which their change, and hence my existence in the time in which they change, can be determined.”

Remark 1. In the preceding proof we notice that the game idealism played is turned back against it with greater justice. Idealism assumed that the only immediate experience is inner experience, and that outer things are merely inferred from it, but unreliably, as always when one infers determinate causes from given effects. For the cause of the representations we ascribe, perhaps falsely, to outer things may also lie in ourselves. Here, however, it is proved that outer experience is properly immediate*.

B 277 Only through it is possible, not indeed consciousness of our own existence, but its determination in time, that is, inner experience. Certainly the representation “I am,” expressing the consciousness that can accompany all thinking, is what immediately includes the existence of a subject, but not yet any cognition of it, and hence no empirical cognition, that is, no experience. For besides the thought of something existing, cognition also requires intuition, here inner intuition, with respect to which, that is, to time, the subject must be determined. For this, outer objects are absolutely required, so that inner experience itself is consequently possible only indirectly, and only through outer experience.

* The immediate consciousness of the existence of outer things is not presupposed in the preceding theorem but proved, whether or not we can understand the possibility of this consciousness. The question concerning its possibility would be whether we have only an inner sense and no outer sense, but merely outer imagination. It is clear, however, that even to imagine something as external, that is, to present it to sense in intuition, we must already have an outer sense, and thereby immediately distinguish the mere receptivity of an outer intuition from the spontaneity characterizing every act of imagination. For merely to imagine even an outer sense would destroy the very faculty of intuition that imagination is supposed to determine.

Remark 2. All experiential use of our faculty of cognition in determining time agrees perfectly with this. Not only can we determine all time solely through change in outer relations (motion) in relation to what persists in space (for example, the sun’s motion in relation to objects on earth).

B 278 We even have nothing persistent at all that we could place as intuition beneath the concept of a substance except matter. Even this persistence is not drawn from outer experience, but presupposed a priori as a necessary condition of all determination of time, and hence also of the determination of inner sense concerning our own existence through the existence of outer things. Consciousness of myself in the representation “I” is no intuition at all, but a merely intellectual representation of the self-activity of a thinking subject. Hence this “I” has not the least predicate of intuition that, as persistent, could serve as a correlate for determining time in inner sense, as impenetrability does in matter as empirical intuition.

Remark 3. That the existence of outer objects is required for the possibility of a determinate consciousness of ourselves does not imply that every intuitive representation of outer things also includes their existence. Such a representation may very well be merely the effect of imagination, in dreams as well as in madness. But it is so only through the reproduction of former outer perceptions, which, as has been shown, are possible only through the actuality of outer objects. All that was to be proved here is that inner experience in general is possible only through outer experience in general.

B 279 Whether this or that supposed experience is not mere imagination must be established from its particular determinations and by comparison with the criteria of all actual experience.

* * *

Finally, the third postulate concerns material necessity in existence, not merely formal and logical necessity in the connection of concepts. Now no existence of objects of the senses can be cognized wholly a priori, though it can be cognized comparatively a priori in relation to another existence already given. Even then, however, one can arrive only at an existence that must be contained somewhere in the connection of experience of which the given perception is a part. Thus the necessity of existence can never be cognized from concepts, but always only from connection with what is perceived, according to universal laws of experience. Now no existence can be cognized as necessary under the condition of other given appearances except the existence of effects from given causes according to laws of causality. Thus it is not the existence of things, substances, but only that of their state whose necessity we can cognize.

B 280 And we cognize it from other states given in perception, according to empirical laws of causality. It follows that the criterion of necessity lies solely in the law of possible experience: that everything happening is determined a priori by its cause in appearance. Hence we cognize only the necessity of effects in nature whose causes are given to us. The mark of necessity in existence extends no further than the field of possible experience, and even there it does not apply to the existence of things as substances, since these can never be regarded as empirical effects, or as something that happens and arises. Necessity therefore concerns only the relations of appearances according to the dynamical law of causality, and the possibility grounded on this of inferring a priori from some given existence, a cause, to another existence, the effect. Everything that happens is hypothetically necessary: this is a principle that subjects alteration in the world to a law, a rule of necessary existence, without which there would not even be nature. Hence the proposition “Nothing happens by blind chance” (in mundo non datur casus) is an a priori law of nature; likewise, “No necessity in nature is blind, but conditioned and hence intelligible necessity” (non datur fatum).

B 281 Both are laws through which the play of alterations is subjected to a nature of things as appearances, or, what is the same, to the unity of understanding, in which alone they can belong to an experience as the synthetic unity of appearances. Both principles are dynamical. The first is properly a consequence of the principle of causality among the analogies of experience. The second belongs to the principles of modality, adding to causal determination the concept of necessity, though a necessity subject to a rule of understanding. The principle of continuity forbade in the series of appearances (alterations) every leap (in mundo non datur saltus), but also in the sum total of all empirical intuitions in space every gap or chasm between two appearances (non datur hiatus). For this is how one can express the proposition that nothing can enter experience that would prove a vacuum, or even admit it as a part of empirical synthesis. As for the void one might think outside the field of possible experience, the world, it does not fall under the jurisdiction of mere understanding. Understanding decides only questions concerning the use of given appearances for empirical cognition. The void is a problem for ideal reason, which goes beyond the sphere of possible experience.

B 282 It wishes to judge what surrounds and bounds experience itself, and must therefore be considered in the transcendental dialectic. These four propositions (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum) could easily be presented in their order, like all principles of transcendental origin, according to the order of the categories, with each assigned its proper place by proof. But the reader, now practiced, will do this unaided or readily discover the guiding thread. They all unite, however, solely in allowing nothing in empirical synthesis that could impair or disrupt understanding and the continuous connection of all appearances, that is, the unity of its concepts. For in understanding alone is the unity of experience possible, in which all perceptions must have their place.

Whether the field of possibility is greater than the field containing everything actual, and this in turn greater than the multitude of what is necessary: these are engaging questions, requiring a synthetic solution, but they fall solely under the jurisdiction of reason. They amount approximately to asking whether all things as appearances belong together in the sum total and context of a single experience, of which every given perception is a part that can therefore be combined with no other appearances.

B 283 Or they ask whether my perceptions can belong to more than one possible experience in their general connection. Understanding gives experience in general a priori only its rule, according to the subjective and formal conditions of both sensibility and apperception that alone make it possible. Other forms of intuition than space and time, and likewise other forms of understanding than the discursive form of thinking or cognition through concepts, even if possible, cannot in any way be devised or made intelligible by us. But even if we could do so, they would still not belong to experience as the sole cognition in which objects are given to us. Whether there could be perceptions other than those belonging in general to our entire possible experience, and hence an entirely different field of matter, understanding cannot decide: it is concerned only with the synthesis of what is given. Otherwise the poverty of our usual inferences, through which we produce a vast realm of possibility of which everything actual, every object of experience, is only a small part, is glaringly obvious. Everything actual is possible; from this there naturally follows, according to the logical rules of conversion, only the particular proposition that something possible is actual.

B 284 This seems to mean that much is possible that is not actual. It does indeed seem that one could also directly increase the number of possible things beyond that of actual things, because something must be added to possibility to constitute actuality. But I do not know this addition to the possible. For what was to be added beyond it would be impossible. Something can be added only for my understanding beyond agreement with the formal conditions of experience: connection with some perception. What is connected with this according to empirical laws is actual, even if it is not immediately perceived. But that another series of appearances, and hence more than one single all-embracing experience, is possible in thoroughgoing connection with what is given to me in perception cannot be inferred from what is given, still less without anything being given, since without material nothing at all can be thought. What is possible only under conditions that are themselves merely possible is not possible in every respect. Yet it is in this sense that the question is taken when one wishes to know whether the possibility of things extends further than experience can reach.

I have mentioned these questions only to leave no gap in what, according to common opinion, belongs to the concepts of the understanding.

B 285 In fact, however, absolute possibility, valid in every respect, is no mere concept of the understanding and can have no empirical use whatever. It belongs solely to reason, which goes beyond every possible empirical use of understanding. Here we have therefore had to content ourselves with a merely critical remark, while otherwise leaving the matter in darkness until our further proceedings.

As I am about to conclude this fourth number, and with it the system of all principles of pure understanding, I must still give the reason why I have called the principles of modality precisely postulates. I do not wish to take the expression here in the sense some recent philosophical writers have given it, contrary to the sense of the mathematicians to whom it properly belongs: namely, that to postulate means to proclaim a proposition immediately certain without justification or proof. For if we were to concede of synthetic propositions, however self-evident, that they may be imposed on unconditional assent without deduction, on the authority of their own declaration, all critique of the understanding is lost. There is no lack of bold pretensions, and even common belief, which is no credential, does not refuse them.

B 286 Our understanding would then stand open to every delusion, unable to refuse assent to pronouncements that, though illegitimate, demand admission in the same confident tone as actual axioms. Thus whenever a determination is synthetically added a priori to the concept of a thing, such a proposition must unfailingly be accompanied, if not by a proof, then at least by a deduction of the legitimacy of its assertion.

The principles of modality, however, are not objectively synthetic, because the predicates of possibility, actuality, and necessity do not in the least enlarge the concept of which they are asserted by adding anything to the representation of the object. Yet since they are still always synthetic, they are so only subjectively. They add to the concept of a real thing, about which they otherwise say nothing, the cognitive power in which it arises and has its seat. Thus if the concept is connected merely in understanding with the formal conditions of experience, its object is called possible. If it is connected with perception, sensation as the matter of the senses, and determined through perception by means of understanding, the object is actual. If it is determined through the connection of perceptions according to concepts, the object is called necessary.

B 287 Thus the principles of modality state concerning a concept nothing other than the action of the faculty of cognition through which it is generated. Now in mathematics a postulate means a practical proposition containing nothing but the synthesis through which we first give ourselves an object and generate its concept: for example, with a given line to describe a circle from a given point on a plane. Such a proposition cannot be proved, because the procedure it demands is precisely what first generates our concept of such a figure. With precisely the same right, then, we can postulate the principles of modality, because they do not enlarge their concept of things in general*, but merely indicate how it is combined with the cognitive power in general.

* Through the actuality of a thing I certainly posit more than its possibility, but not in the thing; for it can never contain more in actuality than was contained in its complete possibility. Rather, since possibility was merely a positing of the thing in relation to understanding and its empirical use, actuality is at the same time a connection of it with perception.

B 288 General Remark on the System of Principles

It is very remarkable that we cannot understand the possibility of any thing through the mere category, but must always have an intuition at hand in which to exhibit the objective reality of the pure concept of the understanding. Take, for example, the categories of relation. How 1) something can exist only as subject, not as a mere determination of other things, that is, be substance; or how 2) because something is, something else must be, and hence how anything can be a cause at all; or 3) how, when several things exist, something follows for the others from the existence of one of them, and reciprocally, so that a community of substances can take place: none of this can be understood from mere concepts. The same holds of the other categories: for example, how a thing together with many others can be one, that is, a magnitude, and so on. As long as intuition is lacking, then, we do not know whether through the categories we are thinking an object, or whether any object whatever can correspond to them. This confirms that in themselves they are not cognitions at all, but mere forms of thought for making cognitions out of given intuitions.

B 289 This also explains why no synthetic proposition can be made from mere categories. For example: in all existence there is substance, something that can exist only as subject and not as mere predicate; or every thing is a quantum, and so on. Here there is nothing that could serve us in going beyond a given concept and connecting another with it. Hence it has never been possible to prove a synthetic proposition from mere pure concepts of the understanding, for example the proposition that everything contingently existing has a cause. One could never get further than proving that without this relation we could not comprehend the existence of the contingent at all, could not cognize a priori through understanding the existence of such a thing. But it does not follow that this relation is also the condition of the possibility of the things themselves. If we look back at our proof of the principle of causality, we will therefore see that we could prove it only of objects of possible experience: everything that happens, every event, presupposes a cause. Moreover, we could prove it only as a principle of the possibility of experience, and hence of cognition of an object given in empirical intuition, not from mere concepts. It cannot be denied that everyone nevertheless finds the proposition “Everything contingent must have a cause” clearly evident from mere concepts.

B 290 But then the concept of the contingent has already been framed so as to contain not the category of modality, as something whose nonbeing can be thought, but that of relation, as something that can exist only as a consequence of something else. Then, of course, the proposition “What can exist only as a consequence has its cause” is an identical proposition. In fact, when we are to give examples of contingent existence, we always appeal to alterations, not merely to the possibility of thinking the opposite*. Alteration, however, is an event.

B 291 As such it is possible only through a cause, and its nonbeing is therefore possible in itself. Thus we recognize contingency from something’s being able to exist only as an effect of a cause. If a thing is therefore assumed to be contingent, saying that it has a cause is an analytic proposition.

* The nonbeing of matter is easy to think, yet the ancients did not infer its contingency from this. But even the alternation of being and nonbeing of a given state of a thing, in which all alteration consists, does not at all prove the contingency of this state, as though from the actuality of its opposite. For example, a body’s rest following its motion does not yet prove the contingency of that motion merely because the former is the opposite of the latter. For this opposite is here opposed to the other only logically, not realiter. To prove the contingency of its motion, one would have to prove that instead of moving at the preceding point in time the body could then have been at rest, not that it rests afterward; for then both opposites can very well coexist.

Still more remarkable is that, to understand the possibility of things according to the categories and thus exhibit the objective reality of the latter, we need not merely intuitions, but always outer intuitions. If, for example, we take the pure concepts of relation, we find that 1) to give something persistent in intuition corresponding to the concept of substance, and thereby exhibit the objective reality of this concept, we need an intuition in space, of matter, because space alone is persistently determined, while time, and hence everything in inner sense, constantly flows. To present alteration as the intuition corresponding to the concept of causality, we must take motion, as alteration in space, as our example. Indeed, through this alone can we make alterations intuitive to ourselves, although no pure understanding can comprehend their possibility. Alteration is the combination of contradictorily opposed determinations in the existence of one and the same thing.

B 292 How a state opposed to a given state of the same thing can follow from it, no reason can make comprehensible to itself without an example, or even intelligible without intuition. This intuition is that of a point’s motion in space, whose existence in different places, as a succession of opposed determinations, alone first makes alteration intuitive to us. For afterward, even to make inner alterations thinkable, we must represent time, as the form of inner sense, figuratively by a line, and inner alteration by the drawing of this line, motion. We must thus make our own successive existence in different states intelligible through outer intuition. The actual ground of this is that all alteration presupposes something persistent in intuition even to be perceived as alteration, whereas no persistent intuition whatever is found in inner sense.—Finally, the category of community cannot be comprehended in its possibility through mere reason at all; hence the objective reality of this concept cannot be understood without intuition, specifically outer intuition in space. For how is one to think the possibility that, when several substances exist, something as an effect can follow reciprocally from the existence of one to the existence of the others, so that because something is in the first there must also be something in the others that cannot be understood from the latter’s existence alone?

B 293 This is required for community, but is quite incomprehensible among things each completely isolated by its subsistence. Thus Leibniz, in ascribing community to the substances of the world solely as understanding thinks them, needed a deity to mediate it; for he rightly found it incomprehensible from their existence alone. But we can very well make the possibility of community among substances as appearances intelligible to ourselves if we represent them in space, and thus in outer intuition. For space already contains a priori formal outer relations as conditions of the possibility of real relations in action and reaction, and hence of community.—Likewise it can easily be shown that the possibility of things as magnitudes, and thus the objective reality of the category of magnitude, can be exhibited only in outer intuition, and only through this subsequently applied to inner sense as well. But to avoid prolixity I must leave examples of this to the reader’s reflection.

This entire remark is of great importance for confirming our preceding refutation of idealism.

B 294 It is of still greater importance when self-cognition from mere inner consciousness and the determination of our nature without the aid of outer empirical intuitions comes under discussion, for it shows us the limits of the possibility of such cognition.

The final conclusion of this entire section is therefore this: all principles of pure understanding are nothing more than a priori principles of the possibility of experience. All synthetic a priori propositions relate solely to experience; indeed, their very possibility rests entirely on this relation.

The Transcendental Doctrine of the Power of Judgment (Analytic of Principles) Third Chapter

On the Ground of the Distinction of All Objects in General into Phaenomena and Noumena

We have now not only traveled through the land of pure understanding and carefully inspected every part of it, but also measured it and assigned everything within it its place. This land, however, is an island, enclosed by nature itself within unalterable boundaries.

B 295 It is the land of truth—an alluring name—surrounded by a vast and stormy ocean, the true home of illusion, where many a fogbank and many an ice floe soon to melt away falsely promise new lands. Ceaselessly deceiving the seafarer roaming in search of discovery with empty hopes, they entangle him in adventures he can neither abandon nor ever bring to an end. Before we venture onto this sea, however, to search it in every latitude and learn for certain whether anything is to be hoped for there, it will be useful first to cast another glance at the map of the land we are about to leave. We should ask, first, whether we might not after all be content with what it contains, or must be content from necessity if there is nowhere else any ground on which we could settle; and second, by what title we possess even this land and can consider ourselves secure against every hostile claim. Although we have already answered these questions sufficiently in the course of the analytic, a summary survey of their solutions may still strengthen conviction by bringing their grounds together at a single point.

We have seen, namely, that everything understanding draws from itself without borrowing it from experience is nevertheless at its disposal for no purpose other than use in experience.

B 296 The principles of pure understanding, whether constitutive a priori, like the mathematical principles, or merely regulative, like the dynamical ones, contain nothing but, as it were, the pure schema for possible experience. For experience has its unity only from the synthetic unity that understanding originally and of itself gives to the synthesis of imagination in relation to apperception, and to which appearances, as data for a possible cognition, must already stand in relation and agreement a priori. Now although these rules of understanding are not only true a priori but even the source of all truth, that is, of the agreement of our cognition with objects, because they contain the ground of the possibility of experience as the sum total of all cognition in which objects may be given to us, it still seems insufficient merely to be told what is true rather than what we wish to know. If this critical investigation teaches us nothing more than what we would quite naturally have practiced in the merely empirical use of understanding, even without such subtle inquiry, the advantage drawn from it seems not worth the expense and preparation. One can indeed reply that no inquisitiveness is more harmful to the extension of our cognition than that which always wants to know the benefit in advance.

B 297 It wants this before embarking on investigations, and before one could form even the slightest concept of that benefit, even if it were set before one’s eyes. Yet there is an advantage that can be made intelligible, and at the same time important, even to the most difficult and reluctant student of such transcendental inquiry. It is this: understanding occupied solely with its empirical use, without reflecting on the sources of its own cognition, can indeed make very good progress, but cannot accomplish one thing—determine for itself the boundaries of its use and know what may lie within or outside its entire sphere. For precisely this requires the deep investigations we have undertaken. But if it cannot distinguish whether certain questions lie within its horizon or not, it is never secure in its claims and possessions. It can expect only repeated humiliating corrections as it incessantly, and inevitably, oversteps the boundaries of its territory and strays into delusion and deception.

That understanding can make no use of any of its a priori principles, indeed of any of its concepts, except an empirical and never a transcendental use, is therefore a proposition that, if it can be cognized with conviction, promises important consequences.

B 298 The transcendental use of a concept in any principle consists in its being related to things in general and in themselves; its empirical use consists in its being related merely to appearances, objects of a possible experience. That only the latter use is possible anywhere can be seen as follows. Every concept requires, first, the logical form of a concept, of thinking, in general, and second, the possibility of giving it an object to which it relates. Without the latter it has no sense and is entirely empty of content, although it may still contain the logical function of making a concept out of whatever data may be available. Now an object can be given to a concept only in intuition. Even if a pure intuition is possible a priori before the object, this intuition itself can acquire its object, and hence objective validity, only through empirical intuition, of which it is the mere form. Thus all concepts, and with them all principles, however possible they may be a priori, nevertheless relate to empirical intuitions, data for possible experience. Without this they have no objective validity whatever, but are a mere play of imagination or of understanding with their respective representations. Take only the concepts of mathematics as an example, first in their pure intuitions.

B 299 Space has three dimensions; between two points there can be only one straight line, and so on. Although all these principles, and the representation of the object with which that science is concerned, are generated entirely a priori in the mind, they would still mean nothing whatever if we could not always exhibit their significance in appearances, empirical objects. Thus we also require that an abstract concept be made sensible, that is, that its corresponding object be exhibited in intuition. Without this the concept would remain, as we say, without sense, that is, without significance. Mathematics fulfills this demand by constructing the figure, which is an appearance present to the senses, though produced a priori. In the same science the concept of magnitude seeks its support and sense in number, and number in the fingers, the beads of the counting board, or the strokes and points placed before our eyes. The concept, together with the synthetic principles or formulas drawn from such concepts, always remains generated a priori. But their use and relation to supposed objects can ultimately be sought nowhere but in experience, whose possibility as to form they contain a priori.

B 300 That this is also the case with all categories and the principles spun from them is clear from the following: we cannot give a real definition of a single one of them, that is, make the possibility of its object intelligible, without immediately descending to conditions of sensibility, and hence to the form of appearances. Consequently they must be restricted to appearances as their only objects. For if this condition is removed, all significance, all relation to an object, disappears; and no example can make intelligible even to ourselves what sort of thing is actually meant by such concepts.

No one can explain the concept of magnitude in general except perhaps as that determination of a thing through which one can think how many times a unit is posited in it. But this “how many times” rests on successive repetition, and hence on time and the synthesis of the homogeneous in it. Reality can be explained in contrast to negation only if one thinks of a time (as the sum total of all being) that is either filled with something or empty. If I omit persistence, existence at all times, nothing remains to me for the concept of substance but the logical representation of a subject. I imagine I make this real by representing something that can occur only as subject, without being a predicate of anything.

B 301 Yet not only do I know no conditions under which this logical prerogative would belong to any thing; nothing further can be made of it, not the slightest consequence drawn, because no object of the use of this concept is thereby determined. Thus we do not know at all whether it means anything whatever. From the concept of cause, if I omit the time in which something follows something else according to a rule, I would find in the pure category nothing beyond its being something from which the existence of another can be inferred. Not only could cause and effect thereby not be distinguished at all, but since this ability to infer soon requires conditions of which I know nothing, the concept would contain no determination of how it fits any object. The supposed principle “Everything contingent has a cause” certainly presents itself with considerable gravity, as though it possessed its own dignity within itself. But if I ask what you understand by “contingent,” and you answer “That whose nonbeing is possible,” I would like to know how you intend to recognize this possibility of nonbeing unless you represent a succession in the series of appearances, and in it an existence following nonbeing, or the reverse, hence a change. For that the nonbeing of a thing does not contradict itself is a feeble appeal.

B 302 What it appeals to is a logical condition, necessary indeed for the concept, but far from sufficient for real possibility. I can in thought abolish every existing substance without contradicting myself, yet cannot infer from this its objective contingency in existence, the possibility of its nonbeing in itself. As for the concept of community, it is easy to judge that, since the pure categories of substance and causality admit no explanation determining the object, reciprocal causality in the relation of substances to one another (commercium) is equally incapable of it. No one has ever been able to explain possibility, existence, and necessity except through manifest tautology when trying to draw their definitions solely from pure understanding. For the deception of substituting the logical possibility of a concept, its not contradicting itself, for the transcendental possibility of things, an object’s corresponding to the concept, can mislead and satisfy only the inexperienced*.

* In a word, none of these concepts can be supported by anything, and their real possibility thereby demonstrated, if all sensible intuition, the only intuition we have, is removed. Only logical possibility then remains: that the concept, the thought, is possible. But this is not the question; the question is whether it relates to an object and thus means anything.

B 303 From this it follows incontestably that the pure concepts of the understanding can never have a transcendental but always only an empirical use, and that the principles of pure understanding can be related only to objects of the senses in reference to the universal conditions of a possible experience, never to things in general without regard to the way we may intuit them.

The transcendental analytic therefore has this important result: understanding can never accomplish more a priori than to anticipate the form of a possible experience in general. Since what is not appearance cannot be an object of experience, understanding can never overstep the limits of sensibility, within which alone objects are given to us. Its principles are merely principles for the exposition of appearances. The proud name of an ontology that presumes to supply synthetic a priori cognitions of things in general in a systematic doctrine, for example the principle of causality, must give way to the modest name of a mere analytic of pure understanding.

B 304 Thinking is the act of relating a given intuition to an object. If the kind of intuition is in no way given, the object is merely transcendental, and the concept of the understanding has no other than a transcendental use: the unity of thinking a manifold in general. Through a pure category, then, in which abstraction is made from every condition of sensible intuition as the only intuition possible for us, no object is determined. Only the thinking of an object in general is expressed in various modi. Now the use of a concept also requires a function of the power of judgment by which an object is subsumed under it, and hence at least the formal condition under which something can be given in intuition. If this condition of the power of judgment, the schema, is lacking, all subsumption falls away, since nothing is given that could be subsumed under the concept. The merely transcendental use of the categories is therefore in fact no use at all, and has no determinate object, nor even one determinable in form. It follows that the pure category is also insufficient for any synthetic a priori principle, and that the principles of pure understanding have only empirical, never transcendental use.

B 305 Beyond the field of possible experience there can be no synthetic a priori principles whatever.

It may therefore be advisable to express the matter thus: the pure categories, without the formal conditions of sensibility, have merely transcendental significance but no transcendental use, because such use is itself impossible. They lack all the conditions for any use in judgments, namely the formal conditions for subsuming any supposed object under these concepts. Since, then, as merely pure categories they are not to have empirical use, and cannot have transcendental use, they have no use at all when separated from all sensibility. That is, they cannot be applied to any supposed object. Rather, they are merely the pure form of the use of understanding concerning objects in general and of thinking, without our being able through them alone to think or determine any object.

Yet a deception that is difficult to avoid underlies this. In their origin the categories are not grounded on sensibility, as are the forms of intuition, space and time; they therefore seem to permit an application extending beyond all objects of the senses. But they in turn are nothing but forms of thought, containing merely the logical capacity to unite a priori in one consciousness the manifold given in intuition.

B 306 Thus if one removes from them the only intuition possible for us, they can have even less significance than those pure sensible forms through which at least an object is given. By contrast, a way of combining the manifold peculiar to our understanding means nothing whatever unless the intuition in which alone this manifold can be given is added.—Nevertheless, it is already implicit in our concept, when we call certain objects, as appearances, beings of sense (phenomena), distinguishing our way of intuiting them from their character in themselves, that we set over against them, as it were, either these same objects in their character in themselves, though we do not intuit them in that character, or other possible things that are not objects of our senses at all. We regard these as objects thought merely through understanding and call them beings of understanding (noumena). The question now is whether our pure concepts of the understanding have significance with respect to these latter objects and could be a way of cognizing them.

But an ambiguity appears here at once that can occasion great misunderstanding. When understanding calls an object in one relation merely a phenomenon, it simultaneously forms, outside this relation, a representation of an object in itself.

B 307 It therefore imagines that it can also form concepts of such an object, and that, since understanding supplies none but the categories, the object in the latter sense must at least be capable of being thought through these pure concepts of the understanding. This leads it to take the entirely undetermined concept of a being of understanding, as something in general outside our sensibility, for a determinate concept of a being that we can in some way cognize through understanding.

If by noumenon we understand a thing insofar as it is not an object of our sensible intuition, abstracting from our way of intuiting it, this is a noumenon in the negative sense. But if we understand by it an object of a nonsensible intuition, we assume a special kind of intuition, intellectual intuition, which is not ours and whose possibility we cannot even understand. This would be the noumenon in the positive sense.

The doctrine of sensibility is therefore also the doctrine of noumena in the negative sense: of things that understanding must think without this relation to our way of intuiting, and hence not merely as appearances but as things in themselves. Yet in thus separating them understanding also comprehends that it can make no use of its categories in considering them this way.

B 308 The reason is that the categories have significance only in relation to the unity of intuitions in space and time. They can determine precisely this unity a priori through universal concepts of combination only because of the mere ideality of space and time. Where this temporal unity cannot be found, and hence in the case of the noumenon, all use, indeed all significance, of the categories entirely ceases. For even the possibility of things that are supposed to correspond to the categories cannot be understood at all. Here I need only appeal to what I stated at the very beginning of the general remark on the preceding chapter. Now the possibility of a thing can never be proved merely from the noncontradiction of its concept, but only by supporting the concept with a corresponding intuition. If, therefore, we wished to apply the categories to objects not regarded as appearances, we would have to base them on an intuition other than sensible intuition, and the object would then be a noumenon in the positive sense. Since such intuition, intellectual intuition, lies absolutely outside our faculty of cognition, the use of the categories can in no way extend beyond the boundary of objects of experience.

B 309 Beings of understanding do indeed correspond to beings of sense, and there may also be beings of understanding to which our sensible faculty of intuition has no relation at all. But our concepts of the understanding, as mere forms of thought for our sensible intuition, do not reach these in the least. What we call noumenon must therefore, as such, be understood only in the negative sense.

If I remove all thinking through categories from an empirical cognition, no cognition of any object remains. For through mere intuition nothing is thought, and that this affection of sensibility is in me constitutes no relation of such a representation to any object. If, on the other hand, I omit all intuition, the form of thinking still remains: the manner of determining an object for the manifold of a possible intuition. To this extent the categories therefore extend further than sensible intuition, because they think objects in general without yet attending to the particular manner (of sensibility) in which these may be given. But they do not thereby determine a larger sphere of objects, because we cannot assume that such objects can be given without presupposing as possible a kind of intuition other than sensible intuition, which we are in no way entitled to do.

B 310 I call a concept problematic when it contains no contradiction and is also connected with other cognitions as a delimitation of given concepts, but its objective reality cannot be cognized in any way. The concept of a noumenon, of a thing that is to be thought not at all as an object of the senses but as a thing in itself, solely through a pure understanding, is not contradictory at all. For one cannot assert of sensibility that it is the only possible kind of intuition. Further, this concept is necessary to prevent sensible intuition from being extended to things in themselves, and thus to restrict the objective validity of sensible cognition. For the remaining things, to which sensible cognition does not reach, are called noumena precisely to indicate that these cognitions cannot extend their territory over everything understanding thinks. In the end, however, the possibility of such noumena cannot be understood at all, and the region outside the sphere of appearances is empty for us. That is, we have an understanding that problematically extends further than appearances, but no intuition, not even the concept of a possible intuition, through which objects could be given to us outside the field of sensibility and understanding could be used assertorically beyond it.

B 311 The concept of a noumenon is therefore merely a boundary concept, intended to restrict the pretensions of sensibility, and hence of merely negative use. Yet it is not arbitrarily invented, but is connected with the limitation of sensibility, without being able to posit anything positive outside its domain.

The division of objects into phaenomena and noumena, and of the world into a world of sense and a world of understanding, can therefore in no way be admitted in a positive sense, although concepts certainly admit division into sensible and intellectual. For no object can be determined for the latter, and they therefore cannot be proclaimed objectively valid. If we depart from the senses, how shall we make it comprehensible that our categories, which would be the only concepts remaining for noumena, still mean anything at all? For their relation to any object requires that something more than mere unity of thinking be given: a possible intuition to which they can be applied. Nevertheless, taken merely problematically, the concept of a noumenon remains not only admissible but also unavoidable as a concept setting limits to sensibility. But it is then no special intelligible object for our understanding. Rather, an understanding to which it would belong is itself a problem.

B 312 The problem is that of cognizing its object not discursively through categories but intuitively in a nonsensible intuition, of whose possibility we cannot form the slightest representation. In this way our understanding receives a negative extension, that is, it is not limited by sensibility, but rather limits sensibility by calling things in themselves, not regarded as appearances, noumena. Yet it immediately sets boundaries to itself as well, by cognizing them through no categories and hence thinking them only under the name of an unknown something.

In the writings of recent thinkers, however, I find an entirely different use of the expressions mundi sensibilis and intelligibilis*, one departing completely from the sense of the ancients. It presents no difficulty, certainly, but also amounts to nothing but empty wordmongering. In this usage some have chosen to call the sum total of appearances, insofar as it is intuited, the world of sense, but insofar as its connection is thought according to universal laws of understanding, the world of understanding.

B 313 Theoretical astronomy, presenting mere observation of the starry heavens, would represent the former; contemplative astronomy (explained perhaps according to the Copernican system of the world, or even according to Newton’s laws of gravitation) would represent the latter, namely an intelligible world. But such twisting of words is a merely sophistical evasion of a troublesome question, by lowering its meaning to one’s convenience. Understanding and reason can certainly be used with respect to appearances. But the question is whether they still have any use when the object is not appearance, a noumenon. It is taken in this sense when thought in itself as merely intelligible, given solely to understanding and not at all to the senses. Thus the question is whether, beyond that empirical use of understanding, even in the Newtonian representation of the universe, a transcendental use is also possible that relates to the noumenon as an object. We have answered this question negatively.

* One must not replace this expression with “intellectual world,” as is commonly done in German exposition. For only cognitions are intellectual or sensitive. What can be an object only of one or the other kind of intuition, and hence the objects, must be called intelligible or sensible, despite the awkward sound.

Thus when we say that the senses represent objects to us as they appear, but understanding as they are, the latter must be taken not in a transcendental but merely in an empirical sense: as objects of experience must be represented in the thoroughgoing connection of appearances.

B 314 They are not to be represented as what they may be apart from relation to possible experience, and hence to senses in general, as objects of pure understanding. For this will always remain unknown to us, so much so that even whether such transcendental, extraordinary cognition is possible at all remains unknown, at least as a cognition falling under our ordinary categories. In us, understanding and sensibility can determine objects only in combination. If we separate them, we have intuitions without concepts or concepts without intuitions, but in both cases representations that we can relate to no determinate object.

If anyone still hesitates, after all these discussions, to renounce the merely transcendental use of the categories, let him try them in some synthetic assertion. An analytic assertion takes understanding no further. Since understanding is then concerned only with what is already thought in the concept, it leaves undecided whether the concept in itself relates to objects or merely signifies the unity of thinking in general, which abstracts entirely from the manner in which an object may be given. It is enough for understanding to know what lies in its concept; what the concept itself may relate to is indifferent to it.

B 315 Let him therefore try some synthetic and supposedly transcendental principle, such as: everything that is exists as substance or as a determination attaching to it; everything contingent exists as an effect of another thing, its cause; and so on. Now I ask: where will he obtain these synthetic propositions, since the concepts are supposed to hold not in relation to possible experience but of things in themselves, noumena? Where is the third thing always required for a synthetic proposition, in which to connect concepts that have no logical, analytic kinship at all? He will never prove his proposition; indeed, more than that, he will not even be able to justify the possibility of such a pure assertion without referring to the empirical use of understanding, thereby completely renouncing a pure judgment free from the senses. Thus the concept of pure, merely intelligible objects is entirely devoid of all principles for its application, because no way can be devised in which they should be given. The problematic thought that nevertheless leaves a place open for them serves only, like an empty space, to restrict empirical principles, without containing or exhibiting any other object of cognition outside their sphere.

B 316 Appendix On the Amphiboly of Concepts of Reflection Through the Confusion of the Empirical Use of Understanding with Its Transcendental Use

Reflection (reflexio) is not concerned with objects themselves in order to obtain concepts directly from them. It is rather the state of mind in which we first prepare to discover the subjective conditions under which we can arrive at concepts. It is the consciousness of the relation of given representations to our various sources of cognition, through which alone their relation to one another can be correctly determined. The first question before any further treatment of our representations is: in which faculty of cognition do they belong together? Is it in understanding or in the senses that they are connected or compared? Many a judgment is accepted from habit or linked through inclination; but because no reflection precedes it, or at least follows it critically, it passes for a judgment originating in understanding. Not all judgments require investigation, that is, attention to the grounds of truth.

B 317 For if they are immediately certain—for example, between two points there can be only one straight line—no closer mark of their truth can be indicated than what they themselves express. But all judgments, indeed all comparisons, require reflection, that is, a distinction of the cognitive power to which the given concepts belong. The act by which I hold the comparison of representations in general together with the cognitive power in which it is carried out, and by which I distinguish whether they are compared with one another as belonging to pure understanding or to sensible intuition, I call transcendental reflection. The relations in which concepts can belong to one another in a state of mind are those of identity and difference, agreement and opposition, the inner and the outer, and finally the determinable and determination, matter and form. The correct determination of these relations depends on the cognitive power in which the concepts subjectively belong together, whether in sensibility or in understanding. For the difference between these faculties makes a great difference to how the concepts should be thought.

Before all objective judgments we compare concepts for identity (many representations under one concept), in order to form universal judgments; or for their difference, in order to produce particular judgments.

B 318 We compare them likewise for agreement, from which affirmative judgments can arise, and for opposition, from which negative judgments can arise, and so on. For this reason it seems that we should call the concepts listed above concepts of comparison (conceptus comparationis). But when the question concerns not the logical form but the content of concepts—whether the things themselves are identical or different, in agreement or opposed, and so on—things can have a twofold relation to our cognitive power, to sensibility and to understanding. How they are to belong to one another depends on the place in which they belong. Thus transcendental reflection, the relation of given representations to one or the other kind of cognition, alone can determine their relation to one another. Whether things are identical or different, in agreement or opposed, and so on, cannot be settled immediately from the concepts themselves through mere comparison (comparatio), but only through distinguishing the kind of cognition to which they belong, by means of transcendental reflection (reflexio). We could therefore indeed say that logical reflection is mere comparison: in it we abstract entirely from the cognitive power to which the given representations belong, and thus treat them as homogeneous in respect of their seat in the mind.

B 319 Transcendental reflection, however, which concerns the objects themselves, contains the ground of the possibility of objectively comparing representations with one another. It is therefore very different from mere comparison, because the cognitive power to which they belong is not the same. This transcendental reflection is a duty no one can renounce who wishes to judge anything about things a priori. Let us now undertake it; it will shed no little light on the determination of the understanding’s proper business.

1 Identity and Difference. If an object is presented to us several times, but each time with exactly the same inner determinations (qualitas et quantitas), then, if regarded as an object of pure understanding, it is always the very same object: not many things but only one (numerica identitas). But if it is appearance, comparison of concepts is not at issue. However identical everything may be in this respect, the difference of the locations of this appearance at the same time is nevertheless sufficient ground for the numerical difference of the object of the senses itself. Thus with two drops of water we can abstract entirely from every inner difference of quality and quantity; their being intuited simultaneously in different places is enough to regard them as numerically different.

B 320 Leibniz took appearances as things in themselves, hence as intelligibilia, objects of pure understanding, although he called them phenomena because of the confused character of their representations. On that basis his principle of the indiscernible (principium identitatis indiscernibilium) certainly could not be disputed. But since they are objects of sensibility, and understanding has not a pure but merely an empirical use with respect to them, plurality and numerical difference are already supplied by space itself as the condition of outer appearances. For a part of space, although it may be completely similar and equal to another, is nevertheless outside it, and precisely thereby a part distinct from the first, added to it to constitute a greater space. This must therefore hold of everything simultaneously occupying the various positions of space, however similar and equal it may otherwise be.

2 Agreement and Opposition. If reality is represented only through pure understanding (realitas noumenon), no opposition can be thought between realities: no relation in which, combined in one subject, they cancel one another’s consequences, so that 3−3=0.

B 321 By contrast, the real in appearance (realitas phaenomenon) can certainly be in mutual opposition; united in the same subject, one reality can wholly or partly destroy the consequence of the other. Thus two moving forces in the same straight line may pull or push a point in opposite directions; or a pleasure may counterbalance pain.

3 The Inner and the Outer. In an object of pure understanding only what has no relation in its existence to anything different from it is inner. By contrast, the inner determinations of a substantia phaenomenon in space are nothing but relations, and the substance itself is entirely a sum total of mere relations. We know substance in space only through forces active there, either driving other substances into it, attraction, or preventing them from entering it, repulsion and impenetrability. We know no other properties constituting the concept of substance that appears in space and that we call matter. As an object of pure understanding, however, every substance must have inner determinations and forces directed toward inner reality. But what inner accidents can I think other than those offered by my inner sense: what is either itself thinking or analogous to it?

B 322 Hence Leibniz, because he represented all substances as noumena, made them—even the constituents of matter—simple subjects endowed with powers of representation, in a word, monads, after he had in thought removed from them everything signifying outer relation, and hence composition as well.

4 Matter and Form. These are two concepts underlying all other reflection, so inseparably are they combined with every use of understanding. The first signifies the determinable in general, the second its determination, both in the transcendental sense, abstracting from every difference in what is given and in how it is determined. Logicians formerly called the universal matter, and the specific difference form. In every judgment the given concepts may be called the logical matter for the judgment, and their relation through the copula the form of the judgment. In every being its constituents (essentialia) are the matter; the manner in which they are connected in a thing is the essential form. Likewise, with respect to things in general, unbounded reality was regarded as the matter of all possibility, and its limitation (negation) as the form through which one thing differs from another according to transcendental concepts.

B 323 Understanding, namely, first demands that something be given, at least in the concept, in order to determine it in a certain way. Hence in the concept of pure understanding matter precedes form. Leibniz therefore first assumed things, monads, and internally a power of representation in them, in order afterward to ground on this their outer relation and the community of their states, their representations. Thus space was possible only through the relation of substances, and time through the connection of their determinations with one another as grounds and consequences. This would indeed have to be so if pure understanding could relate immediately to objects and if space and time were determinations of things in themselves. But if they are merely sensible intuitions in which we determine all objects solely as appearances, the form of intuition, as a subjective constitution of sensibility, precedes all matter, sensations. Hence space and time precede all appearances and all data of experience, and indeed first make them possible. The intellectual philosopher could not tolerate form’s preceding things themselves and determining their possibility. This was an entirely justified criticism if he assumed that we intuit things as they are, albeit with confused representation.

B 324 But since sensible intuition is a quite special subjective condition underlying all perception a priori, and its form is original, form is given by itself alone. Far from matter, or the things themselves that appear, having to underlie it, as we would have to judge from mere concepts, their possibility rather presupposes a formal intuition, time and space, as given.

Remark on the Amphiboly of Concepts of Reflection

Allow me to call the position we assign a concept either in sensibility or in pure understanding its transcendental location. Judging the position belonging to every concept according to the difference in its use, and providing instructions according to rules for determining this location for all concepts, would thus be transcendental topics. Such a doctrine would thoroughly guard against the surreptitious claims of pure understanding and the deceptions arising from them, by always distinguishing the cognitive power to which concepts properly belong. Every concept, every heading under which many cognitions belong, can be called a logical location. On this rests Aristotle’s logical topics, which teachers of the schools and orators could employ.

B 325 By means of them they could look under certain headings of thought for what best suited the subject at hand, and then reason speciously or chatter at length about it with an illusion of thoroughness.

Transcendental topics, by contrast, contains no more than the four headings of all comparison and distinction listed above. They differ from categories because they present, not the object in terms of what constitutes its concept, magnitude or reality, but only the comparison of representations that precedes the concept of things, in all its variety. This comparison, however, first requires reflection, that is, determining the location to which the representations of the things being compared belong, whether pure understanding thinks them or sensibility gives them in appearance.

Concepts can be compared logically without concern for where their objects belong, whether as noumena for understanding or as phenomena for sensibility. But if we wish to proceed with these concepts to objects, transcendental reflection is first necessary to determine for which cognitive power they are to be objects, whether for pure understanding or for sensibility. Without this reflection I make a very uncertain use of these concepts.

B 326 Supposed synthetic principles arise that critical reason cannot recognize, grounded solely on a transcendental amphiboly, that is, a confusion of the pure object of understanding with appearance.

Lacking such transcendental topics, and hence misled by the amphiboly of concepts of reflection, the celebrated Leibniz erected an intellectual system of the world—or rather believed he cognized the inner constitution of things by comparing all objects solely with understanding and the abstract formal concepts of its thinking. Our table of concepts of reflection affords us the unexpected advantage of setting before our eyes the distinctive features of his doctrine in all its parts, together with the guiding ground of this peculiar cast of mind, which rested on nothing but a misunderstanding. He compared all things with one another merely through concepts and naturally found no differences other than those through which understanding distinguishes its pure concepts from one another. He did not regard the conditions of sensible intuition, which carry their own differences with them, as original. For to him sensibility was only a confused way of representing, not a special source of representations. Appearance was for him the representation of the thing in itself, though distinguished in logical form from cognition through understanding.

B 327 For appearance, owing to its usual lack of analysis, draws a certain mixture of accompanying representations into the concept of the thing, which understanding knows how to separate from it. In a word, Leibniz intellectualized appearances, just as Locke, in a system of noogony, if I may use these expressions, had sensualized all concepts of the understanding, proclaiming them nothing but empirical or abstract concepts of reflection. Instead of seeking in understanding and sensibility two entirely different sources of representations that could judge things with objective validity only in connection, each of these great men held to only one of the two, which in his opinion related immediately to things in themselves, while the other did nothing but confuse or order the representations of the first.

Leibniz accordingly compared objects of the senses with one another as things in general merely in understanding. First, insofar as understanding is to judge them identical or different. Since he thus had in view only their concepts, not their position in the intuition in which alone objects can be given, and entirely disregarded the transcendental location of these concepts—whether the object was to be counted among appearances or things in themselves—the outcome could only be this.

B 328 He extended his principle of the indiscernible, which holds merely of concepts of things in general, to objects of the senses (mundus phaenomenon), and believed he had thereby achieved no slight extension of the cognition of nature. Certainly, if I know a drop of water as a thing in itself in all its inner determinations, I cannot regard any one drop as different from another if its entire concept is identical with the other’s. But if it is appearance in space, it has its location not merely in understanding, under concepts, but in outer sensible intuition, in space. There, physical locations are entirely indifferent to the inner determinations of things: a location = b can receive a thing completely similar and equal to another in location = a just as well as if it differed from it internally to the greatest extent. The difference of locations by itself, without further conditions, makes the plurality and distinction of objects as appearances not merely possible but necessary. Thus that apparent law is no law of nature. It is merely an analytic rule, or comparison of things through mere concepts.

Second, the principle that realities, as mere affirmations, never logically oppose one another is an entirely true proposition concerning the relation of concepts.

B 329 It means nothing whatever, however, with respect to nature, or indeed to any thing in itself, of which we have no concept. For real opposition occurs everywhere that A−B=0: where one reality, combined with another in a subject, cancels the other’s effect. All the obstacles and counteractions in nature constantly display this before our eyes; yet because they rest on forces, they must be called realitates phaenomena. General mechanics can even state the empirical condition of this opposition in an a priori rule by attending to the opposition of directions, a condition of which the transcendental concept of reality knows nothing. Although Herr von Leibniz did not announce this proposition with the pomp of a new principle, he nevertheless used it for new assertions, and his successors expressly incorporated it into their Leibnizian-Wolfian systems. According to this principle, for example, all evils are nothing but consequences of the limitations of creatures, that is, negations, because these are the only things opposed to reality. In the mere concept of a thing in general this is indeed so, but not in things as appearances. Likewise his followers find it not merely possible but natural to unite all reality in one being without any opposition to be feared.

B 330 For they know no opposition other than contradiction, through which the very concept of a thing is abolished. They do not know reciprocal impairment, where one real ground cancels the effect of another, and for which we find the conditions of representing it only in sensibility.

Third, Leibniz’s monadology has no other ground than that this philosopher represented the distinction between inner and outer merely in relation to understanding. Substances in general must have something inner, free from all outer relations and consequently from composition as well. The simple is therefore the foundation of the inner in things in themselves. But the inner aspect of their state cannot consist in location, shape, contact, or motion, all of which are determinations of outer relations. Hence we can ascribe to substances no inner state other than that through which we inwardly determine our own sense: the state of representations. Thus the monads were fashioned, which are to constitute the fundamental material of the entire universe, but whose active force consists solely in representations, through which they are properly active only within themselves.

B 331 For this very reason his principle of the possible community of substances with one another had to be a predetermined harmony, and could not be physical influence. Since everything is occupied only inwardly, with its own representations, the state of representations of one substance could stand in no effective combination whatever with that of another. Rather, some third cause influencing them all had to make their states correspond to one another: not indeed through occasional assistance specially applied in each individual case (systema assistentiae), but through the unity of the idea of a cause valid for all, in which they must all receive their existence and persistence, and hence also their mutual correspondence, according to universal laws.

Fourth, his celebrated doctrine of time and space, in which he intellectualized these forms of sensibility, sprang solely from the same deception of transcendental reflection. If I wish to represent outer relations of things through mere understanding, I can do so only by means of a concept of their reciprocal action; and if I am to connect one state of the same thing with another, this can occur only in the order of grounds and consequences. Thus Leibniz thought space as a certain order in the community of substances, and time as the dynamical succession of their states.

B 332 The distinctive character and independence from things that both seem to possess in themselves he ascribed to the confusion of these concepts. This confusion makes what is merely a form of dynamical relations seem a special, self-subsistent intuition preceding things themselves. Space and time were therefore the intelligible form of the connection of things, substances and their states, in themselves. The things, however, were intelligible substances (substantiae noumena). Nevertheless, he intended these concepts to hold for appearances, because he granted sensibility no kind of intuition of its own, but sought all representation of objects, even empirical representation, in understanding, leaving the senses only the contemptible business of confusing and distorting the representations of understanding.

But even if we could say something synthetically about things in themselves through pure understanding, which is nevertheless impossible, this could not at all be applied to appearances, which do not represent things in themselves. In this latter case, then, I must always compare my concepts in transcendental reflection only under the conditions of sensibility. Space and time will thus be determinations not of things in themselves but of appearances. What things may be in themselves I do not know, nor do I need to know.

B 333 For a thing can never come before me otherwise than in appearance.

I proceed in the same way with the other concepts of reflection. Matter is substantia phaenomenon. I seek what belongs to it inwardly in all parts of the space it occupies and in all the effects it produces, which of course can always be only appearances of outer senses. Thus I have nothing absolutely inner, but only something comparatively inner that itself consists in outer relations in turn. But what is absolutely inner in matter according to pure understanding is also a mere fancy. For matter is no object of pure understanding at all; the transcendental object that may be the ground of this appearance we call matter is a mere something, of which we would not even understand what it was if someone could tell us. For we can understand nothing but what brings with it in intuition something corresponding to our words. If the complaints “We have no insight into the inner nature of things” are to mean that we do not comprehend through pure understanding what the things appearing to us may be in themselves, they are entirely unjust and unreasonable. For they demand that we be able to cognize, hence intuit, things without senses, and consequently that we possess a faculty of cognition entirely different from the human one, not merely in degree but even in intuition and kind.

B 334 Thus we are to be not human beings but beings of whom we ourselves cannot say whether they are even possible, much less how they are constituted. Observation and analysis of appearances penetrate into the interior of nature, and we cannot know how far this may go in time. But those transcendental questions that go beyond nature we could still never answer, even if all nature were revealed to us, since we are not even given the ability to observe our own mind with any intuition other than that of our inner sense. For in the mind lies the secret of the origin of our sensibility. Its relation to an object, and the transcendental ground of this unity, undoubtedly lie too deeply hidden for us, who know even ourselves only through inner sense and hence as appearance, to use so unsuitable an instrument of inquiry to discover anything other than appearances again and again, though it is their nonsensible cause we would like to investigate.

What makes this critique of inferences from mere acts of reflection exceedingly useful is that it clearly demonstrates the nullity of all inferences concerning objects compared with one another solely in understanding.

B 335 At the same time it confirms what we have chiefly insisted on: although appearances are not included as things in themselves among the objects of pure understanding, they are nevertheless the only objects in which our cognition can have objective reality, namely where intuition corresponds to concepts.

When we reflect merely logically, we compare our concepts solely with one another in understanding: whether both contain the very same thing; whether or not they contradict one another; whether something is contained inwardly in the concept or is added to it; and which of the two is to count as given, which merely as a way of thinking the given one. But if I apply these concepts to an object in general in the transcendental sense, without determining further whether it is an object of sensible or intellectual intuition, restrictions immediately appear against going beyond this concept. These overturn all empirical use of the concepts and thereby prove that the representation of an object as a thing in general is not merely insufficient, but, without its sensible determination and independently of empirical conditions, internally conflicting. Thus one must either abstract from every object, as in logic, or, if one assumes an object, think it under conditions of sensible intuition.

B 336 Consequently the intelligible would require a quite special intuition that we do not have, and in its absence is nothing for us; conversely, appearances cannot be objects in themselves either. For if I think merely things in general, the difference of outer relations certainly cannot constitute a difference of the things themselves, but rather presupposes it. If the concept of one is not at all internally distinguished from that of another, I merely place one and the same thing in different relations. Further, by adding one mere affirmation, reality, to another, the positive is increased and nothing is taken away from or canceled in it. Hence the real in things in general cannot be opposed to itself, and so on.

* * *

As we have shown, through a certain misinterpretation the concepts of reflection exert such influence on the use of understanding that they were even able to lead one of the most penetrating of all philosophers into a supposed system of intellectual cognition that undertakes to determine its objects without the addition of the senses. For precisely this reason, uncovering the deceptive cause of the amphiboly of these concepts in occasioning false principles is of great use in reliably determining and securing the boundaries of understanding.

B 337 We must indeed say that what belongs to or contradicts a concept universally also belongs to or contradicts everything particular contained under that concept (dictum de Omni et Nullo). But it would be absurd to alter this logical principle to read: what is not contained in a universal concept is also not contained in the particular concepts standing under it. For these are particular concepts precisely because they contain more than is thought in the universal concept. Yet Leibniz’s entire intellectual system is in fact built on this latter principle. It therefore falls with it, together with all the ambiguity in the use of understanding arising from it.

The principle of the indiscernible was properly grounded on the presupposition that, if a certain distinction is not found in the concept of a thing in general, it is also not found in the things themselves. Consequently all things that do not already differ from one another in their concept, as to quality or quantity, are completely identical (numero eadem). But since the mere concept of any thing abstracts from many necessary conditions of an intuition, a peculiar haste leads to taking what has been abstracted from as something not to be found anywhere.

B 338 Nothing is allowed the thing but what is contained in its concept.

The concept of a cubic foot of space is in itself completely identical wherever and however often I may think it. Yet two cubic feet in space are distinguished merely by their locations (numero diversa). These are conditions of the intuition in which the object of this concept is given; they belong not to the concept, but nevertheless to sensibility as a whole. Likewise there is no opposition in the concept of a thing if nothing negative has been combined with something affirmative, and merely affirmative concepts in combination can produce no cancellation. But in the sensible intuition in which reality, for example motion, is given, conditions are found—opposite directions—from which the concept of motion in general had abstracted. These make possible an opposition that is certainly not logical: a zero = 0 resulting from nothing but positives. One could not say, then, that all reality is mutually in agreement merely because no opposition is found among its concepts*.

B 339 According to mere concepts, the inner is the substrate of all relations or outer determinations. If, therefore, I abstract from all conditions of intuition and hold solely to the concept of a thing in general, I can abstract from every outer relation, and a concept must nevertheless remain of what signifies no relation at all but merely inner determinations. It now seems to follow that in every thing, substance, there is something absolutely inner that precedes all outer determinations by first making them possible. This substrate would therefore be something containing no further outer relations, and consequently simple, since corporeal things are always only relations, at least of parts outside one another. And because we know no absolutely inner determinations except through our inner sense, this substrate would be not only simple but also, by analogy with our inner sense, determined through representations.

B 340 That is, all things would properly be monads, simple beings endowed with representations. All this would be correct if the conditions under which alone objects of outer intuition can be given to us did not involve more than the concept of a thing in general, from which the pure concept abstracts. For here it becomes clear that a persistent appearance in space, impenetrable extension, can contain nothing but relations and nothing absolutely inner, and nevertheless be the primary substrate of all outer perception. Through mere concepts I certainly cannot think anything outer without something inner, precisely because concepts of relation presuppose things given absolutely and are impossible without them. But intuition contains something not found at all in the mere concept of a thing in general, and supplies the substrate that could never be cognized through mere concepts: a space that, with everything it contains, consists solely of formal or also real relations. Thus I cannot say that, because no thing can be represented through mere concepts without something absolutely inner, there is also nothing outer in the things themselves contained under these concepts and in their intuition that does not rest on something absolutely inner.

B 341 For suppose we have abstracted from all conditions of intuition. Then nothing indeed remains for us in the mere concept but the inner in general and its mutual relation, through which alone the outer is possible. But this necessity, grounded solely on abstraction, does not apply to things insofar as they are given in intuition with determinations expressing mere relations without an inner foundation, because they are not things in themselves but merely appearances. Even what we know in matter is nothing but relations; what we call its inner determinations is only comparatively inner. Yet among these are self-subsistent and persistent relations through which a determinate object is given to us. That, if I abstract from these relations, I have nothing further to think does not abolish the concept of a thing as appearance, nor even that of an object in abstracto, but it does abolish every possibility of an object determinable through mere concepts, a noumenon. Certainly it is startling to hear that a thing is to consist entirely of relations. But such a thing is also mere appearance and cannot be thought through pure categories at all; it consists in the mere relation of something in general to the senses.

B 342 Likewise, if we begin with mere concepts, we can hardly think the relations of things in abstracto otherwise than as one’s being the cause of determinations in another, for this is our concept of the understanding of relations themselves. But since we then abstract from all intuition, an entire way in which the manifold can determine its members’ locations falls away: the form of sensibility, space, which nevertheless precedes all empirical causality.

* If one wished to use the usual evasion here, that at least realitates noumena cannot counteract one another, one would still have to give an example of such pure reality free from sense, so that we could understand whether it represents anything at all or nothing whatever. But no example can be taken from anywhere except experience, which never offers more than phenomena. Thus the proposition means nothing further than that a concept containing nothing but affirmations contains nothing negative: a proposition we have never doubted.

If by merely intelligible objects we understand things thought through pure categories without any schema of sensibility, such things are impossible. For the condition of the objective use of all our concepts of the understanding is solely our kind of sensible intuition, through which objects are given to us. If we abstract from this, those concepts have no relation to any object whatever. Indeed, even if we were to assume a kind of intuition other than our sensible one, our functions of thinking would still have no significance at all in relation to it. If we understand by intelligible objects only objects of a nonsensible intuition, to which our categories admittedly do not apply, and of which we can therefore never have any cognition, neither intuition nor concept, then noumena must certainly be admitted in this merely negative sense. They then say nothing more than that our kind of intuition relates not to all things but merely to objects of our senses.

B 343 Consequently its objective validity is bounded, leaving room for some other kind of intuition, and hence also for things as its objects. But the concept of a noumenon is then problematic, that is, the representation of a thing of which we can say neither that it is possible nor that it is impossible, since we know no kind of intuition except our sensible one and no kind of concepts except the categories, neither of which is suited to an extrasensible object. We therefore cannot positively extend the field of objects of our thinking beyond the conditions of our sensibility, and assume, besides appearances, objects of pure thinking, noumena, because they have no positive significance that can be specified. For we must admit of the categories that by themselves they are insufficient for cognition of things in themselves, and without the data of sensibility would be merely subjective forms of the unity of understanding, but without an object. Thinking is indeed not in itself a product of the senses and to that extent is not limited by them; but it does not thereby immediately have a use of its own, pure and without the contribution of sensibility, because it would then be without an object. Nor can the noumenon be called such an object.

B 344 For this signifies precisely the problematic concept of an object for an entirely different intuition and an entirely different understanding from ours, which is therefore itself a problem. Thus the concept of the noumenon is not the concept of an object, but the question unavoidably connected with the limitation of our sensibility: whether there may not be objects entirely detached from its intuition. This question can be answered only indeterminately: since sensible intuition does not relate to all things without distinction, room remains for more and different objects. These therefore cannot be denied outright, but, lacking a determinate concept, since no category is suited to them, neither can they be asserted as objects for our understanding.

Understanding accordingly bounds sensibility without thereby extending its own field. In warning sensibility not to presume to relate to things in themselves but solely to appearances, it thinks an object in itself, but only as a transcendental object that is the cause of appearance and hence not itself appearance. This cannot be thought as magnitude, reality, substance, and so on, because these concepts always require sensible forms in which they determine an object. It is therefore wholly unknown whether this object is to be found in us or outside us, whether it would be abolished together with sensibility or would remain if we removed sensibility.

B 345 If we wish to call this object noumenon because its representation is not sensible, we are free to do so. But since we can apply none of our concepts of the understanding to it, this representation still remains empty for us and serves only to mark the boundaries of our sensible cognition and leave a space that we can fill neither through possible experience nor through pure understanding.

The critique of this pure understanding therefore does not permit it to create a new field of objects beyond those that can encounter it as appearances, or to wander into intelligible worlds, not even into their concept. The error that leads to this in the most plausible way, and can indeed be excused though not justified, lies in making the use of understanding transcendental, contrary to its vocation, so that objects, possible intuitions, must conform to concepts, instead of concepts conforming to possible intuitions, on which alone their objective validity rests. The cause of this in turn is that apperception, and with it thinking, precedes every possible determinate arrangement of representations. Thus we think something in general, and determine it sensibly on one side.

B 346 Yet we distinguish the object represented universally and in abstracto from this way of intuiting it. There then remains for us a way of determining it merely through thinking, which is indeed a mere logical form without content, but nevertheless seems to us a way in which the object exists in itself (noumenon), without regard to intuition, which is limited to our senses.

* * *

Before leaving the transcendental analytic, we must add something that, although of no special importance in itself, may nevertheless seem necessary for the completeness of the system. The highest concept with which a transcendental philosophy is commonly begun is usually the division into the possible and the impossible. But since every division presupposes a concept being divided, a still higher one must be specified: the concept of an object in general, taken problematically, without deciding whether it is something or nothing. Since the categories are the only concepts relating to objects in general, distinguishing whether an object is something or nothing will proceed according to their order and guidance.

1 B 347 Opposed to the concepts of all, many, and one is the concept that cancels everything: none. Thus the object of a concept to which no specifiable intuition corresponds is = nothing, a concept without an object, as with noumena, which cannot be counted among possibilities, though they need not on that account be declared impossible either (ens rationis). The same holds, for example, of certain newly conceived fundamental powers, thought without contradiction but also without an example from experience, and therefore not to be counted among possibilities.

2 Reality is something; negation is nothing, namely a concept of the absence of an object, as with shadow or cold (nihil privativum).

3 The mere form of intuition without substance is in itself no object, but the merely formal condition of an object as appearance, as with pure space and pure time. These are indeed something as forms of intuiting, but are not themselves objects intuited (ens imaginarium).

4 B 348 The object of a concept that contradicts itself is nothing, because the concept is nothing: the impossible, such as a rectilinear figure with two sides (nihil negativum).

The table of this division of the concept of nothing—the parallel division of something follows of itself—would therefore have to be arranged as follows:

Nothing, as

1 Empty concept without an object, ens rationis.

2 Empty object of a concept, nihil privativum.

3 Empty intuition without an object, ens imaginarium.

4 Empty object without a concept, nihil negativum.

We see that a thought-entity, no. 1, is distinguished from a nonentity, no. 4, in that the former may not be counted among possibilities because it is mere invention, though not contradictory, whereas the latter is opposed to possibility because the concept even cancels itself. Both, however, are empty concepts.

B 349 By contrast, the nihil privativum, no. 2, and the ens imaginarium, no. 3, are empty data for concepts. If light had not been given to the senses, one could not represent darkness; and if extended beings had not been perceived, one could not represent space. Negation, as well as the mere form of intuition, is no object without something real.

B 74 Of the Transcendental Doctrine of Elements Second Part The Transcendental Logic

Introduction The idea of a transcendental logic

I. Logic in general

Our cognition has two basic sources in the mind. One is the taking in of representations, which is receptivity to impressions. The other is the power to cognize an object by means of those representations, which is the spontaneity of concepts. Through the first we are given an object. Through the second the object is thought, in relation to that representation, which is only a determination of the mind. So intuition and concepts together are the elements of all our cognition. A concept with no intuition matching it in some way can’t yield a cognition, and neither can an intuition with no concepts. Either kind can be pure or empirical. It is empirical if it includes sensation, which presupposes that the object is really present. It is pure if the representation has no sensation mixed in. Sensation is what we may call the matter of sensible cognition.

B 75 That is why pure intuition holds only the form in which something gets intuited, and a pure concept holds only the form of thinking an object at all. Pure intuitions and pure concepts alone are possible a priori. The empirical ones are possible only a posteriori.

Call the mind’s receptivity, its ability to take in representations when it is affected in some way, sensibility. Then the ability to produce representations on its own, the spontaneity of cognition, is the understanding. Our nature is such that intuition can only be sensible. It holds nothing but the way objects affect us. The ability to think the object of a sensible intuition is the understanding. Neither of these qualities ranks higher than the other. If we had no sensibility, no object would come to us. If we had no understanding, none would be thought. Thoughts with no content are empty, and intuitions with no concepts are blind. So we need to make our concepts sensible, by giving them an object in intuition. We equally need to make our intuitions understandable, by bringing them under concepts. The two abilities, or capacities, can’t swap their jobs either. The understanding can’t intuit a thing, and the senses can’t think a thing. Only when the two unite can cognition arise.

B 76 Still, that is no reason to blend their contributions. There is good cause to keep each carefully apart from the other and to tell them apart. That is why we distinguish aesthetic, the science of the rules of sensibility as such, from logic, the science of the understanding’s rules as such.

Logic can in turn be taken up with either of two aims. It can deal with the understanding’s use in general, or with its use in some particular field. The first sets out the absolutely necessary rules of thinking. Without them the understanding isn’t used at all. They apply whatever the objects are that the understanding may be aimed at. The logic of the particular use gives rules for thinking correctly about one certain kind of object. We can call the first elementary logic. The second is the organon of this or that science. Schools mostly put the second first, as preliminary training for the sciences. Yet in the actual course of human reason it comes last. Reason gets to it only when a science has long been finished and needs just a final touch to be corrected and perfected. That is because you must already know the objects quite well.

B 77 Only then can you give the rule for how to set up a science of them.

General logic is either pure or applied. In pure logic we leave out all the empirical conditions under which our understanding works. Some examples are how the senses influence us, how imagination plays, the laws memory follows, the sway of habit, inclination, and so on. That also removes the sources of prejudice, and in fact every cause that might produce certain cognitions in us or slip them in. Such causes bear on the understanding only in certain circumstances where it is applied, and you need experience to know those circumstances. So a general but pure logic deals only with principles a priori. It is a canon for the understanding and for reason, but only for the formal side of how they are used, no matter what the content is, empirical or transcendental. A general logic counts as applied when it is directed at how the understanding is to be used under the subjective, empirical conditions that psychology teaches us. It therefore has empirical principles, though it is general in covering the use of the understanding with no regard to its objects. This is why it is not a canon for the understanding as such, and not an organon of particular sciences either.

B 78 It serves only as a purgative for the common understanding.

So within general logic, the part that is to be the pure doctrine of reason must be kept strictly apart from the part that is applied logic (which is still general). Only the former is truly a science. It is short and dry, as a school-style presentation of the elements of the understanding has to be. Logicians must always bear two rules in mind here.

1 As general logic, it ignores all content of the understanding’s cognition and every difference among its objects. It deals with the bare form of thinking and with nothing else.

2 Considered as pure logic, it contains no empirical principles. So it takes nothing from psychology (as people have at times been talked into believing), and psychology has no say in the canon of the understanding. Pure logic is a demonstrated doctrine, and every part of it must be certain a priori without exception.

What I call applied logic is not what that word usually means. Normally it would hold certain exercises for which pure logic provides the rule. My applied logic represents the understanding together with the rules that govern its necessary use in concreto. By that I mean its use under the subject’s accidental conditions.

B 79 Those conditions can hinder or help that use, and all of them are given only empirically. This logic treats attention, what gets in its way and what follows from it, where error comes from, and the states of doubt, scruple and conviction, and so on. General and pure logic relates to it the way pure morals relates to the proper doctrine of virtue. Pure morals holds just the moral laws that any free will, as such, must obey. The doctrine of virtue weighs those laws against the obstacles of feelings, inclinations and passions, to which people are more or less subject. It can never be a true, demonstrated science, since like that applied logic it needs empirical and psychological principles.

II. Transcendental logic

As we showed, general logic ignores all content of cognition, that is, every relation of cognition to its object. It looks only at logical form, at how cognitions are related to each other, which is the form of thinking in general. But intuitions come in pure and empirical kinds (as the transcendental aesthetic shows).

B 80 So perhaps thinking about objects might likewise divide into pure and empirical. If so, there would be a logic that doesn’t set aside all content of cognition. A logic holding only the rules for pure thinking of an object would shut out every cognition with empirical content. It would also reach the origin of our cognitions of objects, so far as that origin can’t be attributed to the objects. General logic has nothing to do with that origin. It considers representations solely by the laws that govern how the understanding sets them in relation to each other as it thinks. Whether the representations were first given a priori in us or only empirically makes no difference. It concerns only the form the understanding can give to representations, wherever they may otherwise have come from.

At this point I make a remark whose influence reaches all the investigations that follow, so it should stay in view. Not every a priori cognition should be called transcendental. The name belongs only to a cognition by which we know that certain representations (intuitions or concepts) are used purely a priori, and how, or that they are possible that way. (Here transcendental means an a priori possibility of cognition, or an a priori use of it.)

B 81 So space is not a transcendental representation, and neither is any geometrical determination of space a priori. What can be called transcendental is the cognition that these representations have no empirical origin, along with the cognition of how they can still relate a priori to objects of experience. In the same way, using space for objects in general would also be transcendental. Restrict that use to objects of the senses, though, and it is called empirical. The difference between the transcendental and the empirical thus belongs only to the critique of cognitions. It has nothing to do with how they relate to their object.

We can expect, then, that perhaps there are concepts that refer to objects a priori. They would do so not as pure or sensible intuitions do, but only as acts of pure thinking. They would be concepts, yet neither empirical nor aesthetic in origin. With that in mind, we sketch ahead of time the idea of a science of pure understanding and rational cognition, one by which we think objects entirely a priori. A science of this sort would settle the origin, the range and the objective validity of such cognitions. It would have to be called transcendental logic, because it is concerned just with the laws of the understanding and of reason, and only as those apply to objects a priori.

B 82 Unlike general logic, it doesn’t cover empirical and pure rational cognitions without distinction.

III. How general logic divides into analytic and dialectic

The old, famous question was meant to corner the logicians. People hoped it would force them either to be caught in some wretched quibble or to admit their ignorance, and with it the vanity of their whole art. The question is this: What is truth? The definition of the word truth, that it means cognition agreeing with its object, is granted and taken as given here. What people want to know is the general and reliable criterion for the truth of any cognition.

Knowing what it is reasonable to ask already shows a lot of sense and insight, and it is necessary. A question that is absurd in itself, and demands pointless answers, embarrasses whoever raises it. Sometimes it does more harm. It can lure an unsuspecting listener into absurd answers.

B 83 It also produces a laughable sight: one person (as the ancients put it) milks a he-goat while another holds a sieve underneath.

If truth consists in a cognition’s agreeing with its object, then that agreement must tell this object apart from others. A cognition is false when it fails to agree with the object it refers to, even if it contains something that could be true of other objects. A criterion of truth that was general would have to hold for every cognition, whatever its objects. But clearly any such criterion would have to ignore everything a cognition contains (including its relation to its object), and truth is about exactly that. So to ask for a sign by which to tell that this content is true is impossible and absurd. A sign of truth that is both sufficient and general therefore cannot be given. Earlier we named a cognition’s content its matter. So we have to say that for the truth of a cognition as to its matter, no general mark can be demanded, because that demand contradicts itself.

Now take cognition as to its mere form, with all content set aside. It is just as clear here that a logic must supply criteria of truth.

B 84 It supplies them in the rules it sets out as the general and necessary rules of the understanding. Whatever contradicts those rules is false, since then the understanding goes against its own general rules of thinking, and so against itself. But these criteria bear only on the form of truth, which means the form of thinking in general. As far as they go they are entirely right, but they aren’t enough. A cognition can fit the logical form perfectly, that is, not contradict itself, and still contradict its object. The merely logical criterion of truth is a cognition’s agreement with the general, formal laws of the understanding and of reason. It is the conditio sine qua non (the condition without which there is no truth), and so the negative condition of all truth. But logic can’t go beyond that. It has no touchstone that could detect an error which affects not the form but the content.

General logic takes the entire formal business of the understanding and of reason apart into its elements, and presents these as the principles for any logical assessment of our cognition. So we can give this part of logic the name analytic. For that very reason it is at least the negative touchstone of truth. We have to test and size up every cognition by these rules as to its form first. Only afterwards do we examine its content.

B 85 We examine it to find out whether it holds positive truth about its object. But the mere form of cognition, however perfectly it fits logical laws, is far from enough to establish the cognition’s material (objective) truth. So no one can dare to judge objects or claim anything about them by logic alone. First they must have collected sound information about the objects from outside logic. After that, they can try to use and connect it in a coherent whole according to logical laws. Better still, they can simply test it against those laws. Even so, there is something so tempting in having such a showy art, one that puts the understanding’s form on every one of our cognitions, even when we remain very empty and poor in content. Because of this, that general logic, which is only a canon of assessment, has come to be used as though it were an organon for really producing something. At least it has been used to produce a dazzling show of objective claims. In fact it has been misused. General logic taken as this supposed organon is called dialectic.

The ancients meant quite different things by this label for a science or an art. Still, how they actually used it makes one thing certain. What they called dialectic was only the logic of illusion.

B 86 It was a sophist’s trick for giving an air of truth to one’s ignorance, and even to one’s deliberate dazzling tricks. The trick worked by imitating the thorough method that logic prescribes, and by using logic’s topics to dress up any empty claim. Here is a warning we can take as sure and useful. Treat general logic as an organon, and it is always a logic of illusion, in other words dialectical. For it tells us nothing at all about what a cognition contains. All it gives are the formal conditions for fitting the understanding, and those are completely indifferent to objects. So the suggestion that we use it as a tool (an organon) for spreading and extending our knowledge, at least in appearance, can only lead to chatter. We would be able to assert whatever we like with some show of truth, or attack it just as we please.

Teaching of that kind doesn’t suit the dignity of philosophy at all. That is why people have preferred to file this name, dialectic, under logic as a critique of dialectical illusion. We want it understood that way here too.

B 87 IV. How transcendental logic divides into transcendental analytic and dialectic

In a transcendental logic we single out the understanding, just as the transcendental aesthetic singled out sensibility earlier. We pull out of our cognition only the part of thinking that originates in the understanding alone. This pure cognition, however, can be used only on one condition: objects must be given to us in intuition, so that it has something to apply to. Without intuition, all our cognition has no objects and stays entirely empty. One part of transcendental logic presents the elements of the understanding’s pure cognition. It also presents the principles that any thinking of an object at all depends on. This part is the transcendental analytic, and it is also a logic of truth. For no cognition can go against it without losing all content on the spot, that is, all relation to any object, and so all truth. Now it is very tempting and alluring to use these pure cognitions and principles on their own, even beyond the boundaries of experience. But only experience can hand us the matter (objects) to which those pure concepts of the understanding can be applied.

B 88 Thus the understanding risks putting the bare formal principles of pure understanding to a material use, through empty reasoning. It would end up judging about objects without discrimination, though they aren’t given to us and may not be givable in any way. The analytic is really supposed to be only a canon for judging empirical use. It gets abused if we let it stand as the organon for a general, unlimited use. That happens when someone ventures, relying on pure understanding by itself, to judge synthetically about objects in general, and to assert and decide things about them. Using the pure understanding that way would be dialectical. Hence the second part of transcendental logic has to be a critique of this dialectical illusion. Its name is transcendental dialectic. It isn’t an art of stirring up such illusion dogmatically. (Sadly, that art is very popular, and it consists of many kinds of metaphysical conjuring.) It is a critique that examines understanding and reason in their hyperphysical use. Its job is to expose the false illusion in their groundless pretensions. They claim to discover and extend knowledge, and they think they can manage it through transcendental principles alone. The critique brings those claims down to something modest: judging the pure understanding and protecting it from sophistical dazzle.

B 89 Of the Transcendental Logic First Division The Transcendental Analytic

This analytic takes all our a priori cognition apart into the elements of the pure understanding’s cognition. Four things matter here. 1. The concepts must be pure, not empirical. 2. They must belong to thinking and the understanding, not to intuition and sensibility. 3. They must be elementary concepts, kept clearly distinct from derived ones and from ones assembled from others. 4. Their table must be complete, and between them they must cover the entire territory of the pure understanding. Now, the completeness of a science can’t be trusted when it rests on a rough count of a heap pieced together by trial and error. Completeness can come only from an idea of the understanding’s a priori cognition as a whole, together with the division of its concepts that this idea determines. In other words, it is possible only if the concepts are connected in a system. The pure understanding sets itself completely apart, not just from everything empirical but from all sensibility. It is therefore a unity that stands on its own and suffices for itself.

B 90 No addition from outside can enlarge it. The whole sum of its cognition will thus form a system, grasped and determined under one idea. How complete and how well articulated that system is can serve at the same time as a touchstone for the correctness and genuineness of every piece of cognition that fits into it. This entire part of transcendental logic has two books. One holds the concepts of the pure understanding, and the other holds its principles.

Of the Transcendental Analytic First Book The Analytic of Concepts

By the analytic of concepts I don’t mean analysis of them. Analysis is the usual way of working in philosophical inquiry: you take concepts that come to hand, break them down by their content and make them distinct. I mean something that has seldom been tried, a dissection of the power of understanding itself. The aim is to investigate how concepts a priori are possible, by hunting for them in the understanding alone, where they are born, and by analyzing the understanding’s pure use as a whole.

B 91 That is the proper job of a transcendental philosophy. Anything else is the logical handling of concepts in philosophy generally. We will therefore follow the pure concepts down to their earliest germs and dispositions in human understanding. That is where they lie prepared, until experience gives the occasion for them to unfold. The same understanding then frees them from the empirical conditions attached to them and presents them in their purity.

Of the Analytic of Concepts First Chapter On the guiding thread for discovering all pure concepts of the understanding

When a faculty of cognition is set in motion, various concepts come forward as the occasions vary. They make the faculty known, and they can be gathered into a more or less detailed account, once someone has watched for them over a longer time or with sharper insight. With this mechanical method, as it were, we can never say for sure when the inquiry will be done. What is more, the concepts one finds only on occasion like this turn up in no order at all. They lack systematic unity too.

B 92 In the end they are just paired by likeness and ranked by the size of their content, from simple ones to more composite ones. These rankings are anything but systematic, although in their way they are produced by method.

Transcendental philosophy has an advantage, and an obligation too: it must look for its concepts by a principle. The reason is that they spring pure and unmixed out of the understanding, which is an absolute unity, and so they must hang together under one concept or idea. Such a connection provides a rule. By it we can fix, a priori, the place each pure concept of the understanding has, and how complete the whole set is. Otherwise everything here would be left to taste or chance.

Of the Transcendental Guiding Thread for Discovering All Pure Concepts of the Understanding First Section On the logical use of the understanding in general

Earlier we explained the understanding only in negative terms, as a faculty of cognition that isn’t sensible. Without sensibility, we can have no intuition at all. So the understanding is not a faculty of intuition.

B 93 But apart from intuition there is no way to cognize except by concepts. So the cognition of any understanding, human ones at least, works through concepts. It is not intuitive but discursive. All intuitions, being sensible, depend on affections. Concepts depend on functions instead. By function I mean the unity of the act of arranging various representations under one that they share. So concepts rest on the spontaneity of thinking, as sensible intuitions rest on the receptivity of impressions. The only use the understanding can make of concepts is to judge with them. No representation goes straight to the object except intuition. A concept therefore never relates directly to an object. It relates to another representation of the object, which may be an intuition or may itself be a concept already. Judgment is thus cognition of an object at one remove: the representation of a representation of it. Every judgment has a concept that holds of many things. Among them it takes in a given representation, and that representation is the one related directly to the object. Consider “All bodies are changeable.” The concept of the divisible refers to a number of other concepts. Among them, here, it refers especially to the concept of body. And body in turn is referred to certain appearances that come our way.

B 94 So these objects are represented at one remove, through the concept of divisibility. All judgments are therefore functions of unity among our representations. A higher representation replaces the immediate one in cognizing the object. It takes in the immediate one and several others besides, and in this way many possible cognitions are pulled together into one. We can trace all acts of the understanding back to judgments. So the understanding in general can be pictured as a power to judge. For, as said above, it is a power to think, and thinking is cognition by concepts. Concepts, as predicates of possible judgments, refer to some representation of an object not yet determined. The concept of body, for example, means something such as metal, which that concept can be used to cognize. It is a concept only because other representations fall under it, and by means of them it can refer to objects. So it is the predicate in a possible judgment, such as “Every metal is a body.” We can find all the functions of the understanding, then, if we can present the functions of unity in judgments completely. The next section will show that this can be done quite well.

B 95 Of the Guiding Thread for Discovering All Pure Concepts of the Understanding Second Section

§ 9 On the logical function of the understanding in judgments

Take any judgment and set aside all of its content. Look only at the form of the understanding in it. We then find that the function of thinking in a judgment can be brought under four headings, and that each heading contains three moments. A table can set them out conveniently, as follows.

1 Quantity of judgments: universal, particular, singular

2 Quality: affirmative, negative, infinite

3 Relation: categorical, hypothetical, disjunctive

4 Modality: problematic, assertoric, apodictic

B 96 This division seems to depart from the logicians’ customary technique in a few points, though not essential ones. So the following safeguards against a possible misunderstanding won’t be out of place.

1 Logicians rightly say that when judgments are used in syllogisms, singular judgments can be treated like universal ones. For singular judgments have no extension at all. Precisely for that reason, their predicate can’t be drawn to apply to just some of what is contained under the subject concept while being excepted from the rest. It holds without exception for that concept, just as though it were a concept with general validity and an extension, with the predicate true of everything it means. Now compare a singular judgment with a universally valid one purely as a piece of cognition, in terms of size. The singular stands to the universal as one stands to infinity, so the two differ essentially in themselves. Suppose, then, that I assess a singular judgment (judicium singulare) not only for its inner validity but also, as a cognition in general, for its size relative to other cognitions. It then certainly differs from generally valid judgments (judicia communia), and it deserves a place of its own in a complete table of all the moments of thinking.

B 97 (It would not deserve one in a logic limited merely to the way judgments are used with one another.)

2 Likewise, a transcendental logic must still distinguish infinite judgments from affirmative ones. General logic is right to file them with the affirmative ones, and it does not treat them as a separate item in its division. For general logic ignores the whole content of the predicate (even a negative one). It asks only whether the predicate is laid on the subject or set against it. Transcendental logic goes further. It also weighs what such a logical affirmation, made through a merely negative predicate, is worth and contains. And it asks what that adds to cognition overall. Suppose I had said the soul is not mortal. A negative judgment like that would at least have kept an error out. But now I say that the soul is non-mortal. In logical form I have truly affirmed something, since I place the soul in the unbounded range of beings that do not die. The range of possible beings has the mortal as one part and the deathless as another. So my proposition says only that the soul is among the endless number of things left over once I remove everything mortal. But that merely narrows the infinite sphere of the possible. The mortal is cut away from it.

B 98 Then the soul is placed in the leftover stretch of that space. The space stays infinite even after this exception. More parts can be taken out, and still the soul’s concept does not grow by a bit or receive a positive determination. So as to logical range, these infinite judgments only limit, when we look at the content of cognition generally. To that extent they mustn’t be skipped in the transcendental table of all the moments of thinking in judgments. The function the understanding performs in them might prove important within the territory of its pure cognition a priori.

3 There are three kinds of relation that thinking can have in judgments: a) of predicate to subject, b) of ground to consequence, c) of a divided cognition and the gathered members of the division to each other. The first kind of judgment relates just two concepts. The second relates two judgments, and the third relates several judgments, to one another. Consider the hypothetical statement “If perfect justice exists, the persistently wicked are punished.” It really holds a relation between two statements: perfect justice exists, and the persistently wicked are punished. Whether either statement is true in itself stays undecided here. The judgment thinks only the link of consequence.

B 99 Finally, a disjunctive judgment contains a relation among two or more statements. That relation is not one of succession, but of logical opposition, since the sphere of one rules out the sphere of the other. Yet it is also one of community, since together the spheres fill out the sphere of the cognition proper. So it is a relation among the parts of a cognition’s sphere. Each part’s sphere supplements the other’s, to make up the whole range of the divided cognition. For example: the world is there either by blind chance, by inner necessity, or by an external cause. Each statement occupies one part of the sphere of possible cognition about the existence of a world as such, and together they occupy the whole sphere. Taking the cognition out of any one of these spheres means placing it in another one. And placing it in one sphere means taking it out of the others. So a disjunctive judgment has a certain community of cognitions: they shut each other out, yet by doing so they fix the true cognition as a whole, since together they make up the entire content of one given cognition. That is all I find I need to say about this here, given what follows.

4 Modality in judgments is a quite special function of its own.

B 100 What marks it out is that it adds nothing to the content of the judgment. (Beyond magnitude, quality and relation, nothing else makes up the content of a judgment.) It bears only on the worth of the copula, in its connection to thinking as a whole. In problematic judgments, affirming or denying is taken as merely possible (up to one’s choice). In assertoric ones, it is seen as actual (true). In apodictic ones, it is seen as necessary*. Thus the two judgments whose relation forms a hypothetical judgment (antecedens and consequens) are both only problematic. So are the judgments whose interplay forms the disjunctive (the members of the division). In the example above, “There is perfect justice” is not asserted. It is thought of as a judgment one may take up or not, one that someone could possibly accept, and only the consequence is asserted. Judgments like these can therefore be plainly false and yet, taken problematically, serve as conditions for cognizing truth. In the disjunctive judgment, for instance, “The world exists by blind chance” has only problematic force. That is, someone might accept the proposition for a moment.

B 101 And still it helps us find the true one, the way marking a false path helps among all the paths one could take. The problematic proposition is thus one that expresses only logical possibility (which is not objective). It expresses a free choice to let a proposition count, a purely arbitrary taking of it into the understanding. An assertoric proposition tells of logical actuality, that is, of truth. Take a hypothetical syllogism: the antecedent turns up problematic in the major premise and assertoric in the minor. The assertoric form shows that the proposition is already tied to the understanding by the understanding’s laws. An apodictic proposition thinks of the assertoric one as fixed by these same laws of the understanding, and so as asserting a priori. This is how it expresses logical necessity. Here everything gets absorbed into the understanding by degrees. First one judges something problematically. Then perhaps one accepts it as true, assertorically. Finally one maintains that it is bound to the understanding inseparably, so that it is necessary and apodictic. So we may also name these three functions of modality three moments of thinking in general.

* It’s as though thinking belonged to the understanding in the first case, to the power of judgment in the second, and to reason in the third. This is a remark that will only be cleared up later.

B 102 Of the Guiding Thread for Discovering All Pure Concepts of the Understanding Third Section

§ 10 On the pure concepts of the understanding, or categories

As I have said several times, general logic sets aside all the content of cognition. It waits for representations to be given to it from somewhere else, wherever that is, so that it can first turn them into concepts. That process is analytic. Transcendental logic, in contrast, has a manifold of sensibility a priori laid out before it. The transcendental aesthetic supplies it, so as to give the pure concepts of the understanding some stuff to work on. Lacking it, they would hold no content whatever and be completely empty. Space and time hold a manifold of pure intuition a priori. They are nonetheless among the conditions of our mind’s receptivity, the ones under which alone it can take in representations of objects. So they must always affect the concept of those objects too. But the spontaneity of our thinking demands more. The manifold has first to be gone through in a certain way, taken up, and combined, if a cognition is to come of it. I call this act synthesis.

B 103 By synthesis, in the widest sense, I mean the act of putting different representations together and grasping their variety in one cognition. A synthesis is pure when the manifold comes not from experience but a priori, as with space and time. Before we can analyze our representations at all, they must have been given to us. No concepts can arise analytically as far as their content goes. Synthesizing a manifold, whether it was given empirically or a priori, is what first yields a cognition. At the start that cognition may still be crude and confused, and so call for analysis. Yet synthesis is what actually gathers the elements into cognitions and joins them into a definite content. So it is the first thing we need to look at if we are to judge where our cognition begins.

As we will see later, synthesis in general is simply the work of the imagination. The imagination is a blind but indispensable function of the soul. We would have no cognition at all without it, yet we are hardly ever aware of it. Bringing that synthesis under concepts, however, is a job for the understanding. Only through that does the understanding first give us cognition in the strict sense.

B 104 Pure synthesis, stated in general terms, yields the pure concept of the understanding. By this synthesis I mean the kind that depends on a ground of synthetic unity a priori. Counting is an example (you notice it most with large numbers). It is a synthesis by concepts, since it follows a shared ground of unity, such as the decimal system. So under this concept, the unity in the synthesis of the manifold becomes necessary.

Representations are brought under a concept analytically. (General logic handles that job.) What transcendental logic teaches is different. It teaches how to bring under concepts, not the representations, but their pure synthesis. For the cognition of all objects a priori, the manifold of pure intuition is the first thing that has to be given. The imagination’s synthesis of that manifold comes second, but it still yields no cognition. Third come the concepts that give this pure synthesis its unity. They consist only in the representation of that necessary synthetic unity. They contribute the third element toward cognizing an object that presents itself, and they rest on the understanding.

One function unifies different representations in a judgment.

B 105 That same function also unifies the bare synthesis of different representations in an intuition. Put generally, that is what we call the pure concept of the understanding. So one and the same understanding, by the very same acts through which it produces the logical form of a judgment in concepts by means of analytic unity, also brings a transcendental content into its representations by means of the synthetic unity of the manifold in intuition as such. That is why they are called pure concepts of the understanding: they go to objects a priori. General logic can’t manage that.

In this way the pure concepts of the understanding that arise number exactly as many as the logical functions that the previous table found in every possible judgment. They relate a priori to objects of any intuition at all. For the understanding is used up completely by the functions we have named, and its capacity is fully measured by them. We will call these concepts categories, after Aristotle. Our aim is at bottom the same as his, though in execution it departs from his a great deal.

B 106 Table of Categories

1 Of quantity: unity, plurality, totality.

2 Of quality: reality, negation, limitation.

3 Of relation: inherence and subsistence (substantia et accidens); causality and dependence (cause and effect); community (interaction between what acts and what is acted on).

4 Of modality: possibility—impossibility, existence—nonbeing, necessity—contingency.

This is the register of every original, pure concept of synthesis which the understanding holds within itself a priori. They are the reason it is a pure understanding at all, since only through them can it understand anything about the manifold of an intuition, which means thinking an object of it. The division is produced systematically from one shared principle, namely the power to judge, which amounts to the power to think. It did not turn up piecemeal, from a search for pure concepts launched at random.

B 107 One can never be sure such a search is complete, since completeness is only inferred by induction. And I won’t even mention that, with the second method, one never sees why exactly these concepts, and no others, dwell in the pure understanding. Aristotle’s plan to look for these basic concepts was worthy of a keen mind. But he had no principle. So he scooped them up as they came his way. First he turned up ten, which he called categories (predicaments). Later he thought he had found five more, and added them under the name postpredicaments. Even so his table stayed deficient. It also contains some modi of pure sensibility (quando, ubi, situs, and likewise prius, simul), and one empirical item (motus). These don’t belong in this ancestral register of the understanding at all. Or else it counts derived concepts among the original ones (actio, passio), while some of the derived ones are missing entirely.

As for those derived ones, there is a further point to make. The categories are the true root concepts of the pure understanding, and they have derived concepts of their own that are just as pure. A complete system of transcendental philosophy could not possibly pass these over. In a purely critical essay I am content just to mention them.

B 108 Allow me to call these concepts of the understanding, pure yet derived, the predicables of pure understanding, as opposed to the predicaments. With the original, primitive concepts in hand, the derived and subordinate ones are easy to add on, and the pure understanding’s genealogy can be drawn in full. My concern here is not for the system’s completeness but only for the principles of a system. I am saving the supplement for another undertaking. Still, you can come close to that goal by taking up ontology textbooks. Under the category of causality, for instance, they place the predicables force, action and being acted on. Under community, they place presence and resistance. Under the predicaments of modality they place arising, passing away, change and so on. Categories combined with the modi of pure sensibility, or with one another, give a large number of derived concepts a priori. It would be a useful and not unpleasant labor to take note of these and, where possible, list them completely, but it can be spared here.

I deliberately decline to give definitions of these categories in this treatise, though I may well have them ready. I will break these concepts down later, as far as the doctrine of method I’m working on requires.

B 109 In a system of pure reason, people could fairly demand definitions from me. Here, though, they would only pull attention away from the main point of the inquiry, because they would provoke doubts and attacks. These can safely be deferred to another project without taking anything from the essential aim. Meanwhile the little I have said on the matter makes one thing plain. A complete dictionary, with all the explanations it needs, is possible and also easy to put together. The compartments exist already, and they only need filling. And a systematic topic like the present one makes it hard to miss the spot where a given concept properly belongs. It also shows us at once which spot is still empty.

§ 11

Some neat observations can be made about this table of categories. They could perhaps carry weighty consequences for the scientific form of all cognitions of reason. Here is why. In the theoretical part of philosophy the table is uncommonly useful. It is even indispensable for drawing up the plan of a whole science in full, so long as that science rests on concepts a priori, and for dividing the science mathematically on fixed principles. This is evident from the table itself. It sets out every elementary concept of the understanding in full.

B 110 It even gives the form that a system of them takes in the human understanding. So it gives direction for each moment of a planned speculative science, and for their order as well. I have given a sample of this elsewhere*, too. Here, then, are a few of the remarks.

* Metaphysical Foundations of Natural Science.

The first is that this table has four classes of concepts of the understanding, and that it splits first into two divisions. One division is aimed at objects of intuition, pure and empirical alike. The other is aimed at the existence of those objects, whether in relation to each other or to the understanding.

I would name the first class the mathematical categories and the second the dynamical ones. As you see, only the second class has correlates, and the first has none. This difference has to have a basis in the nature of the understanding.

2nd remark. In every class the number of categories is the same, namely three. This too is worth thinking about, because otherwise any division a priori by concepts has to be a dichotomy. On top of that, the third category in each class always comes from joining the second to the first one in its class.

B 111 Totality, for instance, is just plurality regarded as a unity. Limitation is just reality joined to negation. Community is one substance’s causality in determining another reciprocally. And necessity is just existence given through possibility itself. Do not conclude, however, that the third category is therefore only derived and not a root concept of the pure understanding. For to combine the first and second so as to produce the third concept takes a special act of the understanding. It is not the same act as the one used for the first and second. Number belongs to the category of totality, yet it is not always possible even where the concepts of multitude and of unity are present. The representation of the infinite is an example. Likewise, combining the concept of a cause with that of a substance does not yet make influence understandable at once. By influence I mean how one substance can come to be the cause of something in another substance. This shows that the understanding has to perform a special act here, and the same holds for the rest.

3rd remark. Of just one category, community, which stands under the third heading, the agreement is less obvious than it is for the others. The agreement is with the form that corresponds to it in the table of logical functions.

B 112 That form is the disjunctive judgment.

To be sure of this agreement, we have to notice that in every disjunctive judgment the sphere (everything that falls under the concept) is pictured as a whole split up into parts (the subordinate concepts). The parts are thought of as side by side, not one under another, since none can be contained in another. So they fix one another’s place not in one direction, as in a series, but mutually, as in an aggregate. (Posit one member of the division and all the rest are ruled out, and vice versa.)

We think of a like connection in a whole of things. There one thing is not placed under another as its effect, with the other as the cause of its existence. Instead the things stand side by side, at once and mutually, as causes with regard to fixing each other’s state. (A body whose parts pull on each other and also resist each other is an example.) That is a connection of a wholly different kind from the one found in the bare relation of cause and effect (ground and consequence). In that relation the consequence does not in turn determine the ground, so it does not form a whole with the ground. The creator of the world, for instance, does not form one with the world. The understanding uses the same method when it pictures the sphere of a divided concept.

B 113 It also uses it when it thinks of a thing as divisible. In the first case the members of the division exclude each other and yet are joined in one sphere. In the same way the understanding pictures the parts of a divisible thing. The existence of each part (as a substance) belongs to it to the exclusion of the others, and yet the parts are joined in one whole.

§ 12

The transcendental philosophy of the ancients holds one further chapter. It contains pure concepts of the understanding that are not counted as categories. Even so, they ought to rank, right after the categories, as concepts of objects that hold a priori. But then they would swell the number of categories, which can’t happen. The proposition so famous among the scholastics sets these concepts out: quodlibet ens est unum, verum, bonum (any being whatever is one, true and good). In the conclusions drawn from it, which were only tautologies, this principle has proved very meager indeed. In more recent times it gets hauled out in metaphysics, almost solely for the sake of honor. Still, an idea that has lasted this long, however hollow it seems, always deserves a look at its origin. It suggests that the thought rests on some rule of the understanding, one that has simply, as so often happens, been misread.

B 114 These supposed transcendental predicates of things are just logical requirements and criteria that every cognition of things must meet. They are founded on the categories of quantity: unity, plurality and totality. The difference is this. Strictly, those categories should be taken as material, as belonging to the possibility of the things themselves. But the predicates actually used them in a formal sense only, as part of the logical demand on any cognition. And yet they carelessly made these criteria of thinking into properties of things in themselves. Every cognition of an object has unity of concept. We can call it qualitative unity, to the extent that only the unity of gathering the manifold of cognitions together is meant. The single theme of a play, a speech or a fable is an example. Second comes truth with regard to consequences. A given concept shows more signs of objective reality the more true consequences can be drawn from it. We could call this the qualitative plurality of the marks that belong to a concept as their shared ground (they are not thought as a quantity in the concept). Third and finally comes perfection. It consists in this: conversely, the plurality taken together leads back to the unity of the concept, and fits that concept completely and no other. We may call this qualitative completeness (totality).

B 115 It is clear from this that these logical criteria for the possibility of any cognition transform the three categories of magnitude. In the categories of magnitude, unity in producing a quantum has to be assumed homogeneous throughout. Here the transformation serves only to connect even unlike pieces of cognition in one consciousness, and it does so by the quality of a cognition as a principle. Thus the definition is the test of whether a concept is possible (not whether its object is). A definition needs the concept’s unity and the truth of whatever can first be derived from it. In the end it needs completeness in what has been drawn out. Together these supply what the whole concept requires. A hypothesis likewise has a criterion: the explanatory ground it assumes must be intelligible, or have unity (with no auxiliary hypothesis). The consequences derived from it must be true (consistent with each other and with experience). And the explanatory ground must be complete for them. They then point back to exactly what the hypothesis assumed, neither more nor less. They give back analytically, a posteriori, the very thing that had been thought synthetically a priori, and they agree with it. —So the transcendental table of categories gets no supplement from the concepts of unity, truth and perfection, as if it were somehow lacking. All that happens is that the relation of these concepts to objects is set entirely aside.

B 116 The procedure with them is then brought under general logical rules for how cognition agrees with itself.

Of the Transcendental Analytic Second Chapter On the Deduction of the Pure Concepts of the Understanding

First Section

§ 13 On the principles of a transcendental deduction in general

When legal scholars talk about entitlements and presumptions, they separate two questions in a lawsuit: what is lawful (quid juris) and what is the fact (quid facti). They demand proof on both. The proof that is to show the entitlement, the legal claim, they call the deduction. We use a great many empirical concepts and nobody objects. Even with no deduction we feel entitled to give them a sense and a supposed meaning. We can do so because we always have experience at hand.

B 117 With it we can prove their objective reality. There are also usurped concepts, though, fortune and fate for instance. They go around with nearly everyone’s tolerance. But now and then someone confronts them with the question quid juris. Then we are in no small difficulty about their deduction, because we can name no clear legal ground, whether from experience or from reason, that would clarify the right to use them.

Among the many concepts that make up the very mixed web of human cognition, some are also destined for pure use a priori, entirely apart from experience. The entitlement for these always calls for a deduction, because proofs drawn from experience don’t suffice to make such use lawful. Yet we must still find out how such concepts are able to refer to objects that they take from no experience. I therefore name the explanation of how concepts a priori can relate to objects their transcendental deduction. I set it apart from empirical deduction, which shows how a concept was acquired through experience and through reflection on experience. That kind concerns not lawfulness but the fact from which possession arose.

B 118 We now have two kinds of concepts, very different in character, which agree in this: both relate to objects wholly a priori. They are the concepts of space and time, which are forms of sensibility, and the categories, which are concepts of the understanding. Attempting an empirical deduction of them would be pure wasted labor. That is because what sets their nature apart is exactly that they relate to their objects without borrowing anything from experience to represent them. So if they need a deduction, it must always be transcendental.

Still, one can look in experience for the occasions on which these concepts, like all cognition, are produced, even if not for the principle of their possibility. There the impressions of the senses give the first push to open up our entire power of cognition in regard to them, and to build up experience. Experience has two very different elements. One is a matter for cognition, from the senses. The other is a form for ordering that matter, which comes from the inner well of pure intuiting and thinking. These first get exercised on the occasion of the matter, and they produce concepts. We can trace the first efforts of our cognitive power in this way.

B 119 The aim is to climb from single perceptions to general concepts. Doing so is, no doubt, of great use. The famous Locke deserves credit for first opening the way. But a deduction of pure concepts a priori is never produced by it. It doesn’t lie on that path at all. Their later use is meant to be wholly independent of experience, so they must show a very different birth certificate from descent out of experience. This attempted physiological derivation can’t properly be called a deduction at all, as it concerns a quaestionem facti (a question of fact). So I will call it the explanation of how a pure cognition came to be possessed. It is thus clear that only for these concepts can there be a transcendental deduction, and in no way an empirical one. As for pure concepts a priori, the empirical kind is nothing but idle attempts, which only someone who hasn’t grasped the quite special nature of these cognitions could busy themselves with.

Suppose we grant that the transcendental route is the only possible kind of deduction for pure a priori cognition. That still doesn’t show that this deduction is so absolutely necessary. Earlier we used a transcendental deduction to follow the concepts of space and time all the way back to their sources.

B 120 We also explained their objective validity a priori and fixed it. Even so, geometry moves ahead with sure steps through nothing but a priori cognitions. Its basic concept, space, has a pure and lawful origin, so geometry has no need to ask philosophy for a certificate vouching for it. But in this science the concept is used only for the outer world of the senses. Space is the pure form of our intuition of that world. All geometrical cognition rests on a priori intuition, and that is why it is immediately evident. The objects are given in the intuition a priori (as to their form) by the cognition itself. The pure concepts of the understanding are another matter. Here a need arises that cannot be avoided: to look for a transcendental deduction of them, and of space as well. The reason is this. These concepts speak of objects a priori through predicates of pure thinking, not through predicates of intuition and sensibility. So they relate to objects in general, apart from every condition of sensibility. They aren’t grounded in experience. They also can’t show any object in a priori intuition on which they could base their synthesis before all experience. For these reasons they arouse suspicion about the objective validity and the limits of their use. They make the concept of space ambiguous as well. The cause is a habit of theirs.

B 121 They use it outside the conditions of sensible intuition. That is why a transcendental deduction of space was needed above, too. Before readers take even one step into the field of pure reason, they have to be persuaded that this kind of transcendental deduction cannot be avoided. Otherwise they proceed blindly, wander about in all directions, and still end up back in the ignorance they started from. The reader must also see the unavoidable difficulty clearly ahead of time. Then they won’t complain of obscurity where the subject itself lies deeply hidden, and they won’t lose patience too soon over clearing away the obstacles. That is because what matters is this: either we abandon every claim to insight by pure reason in its favorite territory, the territory beyond the boundaries of all possible experience, completely and for good, or we bring this critical investigation to completion.

Earlier, with the concepts of space and time, we were able without much effort to make clear how these, as cognitions a priori, must still relate to objects of necessity, and how they make possible a synthetic cognition of objects independent of all experience. Such pure forms of sensibility are the only way an object can appear to us. In other words, they are the only way it can be an object of empirical intuition. So space and time are pure intuitions.

B 122 In them lies, a priori, what objects need in order to be possible as appearances. And the synthesis found in them is objectively valid.

The categories of the understanding are different. They show us nothing of the circumstances in which intuition gives us objects. Objects, then, may well show up for us with no need to be tied to any functions of the understanding. The understanding then wouldn’t contain their conditions a priori. Here a difficulty shows up that we didn’t meet in the field of sensibility. How can subjective conditions of thinking have objective validity? That is, how can they supply conditions for the possibility of all cognition of objects? Appearances can, after all, be handed to us in intuition when the understanding’s functions play no part. Take the concept of cause. It means a particular kind of synthesis: when something A is given, something quite different, B, is posited after it according to a rule. Nothing a priori tells us why appearances should hold anything like it. (We can’t point to experiences as proof, since it must be possible to show this concept’s objective validity a priori.) So it is doubtful a priori whether such a concept might be completely empty and find no object anywhere among appearances. Objects of sensible intuition must fit certain conditions.

B 123 These are the formal conditions of sensibility that lie a priori in the mind. That much is clear, because otherwise they wouldn’t be objects for us. But they must also fit the conditions the understanding needs for its synthetic insight in thinking, and the inference to that is not so easy to see. For appearances might well be such that the understanding found them in no way fitting the conditions of its unity. Everything might lie in such confusion that, for example, the sequence of appearances offered nothing to suggest a rule of synthesis and so to match the concept of cause and effect. The concept would then be entirely empty. It would be null, with no meaning at all. Even so, appearances would still present objects to our intuition, since intuition doesn’t need the functions of thinking in any way.

Someone might hope to escape the hard work of these investigations by saying this: experience never stops supplying examples of this kind of regularity among appearances. These give us ample reason to draw the concept of cause out of them, and thereby to prove its objective validity as well. But that overlooks something. The concept of cause can’t arise in this way at all. It has to be rooted wholly a priori in the understanding. Otherwise we must drop it altogether as a mere fantasy.

B 124 What the concept requires is that a thing A be such that another thing B follows from it. This must happen of necessity, and by a rule with no exceptions at all. Appearances do offer cases from which we can get a rule. It is a rule saying what usually happens. But they never show that the result is necessary. That is why putting a cause together with an effect has a special standing, which no empirical statement can express: the effect doesn’t just come in addition to the cause, but is posited by it and follows from it. Strict universality of a rule isn’t a property of empirical rules, either. Through induction they can gain only comparative universality, that is, wide usefulness. But the use of the pure concepts of the understanding would change completely if we wanted to treat them as merely empirical products.

§ 14 Transition to the transcendental deduction of the categories

There are only two cases in which a synthetic representation and its objects can come together, relate to each other necessarily, and, so to speak, meet. Either the object is the only thing that makes the representation possible.

B 125 Or the representation is the only thing that makes the object possible. In the first case the relation is only empirical. The representation can then never be possible a priori. That is how it is with appearances, as far as the sensation in them goes. In the second case, a representation by itself does not produce its object as far as existence goes. (We aren’t talking here about the causality it has through the will.) Still, the representation determines the object a priori when it alone makes it possible to cognize something as an object. Now there are two conditions under which alone the cognition of an object is possible. The first is intuition, by which the object is given, though only as appearance. The second is a concept, by which an object corresponding to that intuition is thought. It is clear from what came before that the first condition, the one under which alone objects can be intuited, does in fact lie a priori in the mind as the ground of the objects, as to their form. Every appearance must therefore fit this formal condition of sensibility. Only through that condition can it appear at all, which is to say, be intuited and given empirically. Now the question is whether concepts also come first a priori, as conditions under which alone something is thought as an object in general, even though it isn’t intuited.

B 126 If they do, then every empirical cognition of objects has to fit such concepts. The reason is that without them nothing could be an object of experience. All experience contains two things: first, the sensory intuition that gives us something, and second, a concept of the object that is given in that intuition or appears in it. Concepts of objects in general will thus lie at the base of all cognition drawn from experience, as a priori conditions. The categories are a priori concepts. Their objective validity will therefore depend on the following: only through them is experience possible (as to the form of thinking). For then they relate necessarily and a priori to objects of experience, since it is only by means of them that any object of experience can be thought at all.

This means the transcendental deduction of every a priori concept rests on one principle, and the whole inquiry has to be aimed at it. It is this: we have to recognize these concepts as a priori conditions that make experiences possible (conditions of the intuition we find in experience, or of the thinking). Concepts that supply the objective ground for the possibility of experience are necessary for exactly that reason. But setting out the experience in which they turn up is not their deduction. It is only an illustration, because on that approach they would still be merely contingent.

B 127 Without this original relation to possible experience, the setting in which all objects of cognition occur, we couldn’t understand at all how they relate to any object.

The famous Locke never considered this. He found pure concepts of the understanding in experience, so he derived them from experience as well. Yet he was so inconsistent that he used them to attempt cognitions that go far beyond every boundary of experience. David Hume recognized that such an attempt would need these concepts to originate a priori. But he couldn’t explain how the understanding is bound to think concepts as necessarily combined in the object when they aren’t combined in the understanding itself. He also never thought of this possibility: through these same concepts the understanding itself might be what produces the experience where its objects turn up. Forced by necessity, he derived the concepts from experience. That is, he derived them from a subjective necessity that arises through frequent association in experience and is finally mistaken for an objective one. In other words, he derived them from habit. After that, though, he was very consistent. He called it impossible to use these concepts, or the principles they lead to, to get past the boundary of experience.

B 128 But the empirical derivation that both men fell back on can’t be squared with the actual a priori scientific cognitions we have, namely pure mathematics and general natural science. So the fact refutes it.

The first of these two famous men threw the doors wide open to fanaticism. Once reason has entitlements on its side, vague appeals to moderation can no longer hold it within limits. The second gave himself up completely to skepticism, once he believed he had found so general a deception in our faculty of cognition, a deception taken for reason. We are now about to try an experiment. Can human reason be steered safely between these two rocks, be given definite boundaries, and still be left open to the whole field of its fitting activity?

First I want to set down the definition of the categories. Each one is a concept of an object as such. Through such a concept, that object’s intuition counts as determined in respect to one of the logical functions in judging. Take the function of the categorical judgment. That function was the relation of a subject to a predicate. Here is an example: “All bodies are divisible.” Yet the merely logical use of the understanding left one thing undetermined.

B 129 It did not say which of the two concepts plays subject and which plays predicate. We can just as well say, “Something divisible is a body.” The category of substance settles this. Put the concept of a body under it, and the question is decided: the empirical intuition of a body must in experience always be taken as a subject, and never as a bare predicate. The same goes for all the other categories.

Of the Deduction of the Pure Concepts of the Understanding Second Section Transcendental Deduction of the Pure Concepts of the Understanding

§ 15 On the possibility of combination in general

An intuition that is purely sensible, which is to say nothing but receptivity, can have a manifold of representations given in it. Its form can already be present in our faculty of representing, a priori. Even so, it is only the manner in which the subject is affected. Combination (conjunctio) is another matter. When a manifold in general is combined, that combination can never reach us through the senses. So it can’t be contained along with the pure form of sensible intuition, either.

B 130 It is an act in which the power of representation shows its spontaneity. To tell this power apart from sensibility, we have to call it understanding. So all combination is an action of the understanding. That holds whether or not we become aware of it, and whether it combines the manifold of intuition or various concepts, and, in the case of intuition, whether the intuition is sensible or nonsensible. We would give this action the general name synthesis. That also points out that we can’t represent anything as combined in the object unless we have first combined it ourselves. Combination is unique among representations: objects never give it to us. Only the subject itself can carry it out, because it is an act of the subject’s own self-activity. It is easy to see here that this action must be originally one, and the same for all combination. And taking apart, which is analysis and seems to be its opposite, always presupposes it. Where the understanding hasn’t combined anything beforehand, it can’t take anything apart either, since the power of representation could be given something as combined only by the understanding.

But the concept of combination brings along more than the concept of the manifold and its synthesis. It also brings the concept of the manifold’s unity. What combination amounts to is a representation of a manifold’s synthetic unity*.

B 131 So the representation of this unity cannot come out of the combination. Rather, it is added to the representation of the manifold, and that is what first makes the concept of combination possible. This unity comes before all concepts of combination, a priori. It is not the category of unity (§ 10), because all categories rest on logical functions in judgments. In those judgments combination, and so unity of given concepts, is already thought. The category therefore already presupposes combination. So we have to look for this unity (as qualitative, § 12) higher still. We must look for it in whatever holds the ground for different concepts being unified in judgments. That same thing holds the ground for the understanding being possible at all, even when it is used only logically.

* Whether the representations are themselves identical, so that one could be thought through another analytically, is not a question here. As long as we are talking about a manifold, the consciousness of one representation must always be told apart from the consciousness of another. All that matters here is the synthesis of this (possible) consciousness.

§ 16 On the original synthetic unity of apperception

The “I think” must be able to go along with all my representations. Otherwise something would get represented in me.

B 132 That something could not be thought at all. And that comes to the same thing as saying the representation would be impossible, or at least would be nothing to me. A representation that can be given before any thinking is called intuition. Every manifold in intuition therefore stands in a necessary relation to the “I think.” It does so in the very subject where that manifold is found. This representation, though, is an act: an act of spontaneity. That is, it cannot be counted as belonging to sensibility. I call it pure apperception, to tell it apart from empirical apperception. I also call it original apperception. It is the kind of self-consciousness that brings forth the representation “I think.” This representation has to be able to go along with all the others. In all consciousness it is one and the same. No further representation can accompany it. I also call the unity of this apperception the transcendental unity of self-consciousness, to mark that cognition a priori is possible from it. If the manifold representations given in some intuition did not all belong to a single self-consciousness, they would not all be mine. Put differently, as my representations they must meet a certain condition, whether or not I am aware of them as mine. Under that condition, and no other, they can be gathered into one general self-consciousness. Otherwise they would not belong to me completely.

B 133 We can draw many conclusions from this original combination.

Namely, a manifold is given in intuition, and its apperception is identical throughout. That identity contains a synthesis of the representations. It is possible only through consciousness of this synthesis. Empirical consciousness, which goes along with different representations, is scattered in itself and has no relation to the identity of the subject. That relation doesn’t come about just because I accompany each representation with consciousness. It comes about because I add one representation to another and am conscious of their synthesis. I can represent the identity of consciousness within these very representations only because I am able to combine a manifold of given representations in a single consciousness. To say it differently: analytic unity of apperception is possible only if some synthetic unity is assumed*.

B 134 So when I think, “All these representations given in intuition belong to me,” I am saying: “I unite them in one self-consciousness, or at least I can.” This thought is not yet awareness of the synthesis of the representations itself. But it does presuppose the possibility of that synthesis. I call all these representations mine only because I can grasp their manifold in one consciousness. Otherwise I would have a self as many-colored and varied as the number of representations I am conscious of. Synthetic unity belongs to the manifold of intuitions, and it is given a priori. That unity is therefore the ground of apperception’s identity, and that identity precedes, a priori, every determinate thought of mine. Combination, however, does not lie in the objects. We cannot borrow it from the objects by way of perception and so bring it into the understanding for the first time.

B 135 It is solely a performance of the understanding. The understanding itself is just the ability to combine a priori, and to bring the manifold of given representations under apperception’s unity. This principle is the highest in all of human cognition.

* All common concepts, as such, carry with them the analytic unity of consciousness. Suppose I think of red in general. Then I represent a property that can be found (as a mark) in something or other, or can be combined with other representations. So I can represent the analytic unity only by way of a synthetic unity that I have thought of beforehand as possible. Suppose a representation is to be thought of as shared by different things. Then it is counted as belonging to things that also have something distinct in themselves, apart from it. It has to be thought beforehand in synthetic unity with other representations, possible ones at least. Only after that can I think of the analytic unity of consciousness in it, the unity that turns it into a conceptus communis, a common concept. That is how the synthetic unity of apperception comes to be the highest point. All use of the understanding has to be fastened to it, including logic as a whole and, after logic, transcendental philosophy. In fact this faculty is the understanding itself.

The principle of apperception’s necessary unity is itself an identity, which makes it an analytic proposition. Still, it declares a synthesis necessary: a synthesis of the manifold given in one intuition. Without it, the thoroughgoing identity of self-consciousness cannot be thought. The I, as a simple representation, gives no manifold at all. A manifold can only be given in intuition, which is different from the I, and it can be thought only by being combined in one consciousness. An understanding in which self-consciousness would at the same time give all the manifold would intuit. Ours can only think, and has to look in the senses for intuition. I am therefore conscious of an identical self in relation to the manifold of representations given me in one intuition. The reason is that I call them all mine, and so they make up one. It comes to this: I have, a priori, a consciousness of a necessary synthesis of them. This is called the original synthetic unity of apperception.

B 136 All the representations given to me stand under it, but they also have to be brought under it by a synthesis.

§ 17 The principle of the synthetic unity of apperception is the highest principle of all use of the understanding

The Transcendental Aesthetic gave us the highest principle for the possibility of any intuition, so far as sensibility goes. It was this: the whole manifold of that intuition comes under space and time as its formal conditions. The supreme principle of the very same thing, in relation to the understanding, is this: all that is manifold in intuition stands under the conditions set by the original synthetic unity of apperception*. Under the first stand all the manifold representations of intuition, insofar as they are given to us. Under the second they stand insofar as they must be able to be combined in one consciousness.

B 137 If that fails, they can yield no thought and no cognition. The given representations would not share the act of apperception, the “I think,” and so they would not be gathered together in one self-consciousness.

* Space and time, together with all their parts, are intuitions. So they are single representations, together with the manifold they contain in themselves (see the Transcendental Aesthetic). They are therefore not mere concepts. A concept contains one and the same consciousness as being in many representations. Space and time contain many representations as being in one, together with the consciousness of them. They therefore show up as composite, and so the unity of consciousness is found in them as synthetic, though still as original. This singleness of theirs matters in application (see § 25).

Speaking generally, the understanding is the faculty of cognitions. A cognition is the determinate way given representations are related to an object. By an object we mean whatever has, in its concept, the manifold of a given intuition united. Any uniting of representations needs consciousness to be one in synthesizing them. So the unity of consciousness is the one thing that makes up the relation of representations to an object, and with it their objective validity and their becoming cognitions. The very possibility of the understanding rests on it.

So the understanding’s first pure cognition is the principle of apperception’s original synthetic unity. All the rest of the understanding’s use is based on it, and it is also entirely independent of all conditions of sensible intuition. Consider space, the bare form of outer sensible intuition. It is not yet any cognition. All it does is provide, a priori, the manifold of intuition for a cognition that may come. To cognize anything in space, a line for instance, I have to draw it.

B 138 So I have to produce, synthetically, a determinate combination of the given manifold. The unity of the action must at the same time be unity of consciousness, found in the concept of a line. Only then is an object (a determinate space) cognized. So the synthetic unity of consciousness is an objective condition of all cognition. I don’t need it merely for my own cognizing of an object. Each intuition must stand under it if it is to become an object for me. Otherwise, and without this synthesis, the manifold would never come together in one consciousness.

As noted, this last proposition is analytic in itself, although it makes synthetic unity a condition for all thinking. It says only this: each of my representations, in whatever intuition is given, must meet one condition. Only if they meet it can I count them as mine, as belonging to the identical self, and gather them as synthetically combined in one apperception under the general expression “I think.”

Still, this principle does not hold for every understanding that could exist. It holds only for an understanding whose pure apperception gives no manifold whatever in the representation “I am.” Take an understanding whose self-consciousness would at the same time give the manifold of intuition.

B 139 Suppose its representation would at the same time make the objects of that representation exist. A special act of synthesizing the manifold into one consciousness would be unnecessary for it. The human understanding, which only thinks and does not intuit, does need it. For the human understanding, though, this principle is unavoidably the first one. It cannot form the slightest concept of any other possible understanding. That other understanding might be one that itself intuited. Or it might have a sensible intuition as its ground, but one of a different kind from the intuition in space and time.

§ 18 What the objective unity of self-consciousness is

The transcendental unity of apperception is the unity through which everything manifold given in an intuition is united into a concept of the object. That is why it is called objective. Do not confuse it with the subjective unity of consciousness. That one is a determination of inner sense. Through that determination the manifold of intuition is given empirically for such a combination. Whether the manifold reaches my empirical awareness as simultaneous or as one thing after another depends on circumstances, that is, on empirical conditions.

B 140 So the empirical unity of consciousness, produced by associating representations, is about an appearance itself, and it is wholly contingent. The pure form of intuition in time is different. Taken simply as intuition in general, which contains a given manifold, it stands under the original unity of consciousness. It does so only because the manifold of intuition is necessarily related to the one “I think.” That is to say, it does so by way of the understanding’s pure synthesis, which lies a priori beneath the empirical synthesis. Only the first unity is objectively valid. We aren’t looking here at empirical unity of apperception. It is derived from the first kind, under given conditions in concreto. It has merely subjective validity. Take two people. One combines the idea of a given word with one thing, and the other combines it with another thing. In the empirical realm, consciousness’s unity is not necessary, and it is not universally valid, regarding what is given.

§ 19 Every judgment’s logical form lies in the objective unity of apperception among the concepts it holds

I have never been able to feel satisfied with the definition that logicians give of a judgment in general. In their words, it is the representation of how two concepts are related.

B 141 I won’t quarrel with them here over what is wrong with that definition. At best it fits categorical judgments but not hypothetical and disjunctive ones, since these contain a relation not of concepts but of judgments themselves. (This oversight in logic has led to a number of awkward results.)* I only remark that the definition leaves open what the relation consists of.

* The drawn-out theory of the four syllogistic figures deals only with categorical inferences of reason. It is nothing more than a trick. Immediate inferences (consequentiae immediatiae) are tucked in among the premises when a pure inference of reason is drawn. That slips in an illusion of extra kinds of inference beyond the one in the first figure. Even so, this trick alone would have had no great success if it had not also managed to give categorical judgments exclusive standing, as the ones to which all others must be traceable. According to § 9, that is false.

I examine more closely how given cognitions are related inside any judgment. I tell this relation, which belongs to the understanding, apart from the relation that follows the laws of the reproductive imagination (which has only subjective validity). What I find is this: a judgment is simply the way of bringing given cognitions under apperception’s objective unity. That is what the little relating word “is” aims at in judgments.

B 142 It separates the objective unity of given representations from the subjective unity. For “is” marks the relation of the representations to original apperception and their necessary unity, even when the judgment itself is empirical and therefore contingent, as in “Bodies are heavy.” By this I don’t mean that these representations belong together necessarily in empirical intuition. My point is that they belong together because apperception is necessarily one when intuitions are synthesized. In other words, they go together according to principles that determine all representations objectively, to the extent that cognition can arise from them. Every one of these principles is derived from the principle of apperception’s transcendental unity. Only this makes the relation a judgment, meaning a relation with objective validity. It is then clearly different from a relation among the same representations that has only subjective validity, for example one that follows the laws of association. By those laws I could say only this: “When I carry a body, I feel the pressure of its weight.” I could not say, “The body itself is heavy.” To say that would be to say the two representations are combined in the object, whatever state the subject is in. It would not be merely that they turn up together in perception, however often that repeats.

B 143 § 20 Every sensible intuition falls under the categories, which are the only conditions for its manifold to join in a single consciousness

A manifold given in a sensible intuition must belong under apperception’s original synthetic unity. Only through that unity can intuition itself be a unity (§ 17). The understanding acts to bring a manifold of given representations under one apperception. These representations may be intuitions, or they may be concepts. That action is the logical function of judgments (§ 19). So the manifold in a single empirical intuition is fixed, in relation to one logical function of judging. Through it the manifold is brought to a consciousness as such. But the categories are just these functions of judging, so far as a given intuition’s manifold is determined in respect of them (§ 13). It follows that the manifold in a given intuition is also bound to stand under categories.

B 144 § 21 Remark

A manifold contained in an intuition that I call mine is represented, through the understanding’s synthesis, as belonging to the necessary unity of self-consciousness. This happens through the category*. What the category shows is that the empirical consciousness of a manifold given in one intuition stands beneath a pure self-consciousness, a priori. That parallels empirical intuition, which stands beneath a pure sensible intuition that also holds a priori.—So the proposition above begins a deduction, and its subject is the pure concepts of the understanding. In that deduction the categories arise in the understanding alone, independent of sensibility. That means I must still set aside how the manifold gets given for an empirical intuition. I look only at the unity that the understanding adds to the intuition by means of the category. Later (§ 26) we will look at how empirical intuition is given in sensibility.

B 145 It will turn out that this unity is exactly the one the category prescribes (see § 20 just above) for any given intuition’s manifold. Once the category’s a priori validity for all objects of our senses is explained in that way, the deduction will at last reach its goal in full.

* The ground of the proof is the represented unity of intuition, by which an object is given. That unity always involves a synthesis of whatever manifold is given for one intuition. It also already holds the relation of this manifold to apperception’s unity.

But there was one point in the proof above that I could not abstract from. It was this: the manifold for intuition has to be given ahead of the understanding’s synthesis, and apart from it. How it is given is left undetermined here. Suppose I tried to conceive an understanding that itself intuited, a divine one, say. It would not represent objects that are given to it. Its very representation would give or produce the objects at the same time. The categories would mean nothing at all for cognition of that kind. They are rules, and rules only, for an understanding whose entire power lies in thinking. What it can do is act: it takes a manifold that has reached it by way of intuition, from some other source, and brings the synthesis of that manifold to apperception’s unity. Such an understanding cognizes nothing by itself. The most it does is combine and arrange the raw stuff of cognition, namely intuition, which the object has to give it. Our understanding has a peculiarity: it can bring about the unity of apperception a priori only by means of the categories.

B 146 And it can do so only by just this kind and number of them. No further ground can be given for this. Equally, we cannot explain why we have exactly these functions of judging and no others. Nor can we explain why time and space are the sole forms of intuition possible for us.

§ 22 The category has no use for cognizing things except its application to objects of experience

Thinking an object and cognizing an object are therefore not the same thing. Cognition takes two things. One is the concept (the category) through which an object as such is thought. The second is the intuition by which the object is given. Suppose no intuition corresponding to the concept could ever be given. In that case the concept would be a thought in form only. It would have no object, and no cognition of any thing could come through it. For as far as I could know, there would be nothing, and nothing that could be, to which my thought could be applied. Every intuition that we can have is sensible (Aesthetic). For us, then, thinking an object as such by a pure concept of the understanding becomes cognition only when that concept is referred to objects of the senses.

B 147 Sensible intuition comes in two kinds. One is pure intuition (space and time). The other is empirical intuition of whatever is represented in space and time immediately as real, by means of sensation. By determining the first, we can get cognitions a priori of objects (in mathematics), but only as to their form, as appearances. Whether any things exist that have to be intuited in this form remains undecided. Mathematical concepts are therefore not cognitions on their own. They become cognitions only if we presuppose things that can show themselves to us solely in the form of that pure sensible intuition. But in space and time, things are given to us only as perceptions, and a perception is a representation that comes with sensation. So they are given through empirical representation. Even when pure concepts of the understanding are applied to a priori intuitions (mathematics does this), they provide cognition only on one condition: those intuitions can themselves be applied to empirical intuitions, and the concepts of the understanding along with them. In the same way the categories, working through intuition, offer no cognition of things except by being possibly applied to empirical intuition. All they do is make empirical cognition possible. And that is called experience. The categories have no other use in cognizing things.

B 148 They can be used only insofar as those things are taken as objects of possible experience.

§ 23

The proposition above is of the greatest importance. It marks out the boundaries within which the pure concepts of the understanding can be used on objects. Earlier, the Transcendental Aesthetic did this for how the pure form of our sensible intuition may be used. Space and time are the conditions that allow objects to be given to us. They hold only for objects of the senses, which means only for experience. Past these boundaries they stand for nothing, because they exist only in the senses and have no reality apart from them. The pure concepts of the understanding are free of this restriction. They reach to objects of intuition as such. It makes no difference whether that intuition resembles ours, provided it is sensible and not intellectual. But stretching the concepts further, beyond our sensible intuition, does us no good. They would then be empty concepts of objects. Through them we can’t judge at all whether such objects are even possible or not. They are bare forms of thought with no objective reality. We lack any intuition to which they could apply the synthetic unity of apperception. That unity is all they contain.

B 149 Without such an intuition they cannot determine an object. Only our sensible and empirical intuition can give them sense and meaning.

Suppose, then, that we assume an object of a nonsensible intuition as given. We can of course represent such an object through all the predicates that the assumption itself carries, namely that nothing belonging to sensible intuition fits it. It is not extended, or in space. Its duration is not time. No change (the succession of determinations in time) is found in it. And so on. But that is no real cognition. I am only indicating how the object’s intuition is not, without being able to say what it does contain. In that case I have given my pure concept of the understanding no possible object whatever. I was unable to give an intuition to match it. I could only say that ours doesn’t hold for it. The chief point, though, is that no category, not even one, could be applied to such a something. Consider the concept of substance, meaning something that can exist as a subject and never as a mere predicate. Whether any thing could match this way of determining a thought, I have no idea, unless empirical intuition supplies a case where it applies. But more of this later.

B 150 § 24 On the application of the categories to objects of the senses in general

Through the understanding alone, the pure concepts of the understanding relate to objects of intuition in general. It is left open whether that intuition is ours or some other one, though still a sensible one. That is precisely why they are only forms of thought. Through them no determinate object has yet been cognized. Their synthesis or combination of the manifold had to do only with apperception’s unity, and so it was the ground of the possibility of cognition a priori, so far as that cognition rests on the understanding. It is therefore not only transcendental but also purely intellectual. In us, though, a certain form of sensible intuition lies underneath, a priori. It rests on the receptivity of the faculty of representation (sensibility). That lets the understanding, being spontaneous, determine inner sense by means of the manifold of given representations, matching apperception’s synthetic unity. Thus it can think, a priori, of the manifold of sensible intuition as having synthetic unity of apperception. It takes this unity as the condition that all objects of our (human) intuition are bound to meet. Through this the categories, which are mere forms of thought, get objective reality.

B 151 They can be applied, that is, to objects that may be given to us in intuition, though only as appearances. For only of appearances are we capable of intuition a priori.

This synthesis is possible and necessary a priori, and it concerns the manifold of sensible intuition. It may be called figurative (synthesis speciosa). The other synthesis is thought in the bare category, for the manifold of an intuition as such. It is called combination by the understanding (synthesis intellectualis). The names keep the two apart. Both are transcendental. The reason is not only that they themselves proceed a priori. They also provide the basis for other cognition a priori to be possible.

Figurative synthesis can aim solely at the original synthetic unity of apperception, which is the transcendental unity thought in the categories. When it does, we must call it the transcendental synthesis of imagination. This sets it apart from the merely intellectual combination. Imagination is our ability to represent an object in intuition when it isn’t there. All our intuition is sensible. For this reason imagination counts as part of sensibility: it can supply a matching intuition for the concepts of the understanding only under that subjective condition. Still, its synthesis exercises spontaneity. Spontaneity determines; sense, by contrast, can only be determined.

B 152 So imagination can determine sense a priori as to its form, in line with the unity of apperception. To that extent imagination is a faculty for determining sensibility a priori. When it synthesizes intuitions as the categories require, that has to be the transcendental synthesis of imagination. This synthesis is something the understanding does to sensibility. It is the first way the understanding gets applied to objects of the intuition we can have, and it is the ground of every other application too. As figurative, this synthesis is distinguished from the intellectual synthesis, which is carried out by the understanding alone, without any imagination. Insofar as imagination is spontaneity, I sometimes also call it productive imagination. I use that name to distinguish it from reproductive imagination. The synthesis of the reproductive kind answers only to empirical laws, those of association. It adds nothing toward explaining how cognition a priori is possible. For that reason it belongs to psychology, not to transcendental philosophy.

* * *

This is the point at which to clear up a paradox. Everyone who read the account of the form of inner sense (§ 6) must have noticed it. It is this: inner sense shows us to our own consciousness only as we appear to ourselves, and not as we are in ourselves.

B 153 The reason is that we intuit ourselves only in the way we are affected from within. That seems contradictory, since we would have to relate to ourselves as passive. That is why psychological systems like to give out inner sense as identical with the faculty of apperception (which we keep carefully apart).

What determines inner sense is the understanding, with its original power to combine the manifold of intuition, that is, to bring it under one apperception (on which its own possibility rests). In us humans the understanding is not itself a power of intuitions. And even when an intuition is given in sensibility, the understanding can’t take it up into itself, so as to combine, so to speak, the manifold of its own intuition. So when the understanding is considered on its own, its synthesis is nothing other than the unity of an action. It is aware of this action as such even without sensibility. By this action it is able to determine sensibility inwardly, with respect to whatever manifold may be given to it in the form of sensibility’s intuition. The understanding, then, acts on the subject whose faculty it is, and that subject is passive. The action goes by the name of transcendental synthesis of imagination. Because of this action we are justified in saying that inner sense is affected.

B 154 Apperception, with its synthetic unity, is anything but the same thing as inner sense. Apperception is the source of all combination. Under the name of the categories it applies to the manifold of intuitions in general, and to objects in general, before any sensible intuition. Inner sense, by contrast, contains only the bare form of intuition, without combination of the manifold in it, and so no determinate intuition yet. No determinate intuition can exist unless we are conscious of the way the manifold is determined. The determining comes from imagination’s transcendental action. That action is the understanding’s synthetic influence on inner sense, and figurative synthesis is what I have named it.

We also always perceive this in ourselves. To think a line, we have to draw it in thought. We can’t think a circle without describing it. We can’t represent the three dimensions of space at all without setting three lines at right angles to each other from the same point. We can’t even represent time without attending, as we draw a straight line (which is to be the outward, figurative representation of time), solely to the action of synthesizing the manifold by which we determine inner sense in succession. In doing so we attend to the succession of this determination within inner sense. Consider motion as an action of the subject.

B 155 Do not take it as a determination of an object*. Motion is thus the synthesis of the manifold in space. And this synthesis is what first gives rise to the very concept of succession. This happens when we abstract from space and attend solely to the action by which we determine inner sense in line with its form. So the understanding doesn’t find a combination of the manifold of that kind already there in inner sense. It produces the combination by affecting inner sense. Now how can the I that thinks be different from the I that intuits itself (since I can represent another kind of intuition as at least possible), and yet be the same subject as the latter? How can I say: “I am an intelligence and a thinking subject. I cognize myself as an object that is thought, insofar as intuition also gives me to myself. Even then I am cognized only as other phenomena are, not as I am for the understanding, but as I appear to myself”? That puzzle is exactly as hard as another one: how can I be an object for myself at all?

B 156 I mean an object of intuition and of inner perceptions. That things really must be this way can be made plain, provided we accept that space is merely the pure form of the appearances of the outer senses. Time is no object of outer intuition. Still, the only way we can picture it is as a line, and only while we draw that line. Without such a presentation we would have no way to recognize that time’s extent is one. The same goes for fixing how long a time lasts, or where something sits in time, for any inner perception. We always have to take that from the changing things that outer objects show us. From all this we must put the determinations of inner sense in order, as appearances in time, in exactly the way we put the outer senses’ determinations in order in space. So suppose we are willing to concede that the outer senses let us cognize objects only to the extent that we are affected from outside. Then we must concede the same about inner sense: it lets us intuit ourselves only as we are affected from within, by ourselves. In inner intuition, then, our own subject is cognized only as an appearance, and not according to what it is in itself∗∗.

* A pure science has no place for the motion of an object in space, and so neither does geometry. That something is movable can’t be cognized a priori, only through experience. Motion taken as the describing of a space is another matter. It is a pure act: a synthesis of the manifold that proceeds step by step, in outer intuition as such, performed by productive imagination. Such motion belongs to geometry, and to transcendental philosophy as well.

∗∗ I don’t see why people find so much difficulty in inner sense’s being affected by ourselves. Any act of paying attention gives us an example. In attention, the understanding determines inner sense each time. It does so to match the combination it is thinking, and the result is the inner intuition that corresponds to the manifold in the understanding’s synthesis. How strongly the mind is commonly affected by this, everyone can notice in themselves.

§ 25

B 157 By contrast, I am conscious of myself in the transcendental synthesis of the manifold of representations in general, and so in the original synthetic unity of apperception. I am conscious neither of how I appear to myself nor of how I am in myself. I am conscious only that I am. This representation is a matter of thinking, not of intuiting. Cognizing ourselves takes more than the action of thinking, which brings the manifold of any possible intuition to the unity of apperception. It also takes a certain kind of intuition, by which this manifold is given. So my own existence is not appearance (much less mere illusion).

B 158 But the determination of my existence* can happen only in line with the form of inner sense, and in the particular way the manifold that I combine is given in inner intuition. So of myself as I am, I have no cognition. I have it only as I appear to myself. Being conscious of oneself is far from cognizing oneself. That holds despite all the categories, which make up the thinking of an object as such by combining the manifold in a single apperception. Cognizing an object other than myself takes more than thinking an object in general (in the category). I also need an intuition by which I determine that general concept. In the same way, to cognize myself I need more than the consciousness, or the fact that I think myself. I also need an intuition of the manifold in me, by which I determine this thought. And I exist as an intelligence that is conscious only of its power of combining.

B 159 With respect to the manifold it is to combine, it is subject to a limiting condition that it calls inner sense. The only way it can make that combination intuitable is through relations of time, and these lie wholly outside the understanding’s concepts proper. So it can cognize itself only as it appears to itself, in view of an intuition (one that cannot be intellectual and given by the understanding itself). It cannot cognize itself as it would if its intuition were intellectual.

* “I think” is the expression of an act: the act of determining my existence. My existence is thereby already given. What that does not give is the way I am to determine it, meaning how I am to posit in myself the manifold that belongs to it. For that, self-intuition is needed. Self-intuition rests on a form given a priori, which is time. Time is sensible, and it belongs to the receptivity of what can be determined. Now suppose I have no further self-intuition of this kind: one that would give me the determining element in myself, the element whose spontaneity is all I am conscious of. Such an intuition would give it before the act of determining, the way time gives what is determinable. In that case I can’t determine my existence as the existence of a self-acting being. All I can do is picture to myself the spontaneity of my thinking, which is to say, of determining. My existence stays determinable only in a sensible way, as the existence of an appearance. Still, it is this spontaneity that makes me call myself an intelligence.

§ 26 Transcendental deduction of the generally possible use of the pure concepts of the understanding in experience

The metaphysical deduction showed where the categories come from a priori: they agree completely with the general logical functions of thinking. The transcendental deduction then presented how they are possible as a priori cognitions of objects of any intuition at all (§§ 20, 21). What has to be explained now is how the categories let us cognize a priori any and all objects that can ever come before our senses. This holds not as to the form of their intuition but as to the laws of their combination. That is, we must explain how the categories can, so to speak, prescribe the law to nature and even make it possible.

B 160 If the categories lacked this fitness, we could not see why everything that comes before our senses has to obey laws arising a priori from the understanding alone.

To begin, a note: I take the synthesis of apprehension to be the composing of a manifold inside an empirical intuition. This makes perception possible, that is, empirical consciousness of that intuition (as appearance).

Space and time, as representations, give us a priori forms for outer and for inner sensible intuition alike. Whenever we apprehend the manifold of appearance by synthesis, it has to conform to those forms, since it can only take place in this form. Yet space and time are not represented a priori merely as forms of sensible intuition. They are represented as intuitions themselves (which contain a manifold), and so with the determination of the unity of that manifold in them (see Transcendental Aesthetic)*. It follows that a unity of synthesis of the manifold, whether outside us or in us, is given a priori already.

B 161 It comes along with these intuitions (but not in them). It is the condition of the synthesis of all apprehension. It is also a combination, and everything that is to be represented as determinate in space or time must conform to it. This synthetic unity can only be one thing: the unity of combining the manifold of any given intuition in one original consciousness, according to the categories. The only difference is that here it is applied to our sensible intuition. So all synthesis through which perception itself becomes possible stands under the categories. Experience is cognition by way of perceptions that are connected. That makes the categories conditions for experience being possible. So they also hold a priori for every object of experience.

* When space is represented as an object, as geometry really needs it to be, it holds more than the bare form of intuition. It also holds a gathering together of the manifold that sensibility’s form supplies, into a single intuitive representation. So the form of intuition gives only manifold, while the formal intuition gives unity of representation. In the Aesthetic I counted this unity as belonging merely to sensibility. I wanted only to note that it comes before all concepts. Even so, this unity presupposes a synthesis that isn’t the senses’ business. That synthesis is what makes any concept of space and time possible in the first place. Space or time is first given as an intuition by way of that synthesis, in which the understanding determines sensibility. The unity of such an intuition therefore belongs a priori to space and time themselves, and not to a concept of the understanding. (§ 24.)

* * *

B 162 Take an empirical intuition of a house. I make it a perception by apprehending its manifold. The necessary unity of space, and of outer sensible intuition in general, lies at the base of this. I sketch the shape of the house, as it were, in keeping with the synthetic unity of the manifold in space. Leave aside the form of space, and this same synthetic unity turns out to have its seat in the understanding. It is the category for synthesizing what is homogeneous in an intuition as such. In other words, it is the category of magnitude. The synthesis of apprehension, meaning perception, has to fit this category in every respect*.

* This is how it gets proved that the empirical synthesis of apprehension must conform of necessity to the synthesis of apperception. The latter is intellectual and is contained wholly a priori in the category. A single spontaneity is at work in both. It puts combination into the manifold of intuition. In the one place it goes under the name of imagination, in the other the name of understanding.

Take another example: I perceive water freezing. I apprehend two states, a fluid state and a solid state, as related to each other in time. But take the time that I put under the appearance, as inner intuition.

B 163 In that time I represent a synthetic unity of the manifold, and I can’t do otherwise. Without it, that relation could not be given determinately in an intuition (with regard to the time sequence). This synthetic unity is an a priori condition. I combine under it the manifold of an intuition as such. Set aside the abiding form of my inner intuition, which is time. What remains of the unity is the category of cause. I apply that category to my sensibility. By it I determine the relation of everything that happens in time as such. So the apprehension in an event of this sort falls under the concept of how effects and causes are related. So does the event itself, so far as possible perception of it goes. And so it is in all other cases.

* * *

Categories are concepts that lay down laws a priori for appearances, and so for nature, understood as the sum total of appearances (natura materialiter spectata). Now a question arises. The categories are not drawn from nature, and nature is not their model, since they would then be merely empirical. So how can we understand that nature must conform to them? That is, how can they determine a priori the combination of nature’s manifold without taking it from nature? Here is the solution to this riddle.

B 164 It is no more puzzling that the laws of appearances in nature have to fit the understanding and its a priori form than that appearances themselves have to fit the a priori form of sensible intuition. That form of the understanding is its power to combine the manifold as such. Laws don’t exist in the appearances any more than appearances exist in themselves. Laws exist only in relation to the subject that the appearances inhere in, and only because that subject has understanding. Appearances likewise exist only in relation to that same being, and only because it has senses. Things in themselves would have their lawfulness of necessity, whether or not an understanding cognizes them. But appearances are only representations of things, and those things exist unknown, as to whatever they may be in themselves. Being mere representations, they are bound by no law of connection other than the one that the faculty doing the connecting lays down. Imagination is the faculty that does the connecting of the manifold of sensible intuition. For the unity of its intellectual synthesis, imagination relies on the understanding. For the variety in apprehension, it relies on sensibility. Every possible perception rests on the synthesis of apprehension. That empirical synthesis itself depends on the transcendental one, and so on the categories. Hence all possible perceptions must, as to how they are combined, stand under the categories.

B 165 So must everything that can ever come into empirical consciousness. That means all appearances of nature. Nature (considered simply as nature in general) depends on the categories as the original ground of its necessary lawfulness (as natura formaliter spectata). The pure power of the understanding, using mere categories, cannot prescribe any further a priori laws to appearances. It stops at the laws on which a nature as such rests, namely the lawfulness of appearances in space and time. Particular laws concern empirically determined appearances. They can’t be fully derived from the categories, even though they all stand under them. Experience has to be added to get to know the particular laws at all. Only the a priori laws instruct us about experience in general and about what can be cognized as an object in it.

§ 27 Result of this deduction of the concepts of the understanding

We can’t think an object except through categories. We can’t cognize a thought object except through intuitions that correspond to those concepts. All our intuitions, however, are sensible. A cognition whose object is given is therefore empirical. Empirical cognition is experience.

B 166 That leaves us with no possible a priori cognition except of objects of possible experience*.

* I want to head off a rash stumble over the harmful consequences that may be feared from this proposition. So let me only remind readers that the categories, in thinking, are not held back by the conditions of our sensible intuition. They have an unbounded field. Only the cognizing of what we think, the determining of the object, needs intuition. When intuition is absent, thinking of the object may still have true and useful effects on how the subject uses reason. But this use of reason is directed not always at determining the object, and so at cognition, but also at determining the subject and its willing. So it can’t be set out here yet.

Now this cognition, though limited to objects of experience, is not for that reason all borrowed from experience. Take both the pure intuitions and the pure concepts of the understanding. These are elements of cognition, and they are found in us a priori. Only two routes are open if we want to think of a necessary agreement between experience and the concepts of its objects. Either experience is what makes these concepts, or else these concepts are what make experience possible.

B 167 The first does not hold for the categories (or for pure sensible intuition either). They are concepts a priori, and so independent of experience. To claim an empirical origin for them would be a kind of generatio aequivoca, or spontaneous generation. Only the second is left (a kind of system of epigenesis of pure reason): the point being that the categories, coming from the understanding’s side, hold the grounds that make any experience possible at all. How the power of judgment is used transcendentally is the subject of the next chapter. That chapter will say more about how the categories make experience possible. It will also cover which principles of its possibility they hand us when they are applied to appearances.

Imagine someone offering a middle path between the only two ways we named. Namely, the categories would be neither first principles of our cognition thought up by ourselves a priori, nor drawn from experience. These would be dispositions for thinking, subjective ones, that were placed in us at the very moment we came to exist. Our Maker would have arranged them so that using them matches precisely the laws of nature that experience follows (a sort of preformation system of pure reason). Besides the fact that there is no end in sight to how far one might push the assumption of predetermined dispositions toward future judgments on such a hypothesis, one thing would settle the case against this middle way.

B 168 On that view, the categories would lack the necessity that is part of what their concept means. Consider cause. Its concept states that a result follows necessarily once a condition is presupposed. The concept would then be false, if all it rested on were some arbitrary subjective necessity, built into us, that makes us combine certain empirical representations by a rule of that kind. I couldn’t say the effect and the cause are combined in the object, meaning that they are combined necessarily. I could only say, “I am built in such a way that I cannot think these representations as connected in any other way.” The skeptic could ask for nothing better. Our insight would then be nothing but sheer illusion, since our judgments would only seem to be objectively valid. And there would be no lack of people who wouldn’t admit this subjective necessity in themselves (it has to be felt). At the very least, one could quarrel with no one over what rests merely on how that person’s subject is organized.

Brief account of this deduction

It lays out the pure concepts of the understanding (and with them all theoretical cognition a priori) as principles of the possibility of experience. Next it presents experience as the determining of appearances in space and time as such.

B 169 Last it presents this determining as derived from the principle of the original synthetic unity of apperception. That principle is the understanding’s form, taken in relation to space and time, the original forms of sensibility.

* * *

I consider the division into numbered sections necessary only up to this point, because we were dealing with the elementary concepts. Now we want to show how these concepts are used. From here the exposition can go on as one continuous argument, without such numbering.

Of the Transcendental Analytic Second Book

The Analytic of Principles

A ground plan underlies general logic, and it coincides exactly with how the higher faculties of cognition are divided. Those faculties are understanding, power of judgment, and reason. So in its analytic, that doctrine deals with concepts, judgments and inferences, exactly in line with the functions and the order of those powers of the mind, which are all included under the broad name of the understanding in general.

B 170 Formal logic of this bare kind sets aside all content of cognition, pure or empirical. It is concerned solely with the form of thinking as such, that is, of discursive cognition. So in its analytic part it can include the canon for reason as well. The form of reason has a reliable prescription of its own. It can be seen a priori, without looking at the special nature of whatever cognition is in use, just by analyzing the acts of reason into their moments.

Transcendental logic can’t imitate general logic in this division, because it is limited to a definite content, namely pure cognitions a priori only. As it turns out, reason has no objectively valid transcendental use. So it doesn’t belong to the logic of truth, that is, the analytic. As a logic of illusion, it calls for a special part of the scholastic system, under the name of transcendental dialectic.

Understanding and power of judgment therefore find, in transcendental logic, their canon for a use that is objectively valid and so true. That puts them in its analytic part. Reason is another story. It tries to settle things about objects a priori and to widen cognition past the boundaries of possible experience.

B 171 In all of this it is dialectical through and through. Its illusory assertions don’t fit into a canon at all, and the analytic is supposed to contain such a canon.

The analytic of principles will therefore be only a canon for the power of judgment. It instructs the power of judgment in applying to appearances the understanding’s concepts. These concepts hold the condition for rules a priori. That is why, in treating the understanding’s actual principles as my topic, I will call the work a doctrine of the power of judgment. It marks this task more exactly.

Introduction On the Transcendental Power of Judgment in General

Define the understanding in general as the faculty of rules. The power of judgment is then the faculty of subsuming things under rules. That is, it tells whether something falls under a given rule (casus datae legis) or not. General logic has no instructions for the power of judgment, and it could not have any. It abstracts from all content of cognition, so nothing is left to it but one task: to take apart, analytically, the bare form of cognition as it appears in concepts, judgments and inferences.

B 172 In this way it arrives at formal rules covering every use of the understanding. Suppose it wanted to show in general how to subsume under these rules, that is, how to tell whether something falls under them or not. That could be done only through another rule. But this rule, just because it is a rule, again needs guidance from the power of judgment. Here we see that the understanding can be instructed and furnished by rules. The power of judgment, by contrast, is a talent of a special sort. It can’t be taught at all. It can only be practiced. That is why the power of judgment is the specific mark of so-called mother wit, and no school can make up for a lack of it. A school can hand a limited understanding plenty of rules, borrowed from other people’s insight, and graft them on, so to speak. But the ability to use them correctly must belong to the pupil, and no rule one might prescribe for this purpose is safe from misuse if the pupil lacks such a natural gift*.

B 173 So a doctor, a judge or a statesman may carry many fine pathological, legal or political rules in their head, to the point where they could become a thorough teacher of them. And yet they can easily slip in applying them. Perhaps they lack natural power of judgment (though not understanding). In abstracto they can see the general rule, but whether a case in concreto belongs under it, they can’t tell. Or perhaps they haven’t been trained enough for this judgment through examples and real business. This is also the one great use of examples: they sharpen the power of judgment. As for the correctness and precision of insight by the understanding, examples usually do it some harm instead. Seldom do they satisfy the rule’s condition adequately (as casus in terminis). Often, too, they sap the understanding’s effort to see rules in all their sufficiency, in general and apart from the particular circumstances of experience. They get us used to using rules more like formulas than like principles.

B 174 So examples are the baby walker of the power of judgment, and anyone who lacks the natural talent for it can never do without one.

* Lack of power of judgment is really what we call stupidity, and nothing can be done about such a defect. A dull or limited mind that lacks nothing except the proper degree of understanding and concepts of its own can be well equipped by learning, even up to scholarship. Such a mind usually lacks judgment too (the secunda Petri). So it is common to find very learned men who, when they put their science to use, keep revealing that incurable lack.

The power of judgment gets no prescriptions from general logic. Transcendental logic is quite different, so much so that it seems its real task is to correct and secure the power of judgment, by definite rules, in the use of the pure understanding. To extend the understanding in the field of pure cognitions a priori, philosophy as a doctrine seems not to be needed at all. Or rather, it seems out of place, since after all attempts so far, little or no ground has been gained that way. As critique it is different. There, philosophy is called up with all its sharpness and skill at testing, to guard against slips of the power of judgment (lapsus judicii) when we use the few pure concepts of the understanding that we have. The benefit is then only negative.

Transcendental philosophy has this distinctive feature. The pure concept of the understanding supplies a rule, or better, the general condition for rules. Transcendental philosophy can, in addition, point out a priori the case where the rule is to be applied.

B 175 It enjoys this advantage over every other teaching science (mathematics excepted), and the cause of it is this: it deals with concepts that are supposed to relate to their objects a priori. So their objective validity can’t be shown a posteriori, since that would leave their dignity entirely untouched. What transcendental philosophy must do instead is spell out the conditions that allow objects to be given in line with those concepts. It must do so through marks that are general yet sufficient. Otherwise the concepts would be without any content, mere logical forms and not pure concepts of the understanding.

The power of judgment gets its transcendental doctrine in two chapters. The first treats the sensible condition that alone allows pure concepts of the understanding to be used. That is the schematism of pure understanding. The second treats synthetic judgments. On those conditions, a priori, these judgments follow from pure concepts of the understanding. They also lie beneath every other a priori cognition. These judgments are the principles of the pure understanding.

B 176 Of the Transcendental Doctrine of the Power of Judgment (or Analytic of Principles) First Chapter On the Schematism of the Pure Concepts of the Understanding

Think of any case where an object is subsumed under a concept. The representation of the object has to be of one kind with the concept. In other words, whatever is represented in the object being subsumed must be something the concept contains. That is all it means to say an object is contained under a concept. Take the empirical concept of a plate and the pure geometrical concept of a circle. They are of one kind, because the roundness thought in the plate can be intuited in the circle.

Pure concepts of the understanding are a different matter. Set beside empirical intuitions, and indeed beside any sensible intuitions, they are not of one kind with them at all, and no intuition will ever contain one of them. So how can intuitions be subsumed under such concepts? How can a category be applied to appearances? Nobody will say of a category, causality for instance, that it can also be intuited.

B 177 Nobody will say that the senses can intuit it, or that it is contained in the appearance. The question is natural and weighty. This is the actual reason why the power of judgment must have a transcendental doctrine. Its task is to show how appearances as such can have pure concepts of the understanding applied to them. Other sciences don’t face this. In them, the concepts that think the object in general are not so different from, or so unlike, the concepts that present it in concreto just as it is given. So no special discussion is needed there of how the first kind is applied to the second.

One thing is clear. A third item has to exist. It must be of one kind with the category on one side and with the appearance on the other, and it has to make the category’s application to the appearance possible. This go-between representation must be pure, with nothing empirical in it. Yet it must be intellectual in one respect and sensible in another. The transcendental schema is such a thing.

A concept of the understanding holds the pure synthetic unity of the manifold as such. Time is what formally conditions the manifold of inner sense. That makes it the formal condition for the connecting of all representations. In pure intuition, time holds a manifold a priori. Now take a transcendental determination of time. It resembles the category, which makes up its unity, in being universal and in resting on a rule a priori.

B 178 But it also resembles the appearance, because time is contained in each empirical representation of a manifold. So the category can be applied to appearances, through the transcendental determination of time. Such a determination serves as the schema for concepts of the understanding. It is what brings the appearances under the category.

After what the deduction of the categories has shown, I hope nobody is unsure how to settle a certain question. Are these pure concepts of the understanding meant only for empirical use, or can they also be used transcendentally? In other words, do they relate a priori only to appearances, as conditions of possible experience? Or can they reach out to objects in themselves, as conditions of the possibility of things as such, with no restriction to our sensibility? The deduction showed several things. First, no concept can exist, or mean anything, unless an object is given for it, or at least for the parts it is made of. So concepts cannot apply to things in themselves, no matter whether or how such things may be given to us. Second, objects are given to us in one way only: as a modification of our sensibility. Third, pure concepts a priori have to hold something besides the function of the understanding found in the category.

B 179 They must also contain formal conditions of sensibility, in particular of inner sense, a priori. These conditions hold the general requirement under which a category can be applied to any object at all. We will name this formal and pure condition of sensibility the schema of the concept of the understanding that is restricted to it in use. And we will call the understanding’s way of handling these schemata the schematism of pure understanding.

By itself, a schema is always just a product of imagination. Even so, a schema must be told apart from an image. The reason is that imagination’s synthesis aims at no single intuition. It aims only at unity in how sensibility is determined. Put five points in a row:..... You then have an image of the number five. Now suppose I just think of a number as such, which might be five or a hundred. Thinking it amounts more to representing a method than to forming an image. The method is a way of picturing a multitude (a thousand, for example) in an image, following a certain concept. If it were the image I had in mind, I could hardly take it in at a glance and compare it with the concept. Consider the representation of a general procedure of imagination. The procedure gives a concept its image.

B 180 I call that representation the schema of the concept.

Our pure sensible concepts rest, in truth, on schemata, not on images of objects. No image would ever fit the concept of a triangle as such. It could not reach the generality of the concept, which lets the concept cover all triangles, right-angled, oblique and the rest. An image would always cover only one part of that range. A triangle’s schema exists only in thought, and nowhere else. It stands for a rule by which imagination synthesizes pure figures in space. Still less does any object of experience, or image of one, ever attain the empirical concept. The empirical concept relates directly to imagination’s schema. That schema is a rule telling how to determine our intuition under a given general concept. Take the concept of a dog. It means a rule: my imagination can follow it to outline a four-footed animal’s shape in a general way. It is not tied to any one particular shape that experience gives me, or to any image I might present in concreto. This schematism of our understanding, where appearances and their bare form are concerned, is a hidden art deep in the human soul. We will hardly ever pry its true tricks from nature and lay them open to view.

B 181 This much we can say. An image is a product of the empirical power of productive imagination. A sensible concept’s schema, as for figures in space, is made by pure imagination a priori. You could call it a monogram. Images first become possible through this schema and in keeping with it. Images can be linked to the concept only through the schema that they mark out, and taken alone they never fully match the concept. A pure concept of the understanding has a schema of another kind. It cannot be turned into any image at all. It is nothing but the pure synthesis that follows a rule of unity according to concepts in general, the rule that the category expresses. It is a transcendental product of imagination. It has to do with how inner sense in general is determined, by the conditions of its form (time), for all representations that are supposed to hang together a priori in one concept, in keeping with the unity of apperception.

Let us skip a dull and tiresome breakdown of what transcendental schemata for pure concepts of the understanding call for. We would prefer to present them following the order of the categories, each linked to its category.

B 182 Space is the pure image of all magnitudes (quantorum) for outer sense. For the senses’ objects in general, time is that image. The pure schema of magnitude (quantitatis), which is a concept of the understanding, is number. A number is a representation that sums up the step-by-step addition of one unit to another, units of the same kind. Number, then, is simply the oneness of synthesizing the manifold of an intuition that is homogeneous, whatever it may be. It comes about by my generating time itself while I apprehend the intuition.

In the pure concept of the understanding, reality means what answers to sensation as such. That means it is whatever has a concept that in itself points to being (in time). Negation is whatever has a concept that represents not-being (in time). The two are set against each other through a difference within one and the same time: it can be filled or empty. Time is only the form of intuition, and so of objects as appearances. So whatever in those objects answers to sensation is the transcendental matter of every object considered as a thing in itself (thinghood, reality). Every sensation has a degree or magnitude. By it the sensation can fill the same time, that is, inner sense in regard to one and the same representation of an object, more or less, until it ends in nothing (= 0 = negatio).

B 183 So there is a relation and a coherence, or better a passage, from reality to negation. This makes every reality representable as a quantum. A reality’s schema is the quantity of something so far as it fills time. That schema is exactly this continuous, uniform production of the reality in time. One either descends in time from a sensation of a certain degree until it vanishes, or climbs gradually from negation up to the sensation’s magnitude.

The schema of substance is the permanence of the real in time. It is the representation of the real as a substratum for the empirical determination of time in general. The substratum stays while everything else changes. (Time itself does not run on. What runs on in time is the existence of whatever can change. To time, which is itself fixed and lasting, there answers in appearance what is fixed in existence, namely substance. Only by substance can succession and simultaneity of appearances be determined with respect to time.)

The schema of cause, and of the causality of a thing as such, is the real, which is always followed by something else whenever it is posited at will. It therefore consists in the succession of the manifold, so far as the succession is subject to a rule.

Community (interaction) is the reciprocal causality of substances regarding their accidents.

B 184 Its schema is the coexistence of the determinations of the one substance with the other’s, following a general rule.

The schema of possibility is the agreement between the synthesis of various representations and the conditions of time in general. An example is that opposites cannot be in one thing at once but only one after the other. So possibility is the determination of a thing’s representation at some time.

The schema of actuality is existence in a determinate time.

The schema of necessity is the existence of an object at all times.

All of this shows what the schema of each category holds and makes representable. For magnitude, the schema contains the creation (synthesis) of time itself as an object is apprehended one part after another. For quality, it contains sensation (perception) synthesized with the representation of time, which is to say the filling of time. For relation, it contains the way perceptions are related to each other at every time (that is, by a rule for determining time). Finally, for modality and its categories, it contains time itself, as the correlate for determining whether and how an object belongs to time. The schemata are therefore nothing but determinations of time a priori, by rules. These rules follow the order of the categories. They bear on the time series and on what time contains.

B 185 They also bear on time’s order, and last on time taken as a whole, for every possible object.

This makes it plain where the schematism of the understanding leads, by way of imagination’s transcendental synthesis. It leads to nothing but the unity of the whole manifold of intuition in inner sense. Indirectly it leads to the unity of apperception, which is a function matching inner sense (a receptivity). Thus the schemata of pure concepts of the understanding are the real and sole conditions under which those concepts relate to objects and so have meaning. The categories end up with no use except a possible empirical one. All they do is subject appearances to general rules of synthesis, resting on a unity that is necessary a priori (because all consciousness has to be united in one original apperception). In that way they make appearances suitable for complete connection in a single experience.

Every cognition we have lies inside the whole of possible experience. Transcendental truth consists in the general relation to that whole. It comes ahead of every empirical truth, and empirical truth is possible only because of it.

Still, one more thing stands out. The schemata of sensibility are what first realize the categories.

B 186 Yet they also restrict the categories, confining them to conditions that lie outside the understanding, in sensibility. A schema is thus really only the phenomenon, or sensible concept of an object, as it fits the category. (Numerus est quantitas phaenomenon, sensatio realitas phaenomenon, constans et perdurabile rerum substantia phaenomenon—aeternitas, necessitas, phaenomena, and so on.) Say we drop a restricting condition. It seems we then widen the concept that was narrowed before. The categories in their pure meaning, free of every condition of sensibility, would then hold of things as they are. Their schemata, in contrast, only show things as they appear. The categories would then have a meaning that depends on no schemata and reaches much further. In fact, once every sensible condition has been put aside, the pure concepts of the understanding do keep a meaning. It is a logical meaning only, that of the bare unity of representations. No object is given to those representations. So they get no meaning either that could provide a concept of an object. Substance is an example. Leave out the sensible determination of permanence, and substance means only a something that can be thought as a subject, without being a predicate of anything else. I can do nothing with that idea.

B 187 It doesn’t show me what determinations belong to the thing that is supposed to count as such a first subject. Without schemata, the categories are only functions the understanding uses for forming concepts. They don’t present any object. Their meaning comes from sensibility, which makes the understanding real by restricting it at the same time.

Of the Transcendental Doctrine of the Power of Judgment (or Analytic of Principles) Second Chapter

System of All Principles of the Pure Understanding

In the last chapter we looked at the transcendental power of judgment only for the general conditions under which, and only under which, it may use the pure concepts of the understanding to form synthetic judgments. Our job now is to set out, in a connected system, the judgments that the understanding really does produce a priori when it works with this critical care. For this, our table of categories must without doubt give us a natural and safe guide. For the categories are the very concepts whose relation to possible experience must make up all pure cognition of the understanding a priori.

B 188 How the categories relate to sensibility in general will therefore lay out all the transcendental principles that govern how the understanding is used, fully and as one system.

Principles a priori have that name for two reasons. They contain the grounds of other judgments, and they are not themselves grounded in any higher or more general cognitions. Still, this second quality doesn’t always excuse them from needing a proof. A proof can’t be carried any further on the side of the object, since the principle itself lies at the base of all cognition of its object. But that doesn’t stop a proof from being possible, and even necessary, if it draws on the subjective sources that make cognition of an object in general possible. Without one, the proposition would fall under the heaviest suspicion of being a claim slipped in by trickery.

Second, we’ll stick to the principles that concern the categories. So the principles of the transcendental aesthetic, which say that space and time are what make all things possible as appearances, don’t belong in the field we’ve marked out. Neither does the restriction on those principles, namely that they can’t be applied to things in themselves. The mathematical principles aren’t a part of this system either. That is because they are drawn from intuition alone, not from a pure concept of the understanding.

B 189 Still, they are synthetic judgments a priori, so we must make room here for the question of how they are possible. We won’t be proving that they’re correct or apodictically certain; they don’t need that. We only want to make it understandable how such evident cognitions a priori are possible, and to deduce that possibility.

We will also have to talk about the principle of analytic judgments. We will set it against the principle of synthetic judgments, which are what we are really concerned with. Putting the two side by side frees the theory of the synthetic ones from every misunderstanding. It also lays their special nature plainly before our eyes.

The System of the Principles of Pure Understanding First Section The Supreme Principle of All Analytic Judgments

Our cognition may have any content, and it may relate to its object in any way. Even so, there is one general condition that all our judgments must meet, though it’s only a negative one: they mustn’t contradict themselves. If they do, they are nothing in themselves, even apart from any object.

B 190 But a judgment can contain no contradiction and still tie concepts together in a way the object doesn’t allow. Or it may have no ground at all, whether a priori or a posteriori, to justify making it. So a judgment can be free of every inner contradiction and still be false, or without ground.

“A predicate that contradicts a thing can’t belong to that thing.” This proposition is called the principle of contradiction. It is a universal criterion of truth, though only a negative one. It does, however, belong to logic and to nothing else, since it holds of cognitions simply as cognitions, whatever they’re about. And what it says is that contradiction wipes them out and cancels them completely.

The principle can be used positively, too. It doesn’t just serve to banish falsehood and error where these rest on a contradiction. It also lets us recognize truth. If a judgment is analytic, whether it affirms or denies, the principle of contradiction is always enough to recognize its truth. Here’s why. Take whatever our cognition of the object already contains as a concept and thinks in it. Its opposite will always be correctly denied of the object. The concept itself, on the other hand, has to be affirmed of it.

B 191 The reason is that the opposite of the concept would contradict the object.

So we have to grant the principle of contradiction the status of universal, fully adequate principle for all analytic cognition. But that’s as far as its authority and usefulness go, as a criterion of truth that suffices. No cognition can go against it without wiping itself out. That makes the principle a conditio sine qua non, a condition without which nothing could be true. But it does not make the principle what determines whether our cognition is true. Our real business is just the synthetic part of cognition, so we’ll always be careful never to act against this principle, which can’t be broken. But when it comes to the truth of cognition of that kind, we can never hope to learn anything from it.

Here is a formula of this famous principle (a purely formal one, empty of all content) that does contain a synthesis. The synthesis got into it through carelessness, and quite needlessly. The formula says: “It’s impossible for something to be and not be at once.” The word “impossible” adds apodictic certainty, and that was unnecessary. The certainty ought to follow from the proposition by itself. On top of that, the formula is affected by the condition of time.

B 192 It says, in effect: a thing = A, which is something = B, can’t at the same time be non B. But it can very well be both, B and non B, one after the other. Example: someone who is young can’t be old at the same time. Yet one and the same person can be young at one time, and at another time not young, which means old. Now the principle of contradiction is purely logical. It mustn’t limit what it says to relations of time. So a formula like this one runs against the principle’s whole point. The misunderstanding comes only from this. First people split a predicate off from a thing’s concept. Then they join its opposite to that predicate. This never yields a contradiction with the subject. It yields one only with the subject’s predicate, the one that was joined to it synthetically. And even that happens only when the first and second predicates are set down at the same time. Say I claim that an unlearned person is not learned. Then I must add the condition “at once,” because someone unlearned at one time may well be learned at another. Say instead that no unlearned person is learned. Then the proposition is analytic, because the mark (being unlearned) now helps form the concept of the subject. The negative proposition then follows straight from the principle of contradiction, with no need to add “at once.”

B 193 That’s also why I changed the formula above: so that it shows clearly what an analytic proposition is.

The System of the Principles of Pure Understanding Second Section The Supreme Principle of All Synthetic Judgments

Explaining how synthetic judgments are possible is a task that general logic has nothing to do with. It isn’t even allowed to know the task’s name. In a transcendental logic, though, it is the most important job of all. It is even the only job, when the question is the possibility of synthetic judgments a priori, along with the conditions and the extent of their validity. For once it is done, transcendental logic can fully meet its aim, which is to fix the extent and the boundaries of the pure understanding.

In an analytic judgment I stay with the concept I’ve been given and settle something about it. If the judgment affirms, I give the concept nothing except what it already held in thought. If it denies, I just shut out the concept’s opposite. In synthetic judgments, though, I must go outside the given concept. I have to consider something entirely different from what was thought in it, and consider how that stands in relation to the concept.

B 194 That relation is never one of identity or of contradiction. And you can’t tell from the judgment itself whether it’s true or mistaken.

Suppose we grant that to compare a given concept synthetically with another, we have to step outside it. Then a third thing is required, and only within it can two concepts be synthesized. But what could this third thing be, this medium of all synthetic judgments? It is nothing but the whole collection that contains all our representations: inner sense, together with its form a priori, which is time. The synthesis of representations depends on imagination. Their synthetic unity, which judgment needs, depends on the unity of apperception. So here is where we have to look for what makes synthetic judgments possible. All three of these hold sources of representations a priori, so this is also where we must look for the possibility of pure synthetic judgments. Given these grounds, such judgments are even necessary, if any cognition of objects is to come about that depends on nothing but the synthesis of representations.

For a cognition to have objective reality, that is, to refer to an object and have meaning and sense in it, the object must be able to be given in some way. Without that, concepts are empty. With them you have thought, yes.

B 195 But in fact that thinking cognized nothing; you’ve only played with representations. Now, giving an object (not merely in an indirect way, but by presenting it directly in intuition) comes down to relating its representation to experience, actual or at least possible. Even space and time are as free of everything empirical as concepts can be, and it’s certain that they are represented in the mind completely a priori. Even so, they would have no objective validity, sense or meaning unless we could show that they must be used on objects of experience. Indeed, our representation of them is just a schema, and a schema always points back to the reproductive imagination, the faculty that summons the objects of experience. Without those objects the representation would mean nothing. The same goes for every concept, without exception.

So the possibility of experience is what gives objective reality to all our cognitions a priori. Experience, in turn, rests on the synthetic unity of appearances. That means it rests on a synthesis that goes by concepts of the object of appearances as such. Without that synthesis, appearances wouldn’t even amount to cognition. They’d be a rhapsody of perceptions that wouldn’t fit together within any context ruled by a thoroughly connected (possible) consciousness. They wouldn’t fit the transcendental, necessary unity of apperception either.

B 196 Experience therefore has principles of its form lying beneath it a priori. These are general rules for unity in the synthesis of appearances. As necessary conditions, they can always be shown to have objective reality in experience, even in its very possibility. Apart from this relation, synthetic propositions a priori are altogether impossible. There’s no third thing for them, no pure object, where the synthetic unity of their concepts could show objective reality.

In synthetic judgments about space as such, and about the shapes productive imagination sketches in it, we can know a great deal a priori. We don’t actually need any experience for that. Even so, this cognition would be nothing at all. It would be an occupation with a mere figment of the brain, unless space counts as a condition of the appearances that supply the stuff of outer experience. So these pure synthetic judgments refer to possible experience, or rather to the possibility of experience itself, though only indirectly. They rest the objective validity of their synthesis on that alone.

Experience, as empirical synthesis, is the only way of cognizing that lends reality to all other synthesis, through its own possibility. So that other synthesis, as cognition a priori, has truth in only one way.

B 197 Its truth, its agreement with the object, comes only from containing nothing more than the synthetic unity of experience in general requires.

The highest principle of all synthetic judgments, then, is this: any object stands under the conditions that are necessary if the manifold of intuition is to have synthetic unity within a possible experience.

This is how synthetic judgments a priori become possible. We start from the formal conditions of intuition a priori, plus the synthesis of imagination, plus the necessary unity of that synthesis in a transcendental apperception. We relate all of them to a possible cognition by experience as such. Then we can say that the conditions for the possibility of experience as such are the same conditions that make the objects of experience possible. That is why they have objective validity in a synthetic judgment a priori.

The System of the Principles of Pure Understanding Third Section Systematic Presentation of All Its Synthetic Principles

The fact that there are principles anywhere is owed entirely to the pure understanding. It is more than the faculty of rules for what happens.

B 198 It is itself the source of principles, which make everything that can ever show up for us as an object stand necessarily under rules. Without rules like these, appearances could never provide cognition of an object matching them. Even natural laws, when we regard them as basic laws of how the understanding is used empirically, bring along an expression of necessity. At the very least they suggest that they’re settled by grounds that hold a priori, before any experience. And yet every law of nature, without exception, is subordinate to higher principles of the understanding, because it only applies them to particular cases of appearance. Only these higher principles give us the concept that contains the condition for a rule in general, and in a way its exponent. Experience gives us the case that falls under the rule.

There is really no danger of mistaking merely empirical principles for principles of the pure understanding, or the other way around. That is because the pure principles are marked by a necessity according to concepts. Any empirical proposition lacks that necessity, however generally it may hold, and the lack is easy to notice. So this mix-up is easy to avoid. But there are some pure principles a priori that I still wouldn’t assign specifically to the pure understanding. My reason is that they are not drawn from pure concepts.

B 199 They are drawn from pure intuitions (though by means of the understanding). And understanding is the faculty of concepts. Mathematics has principles of this kind. But their application to experience, and with it their objective validity, still always rests on the pure understanding. So does the possibility of such synthetic cognition a priori (the deduction of it).

That’s why the principles of mathematics won’t be listed among mine. What I will list are the principles on which the possibility of mathematics and its objective validity a priori are founded. They should be seen as the principium, the source, of the mathematical principles. They begin with concepts and move toward intuition. They do not begin with intuition and move toward concepts.

When pure concepts of the understanding are applied to possible experience, their synthesis is used in one of two ways: mathematically or dynamically. The reason is that the synthesis is directed partly at intuition alone and partly at the existence of an appearance as such. The conditions of intuition a priori are completely necessary for any possible experience. The conditions for objects of some possible empirical intuition actually existing are merely contingent in themselves. So the principles that govern mathematical use will state something unconditionally necessary, that is, apodictic. The principles of dynamic use will carry a character of necessity a priori too. But that necessity holds only on the condition that empirical thinking goes on in some experience.

B 200 So they carry it only mediately and indirectly, and they lack the immediate evidence that the mathematical principles have (although this doesn’t harm their certainty, which extends to experience in general). We’ll be able to judge this better at the close of this system of principles.

The table of categories points us quite naturally to the table of principles. The principles, after all, are just rules for putting the categories to objective use. So the principles of the pure understanding, all of them, are

1 Axioms of intuition

2 Anticipations of perception

3 Analogies of experience

4 Postulates of empirical thinking in general

I chose these names with care, so that the differences in evidence and in the way these principles are carried out wouldn’t slip by unnoticed. But it will soon be clear that they do differ.

B 201 In evidence, and in how they determine appearances a priori, the principles of quantity and quality (if we look only at the form of the latter) stand sharply apart from the other two. The first two admit of intuitive certainty. The other two admit only of discursive certainty. But both kinds can be completely certain. So I will call the first group the mathematical principles and the second the dynamic principles*.

B 202 Please notice, though, that I have in mind neither the principles of mathematics (in the first case) nor those of general, physical dynamics (in the second). I mean only the principles of the pure understanding, in relation to inner sense, whatever representations are given in it. These are what give all those other principles their possibility. So I’m naming them for how they’re applied, more than for what they contain. Now I’ll consider them in the same order the table presents them.

* Combination (conjunctio) comes in two kinds: composition (compositio) and connection (nexus). Composition is the synthesis of a manifold that doesn’t have to belong together. Take the two triangles you get when a diagonal cuts a square in half. By themselves they don’t have to belong together. That is also how things of the same kind are synthesized in everything that can be treated mathematically. (This synthesis can itself be split into aggregation and coalition. The first deals with extensive magnitudes, the second with intensive ones.) The second kind of combination, connection (nexus), is the synthesis of a manifold whose parts do have to belong together. An accident belongs to some substance this way, and an effect to its cause—so such a manifold is also represented as combined a priori, even though its parts are different in kind. This combination is not arbitrary. I call it dynamic because it concerns how the existence of the manifold is combined. (This kind splits again, into the physical kind, which joins appearances to one another, and the metaphysical kind, which joins them in the faculty of cognition a priori.)

1 Axioms of Intuition

The principle for these is: all intuitions are extensive magnitudes.

Proof

Each appearance has, in its form, an intuition in space and time, and that intuition lies beneath all of them a priori. So the only way to apprehend them, meaning to take them into empirical consciousness, is through the synthesis of the manifold. This synthesis produces the representation of a definite space or time. It does so by composing what is of one kind.

B 203 And it brings with it consciousness of the synthetic unity of that (homogeneous) manifold. Now consciousness of a homogeneous manifold in intuition as such is the concept of a magnitude (quanti), to the extent that this consciousness is what first makes representing an object possible. So even the perception of an object, taken as appearance, depends on the very same synthetic unity in the manifold of the given sensible intuition. Through that unity we think the unity of composition of the homogeneous manifold in the concept of a magnitude. In other words, all appearances are magnitudes, and specifically extensive ones. They appear as intuitions in space or time. So the synthesis that represents them has to be the one that also determines space and time as such.

I call a magnitude extensive when representing its parts is what makes it possible to represent the whole (so the representation of the parts necessarily comes first). However short a line is, I can’t picture it without drawing it in my thought. That means generating all its parts one by one from a point, and only in this way sketching the intuition at all. Time is exactly the same, even the tiniest bit of time. All I think in it is the step-by-step advance from one instant to the next. Out of all the parts of time and their being added together, a definite stretch of time finally results. Space or time is the bare intuition in all appearances.

B 204 So every appearance, as an intuition, is an extensive magnitude: it can be cognized in apprehension only by a successive synthesis, from part to part. Hence all appearances are already intuited as aggregates (collections of parts given beforehand). This isn’t so for every kind of magnitude. It’s so only for magnitudes that are represented and apprehended by us as extensive.

Geometry, the mathematics of extension, and its axioms are built on this successive synthesis by productive imagination as it produces shapes. The axioms express the conditions of sensible intuition a priori. Only under these conditions can a pure concept of outer appearance get its schema. For example: two points allow just one straight line; two straight lines can’t enclose a space; and so on. These are the axioms, and they properly concern only magnitudes (quanta) as such.

Now take magnitude in the sense of quantitas, the answer to the question “How big is it?” Several propositions about this are synthetic and immediately certain (indemonstrabilia). Even so, strictly speaking, none of them is an axiom. Consider the statements that adding equals to equals, or subtracting equals from equals, gives equals. These are analytic, since I am directly aware that one way of generating a magnitude is the same as the other.

B 205 But axioms are supposed to be synthetic propositions a priori. The evident propositions about relations of number are synthetic, to be sure. But they aren’t universal the way geometry’s propositions are. For exactly that reason they aren’t axioms either; call them numerical formulas. The statement 7+5=12 is not analytic. In the representation of 7, in that of 5, and in the representation of putting the two together, I nowhere think the number 12. (Whether I’m supposed to think it in adding the two isn’t at issue here. With an analytic proposition, the only question is whether the predicate is really thought in what I represent as the subject.) The proposition is synthetic, but it’s still a single, particular proposition. Since we look here only at the synthesis of what is of one kind (units), the synthesis can only go one way, even though these numbers can be used generally afterward. Take the statement that a triangle can be drawn from three lines, two of which together are longer than the third. What I have here is nothing but the function of productive imagination, which is free to draw the lines longer or shorter and to let them meet at any angles you like. The number 7, on the other hand, can arise in only one way, and so can 12, which is produced by combining that number with 5.

B 206 Propositions like these shouldn’t be called axioms (there would be infinitely many then), but numerical formulas.

This transcendental principle behind the mathematics of appearances gives our a priori cognition a large extension. For it alone lets pure mathematics, with all its precision, be applied to objects of experience. Without the principle that would not be so obvious, and it has even stirred up quite a few objections. Appearances are not things in themselves. Empirical intuition is possible only by way of pure intuition (of space and time). So what geometry says about pure intuition holds without argument for empirical intuition, too. We have to drop the evasions that say objects of the senses needn’t follow the rules of construction in space (the infinite divisibility of lines or angles, for instance). That would take objective validity away from space, and with it from all of mathematics. We would no longer know why mathematics applies to appearances, or how far. The synthesis of spaces and times, which are the essential form of all intuition, is the very thing that makes it possible to apprehend an appearance, and so makes outer experience possible, and with it all cognition of the objects of that experience. Whatever mathematics proves about that synthesis in its pure use must hold necessarily for apprehension of appearances as well.

B 207 All objections to this are the tricks of a reason that has been taught wrongly. It mistakenly thinks it can pull the objects of the senses free of the formal condition that our sensibility imposes. It pictures them as things in themselves, given to the understanding, even though they are only appearances. In that case, of course, nothing could be known about them a priori by synthesis, not even through pure concepts of space. And geometry itself, the science that fixes those concepts, wouldn’t be possible.

2 Anticipations of Perception

Their principle is this: in every appearance what is real, the object of sensation, has an intensive magnitude, which is to say a degree.

Proof

Perception is empirical consciousness, meaning consciousness that includes sensation. As objects of perception, appearances are no pure intuitions, no merely formal ones like space and time, since those can’t be perceived in themselves at all. So an appearance holds more than intuition. It also holds the matter for some object as such (this is what represents something existing in space or time). That matter is the real of sensation. It is a purely subjective representation. All we can be aware of through it is that the subject is affected.

B 208 And we relate it to an object as such. Now a gradual transition is possible from empirical consciousness to pure consciousness. The real of empirical consciousness fades away completely, and what remains is a merely formal consciousness (a priori) of the manifold in space and time. So there is also a synthesis that generates the magnitude of a sensation, beginning at pure intuition = 0 and running up to any magnitude you like. Sensation in itself is no objective representation at all. It contains no intuition of space and none of time. So it has no extensive magnitude. But it does have a magnitude, which comes to it through apprehension. In apprehension, empirical consciousness can grow in some stretch of time from nothing = 0 up to its given amount. So sensation has an intensive magnitude. And correspondingly an intensive magnitude, a degree of influence on the sense, has to be ascribed to every object of perception, insofar as it contains sensation.

If a cognition lets me know and fix a priori something that belongs to empirical cognition, we can name it an anticipation. No doubt this is the sense in which Epicurus used his word προληψις. But there is something in appearances that can never be cognized a priori. It is also exactly what separates the empirical from cognition a priori.

B 209 That is sensation, the matter of perception. It follows that sensation is the very thing that cannot be anticipated. On the other hand, the pure determinations in space and time, concerning both shape and magnitude, we could call anticipations of appearances. They represent a priori what is always going to be given a posteriori in experience. But suppose something turns out to be knowable a priori of every sensation as sensation in general (without any particular one being given). That would deserve the name “anticipation” in an outstanding sense, because it seems odd to get ahead of experience in just the part that makes up its matter, which we can get only from experience. And that is truly how things stand here.

Apprehension through sensation alone fills just one instant (if I set aside the succession of many sensations). As something in the appearance, it is not apprehended by a successive synthesis moving from parts to the whole representation. So it has no extensive magnitude. If the sensation is absent in that instant, the instant would be represented as empty, hence = 0. Reality (realitas phaenomenon) is what answers to sensation in empirical intuition. What answers to the lack of sensation is negation = 0.

B 210 But every sensation can be diminished, so that it fades and gradually disappears. That gives a continuous chain of many possible intermediate sensations linking reality in appearance to negation. Their differences from one another are always less than the gap from the given sensation down to zero, that is, to complete negation. In other words, the real in an appearance always has a magnitude. We just don’t meet that magnitude in apprehension, because apprehension by mere sensation happens in an instant, not by the successive synthesis of many sensations, and so it doesn’t go from parts to the whole. The real thus does have a magnitude, though not an extensive one.

A magnitude that is apprehended only as a unit, and in which plurality can be represented only as an approach to negation = 0, I call intensive. Every reality in appearance, then, has an intensive magnitude, a degree. If we regard this reality as a cause (whether of a sensation or of some other reality showing up in appearance, an alteration for instance), the degree of the reality as a cause is called a moment, the moment of gravity for example. It is called that because a degree names only a magnitude whose apprehension is instantaneous, not successive. I mention this only in passing, because I don’t yet have to deal with causality.

B 211 So every sensation, and with it every reality in appearance, has a degree, no matter how small it is. That is, it has an intensive magnitude, and there is always room to reduce it further. Reality and negation are linked by an unbroken chain of possible realities, and of possible smaller perceptions. Take any color, red for instance. Its degree, however small, is never the smallest one. Heat is the same, and so is the moment of gravity, and so on, everywhere.

Continuity is what we call it when no part of a magnitude is the smallest possible, that is, no part is simple. Space and time are quanta continua. We never get a part of them except by fencing it in with boundaries, the points and instants. So any part you give is itself a space, or a time. Space is therefore made up of nothing but spaces, and time of nothing but times. A point or an instant is only a boundary, a mere position marking where something is limited. Positions, however, always presuppose the intuitions they’re supposed to limit or determine. And you can’t build space or time out of mere positions, as if they were ingredients that could be given ahead of space or time. We may also call magnitudes of this kind flowing, because the synthesis (of productive imagination) that generates them is a progress through time.

B 212 Time’s continuity is what we usually mark with the word “flowing” (or “flowing away”).

Appearances in general are therefore all continuous magnitudes, extensive ones in their intuition and intensive ones in mere perception (sensation, and so reality). Suppose the synthesis of an appearance’s manifold breaks off. Then we have an aggregate of many appearances, and not properly one appearance as a quantum. An aggregate isn’t produced by simply carrying on one kind of productive synthesis. It is produced by repeating a synthesis that keeps stopping. Calling 13 thalers a quantum of money is right only on one reading: that I mean what one mark of fine silver contains. A mark of fine silver is a continuous magnitude. No part of it is the smallest; any part could make a coin, and that coin would always contain material for smaller ones. But if I take that name to mean 13 round thalers, counted as that many coins (their silver content being whatever it may be), then calling it a quantum of thalers is improper. I have to call it an aggregate, a number of coins. Every number needs unity as its base. So an appearance, as a unity, is a quantum, and as a quantum it is always a continuum.

Now all appearances, considered extensively or intensively, are continuous magnitudes.

B 213 Given that, the claim that every alteration (a thing’s passing from one state into another) is continuous as well could be proved here easily, with mathematical evidence. It could, if the causality of an alteration in general did not lie completely beyond the boundaries of transcendental philosophy and presuppose empirical principles. The understanding tells us nothing a priori about whether a cause is possible that changes the state of things, meaning one that sets them to the opposite of some given state. There are two reasons. First, the understanding doesn’t see how such a thing could be possible. (We lack that insight in several cognitions a priori, too.) Second, being open to change affects only certain determinations of appearances, which only experience can teach, while their cause is found in what doesn’t change. And here all we have to work with are the pure basic concepts of all possible experience, with nothing empirical allowed among them. So we can’t jump ahead to general natural science, which rests on certain basic experiences, without damaging the unity of the system.

Still, we have plenty of proof of how much influence our principle has. It anticipates perceptions, and it even makes up for their absence, to the point of shutting the door on all false conclusions that could be drawn from their absence.

B 214 Perception shows every reality with a degree, and an endless series of ever lower degrees runs between it and negation. Still, every sense must have some definite degree of receptivity for sensations. Given both, no perception is possible, and so no experience either, that would prove a total absence of everything real in the appearance. It doesn’t matter whether the proof would be direct or indirect, or what detour of reasoning one takes. In other words, experience can never give a proof of empty space or empty time. That is because, first, a total absence of the real in sensible intuition can’t itself be perceived. Second, it can’t be concluded from any single appearance and the differences in its degree of reality. And it must never be assumed in order to explain one. Even if the whole intuition of a given space or time were real through and through, with no part empty, there would still have to be infinitely many different degrees in which space or time is filled. That is because each reality has its degree, and that degree can drop by infinite steps all the way to nothing (the empty) while the appearance’s extensive magnitude stays the same. So the intensive magnitude can be smaller or greater in different appearances, even when the extensive magnitude of the intuition is the same.

B 215 Here’s an example. Nearly all natural philosophers see a big difference in how much matter of different kinds there is in the same volume. They see it partly in the moment of gravity, or weight, and partly in the moment with which it resists other matter in motion. From this they all draw the same conclusion: this volume (the extensive magnitude of the appearance) must be empty in every kind of matter, though to different degrees. Which of these investigators of nature, who are mostly mathematicians and mechanists, would ever have guessed that their conclusion rests entirely on a metaphysical assumption, one they claim so firmly to avoid? Yet that’s what it does, because they assume that the real in space is the same everywhere (I won’t call it impenetrability or weight here, since those are empirical concepts) and that it can be told apart only by extensive magnitude, which means by amount. They couldn’t have had any ground in experience for this assumption, which makes it purely metaphysical. Against it I set a transcendental proof. It isn’t meant to explain the difference in how space is filled. But it entirely removes the supposed need for the assumption, namely that the difference can only be explained by positing empty spaces. And it has the merit of leaving the understanding free, at least, to think this variety in another way as well.

B 216 It has that merit in case the explanation of nature should ever make some hypothesis necessary for this. For we can see that equal spaces may be filled perfectly by different matters, so that not a single point in either lacks their presence. Still, whatever is real, at the same quality, has some degree (of resistance or of heaviness). That degree can keep getting smaller without end, without any decrease in extensive magnitude or amount, before it passes into the empty and vanishes. In the same way, an expansion that fills a space, such as heat, and likewise any other reality (in appearance), can shrink in degree without end, without leaving even the smallest part of that space empty. It can still fill the space with these lower degrees every bit as well as another appearance fills it with higher ones. I don’t mean here to claim that things really are like this with different matters and their specific gravity. I only want to show, using a principle of pure understanding, that our perceptions are of a kind that makes such an explanation possible. And I want to show that people go wrong in assuming that the real in appearance has equal degrees everywhere and varies only through aggregation and extensive magnitude, and even claim, supposedly, to assert this by a principle of the understanding a priori.

B 217 Still, to an investigator who is used to the transcendental, and has become careful because of it, this anticipation of perception always seems striking. It also stirs some doubt that the understanding can anticipate a synthetic proposition like this one, on the degree that every real thing in appearances has, and so on the possibility of an inner difference in sensation itself (once we set aside its empirical quality). So there remains a question that deserves an answer: how can the understanding rule synthetically, a priori, on appearances, and even anticipate them in just the point that is strictly and merely empirical, namely sensation?

Sensation’s quality is always purely empirical. It can’t be represented a priori at all (colors, tastes, and the like). But what is real and corresponds to sensations as such, as opposed to negation = 0, stands for something whose concept in itself contains being. It signifies only the synthesis in an empirical consciousness as such. For in inner sense, empirical consciousness can be pushed up from 0 to whatever higher degree you like. So one and the same extensive magnitude of intuition (an illuminated surface, say) can produce as strong a sensation as a whole collection of other, less illuminated surfaces put together.

B 218 We can therefore abstract entirely from the appearance’s extensive magnitude. Even then, in the bare sensation at a moment, we can represent a synthesis of steady rise, starting at 0 and reaching the empirical consciousness we’re given. So all sensations, as such, are given only a posteriori. But the property they have of possessing a degree can be known a priori. It is remarkable that of magnitudes in general we can know only one quality a priori, continuity. Of all quality (the real in appearances), we can know nothing a priori except its intensive quantity, which is that it has a degree. Everything else is left to experience.

3 Analogies of Experience

Their principle: only if we represent perceptions as necessarily connected is experience possible.

Proof

Experience is empirical cognition, cognition that determines an object by way of perceptions. So it is a synthesis of perceptions. This synthesis isn’t itself contained in perception. It contains the synthetic unity of the perceptions’ manifold in one consciousness. That unity is what is essential to cognition of the objects of the senses, that is, to experience.

B 219 Experience is not just intuition or sensation of the senses. Now it’s true that in experience perceptions come together only by chance. No necessity in their connection shows up from the perceptions themselves, and none can. That’s because apprehension merely puts together a manifold of empirical intuition. Nothing in it represents the appearances it puts together, in space and time, as existing together of necessity. But experience is cognition of objects through perceptions. So the way the manifold’s existence is related has to be represented in experience. It has to be represented not the way the manifold is assembled in time, but the way it objectively stands in time. Time itself, though, can’t be perceived. So the existence of objects in time can only be determined by combining them in time as such, and so only through concepts that are connected a priori. Such concepts always carry necessity with them. Therefore experience is possible only if we represent perceptions as necessarily connected.

The three modi, or modes, of time are persistence, succession and simultaneity. So there are three rules for all the time relations of appearances. By them the existence of each appearance can be fixed in terms of the unity of all time. These rules come before all experience, and they first make it possible.

B 220 The common principle of the three analogies is grounded in the necessary unity of apperception. This unity covers every possible empirical consciousness (that is, perception), whenever it occurs. And since this unity lies at the base a priori, the principle rests too on the synthetic unity of all appearances in their time relations. For original apperception refers to inner sense (the sum of all representations), and specifically to its form a priori, meaning the relation of the manifold of empirical consciousness in time. Now in original apperception, all of this manifold is to be united in accordance with its time relations. That is what the transcendental unity of apperception says a priori, and under it stands everything that is to belong to my cognition (that is, my one cognition) and so be able to become an object for me. This synthetic unity in the time relation of all perceptions is determined a priori. So the law is that empirical determinations of time all have to answer to rules for the general determination of time. The analogies of experience, which we’re about to take up, have to be rules of exactly this sort.

What is special about these principles is that they don’t deal with appearances, or with the synthesis behind their empirical intuition. They look only at existence and at how appearances relate to one another as regards that existence.

B 221 Now the way something gets apprehended in an appearance can be fixed a priori, so that the rule for its synthesis can supply this intuition a priori in any empirical example at hand, that is, bring it about. But the existence of appearances can’t be cognized a priori. Suppose we managed to infer some existence by this route. We still wouldn’t know it determinately. We couldn’t anticipate what makes its empirical intuition different from others.

I called the two earlier principles mathematical, because they entitled us to apply mathematics to appearances. They concerned appearances only as to their bare possibility. They taught how appearances can be produced, both as to what is intuited and as to the real that is perceived in them, by the rules of a mathematical synthesis. In both cases, therefore, numerical magnitudes can be put to use, and with them the determination of an appearance as magnitude. For instance, I could compose the degree of the sensations that sunlight causes from about 200,000 illuminations by the moon, and present it as determined a priori, that is, construct it. That’s why we can call the first principles constitutive.

It has to be quite different with the principles that are meant to put the existence of appearances under rules a priori. For existence can’t be constructed.

B 222 So these principles can only bear on the relation of existence, and the most they can offer are regulative principles. There’s no room here for axioms or anticipations. Suppose one perception is given to us in a time relation to others (which stay indeterminate). We won’t be able to say a priori which other perception that is, or how large. We can say only how that other perception is necessarily combined with the given one as regards existence, in this modus of time. In philosophy, “analogy” means something very different from what it stands for in mathematics. There it is a formula that asserts the equality of two relations of magnitude, and it is always constitutive: given two terms of the proportion, the third is thereby given, which is to say it can be constructed. In philosophy, an analogy is the equality of two relations that are not quantitative but qualitative. With three terms given, all I can know and give a priori is how a fourth term would be related to them. The fourth term itself I can neither know nor give a priori. But I do have a rule for looking for it in experience, and a mark for finding it there. An analogy of experience will thus be just a rule by which unity of experience is to arise out of perceptions (not the way perception itself arises, as empirical intuition as such). As a principle about objects (of appearances) it holds not constitutively, only regulatively.

B 223 The very same holds for the postulates of empirical thinking in general. Taken together, they concern the synthesis of intuition alone (appearance’s form), of perception (its matter), and of experience (how those perceptions relate). They too are only regulative principles. They differ from mathematical principles, and those are constitutive. The difference lies not in certainty, which is settled a priori for both, but in the kind of evidence: in how intuitive they are (and so also in whether they can be demonstrated).

One thing was remarked about all synthetic principles, and it deserves special notice here: these analogies can only be proved as principles of the empirical use of the understanding, not the transcendental use. That’s the only meaning and validity they have, and so it’s the only way they can be proved. It follows that appearances don’t get subsumed straight under the categories, but only under their schemata. Suppose the objects these principles apply to were things in themselves. Then we couldn’t cognize anything about them synthetically a priori. But they are nothing except appearances. Full cognition of them is where all principles a priori finally have to end up, and that is nothing but possible experience. So these principles can aim at nothing except conditions for the unity of empirical cognition within the synthesis of appearances.

B 224 This synthesis is thought only through the schema belonging to the pure concept of the understanding. Of its unity, as a synthesis as such, the category contains the function that no sensible condition restricts. These principles give us the right to put appearances together only in a way that is analogous to the logical, general unity of concepts. In the principle itself we do use the category. But in carrying it out, when we apply it to appearances, we put its schema in the category’s place as the key to its use. Or better, we set the schema next to the category as a restricting condition, calling it a formula of the category.

A. First Analogy

Principle of the Persistence of Substance

Whatever changes among appearances, substance persists. Its quantum is neither increased nor reduced in nature.

Proof

All appearances are in time. Only in time, as their substrate (the lasting form of inner intuition), can being simultaneous and following one another be represented at all.

B 225 So time, which all change of appearances has to be thought in, remains and does not change. For it is that in which being after one another and being together can be represented only as ways time is determined. Time can’t be perceived by itself. So among the objects of perception, the appearances, there has to be a substrate to find. It represents time as such, and in apprehension all change or simultaneity can be perceived through the appearances’ relation to it. Now the substrate of everything real, that is, of everything that belongs to the existence of things, is substance. Anything that has to do with existence can only be thought of as a determination of substance. Therefore what lasts, and what alone lets us determine all the time relations of appearances, is substance in the appearance: its real, the substrate under all change that never varies. And since substance can’t change in existence, its quantum in nature can’t be increased or reduced either.

Our apprehension of the manifold of an appearance is always successive, so it is always changing. By it alone we can never decide if the parts of this manifold, taken as an object of experience, exist together or follow one another, unless something lies at its base that always is: something enduring and lasting.

B 226 All change and all simultaneity are just the different modi of time, the ways that lasting thing exists. Time relations are possible only in what lasts (there are just two relations in time, simultaneity and succession). In other words, what lasts is the substratum of the empirical representation of time itself, and only on it can time be determined at all. Persistence is how time as such gets expressed: the constant correlate of every appearance’s existence, of all change and all accompaniment. For change doesn’t touch time itself, only the appearances in time. (And being simultaneous isn’t a modus of time itself, since in time there are no parts that are simultaneous. All are one after another.) If we ascribed succession to time itself, we’d have to think of yet another time in which that succession could happen. Only through what lasts does existence get a magnitude, called duration, in the different parts of the series of time one after another. In mere succession existence is always vanishing and starting up, and never has the slightest magnitude. Without this lasting thing, then, there are no time relations. Time can’t be perceived in itself. So this lasting thing in appearances is the substratum for fixing anything in time. It is thus also the condition that makes possible any synthetic unity of perceptions, meaning experience.

B 227 On this lasting thing, any existence and any change in time can only be viewed as a modus of how what remains and lasts exists. So in all appearances, the object itself is what lasts, that is, substance (phaenomenon). Whatever changes, or could change, has to do only with how this substance (or these substances) exists, so only with their determinations.

I find that people have always assumed this persistence as a substratum of all change in appearances, and always will take it as beyond doubt. That goes for the ordinary understanding as much as for the philosopher. The philosopher just says it a little more precisely: in every alteration within the world, the substance stays and only the accidents change. But I find no one making even an attempt to prove a proposition that is so thoroughly synthetic. It also seldom stands, as it ought to, at the head of the laws of nature that are pure and rest wholly a priori. In truth, the proposition that substance persists is a tautology. For it’s only this persistence that gives us a reason to apply the category of substance to appearance. What would have had to be proved is that in every appearance there is something lasting, and that what can change is nothing but a determination of that thing’s existence.

B 228 But a proof like that can’t be given dogmatically, that is, out of concepts, since it concerns a synthetic proposition a priori. And nobody ever thought that propositions of this kind hold only in relation to possible experience, and can therefore be proved only by a deduction of that experience’s possibility. So it’s no wonder that the proposition was put at the base of all experience (people feel its need in empirical cognition) but never proved.

A philosopher was asked how much smoke weighs. The philosopher answered: take the weight of the ashes that are left from the weight of the wood that burned, and the difference is the weight of the smoke. So the philosopher took it as beyond dispute that even in fire matter (substance) doesn’t perish; only its form is modified. In the same way, the proposition “nothing comes from nothing” was just one more consequence flowing from the principle of persistence, or rather from the principle that the real subject of appearances exists forever. For if what we choose to call substance in an appearance is to be the true substratum for fixing everything in time, then all existence, past and future alike, has to be fixable in it, and in it alone. That is why we can give an appearance the name substance only because we assume that its existence holds at all times.

B 229 The word “persistence” doesn’t even capture this well, because it looks more toward future time; still, the inner necessity of lasting is bound up inseparably with the necessity of having always been, so the word can stay. Gigni de nihilo nihil (nothing comes from nothing) and in nihilum nil posse reverti (nothing can go back into nothing) were two propositions that the ancients always linked together. Today people sometimes pull them apart, by mistake. They imagine these propositions are about things in themselves. They fear the first one could clash with the world’s being dependent on a highest cause (even as to its substance). That worry is groundless, since we are talking only about appearances in the field of experience. The unity of such appearances would never be possible if we let new things (as to substance) come into being. We would then lose the one thing that can represent the unity of time, namely the identity of the substratum, in which alone all change has complete unity. This persistence is, after all, only our way of representing the existence of things (in appearance).

The determinations of a substance are nothing but particular ways for it to exist, and they’re called accidents. Accidents are always something real, since they have to do with the existence of the substance. (Negations are determinations too, but they only express that something is missing in the substance.)

B 230 Now suppose we credit this real element in the substance with a separate existence (motion, say, as an accident of matter). Then we call that existence inherence, as opposed to the substance’s existence, which we call subsistence. But this causes many misreadings. It is more exact and more correct to describe an accident only by saying how a substance’s existence is determined in a positive way. Even so, given the conditions that govern the logical use of our understanding, we cannot avoid setting apart, so to speak, whatever in a substance’s existence can change while the substance stays. We have to look at it in relation to what truly lasts, and is the root. That’s why this category sits under the heading of relations: it is more the condition of relations than something that holds a relation in itself.

This persistence also lets us correct the concept of alteration. Coming into being and passing away aren’t alterations of the thing that comes into being or passes away. Alteration is one way of existing that follows another way of existing in the very same object. So whatever alters, lasts, and only its state changes. This change touches only determinations, which can stop or start. We can therefore say, in a phrase that sounds a little paradoxical, that only what lasts (substance) is altered.

B 231 What can vary undergoes no alteration but a change, since some determinations stop and others start.

So alteration can be perceived only in substances. Coming into being or passing away in the strict sense, not just as a determination of what lasts, can’t be a possible perception at all. For the lasting thing is what makes it possible to represent the passage from one state to another, and from non-being to being, and such passages can be known empirically only as shifting determinations of what remains. Suppose something simply began to be. Then you would need a point of time at which it wasn’t. But to what would you fasten that point, if not to something already there? For an earlier empty time is no object of perception. If you tie the coming into being to things that existed beforehand and last until that which comes to be, then the later thing was merely a determination belonging to the earlier one, the lasting thing. Passing away works the same way, because it presupposes an empirical representation of a time in which the appearance is gone.

Substances, as they appear, are what underlies every determination of time. If some came to be and others passed away, that would remove the single condition of the empirical unity of time.

B 232 Appearances would then relate to two kinds of time, with existence flowing along in both side by side. That is absurd. There is only one time, and all the different times have to be set in it, not together but one after another.

So persistence is a necessary condition. Only under it can appearances be determined as things or objects within a possible experience. We’ll have a chance later to say what needs saying on the empirical criterion for this necessary persistence, and so for the substantiality of appearances.

B. Second Analogy

Principle of Succession in Time According to the Law of Causality

Every alteration happens in line with the law that links cause and effect.

Proof

(The previous principle showed that all appearances of temporal succession are only alterations, that is, a successive being and non-being of the determinations of the substance that persists. So it also showed that the being of the substance itself, as following its non-being, or its non-being, as following its existence, does not take place.

B 233 In other words, a substance itself neither comes to be nor passes away. That principle could also have been put this way: Every change of appearances (every succession of them) is only alteration. For coming to be and passing away of a substance are not alterations of it, because the concept of alteration presupposes one and the same subject existing with two opposite determinations, and therefore persisting.—After this preliminary remark, the proof follows.)

I notice that appearances follow one another. That is, at one time a state of things exists whose opposite existed in the state before. So what I’m really doing is connecting two perceptions in time. But connecting isn’t something bare sense and intuition can do. Here it’s the product of a synthesizing power of imagination, which fixes inner sense with respect to time. This power can combine the two states in either of two ways, so that either one or the other comes first in time. For time can’t be perceived by itself, and so we can’t settle, empirically in relation to time as it were, what goes before and what follows in the object. All I’m conscious of is that my imagination sets one state first and the other after. I’m not conscious of one state coming before the other in the object.

B 234 Put differently, mere perception leaves the objective relation of the successive appearances open. For that relation to be recognized as settled, we have to think the relation between the two states in such a way that it settles as necessary which of them must be placed first and which second, and not the reverse. A concept that carries necessity of synthetic unity along with it can be nothing but a pure concept of the understanding. It doesn’t lie in perception. Here the concept is that of how a cause relates to its effect. The cause fixes the effect in time as its consequence, rather than as something that might merely come first in imagination (or might not be perceived at all). So experience of appearances, that is, empirical cognition of them, is possible only because we subject the succession of appearances, and with it every alteration, to the law of causality. And that means appearances themselves can be objects of experience only under that same law.

Apprehension of the manifold of an appearance always goes step by step. The representations of the parts come one after another. Whether the parts also come one after another in the object is a separate matter for reflection, and the first doesn’t include it. We can, of course, call anything an object, even any representation, so long as we’re conscious of it.

B 235 But what the word means when applied to appearances takes deeper study. We’re not asking about appearances as objects in the sense of being representations. We’re asking what it means to say they designate an object. As mere representations that are also objects of consciousness, they’re no different from apprehension, which is their being taken into the synthesis of imagination. So the manifold of appearances, we have to say, gets produced in the mind step by step, every time. If appearances were things in themselves, nobody could infer, from the order in which the representations of their manifold arrive, how it is combined in the object. We only ever deal with our own representations. How things in themselves might be (apart from the representations by which they affect us) is completely outside our sphere of cognition. Appearances aren’t things in themselves, though they’re all that can be given to us to cognize. So I have to say how the manifold is combined in time within the appearances themselves, even though our representation of it in apprehension is always step by step. Take a house standing in front of me. Apprehending the manifold in its appearance goes step by step. Now, is the manifold of the house also step by step in itself? Of course no one will say so.

B 236 But once I push my concepts of an object up to the transcendental meaning, the house is not a thing in itself at all. It’s only an appearance, which is to say a representation, and its transcendental object is unknown. So what is the question really asking when it wants to know how the manifold in the appearance itself (which is nothing in itself) might be combined? Here what lies in the successive apprehension counts as representation. The appearance that’s given to me, though it’s nothing more than a sum of those representations, counts as their object. My concept, which I pull out of the representations of apprehension, is supposed to agree with that object. We see quickly that agreement of cognition with its object is truth. So all we can ask about here is the formal conditions of empirical truth. Appearance, set against the representations of apprehension, can be represented as their distinct object only if it falls under a rule. That rule sets it apart from any other apprehension, and it makes one way of combining the manifold necessary. Whatever in the appearance carries the condition for this necessary rule of apprehension, that is the object.

Now back to our task. Something happens when something, or some state, comes to be that wasn’t there before.

B 237 We can’t perceive that empirically unless an earlier appearance exists that doesn’t contain the state. For a reality following an empty time, a coming to be that no state of things precedes, can be apprehended no more than empty time itself. So any apprehension of an event is a perception that follows another one. But every synthesis of apprehension is like that, as the house example showed earlier. So this doesn’t yet set it apart from other apprehensions. Something else, though, I do notice. Take an appearance that involves something happening. Call the earlier state of the perception A and the later one B. B can then only follow A in apprehension. Perception A can’t follow B; it can only come before it. For example, I see a ship floating downstream. My perception of its position farther down follows my perception of its position farther up the river’s course. And in apprehending this appearance it’s impossible to perceive the ship first lower down and afterward higher up. The order in which perceptions succeed each other in apprehension is therefore fixed here, and apprehension is bound by it. In the earlier house example, my perceptions could start at the top and finish at the ground.

B 238 They could just as well start from the bottom and finish at the top, or take in the manifold of empirical intuition from the right or from the left. No fixed order in the series of these perceptions made it necessary for me to begin at one point rather than another in order to combine the manifold empirically. But when I perceive something happening, this kind of rule is always found. It makes it necessary that these perceptions succeed each other in a set order as this appearance is apprehended.

So in our case I have to derive the subjective sequence of apprehension from the objective sequence of the appearances. Otherwise the subjective sequence is wholly undetermined and doesn’t tell any appearance from another. By itself it proves nothing about how the manifold is connected in the object, because it’s entirely arbitrary. The objective sequence will therefore be found in the order of the manifold of the appearance. By that order, apprehending the one (what happens) follows, by a rule, apprehending the other (what precedes). Only then am I entitled to claim something about the appearance itself, and not just about my apprehension: that there’s a sequence in the appearance. That amounts to saying I can’t carry out the apprehension in any order but this very one.

So, by a rule of this kind, what precedes an event has to contain the condition for a rule.

B 239 It is a rule by which that event follows always and of necessity. The reverse doesn’t hold. I can’t go back from the event and fix (by apprehension) what precedes it. For no appearance returns from a later point of time to an earlier one, even though it does refer to some earlier one. Going forward from a given time to the determinate time after it, on the other hand, is necessary. Because something does follow, I must relate it of necessity to something else in general that comes before, and which it follows by a rule, that is, of necessity. In this way the event, as the conditioned, gives reliable direction to some condition, and the condition determines the event.

Suppose nothing came before an event that it was bound to follow by a rule. Then every sequence in perception would lie only in apprehension. It would be merely subjective, and it would settle nothing objectively about which of the perceptions has to be the earlier and which the later. We would have nothing but a play of representations related to no object. Our perception wouldn’t set one appearance apart from another as regards time relation. The reason is that the succession in apprehending is the same everywhere, so nothing in the appearance determines it.

B 240 Nothing makes any given sequence objectively necessary. So I won’t say that two states follow each other in the appearance. I’ll say only that one apprehension follows another. That’s merely subjective. It determines no object, and so it can’t pass for cognition of any object (not even of one within appearance).

Whenever we experience something happening, we presuppose that there is something earlier which it follows by a rule. Without that, I wouldn’t say the object follows. A bare sequence in my apprehension, not fixed by a rule in relation to something earlier, gives no right to claim a sequence in the object. So I always act with a rule in view: the rule by which appearances, in their order of succession (which is to say, as they take place), are determined by the previous state. That’s how I give objective status to my subjective synthesis (the one belonging to apprehension). And only on this presupposition is it possible even to experience something that happens.

This does seem to clash with every remark ever made about how our understanding proceeds. According to those remarks, we are led to a rule only by perceiving and comparing the matching sequences of many events after earlier appearances.

B 241 That rule says certain events always follow certain appearances, and it’s what first prompted us to form the concept of cause. If so, the concept would be merely empirical. The rule it provides, “whatever happens has a cause,” would be as much a matter of chance as experience itself. Its universality and necessity would be made up, with no true general validity, since they would rest on induction and not on anything a priori. But this is how it goes with other pure representations a priori too (space and time, for instance). We can extract these from experience as clear concepts only because we’d already put them into it, and so brought experience about through them in the first place. Granted, the logical clarity of the idea, a rule that governs the course of events, taken as the concept of cause, is possible only after we’ve used it in experience. But taking account of such a rule, as the condition for the synthetic unity of appearances in time, is what grounded experience in the first place. So it came before experience, a priori.

What matters, then, is to show with an example that even in experience we ascribe the sequence of an event (where something happens that wasn’t there before) to the object only under one condition.

B 242 We distinguish it from the subjective sequence of our apprehension only when a rule lies at the base. This rule forces us to follow this particular order of perceptions rather than any other. And in fact this compulsion is what first makes it possible to represent a succession in the object.

Representations exist in us, and we can become conscious of them. However far this consciousness reaches, and however exact or precise it is, they still remain only representations: inner determinations of our mind within one time relation or another. How, then, do we get to positing an object for these representations? How do we give them an objective reality beyond their subjective reality as modifications, though I couldn’t say what kind? Objective meaning can’t consist in a relation to another representation (one of the sort we’d call a representation of the object). If it did, the question would simply return: how does that representation, in turn, step outside itself and gain objective meaning beyond the subjective meaning that belongs to it as a determination of a state of mind? Suppose we examine what new quality our representations receive from being related to an object, and what rank they acquire by that. We find it does nothing more than make the combination of the representations necessary in a certain way, and put them under a rule.

B 243 And conversely, they get objective meaning only because a certain order in the time relation of our representations is necessary.

When appearances are synthesized, the manifold of representations always arrives one item after another. No object is represented by that alone, since this sequence is common to all apprehensions and sets nothing apart from anything else. But suppose I perceive, or take for granted, that this sequence involves a relation to the earlier state, from which the representation follows by a rule. Then something presents itself as an event, as something that happens. In other words, I cognize an object, and I have to put it at a certain determinate place in time. Given the earlier state, that place can’t be assigned to it any other way. So when I perceive that something happens, that representation holds, to begin with, the thought that something comes before. After all, it’s in relation to that earlier something that the appearance gets its time relation: to exist after a prior time in which it wasn’t. But it can get its determinate place in time within this relation only if something is presupposed in the earlier state which it always follows, that is, follows by a rule. From this we get two results. First, I can’t turn the series around and put what happens ahead of what it follows.

B 244 Second, once the earlier state is posited, this determinate event inevitably and necessarily follows. The upshot is that an order arises among our representations. In that order, the present (as something that has come to be) points back to some earlier state, as a correlate (still undetermined) of this given event. That correlate, however, relates to the event as its consequence, determining it, and connects it of necessity with itself in the series of time.

Suppose our sensibility is under a necessary law, and so a formal condition of all perceptions: the earlier time necessarily determines the later one (I can only reach the later time by going through the earlier). Then it is also an indispensable law for how we represent the series of time empirically. Appearances from past time fix whatever exists in the time that follows. And those later appearances, as events, occur only to the extent that the earlier ones fix their existence in time, that is, settle it by a rule. For it is only in the appearances that we can recognize this continuity in how times connect empirically.

Understanding is part of all experience and of its possibility. Its first contribution is not to give objects distinct representations, but to make representing an object possible at all. Here’s how it does that.

B 245 It carries the order of time over to appearances and to their existence. It assigns each appearance, as a consequence, a place in time fixed a priori in relation to the earlier appearances. Without such a place the appearance wouldn’t match time itself, which fixes the place of all its parts a priori. This fixing of place can’t be taken over from the way appearances relate to absolute time (that is no object of perception). It works the other way around: appearances have to fix each other’s places in time itself, and make those places necessary in the order of time. In other words, whatever follows or happens must follow, by a general rule, what the earlier state contained. This gives a series of appearances. By means of the understanding, the series produces in the sequence of possible perceptions the same order and unbroken connection that we find a priori in time, the form of inner intuition, where all perceptions would have to have their places, and it makes that order necessary.

So the fact that something happens is a perception belonging to a possible experience. It becomes actual when I treat the appearance as fixed in its place in time, and thus as an object one can always come upon, by a rule, in the connection of perceptions.

B 246 This rule for fixing something in the time sequence is as follows: the condition under which the event always follows (that is, follows of necessity) is to be found in what comes before. The principle of sufficient reason, then, is the ground of possible experience, that is, of objective cognition of appearances as regards how they relate in the order of time.

The proof of this proposition rests on just these points. All empirical cognition involves the synthesis of the manifold by imagination, and that synthesis always works in sequence. That is, representations always come one after another in it. But imagination doesn’t fix the order of the sequence at all (what has to come first and what has to follow), and a series of representations can be run through backward as easily as forward. Now if this synthesis is a synthesis of apprehension, covering the manifold of a given appearance, the order is settled in the object. More exactly, it contains an ordering of the step-by-step synthesis, and that ordering determines an object. By that order, one thing has to come first, and when it is posited, the other has to follow of necessity. For my perception to hold cognition of an event, where something truly happens, it has to be an empirical judgment. In it we think of the sequence as fixed.

B 247 That is, we think of it as presupposing another appearance earlier in time, which it follows of necessity, or by a rule. Otherwise, if I posited the earlier thing and the event didn’t have to follow it, I’d have to take the event for a subjective play of my imaginings. And if I still pictured something objective in it, I’d have to call it a mere dream. So the relation of appearances (as possible perceptions), by which what follows (what happens) is determined in its existence by something earlier, necessarily and by a rule in time, is the relation of cause to effect. It is the condition under which our empirical judgments about the series of perceptions have objective validity, and so empirical truth, and thus experience. For this reason the principle that governs causal relations within the sequence of appearances holds for all objects of experience as well (under the conditions of succession). It is itself the ground of what makes such experience possible.

A further worry comes up here, and it has to be cleared away. In our formula, the proposition of causal connection among appearances is limited to their sequence. Yet when we use it we find it fits their accompaniment too, so that cause and effect can be simultaneous. For instance, a room is warm. The open air is not.

B 248 I search for the cause and come upon a heated stove. Now the stove is the cause, and it exists at the same time as its effect, the warmth in the room. So there is no sequence in time here between cause and effect. They are simultaneous, and the law still applies. Most efficient causes in nature coexist with their effects. The effects follow each other in time only because a cause can’t complete its whole effect in a single instant. But at the instant it first arises, an effect is always simultaneous with its cause’s causality, because if the cause had stopped being even an instant sooner, the effect would never have come about. We must keep in mind that what counts is the order of time, not its running out. The relation holds even if no time has gone by. The gap in time between the cause’s causality and the effect that follows right away may shrink to nothing (so they’re simultaneous), yet how one stands to the other can still always be fixed in time. A ball lies on a stuffed cushion and presses a dimple into it. If I treat the ball as cause, it’s simultaneous with its effect. Still, I tell them apart by the time relation in their dynamic connection. For when I put the ball on the cushion, the dimple follows the cushion’s earlier smooth shape.

B 249 But if the cushion has a dimple (I don’t know how), no lead ball follows.

So succession in time is, after all, the only empirical criterion for telling an effect, in terms of the causality of the cause that comes before it. The glass causes the water to climb above its level surface, even though the two appearances occur together. For the moment I scoop water out of a larger container with the glass, something results: the horizontal level the water had there changes into the concave one it takes on in the glass.

Causality leads to the concept of action, action leads to the concept of force, and through force we arrive at the concept of substance. My critical project goes only to the sources of synthetic cognition a priori. I don’t want to burden it with analyses that only clarify concepts (and don’t extend them). So I leave the detailed treatment of them to a future system of pure reason. Such analysis is, after all, abundantly available even in the textbooks of this kind that we already have. But I can’t pass over the empirical criterion of a substance, to the extent that substance seems to show itself not through the appearance’s persistence but better and more easily through action.

B 250 Where there is action, and so activity and force, there is also substance, and that is where the seat of this fruitful source of appearances has to be looked for. That’s well put. But if you must explain what you mean by substance, and want to avoid a bad circle, the answer isn’t so easy. How can anyone conclude straight from action to the persistence of the one who acts, which is such an essential and distinctive mark of substance (phaenomenon)? Given what we’ve said before, though, answering the question isn’t so hard, even though by the ordinary method (dealing with your concepts merely analytically) it would be impossible. Action already means how the subject of causality stands toward the effect. Every effect consists in what happens, and so in what can change, marking time by succession. So the ultimate subject of the effect is what lasts, the substratum of everything changing, that is, substance. For the principle of causality makes actions the original ground of every change among appearances. They can’t, then, reside in a subject that itself changes, because other actions, and another subject to determine that change, would be needed. By virtue of this, action proves substantiality as a sufficient empirical criterion.

B 251 I don’t have to go looking first for the subject’s persistence through compared perceptions. That wouldn’t even work well this way, given the thoroughness that the scale and strict universal validity of the concept demand. For it is a secure conclusion that the first subject of the causality of all coming to be and passing away cannot itself come to be or pass away (in the field of appearances). That conclusion ends up at empirical necessity and persistence in existence, and so at the concept of a substance as appearance.

When something happens, the mere coming to be, leaving aside what comes to be, is already an object of investigation in itself. The passage from the non-being of a state to that state, even supposing the state held no quality in the appearance, needs investigating all on its own. As the discussion under A showed, this coming to be does not touch the substance (which doesn’t come to be) but its state. It is merely alteration, and not origin from nothing. If this origin is regarded as the effect of a foreign cause, it’s called creation. Creation can’t be allowed as an event among appearances, because its mere possibility would wreck the unity of experience. It’s different if I consider all things as things in themselves instead of as phenomena.

B 252 And I may regard them as objects of the mere understanding. Then, although they are substances, they can still be seen as dependent on a foreign cause for their existence. But that would bring in entirely different meanings of words, and it wouldn’t fit appearances, as possible objects of experience.

How anything at all can be altered, and how a state at one point of time can be succeeded by its opposite at a different point: of that we have not the slightest concept a priori. We’d need knowledge of actual forces for that, and such knowledge can only be given empirically. Moving forces are an example, or what comes to the same, certain successive appearances (motions) that point to such forces. But the form of any alteration is another matter. By form I mean the condition under which alone alteration can occur as the coming to be of another state (no matter what its content is, that is, no matter which state is being altered). This form, and with it the succession of the states themselves (what has happened), can be examined a priori, using the causal law and the conditions that time imposes*.

* Notice that I’m not talking about alteration of certain relations in general, but about alteration of state. So a body that moves uniformly doesn’t alter its state (of motion) at all, but it does if its motion speeds up or slows down.

B 253 When a substance goes from a state a to another state b, the point of time of the second state differs from that of the first, and comes after it. Likewise the second state differs from the first, in which reality (in appearance) was missing, just as b differs from zero. So even if state b differed from a only in size, the alteration would be the arising of b-a, which was not in the previous state, and relative to which that state is = 0.

So the question is how a thing goes from a state = a to another state = b. Between two instants there’s always some time. Between two states at those instants there’s always a difference, and it has a magnitude (every part of an appearance is itself a magnitude). Every transition from one state to another therefore happens in a stretch of time lying between two instants. The earlier instant settles which state the thing is leaving, the later one which state it reaches. Both are therefore boundaries of the time an alteration takes, and so also of the state in between them. As such, they belong to the alteration as a whole. Now every alteration has a cause, and the cause shows its causality throughout the whole time the alteration goes on. So the cause doesn’t produce its alteration abruptly (at once, in one instant). It produces it in time.

B 254 While time runs on from the opening instant a until it is complete in b, the magnitude of the reality (b-a) is likewise being generated, passing through all the smaller degrees between the first and the last. Every alteration is therefore possible only through the continuous action of causality. When that action is uniform it’s called a moment. The alteration doesn’t consist of such moments. It is produced by them, as their effect.

This is the law of continuity of all alteration. Its ground is this. Neither time nor an appearance within time is made of smallest parts. And yet the thing’s state, as it alters, passes through all these parts, like elements, on its way to the second state. In the real of appearance there is no smallest difference, and in the magnitude of times there is none either. That’s how the new state of reality develops out of the first, where it was absent, through every one of its infinitely many degrees. The gaps between these degrees are each smaller than the gap between 0 and a.

What use this proposition may have in the study of nature is no business of ours here. But how such a proposition can be possible entirely a priori, when it seems to extend our cognition of nature so far, calls for close examination. That’s so even though it’s plain to see that the proposition is real and correct.

B 255 And so one might think one need not ask how it was possible. For there are so many baseless claims to extend our cognition by pure reason that we must take it as a general principle to be deeply suspicious. Without documents that can supply a thorough deduction, we must neither believe nor accept anything like that, not even when the dogmatic proof is as clear as can be.

Our empirical cognition never grows, and perception never advances, except by extending the determination of inner sense. That is a progress through time, whatever the objects are, appearances or pure intuitions. This progress determines everything, and nothing further determines it. That is, its parts exist only in time, and only by being synthesized. They aren’t given ahead of that synthesis. So whenever perception moves on to something later in time, time gets determined, because the perception is being produced. Time is always a magnitude, and so are all its parts. So what is produced is a perception that has magnitude, built up through every degree from zero to the degree it finally has. None of those degrees is the smallest. That shows how we can cognize a law of alterations a priori, as far as its form goes.

B 256 We only anticipate our own apprehension, whose formal condition is there in us before any appearance is given, so we must be able to cognize it a priori.

Time carries the sensible a priori condition that makes it possible to move continuously from what exists to whatever comes next. The understanding does the same kind of job. By way of the unity of apperception, it carries the a priori condition for a continuous determination of every position that appearances can take in this time. It does this through the series of causes and effects. A cause always draws its effect’s existence after it. That is how empirical cognition of time relations becomes valid for any time at all, that is, universally, and so objectively valid.

C. Third Analogy

Principle of Simultaneity, by the Law of Interaction, or Community

All substances, in so far as we can perceive them in space as existing at the same time, are in thoroughgoing interaction.

Proof

Simultaneity is what we have when, in empirical intuition, perceiving one thing can be followed by perceiving the other, and the reverse.

B 257 (In the temporal sequence of appearances this can’t happen, as the second principle showed.) So I may begin by perceiving the moon and move on to the earth, or begin with the earth and move on to the moon. These perceptions can follow each other in either direction. That’s why I say the two exist at the same time. Now simultaneity is the existence of a manifold in the same time. But time itself can’t be perceived. So I can’t see that things are placed in the same time and conclude from it that perceptions of them can follow each other either way. Imagination’s synthesis in apprehension would give me only this: each perception is present in me while the other is absent, and the reverse. It wouldn’t tell me that the objects are simultaneous. That would mean: when one exists, the other exists in the same time, and it has to be so, or the perceptions couldn’t follow each other both ways. So a concept of the understanding is needed. It must be about the reciprocal sequence of determinations in these things, which exist together though outside one another. With it we can say that the two-way sequence of perceptions has its basis in the object, and so represent the simultaneity as objective. Now consider a relation between substances in which one contains determinations.

B 258 The ground of those determinations is contained in the other. That is the relation of influence. And when the second in turn contains the ground of determinations in the first, the relation is community, or interaction. So experience can recognize substances in space as simultaneous only if we presuppose that they interact. That interaction is therefore also the condition for the things themselves to be possible as objects of experience.

Simultaneous things exist in one and the same time. How do we know they do? By this test: it must make no difference in what order the synthesis of apprehension runs through this manifold. We might go from A through B, C and D to E, or just as well from E back to A. Suppose instead the things came one after another in time, in the order that starts at A and ends at E. Then we couldn’t start apprehension with the perception of E and go back to A. A already belongs to past time. So it can’t be an object of apprehension any more.

Now suppose a manifold of substances taken as appearances, with every one of them fully isolated. None acts on any other, and none gets influences back from another. I say then that nobody could ever perceive that they exist together.

B 259 And no path of empirical synthesis could lead from one’s existence to another’s. Imagine them cut off from each other by completely empty space. A perception that travels in time from one to the other could, with a later perception, fix the second one’s existence. But it couldn’t tell apart two cases: the second appearance objectively comes after the first, or it is rather simultaneous with it.

Besides bare existence, then, something else must be there. Through it A fixes B’s place in time, and B fixes A’s. Only so can substances we think of as co-existing be represented in empirical terms as existing together. Now one thing fixes another’s place in time only by being a cause, either of that other or of its determinations. So each substance (a substance can be a consequence only with regard to its determinations) has to hold two things. It must exercise causality over certain determinations in the other, and it must take in the effects of the other’s causality. In short, they must be in dynamic community, directly or indirectly, if their being simultaneous is ever to be cognized in some possible experience. Now whatever objects of experience can’t do without, if experience of them is to be possible, is necessary for them.

B 260 So all substances in appearance, in so far as they are simultaneous, necessarily stand in thoroughgoing community of interaction with one another.

The word “community” is ambiguous in our language. It can mean communio, a sharing in common, but it can also mean commercium, an exchange. Here we use it in the second sense, as a dynamic community. Without that, even the community of place (communio spatii) could never be cognized empirically. It’s easy to see from our experiences that only continuous influences at every point of space can lead our sense from one object to another. The light that plays between our eye and the heavenly bodies produces an indirect community between us and them, and so proves that they exist at the same time. We can’t change our place empirically (that is, perceive the change) unless matter everywhere makes it possible to perceive where we are. And this matter can show its own simultaneity, and so the coexistence of even the most distant objects (though only indirectly), only by means of its reciprocal influence. If there were no community, each perception (of an appearance in space) would break off from the next. The chain of empirical representations that we call experience would start from scratch with every new object.

B 261 Nothing earlier would connect with it even slightly, or stand in any time relation to it. I don’t mean to refute empty space by this. It can exist wherever perceptions don’t reach, so that no empirical cognition of simultaneity takes place. But then, for all our possible experience, it is no object at all.

An illustration may help. In our mind, every appearance that belongs to a possible experience must stand in community of apperception (communio). If objects are to be represented as connected and existing together, they must also fix each other’s places in a single time, and so form a whole. Now suppose that this community in the subject is to have an objective ground, or to apply to appearances taken as substances. Then the perception of one must make the perception of the other possible, as its ground, and the same the other way round. That is so that the succession always present in perceptions, as apprehensions, isn’t ascribed to the objects, and the objects can instead be represented as existing together. But that is a reciprocal influence, that is, a real community (commercium) of substances. Without it, experience couldn’t contain the empirical relation of simultaneity.

B 262 Through this commercium, appearances that are outside one another and still connected form a composite (compositum reale). Composites like this become possible in many ways. The three dynamic relations that all others come from are therefore inherence, consequence and composition.

* * *

That makes three analogies of experience. All they do is give principles for determining how appearances exist in time. They cover time’s three modi (modes). The first is how an appearance stands to time itself, taken as a magnitude: the magnitude of existence, which is duration. The second is how appearances stand to one another in time, taken as a series: one after another. The third is how they stand in time taken as the sum of all existence: at the same time. This unity of time-determination is dynamic through and through. That is, we don’t treat time as something in which experience can directly assign each existing thing its place. That can’t be done, since absolute time is no object of perception, so there is nothing to hold appearances up against. Instead it is the rule of the understanding that gives each appearance its place in time. Only by this rule can the existence of appearances take on synthetic unity according to time relations. So the rule works a priori, and it is valid for every time, whichever one.

B 263 When we speak of nature (in the empirical sense), we mean appearances as linked together in their existence by necessary rules, that is, by laws. So certain laws, and a priori ones, are what first make a nature possible. Empirical laws operate and can be found only through experience, and only in line with those original laws, which are what first make experience possible. What our analogies really show, then, is nature’s unity, in the way all appearances hang together, expressed through certain exponents. Each exponent says only how time (in so far as it takes in all existence) relates to the unity of apperception, which can exist only in synthesis by rules. Taken together, the analogies say this: all appearances lie within one nature, and must. Without that unity a priori, experience could have no unity, and objects within it could not be determined.

A remark is needed about the kind of proof we used for these transcendental laws of nature, and what is special about it. The remark should also be very important as a guide for anyone who tries to prove an a priori proposition that is both intellectual and synthetic. Suppose we had wanted to prove the analogies dogmatically, that is, from concepts. We would have had to prove that everything that exists is found only in what persists.

B 264 We would have had to prove that every event presupposes something in the earlier state, on which it follows by a rule. And we would have had to prove that in a manifold of coexisting things the states are simultaneous with respect to each other by a rule (they stand in community). All that effort would have been entirely wasted. From one object and its existence, we can never reach the existence of another, or its way of existing, by means of the mere concepts of these things. It makes no difference how we take them apart. So what did we have left? The possibility of experience, a cognition in which every object must finally be able to be given to us, if our representation of it is to have objective reality. The essential form of this third thing is the synthetic unity of apperception across all appearances. In it we found a priori conditions for determining time thoroughly and necessarily for all existence in appearance. Without them, no empirical determination of time could be made either. We also found rules of a priori synthetic unity, which let us anticipate experience. People lacked this method. They also imagined they could prove dogmatically the synthetic propositions that the understanding’s use in experience recommends as its principles. That is why the principle of sufficient reason has been given proofs so often, and always in vain.

B 265 Nobody thought of the other two analogies, even though people always silently relied on them*, since nobody had the guiding thread of the categories. Only that thread can uncover each gap the understanding has, whether in its concepts or in its principles, and make the gap visible.

* The unity of the whole world, in which all appearances are supposed to be connected, is plainly just a conclusion from the principle of community among all coexisting substances, which has been assumed in secret. If substances were isolated, they would not form a whole as its parts. And suppose their connection (the manifold’s interaction) were not necessary already, for the sake of simultaneity. Then we couldn’t reason from simultaneity, a merely ideal relation, to that connection as a real one. Still, we showed in its place that community is really the ground of the possibility of empirical cognition of coexistence. So what we are actually doing is to infer back from that cognition to community, which is its condition.

4 The Postulates of Empirical Thinking in General

1 What fits the formal conditions of experience, as regards both intuition and concepts, is possible.

2 B 266 Whatever connects with experience’s material conditions (sensation) is actual.

3 Whatever has its connection with the actual determined by the general conditions of experience is (exists) necessarily.

Explanation

The categories of modality have one special trait. When they are attached to a concept as predicates, they add nothing to it as a determination of the object. They only express how the concept stands toward the faculty of cognition. Even if a thing’s concept is already complete, I can still ask whether the thing is merely possible, or actual too, and if actual, whether it’s even necessary. No further determinations of the object itself are thought by this. The question is only how the object, with all its determinations, stands toward the understanding and its empirical use; toward the empirical power of judgment; and toward reason, where reason is applied to experience.

That is exactly why the principles of modality only explain what possibility, actuality and necessity mean when they are applied in experience. They also restrict every category to merely empirical use, and they refuse to allow any transcendental use.

B 267 For if these concepts aren’t meant to be merely logical, expressing the form of thinking in an analytic way, but are meant to be about things and about their possibility, actuality or necessity, then they have to point to possible experience, and to the synthetic unity found there. That is the only place where objects of cognition are given.

So the postulate of the possibility of things asks for this: a thing’s concept must fit the formal conditions of experience in general. Those conditions are the objective form of experience in general, and they hold all the synthesis that cognizing objects takes. Any concept that takes a synthesis into itself must count as empty, and it refers to no object, unless the synthesis belongs to experience. There are two ways it can. Either the synthesis is borrowed from experience, and then we call the concept empirical. Or it is a synthesis on which experience as such (its form) depends, as an a priori condition. Then the concept is pure, yet it still belongs to experience, since its object can be met with only there. After all, where would we find the mark of possibility for an object that we think through an a priori synthetic concept? It could only come from the synthesis that forms the empirical cognition of objects. It is true that a concept like this has to be free of contradiction.

B 268 That is a necessary logical condition. But it falls far short of what objective reality needs, I mean the possibility of an object like the one the concept thinks. Consider a figure bounded by two straight lines. Its concept has no contradiction in it. The concepts of two straight lines and of their coming together contain no negation of a figure. The impossibility lies elsewhere. It is not in the concept itself but in constructing it in space, that is, in the conditions of space and how space is determined. Those conditions have objective reality in their turn. They relate to possible things, since they contain the form of experience as such a priori.

Now let’s see how far this postulate of possibility reaches and what difference it makes. I might picture a thing that persists, so that all its changes belong only to its state. From that concept alone, I could never cognize that such a thing is possible. Or I might picture something built so that, once it is posited, something else always follows without fail. There is surely no contradiction in thinking that. But it tells me nothing about whether any possible thing has such a property (causality). Or, last, I might picture several things (substances).

B 269 They would be made so that the state of one brings a consequence in the state of another, and the reverse. Whether things can stand in such a relation cannot be read off these concepts at all, since the synthesis in them is merely arbitrary. The only way to recognize the objective reality of these concepts, that is, their transcendental truth, is that they express a priori how perceptions relate in any experience. Of course, cognizing their reality in this way is independent of experience. But it does depend on a relation to the form that any experience has, and to the synthetic unity that alone lets objects be cognized empirically.

Suppose, on the other hand, that we tried to invent brand-new concepts of substances, forces and interactions, out of the material perception offers us, without taking from experience any example of how such things are connected. We would end up with sheer fantasies. Nothing marks their possibility, because we never made experience our teacher or took these concepts from it. Concepts invented like this can’t get their mark of possibility a priori, as the categories do, as conditions that all experience depends on. They can get it only a posteriori, as marks that experience itself hands over.

B 270 So their possibility has to be cognized empirically, after the fact, or it can’t be cognized at all. Take a substance that is permanently present in space without filling it (the halfway thing between matter and thinking beings that some people wanted to bring in). Or take a fundamental power, special to our mind, of seeing the future ahead of time (not just working it out). Or, finally, take a power of the mind to share thoughts with other people, however far away they are. The possibility of such concepts has no basis whatever. It can’t be based on experience and the laws we know from it. Without that basis, each concept is an arbitrary combination of thoughts. No contradiction is in it. But it has no claim to objective reality, and so none to the possibility of an object of the sort we are trying to think here. About reality in particular, it is surely obvious that we should not try to think it concretely without the help of experience. Reality can bear only on sensation, which is the matter of experience. It has nothing to do with the form of the relation, and that form is what one could play games with in fictions.

But I will pass over everything whose possibility can be learned only from its actually showing up in experience. Here I look only at the possibility that things get from concepts a priori.

B 271 On these I go on asserting that their possibility never comes from such concepts by themselves. It always comes only from their serving as formal and objective conditions of experience in general.

It does look as if a triangle’s possibility could be known from its concept itself (the triangle is surely independent of experience). After all, we really can give it an object entirely a priori; that is, we can construct it. But that gives us only the form of an object. The triangle would still be nothing but a product of imagination, and whether its object is possible would remain doubtful. For that, something more is needed: the figure must be thought under conditions that all objects of experience rest on, and nothing else. Space is a formal condition of outer experience, and it is a priori. Also, when we build a triangle in imagination, the shaping synthesis we use is entirely the same as the one we use in apprehending an appearance, to form an experiential concept of it. These two facts alone connect the thought of such a thing’s possibility with the concept. The same goes for continuous magnitudes, and for magnitudes at all. Their concepts are all synthetic, so their possibility is never clear from the concepts themselves.

B 272 It becomes clear only when the concepts are taken as the formal conditions by which objects get determined in experience at all. And where would we look for objects that match the concepts, if not in experience, which is the only way objects are given to us? Still, we can cognize and describe the possibility of things without first bringing in experience itself. We do it only through the formal conditions under which anything in experience gets determined as an object. That makes it fully a priori. But it holds only in relation to those conditions and inside their boundaries.

To know that things are actual, the postulate demands perception, and with it sensation we are conscious of. It need not be a direct perception of the same object whose existence we are trying to cognize. But the object must be connected with some actual perception, following the analogies of experience, which lay out every real connection within experience at all.

You can’t find any mark of a thing’s existence in the bare concept of the thing. The concept may be so complete that nothing at all is lacking for thinking the thing with every one of its inner determinations. Existence still has nothing to do with all of that. It depends only on this: is such a thing given to us, in such a way that perceiving it could come ahead of the concept?

B 273 The concept coming before perception means just that the thing is possible. Perception, which supplies the stuff of the concept, is the one mark of actuality. Still, we can cognize that a thing exists even before we perceive it, and so cognize it a priori in a comparative way. This works whenever the thing is connected with certain perceptions by the principles of empirical connection (the analogies). In that case the thing’s existence is connected with our perceptions within a possible experience. With the analogies as guide, we can move from our actual perception to the thing, along the series of possible perceptions. In this way we cognize that a magnetic matter runs through all bodies, from perceiving iron filings being pulled. Our organs make it impossible to perceive this matter directly. Still, under the laws of sensibility, and given how our perceptions fit together, we would meet a direct empirical intuition of it somewhere in experience, if our senses were finer. The coarseness of our senses has no bearing on the form of possible experience at all. So we can cognize that things exist exactly as far as perception and its attachments reach, following empirical laws. Suppose we don’t begin from experience.

B 274 Or suppose we don’t proceed by the laws of empirical connection among appearances. Then we flatter ourselves in vain when we try to guess or discover that any thing exists. Idealism, though, raises a mighty objection to these rules, which prove existence by indirect means. This is the right place to refute it.

Refutation of Idealism

By idealism I mean the material kind. It is the theory that says objects in space outside us either can only be doubted and can’t be proved, or are false and impossible. The first is the problematic idealism of Descartes, which holds just one empirical assertion (assertio) to be beyond doubt: I am. The other is Berkeley’s dogmatic idealism, which declares space, along with all the things it is attached to as an inseparable condition, to be something impossible in itself. So it also calls the things in space mere imaginings. Dogmatic idealism cannot be avoided if we take space to be a property that belongs to things in themselves. Then space and everything it is the condition of would be a non-thing. But we removed the basis for this idealism in the Transcendental Aesthetic. The problematic kind says nothing about that.

B 275 It merely claims that we can’t prove an existence beyond our own through immediate experience. This is reasonable, and it suits a thorough philosophical way of thinking, namely to allow no decisive judgment until a sufficient proof has been found. So the proof that is asked for must show that we also have experience of outer things, and not merely imagination. That can hardly be done in any way except by proving that even our inner experience, the one Descartes does not doubt, is possible only if outer experience is presupposed.

Theorem

Mere consciousness of my own existence, though a consciousness that is empirically determined, proves that objects exist in space outside me.

Proof

I am aware that my existence is determined in time. Determining time always presupposes something persistent in perception. That persistent element can’t be something in me, because only through it can my existence in time first be determined 1). So perceiving this persistent element requires a thing outside me. A mere representation of such a thing won’t do. It follows that my existence in time can be determined only because actual things exist that I perceive outside me.

B 276 Now consciousness in time is, of necessity, combined with consciousness of how this time-determination can be possible. Thus the existence of things outside me, which is the condition of time-determination, is also necessarily combined with it. That is, my consciousness of my own existence is at once an immediate consciousness that other things exist outside me.

1 Kant’s preface to this second edition says the sentence should be changed to read: “But this persistent element can’t be an intuition in me. All the grounds that determine my existence and can be found in me are representations. As representations they need something persistent, distinct from themselves, in relation to which their change, and with it my existence in the very time they change in, can be determined.”

Remark 1. The proof above shows that idealism’s own game is turned back on it, and with better right. Idealism claimed that the only immediate experience is inner. Outer things, it said, are merely inferred from it. But such an inference is shaky, as it always is when we reason from given effects to definite causes. The cause of the representations we ascribe to outer things, perhaps falsely, could lie in us. Here, however, the proof shows that outer experience is in fact immediate*.

B 277 It also shows that only through outer experience is something else possible: not consciousness of our own existence, but the determination of that existence in time, that is, inner experience. Admittedly the representation I am, which expresses the consciousness that can go along with all thinking, immediately includes the existence of a subject. But it is not yet a cognition of the subject, and so not an empirical cognition, that is, not experience. Experience takes more than the thought of something existing. It also takes intuition, in this case inner intuition, in relation to which (time) the subject must be determined. For that, outer objects are altogether required. Inner experience itself is therefore possible only indirectly, and only by way of outer experience.

* The theorem above doesn’t presuppose that we are immediately conscious of the existence of outer things. It proves this, whether we can understand how such consciousness is possible or not. The question about its possibility would be this: do we have an inner sense only, with no outer sense, and merely an imagination of outer things? But it is clear that we need an outer sense already, just to imagine something as outside us, that is, to put it before sense in intuition. With that sense, we must be able to tell directly between two things: an outer intuition, which merely receives, and the spontaneity that marks every act of imagination. For imagining even an outer sense would wipe out the very capacity for intuition that imagination is supposed to determine.

Remark 2. Everything our faculty of cognition does with experience, when it determines time, agrees perfectly with this. Time can be determined only by way of change in outer relations (motion), measured against something that persists in space (the sun’s motion, for instance, against the objects of the earth).

B 278 Beyond that, we have nothing persistent at all that could stand under the concept of a substance as its intuition, other than matter. And this persistence is not taken from outer experience either. It is assumed a priori, since every time-determination needs it as a condition. That means it is also assumed as the way inner sense gets determined, for our own existence, by way of the existence of outer things. When I am conscious of myself in the representation I, that is not an intuition. It is an intellectual representation only, of a thinking subject acting by itself. So this I has no predicate of intuition at all that could be persistent and serve as the correlate for time-determination in inner sense. Take impenetrability in matter, which is an empirical intuition: that is the kind of predicate I mean.

Remark 3. For a determinate consciousness of ourselves to be possible, outer objects have to exist. That does not mean every intuitive representation of outer things includes their existence. Such a representation may be nothing but a product of imagination, as in dreams and in madness. Even so, imagination produces it only by reproducing earlier outer perceptions, and, as we have shown, those are possible only because outer objects are actual. What had to be proved here was only this: inner experience at all is possible only through outer experience at all.

B 279 Whether this or that supposed experience is really just imagination has to be settled by looking at its particular determinations and by holding it up to the criteria of all actual experience.

* * *

Now the third postulate. It is about material necessity in existence, not the merely formal, logical necessity that holds in how concepts are connected. We can never cognize any existence of objects of the senses entirely a priori. We can cognize it comparatively a priori, in relation to some other existence that is already given. Even then, what we reach is only an existence that has to lie somewhere in the experience-context to which the given perception belongs as a part. So necessity of existence is never something we learn from concepts. We learn it only from its connection with what is perceived, following the general laws of experience. And in that way only one existence can be cognized as necessary, given other appearances: the existence of effects, from causes that are given, according to laws of causality. So what we can cognize as necessary is never the existence of things (substances) themselves. It is the existence of their state, and that alone.

B 280 We come to know it from other states that perception gives us, by way of the empirical laws of causality. This means the criterion of necessity lies entirely in the law of possible experience: whatever happens is determined a priori in appearance by its cause. The only necessity we can cognize in nature, then, is that of effects whose causes are given to us. The mark of necessity in existence stops where possible experience stops. Even inside that field it does not hold of the existence of things as substances, because we can never see substances as empirical effects, as something that happens and arises. Necessity thus concerns only how appearances relate under the dynamic law of causality. It also concerns the possibility, which rests on that law, of inferring a priori from one given existence (a cause) to another (its effect). Everything that happens is hypothetically necessary. That principle puts change in the world under a law. In other words, it puts it under a rule of necessary existence, and without such a rule there would not even be a nature. So here is an a priori law of nature: nothing comes about through mere blind accident (in mundo non datur casus). So is this one: no necessity in nature is blind; it is conditioned, and therefore intelligible, necessity (non datur fatum). Both of these are laws.

B 281 Through them the play of alterations is brought under a nature of things (as appearances). Or, to say the same, they bring it under the unity of the understanding, since only there can alterations belong to an experience, which is the synthetic unity of appearances. Both principles are among the dynamic ones. The first really follows from the causality principle (among the analogies of experience). The second falls under modality’s principles. Those add to the determination by cause the concept of necessity, which stands under a rule of the understanding. The principle of continuity ruled out any leap in the series of appearances (alterations): in mundo non datur saltus. It also ruled out any gap or chasm between two appearances in the whole of empirical intuitions in space: non datur hiatus. The proposition can be put this way: nothing that would prove a vacuum, or merely allow one as part of the empirical synthesis, can come into experience. What about emptiness that one might think of beyond the field of possible experience (the world)? That does not come under the jurisdiction of the mere understanding. The understanding decides only questions about using given appearances for empirical cognition. Emptiness is a task for ideal reason, which steps out past the sphere that possible experience covers.

B 282 It wants to judge what surrounds and bounds that sphere, and so emptiness has to be weighed in the Transcendental Dialectic. We could easily set out all four of the propositions here (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum), like all principles of transcendental origin, in an order that follows the order of the categories, and prove each one’s place. But a practiced reader will do this alone, or will easily find the guiding thread. All four serve a single aim: to admit nothing into the empirical synthesis that could harm or cut into the understanding, or the way all appearances hang together without a break, which is the unity of its concepts. For only in the understanding is the unity of experience possible, the unity in which every perception must have its place.

Is the field of the possible larger than the field that holds everything actual? And is that field in turn larger than the stock of what is necessary? These are neat questions, and their solution would be a synthetic one. But they too come only under reason’s jurisdiction. They ask, more or less, whether all things as appearances belong together to the totality and context of one single experience, so that every given perception is a part of it and could not be combined with any other appearances.

B 283 Or they ask if my perceptions may be spread over more than one possible experience (as connected in general). The understanding supplies a priori only the rule for experience as such. That rule follows from the subjective, formal conditions, both of sensibility and of apperception, which alone make experience possible. Other forms of intuition (besides space and time) might be possible, and so might other forms of understanding (besides the discursive one of thinking, or of cognizing through concepts). Yet we can neither think them up nor make them comprehensible to ourselves in any way. And even if we could, they would not belong to experience, which is the only cognition where objects are given to us. Might there be perceptions beyond all that belongs to our possible experience, and so a wholly different field of matter? The understanding can’t decide that. The only thing it deals with is the synthesis of whatever is given. In other respects the poverty of our ordinary inferences stands out: by them we produce a vast realm of the possible, and everything actual (every object of experience) is supposed to be only a small part of it. Everything actual is possible. By the logical rules of conversion, it follows quite naturally that the merely particular proposition holds: some things possible are actual.

B 284 That seems to mean: many things are possible that are not actual. It also looks as if one might simply say that the number of the possible exceeds the number of the actual, because something must be added to the possible to make the actual. But I know of no such addition to the possible. Whatever was to be added to it would be impossible. Only to my understanding can something be added beyond fitting the formal conditions of experience, namely a connection with some perception. If something is connected with a perception by empirical laws, it is actual, though nobody perceives it directly. But what is given gives us no way to infer that some other series of appearances is possible, one in thoroughgoing connection with what my perception supplies, and so more than a single experience embracing everything. Even less can we infer it when nothing is given at all, since without material nothing can be thought anywhere. Something that is possible just on conditions which are themselves only possible is not possible in every respect. But that is the sense in which the question is meant, when we want to know whether the possibility of things reaches further than experience does.

I touched on these questions merely so that nothing would be missing from what, in common opinion, counts among the concepts of the understanding.

B 285 In fact absolute possibility, which holds in every respect, is not a mere concept of the understanding, and cannot have empirical use in any way. It belongs to reason alone, and reason reaches past any empirical use the understanding could possibly have. So here we had to be satisfied with a critical remark and nothing more. For the rest, we have left the matter in obscurity until we proceed further in the future.

I am closing this fourth part, and with it the whole system of principles of the pure understanding. So I owe the reason why I called the principles of modality postulates. I don’t want to take the word here as some recent philosophical authors have taken it. They go against the mathematicians, to whom the word really belongs. For these writers, to postulate means to offer a proposition as immediately certain, with no justification or proof. For suppose we had to concede this for synthetic propositions, however evident they are: that you may demand unconditional approval for them without any deduction, on the strength of what they themselves declare. Then every critique of the understanding is lost. Bold claims are plentiful, and ordinary belief (which is not a letter of credit) does not turn them away.

B 286 So our understanding would lie open to every delusion. It could not refuse its approval to pronouncements which, though without right, demand in the same confident tone to be admitted as true axioms. So when a determination is added a priori and synthetically to the concept of a thing, a proposition of that kind must unfailingly have a deduction of the legitimacy of its claim added to it, if not a proof.

The principles of modality are not objectively synthetic. The predicates possibility, actuality and necessity don’t add anything to the concept they are said of; they put nothing further into the representation of the object. But since they are nonetheless always synthetic, they can be so only subjectively. That is, they add something to the concept of a thing (a real thing), though otherwise they say nothing about it. What they add is the faculty of cognition in which the concept arises and has its place. If it is merely connected, within the understanding, with the formal conditions of experience, we call its object possible. If the concept is bound up with perception (sensation, the matter of the senses), and perception, by way of the understanding, determines it, the object is actual. Suppose the connection of perceptions determines it, according to concepts.

B 287 Then the object is called necessary. So the principles of modality say nothing about a concept except the act of the faculty of cognition that produces it. Now in mathematics, the word postulate means a practical proposition. It contains only the synthesis by which we first get ourselves an object and generate its concept. One example is to draw a circle on a plane, starting from a given point, with a given line. A proposition of this kind can’t be proved, because the procedure it asks for is exactly the way in which we first produce the concept of such a figure. That gives us exactly the same right to postulate the principles of modality. They don’t increase their concept of things in general*, but only show how that concept is combined with the faculty of cognition.

* When I say a thing is actual, I posit more than I do by saying it is possible. But the more is not in the thing. A thing can never hold more in its actuality than its complete possibility already held. Rather, since possibility was only a way of positing the thing with respect to the understanding (its empirical use), actuality at the same time connects the thing with perception.

B 288 General Remark on the System of Principles

Something here deserves special notice. We can’t see that any thing is possible just from the bare category. An intuition must always be at hand, because only in it can a pure concept of the understanding show that it has objective reality. Take the categories of relation, for example. 1) How can something exist purely as a subject, without being just a determination of other things? That is, how can it be a substance? Or 2) how can it be that, because something is, something else must be, so that something can be a cause at all? Or 3) when several things exist, how can the existence of one of them have some result for the rest, and the reverse, so that substances can stand in community? None of this can be seen from mere concepts. The same holds for the other categories too. For example, how can one thing be the same as many things together, that is, be a magnitude, and so on? So as long as intuition is missing, we don’t know whether we are thinking an object through the categories, or whether any object at all could correspond to them. This confirms that by themselves they are no cognitions at all. They are mere forms of thought, and their job is to turn given intuitions into cognitions.

B 289 —This is also the reason that mere categories can never yield a synthetic proposition. For example: in all existence there is substance, that is, something that can exist only as a subject and not as a mere predicate. Or: each thing is a quantum, and so forth. In such propositions nothing helps us go beyond a given concept and connect another one with it. That is also why every attempt has failed to prove a synthetic proposition out of pure concepts of the understanding alone. One example is the proposition that everything that exists contingently has a cause. Nobody ever got further than showing this: without that relation, we would be unable to grasp the contingent’s existence at all. That is, we couldn’t cognize a priori through the understanding that such a thing exists. But that does not make the same relation a condition for the things themselves to be possible. Think back to how we proved the causality principle. You will see that we could prove it only for objects of possible experience: whatever happens (any event whatever) presupposes a cause. And the only way we could prove it was as a principle that makes experience possible, and so makes it possible to cognize an object that empirical intuition gives us. We couldn’t prove it from mere concepts. Still, nobody can deny that the saying “anything contingent must have a cause” is plain to everyone from mere concepts.

B 290 In that case, though, we have already built the concept of the contingent so that it contains not the category of modality (what could be thought not to exist) but the category of relation (what can exist only as the consequence of another thing). And then, of course, the proposition is an identical one: anything that can only exist as a consequence has a cause. In fact, whenever we are asked for examples of contingent existence, we always point to alterations, and not just to the possibility of thinking the opposite*. An alteration is an event.

B 291 Taken as an event, it is possible only by way of a cause, so its nonbeing is possible in itself. This is how we recognize contingency: something can exist only as the effect of a cause. So if we assume a thing to be contingent, then “it has a cause” is an analytic proposition.

* We can easily think of the nonexistence of matter, but the ancients didn’t infer its contingency from that. Even the alternation of being and nonbeing in a given state of a thing, which is what all alteration consists in, doesn’t prove that the state is contingent, as if proving it from the actuality of its opposite. Take a body’s rest following motion. That doesn’t yet prove the contingency of its motion, on the ground that rest is the opposite of motion. For here the opposite stands against the other only in a logical way, not realiter, in actual fact. To prove the contingency of the motion, we would have to prove that at the earlier point in time the body could have been at rest instead of moving. Proving that it rests afterward would not do; for in that case both opposites can well exist side by side.

More remarkable still is this: to understand how things are possible according to the categories, and so to show that the categories have objective reality, we need not just intuitions but always outer intuitions. Take the pure concepts of relation, for example. We find that 1) the concept of substance needs something persistent to correspond to it in intuition (and that is what shows the concept’s objective reality). For that we need an intuition of matter in space, since space determines everything in a persisting way, while time, and so everything in inner sense, keeps flowing. Alteration is the intuition that corresponds to the concept of causality. To exhibit it, our example has to be motion, which is alteration in space. Only through motion can we make alterations, whose possibility no pure understanding can grasp, something we can see in intuition. Alteration is the combination of determinations that contradict each other, in the existence of a single thing.

B 292 How can a state of a thing be followed, in the same thing, by a state that is its opposite? No reason can make this graspable without an example. It can’t even make it understandable without an intuition. That intuition is the motion of a point in space. The point’s existing in different places (as a sequence of opposite determinations) is the first thing, and the only thing, that makes alteration visible to us in intuition. Afterwards, to make even inner alterations thinkable, we have to picture time, the form of inner sense, in a figure, as a line. We picture inner alteration as the drawing of this line (motion). So we grasp our own successive existence in different states by way of outer intuition. The real reason for this is that every alteration presupposes something persistent in intuition, if it is to be perceived even as alteration. But inner sense contains no persistent intuition at all.—Finally, take the category of community. Mere reason cannot grasp how it is possible. So we can’t see the objective reality of this concept without intuition, and outer intuition in space at that. How are we to think the possibility of this: several substances exist, and from the existence of one something follows (as effect) for the existence of the others, and the reverse? Because something is in the first, something must also be in the others.

B 293 And it can’t be understood from the existence of the others alone. Community requires exactly this. But among things that each isolate themselves wholly through their own subsistence, it can’t be grasped at all. That is why Leibniz called in a deity as go-between. Leibniz ascribed community to the world’s substances only as the understanding alone thinks them. And from their existence alone, community seemed to Leibniz, rightly, impossible to grasp. But we can make the possibility of community (of substances as appearances) quite graspable if we represent it in space, that is, in outer intuition. For space contains a priori the formal outer relations that are conditions of real ones (in action and reaction, and so of community).—It is just as easy to show this for the possibility of things as magnitudes. The category of magnitude, too, can show its objective reality only in outer intuition, and only by means of that intuition can it later be applied to inner sense. To avoid going on at length, I must leave it to the reader to think up examples.

This whole remark is very important. It confirms our earlier refutation of idealism. But it matters even more for another reason.

B 294 We will come to self-knowledge drawn from mere inner consciousness and from the determination of our nature, without the help of outer empirical intuitions. When we do, this remark will show us the limits on the possibility of such cognition.

The last conclusion of this whole section, then, is that all principles of the pure understanding are no more than principles, a priori, for experience to be possible. Every synthetic a priori proposition refers to experience alone, and the possibility of such propositions depends wholly on that reference.

Of the Transcendental Doctrine of the Power of Judgment (Analytic of Principles) Third Chapter

The Ground for Distinguishing All Objects in General into Phaenomena and Noumena

We have now journeyed through the land of pure understanding. We looked closely at each part. We have also measured it out and given everything in it its place. But this land is an island, shut in by nature itself within boundaries that can’t be changed. It is the land of truth (a charming name).

B 295 Around it lies a wide and stormy ocean, the real home of illusion. Out there, many a fog bank and many a block of ice that soon melts passes itself off as new land. They keep deceiving a seafarer who roams about hunting for discoveries, and they offer nothing but empty hopes. The seafarer is drawn into adventures that can’t be dropped and can’t be finished. Before we dare to go out on that sea, to search it in every latitude and make sure whether anything there is worth hoping for, it will be useful to look once more at the map, before we leave this land behind. We should ask first whether we might be content with what the land holds, or even must be content out of need, if nowhere else offers ground where we could settle. We should ask second by what title we hold this land ourselves, and how we can keep it safe against all hostile claims. We have already answered these questions well enough in the course of the Analytic. But a short summary of the answers can strengthen our conviction, by bringing their separate points together in one place.

What we have seen is this: anything the understanding draws out of itself, without borrowing it from experience, serves it for nothing except use in experience.

B 296 The principles of pure understanding may be constitutive a priori (the mathematical ones) or only regulative (the dynamical ones). Either way, all they hold is, so to speak, the pure schema for a possible experience. Experience has its unity from only one source: the synthetic unity that the understanding gives, originally and by itself, to the imagination’s synthesis with respect to apperception. Appearances, as data for a possible cognition, already have to relate and conform to that unity a priori. These rules of the understanding are not only true a priori. They are the very source of all truth, which is our cognition’s agreement with objects, since they hold the ground that makes experience possible, and experience is the sum of all cognition in which objects can be given to us. Even so, being told only what is true doesn’t seem to us enough. We want to be told what we are eager to know. Now suppose this critical inquiry teaches us nothing beyond what we would have done on our own in the merely empirical use of the understanding, with no such subtle research. Then the benefit seems not worth the effort and preparation. To that one can reply, it’s true, that no rash curiosity does more harm to the growth of our cognition than the kind that insists on knowing the use beforehand, before beginning an inquiry.

B 297 Before the inquiry, one can’t form even the faintest notion of that use, even when it is put in front of one’s eyes. There is, however, an advantage that even the hardest and most unwilling student of such transcendental research can be made to understand and care about. An understanding busy only with its empirical use, and not pondering where its own cognition comes from, can get on very well. But there is one thing it can’t do. It cannot fix for itself the boundaries of its own use, or know what may lie inside or outside its whole sphere. That takes exactly the deep investigations we have made. And if the understanding can’t distinguish whether some questions lie in its horizon or not, it is never sure of its claims and possessions. It can only expect many shameful corrections, as it keeps crossing the borders of its territory (which is unavoidable) and wanders into delusion and dazzling tricks.

Here is a proposition with important consequences, if we can really see it to be true: the understanding can make only empirical use of all its principles a priori, and of all its concepts too, and never transcendental use.

B 298 A concept is used transcendentally in a principle when the principle applies it to things in general, things in themselves. It is used empirically when the principle applies it merely to appearances, that is, to objects of a possible experience. Only the second use can ever take place anywhere. We see this as follows. Every concept needs two things. The first is the logical form that any concept (any act of thinking) has. The second is that it must be possible to give the concept an object to refer to. Without the second, the concept means nothing and holds no content at all. All it keeps is the logical function of making a concept from whatever data there happen to be. Now there is only one way to give a concept its object: in intuition. Although a pure intuition is possible a priori even before the object, that intuition itself can get its object, and with it objective validity, only through empirical intuition, whose mere form it is. So every concept, and every principle with it, however possible a priori, still refers to empirical intuitions, that is, to data for possible experience. Without that, they have no objective validity whatever. They are only a game, played by imagination or understanding with its own representations. Take the concepts of mathematics, and begin with their pure intuitions.

B 299 Space has three dimensions. Between two points there can be only a single straight line. And so on. All these principles are produced in the mind entirely a priori, and so is the representation of the object that this science works on. Yet they would mean nothing if we could not always show their meaning in appearances (empirical objects). That is why an abstract concept has to be made sensible: the object that corresponds to it must be shown in intuition. Otherwise the concept would stay (as the saying goes) without sense, which means without meaning. Mathematics meets the demand by constructing the figure. A figure is an appearance, and the senses can face it, though it was brought about a priori. That same science has the concept of magnitude find its footing and sense in number. Number in turn seeks it in fingers, in the beads of an abacus, or in strokes and dots placed before the eyes. The concept itself is always generated a priori, and so are the synthetic principles or formulas built from such concepts. But using them, and relating them to supposed objects, can be looked for in the end only in experience. Those a priori concepts and principles contain the possibility of that experience, as far as its form goes.

B 300 The same is true of all the categories, and of the principles spun out of them. This also becomes clear from the following. We can’t give a real definition of even one category, that is, we can’t explain how its object could be possible, without at once stepping down to conditions of sensibility, and thus to the form of appearances. The categories must therefore be restricted to appearances, which are their only objects. Take that condition away, and all meaning, which is relation to the object, falls away. No example can then help us grasp what thing could really be meant by concepts like these.

Nobody can explain the concept of magnitude as such, except roughly as follows: magnitude is what makes it possible to think a thing by how many times a unit has been put into it. But this “how many times” depends on successive repetition, and so on time and on synthesis (of what is of the same kind) in time. Reality, as opposed to negation, can be explained only by imagining a time (the sum of all being) that is either full of something or empty. Suppose I drop persistence (which is existence at all times). Then the concept of substance has nothing left except the logical representation of a subject. I try to make it real by representing something that can occur merely as a subject (without being the predicate of anything).

B 301 Yet I can’t name any conditions under which a thing would have this logical advantage. Worse, nothing further can be made of it, and not the slightest conclusion can be drawn, since no object of use is thereby fixed for this concept, and so we don’t know at all whether it means anything. Take the concept of cause (leaving out time, in which one thing follows another by a rule). In the pure category I would find only that a cause is something from which the existence of something else can be inferred. Then cause and effect could not be told apart. And since inferring soon takes conditions I know nothing about, the concept would have no determination for how it fits any object. The so-called principle “everything contingent has a cause” enters with quite a solemn air, as if its dignity lay in itself. But if I ask, “What do you mean by contingent?” and you answer, “Something whose nonbeing is possible,” then I would like to know how you will recognize this possibility of nonbeing. You will have to picture, in the series of appearances, a succession, and in the succession an existence that follows on nonbeing (or the other way round), and so a change. For to say that a thing’s nonbeing does not contradict itself is a lame appeal to a logical condition.

B 302 The condition is necessary for the concept, but far from enough for real possibility. Indeed, I can cancel any existing substance in thought without contradicting myself. Yet I can’t infer from this its objective contingency in its existence, that is, the possibility of its nonbeing in itself. Now take the concept of community. It is easy to see that the pure categories of substance and of causality admit no explanation that determines their object. The reciprocal causality of substances toward one another (commercium) is equally incapable of one. Possibility, existence and necessity have never yet been explained otherwise than by obvious tautology, if the definition was to come from pure understanding alone. For the trick of substituting the logical possibility of the concept (which does not contradict itself) for the transcendental possibility of things (where an object corresponds to the concept) can deceive and satisfy only the inexperienced*.

* In short, nothing can back up any of these concepts, so their real possibility can’t be shown, if all sensible intuition (the only one we have) is removed. Then only logical possibility is left, that is, that the concept (thought) is possible. But that is not what is at issue. What is at issue is whether the concept refers to an object, and so means anything at all.

B 303 It follows beyond dispute that the pure concepts of the understanding are never to be used transcendentally; their use is always and only empirical. It also follows that the principles of the pure understanding can be applied only to the general conditions of a possible experience, that is, to objects of the senses. They can never be applied to things in general (without regard to how we might intuit them).

So the Transcendental Analytic leaves us with an important result. A priori, the understanding can do no more than anticipate the form of any possible experience. And whatever is not an appearance can’t be an object of experience. So the understanding can never step over the limits of sensibility, the only place where objects are given to us. Its principles only set out appearances. The proud name of an ontology claims to offer, in a systematic doctrine, synthetic cognitions a priori about things in general (the principle of causality, for example). That name has to give way to the modest one: a mere analytic of the pure understanding.

B 304 To think is to relate a given intuition to an object. If the kind of intuition is not given in any way, the object is only transcendental, and the concept of the understanding can have no use other than a transcendental one: the unity of thinking a manifold as such. A pure category leaves out every condition of sensible intuition, the only intuition we can have. So no object is determined through a pure category. It merely expresses, in various modi (modes), the thinking of an object as such. Now using a concept also takes a function of the power of judgment: an object has to be subsumed under the concept. That means at least the formal condition that something must meet to be given in intuition. If the power of judgment lacks this condition (the schema), no subsumption can happen, because nothing is given to bring under the concept. Categories used only transcendentally are therefore, in fact, not used at all. They have no determinate object, nor even one that could be determined as to form. From this it follows that a pure category is not enough for any synthetic principle a priori. It follows too that the principles of the pure understanding have only empirical use, never transcendental use.

B 305 Beyond the reach of possible experience, there are no synthetic principles a priori at all.

It may therefore be wise to say it this way: without the formal conditions of sensibility, the pure categories have only transcendental meaning, and they have no transcendental use. Such use is impossible in itself, because they lack all the conditions of any use (in judgments). Those are the formal conditions for placing some supposed object under these concepts. As mere pure categories they are not supposed to have empirical use, and they cannot have transcendental use. So if we detach them from all sensibility, they have no use whatsoever. They can’t be applied to any supposed object. What they are is only the pure form for using the understanding on objects as such, and for thinking. By them alone, however, we can neither think nor determine any object.

A deception lies under this, and it is hard to avoid. By their origin the categories do not rest on sensibility, as the forms of intuition, space and time, do. So they seem to permit an application that reaches beyond all objects of the senses. But they too are only forms of thought. They contain only the logical power to unite, in one consciousness a priori, the manifold given in intuition.

B 306 If the only intuition possible for us is taken from them, they have still less meaning than those pure sensible forms. The sensible forms at least give an object. A way of combining the manifold that belongs to our understanding means nothing at all if the intuition, the only place the manifold can be given, does not come along.—Still, our concept itself already says something. When we call certain objects appearances, beings of sense (phaenomena), we distinguish how we intuit them from what they are in themselves. That already means we set something over against them, as it were. It might be those very objects, according to how they are constituted in themselves, although we don’t intuit them in that constitution. Or it might be other possible things that our senses can never have as objects, things we think as objects through the understanding alone. These we call beings of understanding (noumena). Now the question comes up: do our pure concepts of the understanding mean anything with respect to the latter, and could they be a way of cognizing them?

Right at the start, however, an ambiguity appears here that can lead to a great misunderstanding. When the understanding calls an object a phaenomenon, only in a certain respect, it also forms for itself, apart from that respect, a representation of an object in itself.

B 307 So it supposes it can form concepts of an object of that sort as well. The understanding supplies no concepts other than the categories. So it supposes that the object in this second sense must at least be thinkable through these pure concepts of the understanding. This leads it astray. It takes the wholly indeterminate concept of a being of understanding, meaning a something in general outside our sensibility, to be a determinate concept of a being we can cognize in some way through the understanding.

Take noumenon to mean a thing to the extent that our sensible intuition does not take it as an object, because we abstract from our way of intuiting it. Then we have a noumenon in the negative meaning of the word. Take it instead to mean an object of a nonsensible intuition. Then we assume a special way of intuiting, namely the intellectual one. That way is not ours, and we can’t even see that it is possible. This would be a noumenon in the positive meaning.

The teaching about sensibility is at once the teaching about noumena in the negative sense. These are things the understanding has to think of without any tie to our way of intuiting. So it has to think of them as things in themselves, and not just as appearances. But once the understanding sets them apart like this, it also sees that it can’t use its categories to look at them that way.

B 308 The categories mean something only when they’re tied to the unity that intuitions have in space and time. And they can fix that unity a priori, through general concepts of combination, only because space and time are merely ideal. Where this unity of time can’t be found, which is the case with the noumenon, the categories stop being usable and stop meaning anything at all. We can’t even see how the things that are supposed to match the categories could be possible. So all I can do is point back to what I said at the very start of the general remark on the previous chapter. Now, no thing’s possibility can be proved merely because its concept doesn’t contradict itself. It can be proved only by backing the concept with an intuition that corresponds to it. Suppose we wanted to use the categories on objects that we don’t treat as appearances. Then we’d have to base the categories on some intuition that isn’t the sensible kind. That object would count as a noumenon in the positive meaning of the word. But an intuition like that, an intellectual intuition, lies entirely outside our power of cognition. So the categories can’t be used on anything beyond the boundary of the objects of experience. Beings of the understanding do, to be sure, correspond to beings of the senses.

B 309 There may even be beings of the understanding that our sensible power of intuition has no relation to at all. Our concepts of the understanding, though, are only forms of thought for our sensible intuition. They don’t reach those beings in the slightest. So whatever we call a noumenon has to be understood as one only in the negative sense.

Take an empirical cognition and subtract all the thinking done through categories. No cognition of any object is left, because nothing at all is thought through mere intuition. That my sensibility is affected in this way gives that representation no relation to any object. Now suppose I leave out all intuition instead. What’s left then is the form of thinking: the way of settling on an object for whatever manifold a possible intuition offers. In this respect the categories reach further than sensible intuition does. They think objects as such, without yet looking at the particular manner (of sensibility) in which those objects might be given. But that doesn’t give them a bigger sphere of objects. We can’t suppose such objects could be given unless we also suppose that some intuition other than the sensible kind is possible. And we have no right to suppose that.

B 310 I use the word problematic for a concept that holds no contradiction, hangs together with other cognitions as a way of bounding given concepts, and has an objective reality that can’t be cognized in any way. The concept of a noumenon is like that. A noumenon is a thing meant to be thought of as it is in itself, by pure understanding alone, and not as something the senses can take as an object. The concept isn’t contradictory at all, since we can’t claim that sensibility is the only possible kind of intuition. The concept is also necessary. It keeps sensible intuition from being stretched over things in themselves, and so it keeps the objective validity of sensible cognition limited. (Whatever sensible cognition doesn’t reach gets called noumena for just this reason: to show that such cognitions can’t extend their territory over everything the understanding thinks.) In the end, though, we can’t see how such noumena could be possible. And whatever lies beyond the sphere of appearances is, for us, empty. We have an understanding that reaches further than appearances do, but only problematically. What we lack is any intuition, or even the concept of a possible one, that could give us objects beyond sensibility’s field. Without that, we can’t use the understanding assertorically outside that field either.

B 311 So the concept of a noumenon is only a boundary concept. Its job is to rein in the presumption of sensibility, and so it has a negative use only. But it isn’t made up at random. It is tied to the limiting of sensibility, though it can’t set up anything positive outside sensibility’s range.

In a positive sense, we can’t allow objects to be divided into phaenomena and noumena, or the world to be split into one world for the senses and another for the understanding. Concepts, it’s true, can be divided into sensible and intellectual ones. But we can’t assign any object to the intellectual ones, so we can’t pass them off as objectively valid. Once we leave the senses, how can we make it clear that our categories still mean anything at all? They would be the only concepts left for noumena. For the categories to relate to any object, something more than the mere unity of thinking is needed. A possible intuition must also be given, one they can be applied to. Even so, the concept of a noumenon, taken merely problematically, stays not only admissible but unavoidable, as a concept that puts sensibility within limits. But then it isn’t a special intelligible object for our understanding. What it points to is an understanding to which such an object would belong, and that understanding is itself a problem (Problema). Such an understanding would not cognize its object discursively, working through categories.

B 312 It would cognize it intuitively, in a nonsensible intuition. We can’t form the slightest representation of how that could be possible. In this way our understanding gets a negative extension. Sensibility doesn’t set limits for the understanding. Instead, the understanding sets limits for sensibility, by giving the name noumena to things in themselves (things not viewed as appearances). But it also sets boundaries for itself right away: it won’t cognize those things through any categories, and so it can think of them only by the name “unknown something.”

In the writings of more recent authors, however, I find that the expressions mundi sensibilis and intelligibilis* (of a sensible and of an intelligible world) are used in a quite different way. It departs completely from the sense the ancients gave them. It involves no difficulty, of course, but nothing is found in it except empty haggling over words. Some have liked to call the sum of appearances the world of the senses, in so far as it is intuited, though the connection of appearances can also be thought according to general laws of the understanding.

B 313 In that respect they have liked to call it the world of the understanding. Theoretical astronomy, which just reports observation of the starry sky, would present the first. Contemplative astronomy would present the second, an intelligible world. That second kind might be astronomy explained by the Copernican world-system, or even by Newton’s laws of gravitation. But twisting words like this is only a sophist’s trick for dodging a hard question: you shrink its meaning until it’s comfortable to answer. Of course understanding and reason can be applied to appearances. What we’re asking is whether they’re any use at all when the object isn’t an appearance (a noumenon). That is how one takes an object when it is thought of in itself as merely intelligible, that is, as given to the understanding alone and not to the senses at all. So the question is this: besides that empirical use of the understanding (even in Newton’s picture of how the world is built), is a transcendental use also possible, one that goes to the noumenon as an object? We have answered that question in the negative.

* We must not use the expression “intellectual world” in its place, as people commonly do in German presentations. Only cognitions are intellectual or sensitive. But what can be an object of only one or the other kind of intuition—that is, objects—must be called intelligible or sensible, however harsh that sounds.

So when we say that the senses show us objects as they appear while the understanding shows them as they are, we must take the second part in an empirical sense, not a transcendental one. It means how objects must be represented as objects of experience, in the thoroughgoing connection of appearances.

B 314 It doesn’t mean what they might be apart from any relation to possible experience, and so to the senses in general, that is, as objects of pure understanding. That will always stay unknown to us. We can’t even tell whether this kind of transcendental (extraordinary) cognition could exist at all, at least one that works under our ordinary categories. For us, understanding and sensibility determine objects only when they are combined. Pull them apart and we are left with intuitions lacking concepts, or concepts lacking intuitions. In both cases we have representations that we can’t relate to any determinate object.

Suppose someone, even after all this, can’t bring themselves to give up the purely transcendental use of the categories. Let them test the categories in some synthetic assertion. For an analytic assertion doesn’t take the understanding any further. All it handles is what the concept already holds in thought. So it never settles whether the concept itself is about objects, or whether it just stands for the unity of thinking as such (a unity that ignores entirely how an object might be given). Knowing what its concept contains is all it needs. What the concept itself may be about makes no difference to it.

B 315 So let them take a synthetic principle that is supposed to be transcendental, such as this: everything that is exists as a substance or as a determination attached to a substance; everything contingent exists as the effect of another thing, namely its cause; and so on. Now I ask: where will they get these synthetic propositions from, when the concepts are meant to hold of things in themselves (noumena) and not in relation to possible experience? Every synthetic proposition needs a third element, to connect concepts that aren’t logically (analytically) related at all. Where is it here? They will never prove their proposition. More than that: they couldn’t even defend the possibility of a pure claim like this without turning to the empirical use of the understanding. That would mean giving up completely on pure judgment free of the senses. So the concept of purely intelligible objects is wholly empty of principles for applying it. We can’t think up any way in which such objects could be given. The problematic thought still keeps a place open for them. But all it does, like an empty space, is to put limits on the empirical principles. It contains no other object of cognition outside their sphere, and shows none.

B 316 Appendix The Amphiboly of Concepts of Reflection Through Confusing the Empirical Use of Understanding with the Transcendental

Reflection (reflexio) doesn’t deal with the objects themselves in order to get concepts directly from them. It is the frame of mind we get into first, when we get ready to discover the subjective conditions that let us arrive at concepts. It is the consciousness of how given representations relate to our different sources of cognition. Only through this can their relation to one another be determined correctly. Before we do anything else with our representations, the first question is this: in which power of cognition do they belong together? Are they being connected or compared in front of the understanding, or in front of the senses? Many a judgment is accepted out of habit, or tied together by inclination. But no reflection comes before it, or at least follows it critically, and so it passes for a judgment that originated in the understanding. Not every judgment calls for investigation, meaning a look at the grounds of its truth.

B 317 Some judgments are certain at once. Take “Between two points there can lie just one straight line.” For a judgment like that, no closer mark of truth can be given than what it states itself. But all judgments, indeed all comparisons, need reflection, that is, a distinction of the power of cognition to which the given concepts belong. There is an act in which I hold the comparison of representations up against the power of cognition where the comparison takes place. In that act I also tell whether the representations are compared as things that belong to pure understanding or to sensible intuition. I call this act transcendental reflection. In a state of mind, concepts can be related to one another in these ways: sameness and difference; agreement and conflict; the inner and the outer; and last, the determinable and its determination (matter and form). Getting this relation right depends on which power of cognition the concepts subjectively belong together in, sensibility or understanding. For the difference between these two powers makes a great difference in how we should think the relations.

Before making any objective judgments, we compare concepts. We look for sameness (of many representations under one concept), which serves general judgments, or for their difference, which serves to produce particular ones.

B 318 We look for agreement, from which affirmative judgments can come, and for conflict, from which negative judgments can come, and so on. On this ground, it seems, we ought to call the concepts just named concepts of comparison (conceptus comparationis). But sometimes the logical form isn’t what matters. What matters is what the concepts contain, that is, whether the things themselves are the same or different, in agreement or in conflict, and so on, things can stand in a twofold relation to our power of cognition, namely to sensibility and to understanding. And how they are supposed to belong to one another is settled by the place where each of them belongs. So only transcendental reflection, that is, the relation of given representations to one kind of cognition or the other, can determine how they relate to each other. Whether things are the same or different, in agreement or in conflict, and so on, can’t be settled directly from the concepts themselves by mere comparison (comparatio). It can be settled only after we tell apart the kind of cognition they belong to, by means of a transcendental reflection (reflexio). So one could indeed say that logical reflection is a mere comparison. In it we abstract completely from the power of cognition to which the given representations belong. So as far as their seat in the mind goes, we have to treat them as being of one kind.

B 319 Transcendental reflection is different. It goes to the objects themselves, and it holds the ground that makes an objective comparison of representations with one another possible. So it is very different from logical comparison, because the power of cognition the representations belong to is not the same. This transcendental reflection is a duty that no one can get out of who wants to judge anything about things a priori. We’ll take it up now, and it will shed no small amount of light on what the understanding’s real business is.

1 Sameness and difference. Suppose an object shows up before us on several occasions, and each time its inner determinations are exactly alike (qualitas et quantitas). If pure understanding is what takes it as its object, then it is always the same object. It is not many things but only one thing (numerica identitas). But if it is an appearance, comparing concepts doesn’t matter at all. The concepts may match in every respect. Even so, if the appearance is in different places at the same moment, that is reason enough to count the object (of the senses) as numerically different. Take two drops of water. We can set aside every inner difference between them, in quality and in quantity. It’s enough that they are intuited in different places at once for us to hold them numerically different.

B 320 Leibniz took appearances to be things in themselves, and so to be intelligibilia, that is, objects of pure understanding. (He did give them the name of phenomena, because the representations of them are confused.) Given that, nobody could really contest his proposition of the indiscernible (principium identitatis indiscernibilium). But appearances are objects of sensibility, and the understanding is used on them not purely but only empirically. Space is the condition of outer appearances, and space by itself already gives us multiplicity and numerical difference. One part of space may be perfectly similar and equal to another. Still, it lies outside that other part, and for exactly that reason it is a different part, one that is added to the first to make a larger space. And that must hold of everything in the various places of space at once, no matter how alike and equal those things are otherwise.

2 Agreement and conflict. When reality is represented by pure understanding alone (realitas noumenon), you can’t think of any conflict among realities. By conflict I mean a relation in which realities, joined in one subject, cancel each other’s consequences, so that 3-3=0. On the other hand, take what is real in appearance (realitas phaenomenon).

B 321 It can certainly be in conflict with other real things. United in the same subject, one can destroy the consequence of another, wholly or in part. Take two moving forces on one straight line, pulling or pushing a point in opposite directions. Or take a pleasure that balances out a pain.

3 Inner and outer. In an object of pure understanding, a thing is inner only if, as far as its existence goes, it has no relation to anything besides itself. A substantia phaenomenon in space is different. Its inner determinations are nothing but relations, and the whole substance is simply a sum of nothing but relations. The only way we know substance in space is through forces working in it. They either drive other things toward it (attraction) or keep them from entering it (repulsion and impenetrability). We know no other properties that make up the concept of the substance that appears in space, which we call matter. But as an object of pure understanding, a substance has to have inner determinations, and forces that have to do with inner reality. What inner accidents can I think of, though, except the ones my inner sense offers me? That is, something that is either itself a thinking or analogous to thinking.

B 322 That is why Leibniz made simple subjects out of all substances, endowed with powers of representation: in a word, monads. He pictured them as noumena. He did the same even with the components of matter, after he had removed in thought everything that could mean outer relation, and with it composition.

4 Matter and form. These two concepts underlie all other reflection, for they are so inseparably combined with each use of the understanding. The first means the determinable in general. The second means its determination. (Both are meant in the transcendental sense, since we abstract from any difference in what is given and in the way it is determined.) Logicians used to call the general the matter and the specific difference the form. In a judgment, we can call the concepts that are given its logical matter, and call their relation (through the copula) the judgment’s form. In any being, the parts it consists of (essentialia) are the matter, and the way they are connected in the thing is the essential form. With regard to things in general, unlimited reality was also regarded as the matter of all possibility. The limiting of it (negation) was regarded as the form by which, according to transcendental concepts, one thing differs from another. The understanding first demands that something be given.

B 323 That must happen at least in the concept, so that the understanding can then determine it in some way. So in the concept of pure understanding, matter comes before form. That is why Leibniz first assumed things (monads), with an inner power of representation in them. On that he then built their outer relation, and the community among their states, meaning their representations. That made space possible only through how substances relate. It made time possible only through how their determinations connect to one another, as grounds and consequences. It would really have to be that way, if pure understanding could relate straight to objects, and space and time were features of things in themselves. Suppose instead that they are only sensible intuitions, ones in which we determine objects purely as appearances. Then the form of intuition (as a subjective feature of sensibility) comes before all matter (sensations). So space and time precede every appearance and every datum of experience, and they are what make those possible at all. The intellectual philosopher couldn’t stand the idea that the form should come before the things themselves and determine their possibility. He was quite right to object, if he thought that we intuit things as they are (even if confusedly).

B 324 But sensible intuition is a very special subjective condition of its own. It underlies every perception a priori. Its form is original. So the form is given on its own. Matter (or the things themselves that appeared) is not the ground, as judging by mere concepts would require. On the contrary, such things are only possible if a formal intuition (time and space) is already given.

Note on the Amphiboly of Concepts of Reflection

Allow me to use the term transcendental place for the position we give a concept, whether in sensibility or in pure understanding. Judging this place, which belongs to each concept according to how it is used, and giving rules for fixing the place of all concepts, would then be the transcendental topic. This doctrine would thoroughly protect us from the stealthy errors of pure understanding and the delusions that spring from them, because it would always tell us which power of cognition a concept properly belongs to. Any concept, any title under which many cognitions fall, can be called a logical place. Aristotle’s logical topic is built on this. Schoolteachers and speakers could use it, going to certain titles of thinking.

B 325 There they could look up whatever best suited the matter at hand. Then, with a show of thoroughness, they could argue cleverly about it or chatter on at length.

The transcendental topic, by contrast, contains nothing more than the four titles of all comparison and distinction that I listed. They differ from the categories in this way. They don’t present the object by what makes up its concept (magnitude, reality). They present only the comparison of representations, in all its variety, which comes before the concept of things. This comparison first needs a reflection, that is, a decision about where the representations of the things we are comparing belong: do they belong to what pure understanding thinks, or to what sensibility gives in appearance?

Concepts can be compared logically without worrying about where their objects belong—whether they are noumena for the understanding or phaenomena for sensibility. But if we want to go with these concepts to the objects, we first need a transcendental reflection about which power of cognition they are supposed to be objects for, pure understanding or sensibility. Without this reflection, my use of these concepts is very unsafe.

B 326 Supposed synthetic principles arise that critical reason can’t accept, and that rest solely on a transcendental amphiboly, that is, on a confusion of an object of pure understanding with an appearance.

Lacking such a transcendental topic, and so deceived by the amphiboly of the concepts of reflection, the famous Leibniz set up an intellectual system of the world. Or rather, he believed he knew the inner nature of things, by comparing all objects only with the understanding and with the abstracted formal concepts of its thinking. Our table of the concepts of reflection gives us an unexpected advantage. It sets before our eyes what is distinctive in his doctrine in all its parts, and at the same time the guiding ground of this peculiar way of thinking, which rested on nothing but a misunderstanding. He set all things beside one another by means of concepts only. Naturally, he found no differences except the ones by which the understanding tells its pure concepts apart. Sensible intuition has conditions that bring differences of their own. He didn’t count these as original. For to him sensibility was nothing more than a muddled way of representing things, not a separate source of representations. Appearance, as he saw it, was just how the thing in itself is represented. It differed from cognition through the understanding in logical form only.

B 327 That is because appearance, as he saw it, usually lacks analysis, and so it draws into the concept of the thing a certain mixture of side-representations, which the understanding knows how to separate out. In short, Leibniz intellectualized appearances, just as Locke, going by a system of noogony, had sensified all the concepts of the understanding (I hope I may use such words). That is, Locke passed them off as nothing but empirical or abstracted concepts of reflection. Instead of seeing understanding and sensibility as two entirely different sources of representations, which give valid judgments about things only when connected, each of these great men clung to just one of them. In his view, that one was directly about things in themselves, and the other only muddled or ordered what the first one supplied.

So Leibniz compared the objects of the senses with one another merely in the understanding, as things in general. First, he compared them insofar as the understanding is to judge them the same or different. All he looked at was their concepts. Their position in intuition, the only place where objects can be given, he ignored. And he left the transcendental place of these concepts (whether the object is to be counted among appearances or among things in themselves) entirely out of account, and so it could not turn out any other way than this.

B 328 He carried his principle of the indiscernible over to the objects of the senses (mundus phaenomenon), although it holds only of concepts of things in general. And he thought he had thereby given our knowledge of nature no small expansion. Of course, suppose a drop of water were a thing in itself, and I knew all its inner determinations. Then I couldn’t count it as different from another drop, if the whole concept of it matched the other’s. But if the drop is an appearance in space, its place is not just in the understanding (under concepts). It is in the sensible outer intuition (in space). And there the physical places don’t matter at all with regard to the inner determinations of things. A place = b can take in a thing perfectly similar and equal to another thing in place = a, just as well as it could if that thing were as different from it inside as could be. The difference of places already makes the multiplicity and distinction of objects, as appearances, not only possible but necessary, without any further conditions. That seeming law, then, is not a law of nature at all. It is merely an analytic rule, a comparison of things through mere concepts.

Second, there is a principle that realities never clash logically, since they are mere affirmations. That is a perfectly true statement about how concepts relate.

B 329 But it means nothing at all, whether for nature or for any thing in itself (we have no concept of such a thing). For real conflict happens wherever A - B = 0. That is, it happens wherever two realities are joined in one subject and one cancels the other’s effect. Nature shows us this constantly in its obstacles and counteractions. Because these rest on forces, they have to be called realitates phaenomena. General mechanics can even state, in an a priori rule, the empirical condition under which this conflict arises. It does so by looking at how directions oppose each other. The transcendental concept of reality knows nothing of that condition. Mr. von Leibniz didn’t announce this principle with much fuss, as a new principle. But he did use it for new claims, and his followers wrote it expressly into their Leibniz-Wolfian systems. By this principle, for instance, every evil is just a consequence of creatures’ limits, that is, of negations. Negations are the only thing that conflicts with reality. (That’s really so when we consider just the concept of a thing in general, but not for things as appearances.) In the same way, those who follow this view think it is not just possible but natural for all reality to come together in a single being, without any fear of conflict.

B 330 They think so because the only conflict they know is contradiction (which cancels the concept of a thing itself). They don’t know the kind where one real ground cancels what another one brings about. And for picturing that kind, we find the conditions only in sensibility.

Third, the only ground of Leibniz’s monadology is that this philosopher pictured the difference between inner and outer purely in relation to the understanding. Substances in general must have something inner. So that inner part must be free of all outer relations, composition included. So the simple is what the inner side of things in themselves is founded on. Now the inner side of a substance’s state can’t consist of place, shape, contact or motion, since all of these are outer relations. So the only inner state we can give to substances is the one by which we ourselves determine our own sense from inside: the state of representations. And so the monads were made. They are meant to be the basic stuff of the whole universe. Their active force consists only in representations, so they are properly active only within themselves.

For the same reason, his principium of how substances can form a community with one another had to be a pre-established harmony.

B 331 It could not be physical influence. Everything is busy only with its inside, that is, with its own representations. So the state of one substance’s representations could not be combined in any effective way with that of another. Some third cause had to flow into all of them together and make their states match one another. This could not be done by occasional help, supplied separately in each single case (systema assistentiae). It had to come from the unity of the idea of one cause valid for all. In that cause they all have to get their existence and their continuing, and their correspondence with each other as well, all under general laws.

Fourth, he made a famous doctrine out of time and space, treating these forms of sensibility as intellectual. That doctrine came from the very same deception of transcendental reflection. If I try to represent the outer relations of things through the understanding alone, I can do it only through a concept of how they act on one another. And if I want to connect one state of a thing with another state of that same thing, that can only be done by the order of grounds and consequences. So for Leibniz, space was a certain order among substances in community, and time was the dynamic succession of their states. Both appear to have something peculiar about them.

B 332 That something is independent of things. He blamed it on the confusion in those concepts. Because of the confusion, what is only a form of dynamic relations is taken for an intuition of its own, existing by itself and coming before the things themselves. In that case space and time were the intelligible form in which things (substances and their states) are connected in themselves. And the things were intelligible substances (substantiae noumena). All the same, he wanted these concepts to be valid for appearances, because he would not grant sensibility an intuition of its own kind. He sought every representation in the understanding, even the empirical representation of objects. The senses were left with only the despised job of muddling and distorting the understanding’s representations.

Suppose we could say something synthetic about things in themselves through pure understanding (though that is impossible). It still couldn’t be stretched to cover appearances, since appearances don’t represent things in themselves. In that case, then, in transcendental reflection, I will always have to compare my concepts under the conditions of sensibility alone. Space and time will then be determinations of appearances, not of things in themselves. What things in themselves may be, I don’t know, and I have no need to.

B 333 A thing can only ever reach me in appearance.

I treat the other concepts of reflection the same way. Matter is substantia phaenomenon. What belongs to it on the inside I look for in every part of the space it fills and in every effect it has, and these, naturally, can only ever be appearances of the outer senses. So nothing I find is absolutely inner. It is all inner only by comparison, and it in turn is made of outer relations. And the absolutely inner side of matter, as pure understanding would define it, is a mere whim too. For matter is not an object for pure understanding at all. The transcendental object, though, which may be the ground of the appearance we call matter, is nothing but a bare something. If someone could tell us what it is, we still wouldn’t understand. We understand only what brings along, in intuition, something matching our words. Suppose people complain, “We can’t see the inner side of things at all,” and mean by this, “We don’t grasp by pure understanding what the things that appear to us may be in themselves.” Then the complaint is quite unfair and unreasonable.

B 334 It demands that we cognize things, and so intuit them, without senses, and that our power of cognition be wholly unlike the human one. It would differ not merely in degree, but also in intuition and kind. We would then be not humans but beings that we can’t even say are possible, let alone describe. Observation and analysis of appearances do reach into the inside of nature, and nobody can say how far that will go over time. The transcendental questions reach beyond nature. We could never answer them, even if all of nature were uncovered for us. We can’t even observe our own mind by any intuition other than inner sense. The secret of where our sensibility comes from lies in the mind. How sensibility relates to an object, and what the transcendental ground of that unity is, surely lie hidden too deeply. Even ourselves we know only by inner sense, and so only as appearance. With a tool so badly suited to inquiry, all we could ever find is more appearances. What we would like to explore is their nonsensible cause.

This critique of inferences drawn from mere acts of reflection is extremely useful because it makes clear that inferences about objects, drawn from merely comparing them in the understanding, are void.

B 335 It also confirms what we mainly stressed: appearances, though they aren’t things in themselves and so don’t figure among the objects of pure understanding, are still the only place where our cognition can have objective reality, that is, where an intuition matches the concepts.

When we reflect in a purely logical way, we only compare our concepts with each other in the understanding. We ask whether both contain the same thing, whether they contradict each other or not, whether the concept holds something inside itself or has it added on, and which of the two counts as given, and which is only a way of thinking about the given one. Now suppose I use these concepts for an object as such, taken transcendentally, without deciding if it’s an object for sensible intuition or for intellectual intuition. Restrictions show up at once (don’t go beyond this concept), and they turn every empirical use of the concepts upside down. What they show is that to represent an object merely as a thing in general is worse than inadequate. Take away the sensible determination and every empirical condition, and the representation conflicts with itself. So we must either abstract from every object (that is what logic does) or, if we assume one, think of it under the conditions of sensible intuition. The intelligible would then call for a quite special intuition.

B 336 We lack any such intuition, and without it the intelligible is nothing for us. On the other hand, appearances can’t be objects in themselves either. If I think merely of things in general, differences in outer relations can’t make for a difference in the things themselves. Such differences presuppose one instead. And if the concept of one thing isn’t inwardly different at all from the concept of another, I am only putting a single thing into different relations. Also, when one mere affirmation (reality) is added to another, the positive grows, and nothing is removed or canceled. So what is real in things in general can’t conflict with itself, and so on.

* * *

The concepts of reflection, as we have shown, exert a certain misleading influence on how the understanding is used. They managed to lure one of the sharpest of all philosophers into building a supposed system of intellectual cognition. Such a system sets out to determine its objects without the senses taking any part. That is exactly why it is so useful to lay bare the deceptive cause of these concepts’ amphiboly, which gave rise to false principles. It lets us fix and secure the understanding’s boundaries reliably.

B 337 We must grant that whatever belongs to a concept universally, or conflicts with it, belongs to or conflicts with every particular thing that falls under the concept (dictum de Omni et Nullo). But it would be absurd to turn this logical principle around to read: what is not contained in a general concept is not contained in the particular concepts under it either. Those are particular concepts exactly because they contain more than the general concept thinks. Yet Leibniz’s whole intellectual system is actually built on that last principle. It collapses with it, and so does all the ambiguity in the use of the understanding that comes from it.

The principle of the indiscernible really rested on this assumption: if the concept of a thing in general shows no certain distinction, then none is to be found in the things themselves. So all things that don’t already differ in their concept (in quality or quantity) are completely one and the same (numero eadem). But the mere concept of a thing leaves out many conditions that an intuition necessarily needs. By a strange hastiness, what was left out is taken for something not to be found anywhere.

B 338 And the thing is allowed nothing except what its concept contains.

Think of a cubic foot of space, wherever and however often you like. The concept is in itself entirely the same each time. Yet two cubic feet in space differ from each other only in where they are (numero diversa). The places are conditions of the intuition that gives us the object of this concept. They aren’t part of the concept, but they are part of sensibility as a whole. Likewise, a thing’s concept contains no conflict as long as nothing negating has been joined to something affirming. Concepts that are merely affirmative, when combined, can’t cancel anything. But sensible intuition is where reality (motion, for example) is given, and it contains conditions that the concept of motion in general leaves out: opposite directions. These make a conflict possible, though not a logical one, in which pure positives produce a zero = 0. So one couldn’t say that all reality agrees with itself just because its concepts show no conflict*. Now think in terms of mere concepts alone.

B 339 In those terms, the inner is the substratum of every relation, that is, of every outer determination. So I can set aside every outer relation, once I leave out all conditions of intuition and hold to the bare concept of a thing in general. Even so, I must still have a concept left of what is no relation at all but only inner determinations. It now seems to follow that every thing (substance) has something in it that is absolutely inner. This inner part comes before all outer determinations, because it first makes them possible. So the substratum would contain no outer relations at all, and would therefore be simple. (Bodily things are always only relations, after all, at least relations of parts outside one another.) And we know no absolutely inner determinations except those of our inner sense. So this substratum would not only be simple. It would also be determined by representations, following the pattern of our inner sense.

B 340 In other words, all things would really be monads: simple beings endowed with representations. All this would be quite right, except for one thing. Only under certain conditions can objects of outer intuition be given to us, and the pure concept leaves those conditions out. Those conditions take in more than just the concept of a thing in general. For we find that something that persists as an appearance in space (impenetrable extension) can hold nothing but relations, nothing absolutely inner, and yet still be the first substratum of all outer perception. By mere concepts, I really can’t think of anything outer without something inner. That’s because concepts of relation presuppose things that are simply given, and can’t exist without them. But intuition holds something that the concept of a thing in general lacks altogether. It supplies the substratum that mere concepts could never make known: a space which, with everything in it, consists of nothing but formal, or even real, relations. So I can’t say: since mere concepts can’t represent a thing without an absolutely inner side, there’s likewise nothing outer in the things themselves that fall under these concepts, or in their intuition, with no absolutely inner ground beneath it. Suppose we have set aside all conditions of intuition.

B 341 Then the mere concept leaves us only the inner in general and the relations of the inner things among themselves, which alone make the outer possible. But this necessity rests purely on abstraction. It doesn’t hold for things when they are given in intuition through determinations that only express relations, with no inner ground beneath them. The reason is that they aren’t things in themselves but merely appearances. Everything we know of matter is relations. (What we call matter’s inner determinations are inner only by comparison.) Among them, though, are some that stand on their own and persist, and through these a determinate object is given to us. If I set these relations aside, there is nothing left for me to think. That doesn’t cancel the concept of a thing as appearance, or the concept of an object in the abstract. What it does cancel is all possibility of an object that mere concepts could determine, that is, a noumenon. It does give one pause to hear that a thing might consist wholly of relations. But a thing like that is a mere appearance, and pure categories can’t think it at all. It consists in nothing more than how something in general stands to the senses. Likewise, if we start from mere concepts, we can think the relations of things in the abstract in no other way.

B 342 It has to be this: one thing is the cause of determinations in another. For that is our concept of the understanding for relations itself. But then we are abstracting from all intuition. One whole way in which the manifold can fix one another’s place falls away, namely the form of sensibility (space), which comes before all empirical causality.

* Suppose someone used the usual way out here and said that at least noumenal realities (realitates noumena) can’t work against one another. Even then one would have to produce an example of such a pure reality, free of the senses. Only that would show whether it stands for anything or for nothing. But an example can come from nowhere except experience, which gives us nothing beyond phaenomena. So the proposition says only that a concept made of affirmations alone has no negation in it. We’ve never doubted that.

Suppose we mean by merely intelligible objects the things that are thought through pure categories, with no schema of sensibility. Then there can be no such things. Our concepts of the understanding can be used on objects only on one condition: our own kind of sensible intuition, which is what gives us objects. Leave that out, and the concepts refer to no object at all. Even if we assumed some other kind of intuition besides this sensible one of ours, our functions of thinking would mean nothing for it. Now suppose instead that we mean objects of a nonsensible intuition. Our categories don’t hold of them, and so we can never have any cognition of them, neither intuition nor concept. In that merely negative sense, noumena must certainly be allowed. They say only that our kind of intuition doesn’t reach all things, but only the objects of our senses.

B 343 Its objective validity is therefore bounded, and there is room left for some other kind of intuition, and so for things as its objects. But then the concept of a noumenon is problematic. It represents a thing that we can’t call possible or impossible. The only intuition we know is our sensible one, and the only concepts we know are the categories, and neither suits an object beyond the senses. So we can’t broaden the field of what our thinking can be about beyond the conditions of our sensibility, in a positive way. We can’t add objects of pure thinking, that is, noumena, to appearances. Such objects have no positive meaning that we could specify. About the categories we have to admit that they alone are not enough to cognize things in themselves. Without the data of sensibility they would be only subjective forms of the unity of the understanding, with no object. Thinking, to be sure, doesn’t in itself come from the senses, and to that extent it isn’t limited by them either. But that doesn’t make it usable on its own, in a pure way, without sensibility joining in, because then it has no object. And one can’t call the noumenon an object of that sort either. For a noumenon is exactly the problematic concept of some object.

B 344 That object is for an intuition and an understanding of a kind quite different from ours, and that kind of understanding is itself a problem. So the concept of a noumenon isn’t the concept of an object. It is a task that comes inevitably with the limiting of our sensibility: might there be objects entirely free of that intuition? This can be answered only vaguely. Sensible intuition doesn’t extend to all things without distinction. So there is room left for more and other objects. They can’t be denied outright. But we have no determinate concept of them (no category fits), so they can’t be asserted either as objects for our understanding.

So the understanding sets a boundary to sensibility without widening its own field. It warns sensibility not to presume to reach things in themselves, but only appearances. In doing so, it thinks of an object in itself. But it thinks it only as a transcendental object, the cause of the appearance (and so not an appearance itself). We can’t think of it as a magnitude, as reality, as substance, and so on (those concepts always need sensible forms in which to determine an object). So it is entirely unknown whether this object is in us or outside us, and whether it would vanish along with sensibility or remain if sensibility were taken away.

B 345 We may call this object a noumenon, since the representation of it isn’t sensible. That’s up to us. But none of our concepts of the understanding can be applied to it. The representation therefore stays empty for us. Its only use is to show where the boundaries of our sensible cognition lie, and to leave a space open that neither possible experience nor pure understanding can fill.

So the critique of this pure understanding forbids us to invent a new field of objects, other than the ones that can come before it as appearances. It won’t let us wander off into intelligible worlds, or even into the concept of one. The mistake that tempts us most plausibly into this, and that is excusable though not justified, is the following. The understanding is used in a transcendental way, against its purpose. Objects, that is, possible intuitions, are made to follow concepts, when concepts ought to follow possible intuitions (the only thing their objective validity rests on). And the reason for that mistake is that apperception, and thinking with it, comes first, ahead of any possible determinate ordering of representations. We think something in general, and in one respect we determine it sensibly.

B 346 Still, we distinguish the general object, represented in the abstract, from this way of intuiting it. That leaves us a way of determining it by thinking alone. It’s a mere logical form with no content. Yet it looks to us like a way for the object to exist in itself (noumenon), when we ignore the intuition that is limited to our senses.

* * *

Before we leave the transcendental analytic, one more thing needs adding. It isn’t very important in itself, but it seems necessary to complete the system. The highest concept that a transcendental philosophy usually starts from is the division into possible and impossible. But any division presupposes a concept that gets divided. So a higher one has to be named. It is the concept of an object in general. We take it problematically, leaving open whether it is something or nothing. The categories are the only concepts that relate to objects in general. So we will decide if an object is something or nothing by following the order and guidance of the categories.

1 B 347 The concepts of all, many and one have an opposite: the concept that cancels everything, that is, none. So the object of a concept with no intuition that could be specified for it is = nothing. That is a concept without an object, like noumena. They can’t be counted among the possibilities, but they needn’t be declared impossible for that reason (ens rationis). The same goes for certain new fundamental powers that people imagine. They are thought without contradiction, but also without any example from experience, so they too aren’t to be counted among the possibilities.

2 Reality is something. Negation is nothing: it is a concept of an object that is lacking, like shadow or cold (nihil privativum).

3 The mere form of intuition, without substance, isn’t an object in itself. It is only the formal condition of an object (as appearance), like pure space and pure time. They are something, as forms of intuiting, but they aren’t themselves objects that get intuited (ens imaginarium).

4 B 348 If a concept contradicts itself, its object is nothing, because the concept is nothing: the impossible. A straight-lined figure with two sides is an example (nihil negativum).

Here is how the table for dividing the concept of nothing would have to be set out (the parallel division of something follows on its own):

Nothing, as

1 An empty concept without an object: ens rationis.

2 An empty object of a concept: nihil privativum.

3 An empty intuition without an object: ens imaginarium.

4 An empty object without a concept: nihil negativum.

We see that a thing of thought (no. 1) differs from a non-thing (no. 4) in that the first must not be counted among the possibilities, because it is a mere invention (though not a contradictory one). The second is the opposite of possibility, since the concept does away with itself.

B 349 Both, however, are empty concepts. By contrast, the nihil privativum (no. 2) and the ens imaginarium (no. 3) are empty data for concepts. Without light given to the senses, we couldn’t represent darkness, and without perceived extended beings, we couldn’t represent space. Negation and the mere form of intuition alike are not objects without something real.