Transcendental Doctrine of Method

B 733 II. Transcendental Doctrine of Method

B 735 If I regard the sum of all cognition of pure and speculative reason as a building of which we at least have the idea within us, I can say that in the Transcendental Doctrine of Elements we have assessed the building materials and determined what sort of building, of what height and solidity, they will suffice for. Admittedly, we found that, although we had in mind a tower reaching to the heavens, the stock of materials sufficed only for a dwelling spacious enough for our business on the plain of experience and just high enough to survey it; but that that bold undertaking had to fail for lack of material, even without reckoning on the confusion of languages that inevitably divided the workers over the plan and scattered them throughout the world, each to build separately according to his own design. We are now concerned less with the materials than with the plan. Warned not to risk a blind design of our choosing that might exceed all our resources, yet unable simply to abandon the establishment of a secure dwelling, we must draw up the estimate for a building in proportion to the stock given us and at the same time suited to our needs.

By the transcendental doctrine of method, then, I understand the determination of the formal conditions of a complete system of pure reason.

B 736 With this aim we shall be concerned with a discipline, a canon, an architectonic, and finally a history of pure reason. In a transcendental respect, we shall accomplish what the schools seek, but poorly achieve, under the name of practical logic with regard to the use of the understanding in general. For general logic is restricted neither to any particular kind of cognition of the understanding (for example, not to pure cognition), nor to particular objects. Without borrowing knowledge from other sciences, it can therefore do no more than present titles for possible methods and technical expressions used for the systematic aspect of various sciences, acquainting the learner in advance with names whose meaning and use he is to learn only later.

Transcendental Doctrine of Method Chapter One The Discipline of Pure Reason

Negative judgments, negative not merely in logical form but also in content, enjoy no particular esteem with humanity’s thirst for knowledge. They are even regarded as envious enemies of our drive for cognition, which ceaselessly strives for expansion.

B 737 An apology is almost needed to win them mere toleration, and still more to win them favor and high regard.

Logically, we can of course express any propositions we please negatively. But with regard to the content of our cognition in general, as to whether a judgment extends or restricts it, negative judgments have the distinctive task of merely warding off error. Hence negative propositions meant to ward off false cognition where no error is possible are admittedly very true, but empty—that is, wholly unsuited to their purpose—and for that very reason often ridiculous. Such is the proposition of that school orator: Alexander could not have conquered countries without an army.

But where the limits of our possible cognition are very narrow, the temptation to judge great, the illusion presented very deceptive, and the harm resulting from error considerable, the negative side of instruction, which serves merely to protect us from errors, has still greater importance than some positive instruction that might increase our cognition. The constraint through which a constant tendency to deviate from certain rules is restricted and finally eradicated is called discipline. It differs from cultivation, which is meant merely to provide a skill without canceling another already present.

B 738 In developing a talent that already has an impulse of its own to express itself, discipline will therefore make a negative* contribution, while cultivation and doctrine make a positive one.

* I am well aware that scholastic usage commonly treats the name discipline as equivalent to instruction. Yet there are so many other cases in which the former expression, as training, is carefully distinguished from the latter, as teaching, and the nature of things itself so requires us to reserve the only suitable expressions for this distinction, that I wish the word might never be allowed any but a negative meaning.

Everyone will readily concede that temperament, and likewise talents that readily indulge in free and unrestricted movement (such as imagination and wit) need discipline in many respects. But that reason, whose proper task is to prescribe discipline to all other endeavors, should itself need such discipline may certainly seem strange. Indeed, reason has so far escaped this humiliation precisely because, given the solemnity and thorough decorum with which it presents itself, no one could easily suspect it of frivolously playing with imaginings instead of concepts and words instead of things.

No critique of reason is needed in its empirical use.

B 739 For its principles are subjected to continuous examination at the touchstone of experience. Nor is one needed in mathematics, where its concepts must immediately be exhibited in concreto in pure intuition, so that everything unfounded and arbitrary becomes apparent at once. But where neither empirical nor pure intuition keeps reason on a visible track—namely, in its transcendental use according to mere concepts—it so urgently needs a discipline to curb its tendency to extend itself beyond the narrow boundaries of possible experience and keep it from excess and error that even the entire philosophy of pure reason is concerned only with this negative benefit. Individual aberrations can be remedied through censure, and their causes through critique. But where, as in pure reason, an entire system of deceptions and delusions is found, well combined among themselves and united under common principles, an entirely distinctive and indeed negative legislation seems required. Under the name of discipline, this would establish, as it were, a system of caution and self-examination drawn from the nature of reason and the objects of its pure use. No false sophistical illusion could withstand it, but would have to betray itself at once despite every ground offered to excuse it.

B 740 It should be carefully noted, however, that in this second main part of the transcendental critique I direct the discipline of pure reason not toward the content but merely toward the method of cognition from pure reason. The former has already been dealt with in the Doctrine of Elements. Yet reason’s use has so much in common whatever object it is applied to, while, insofar as it is to be transcendental, it is at the same time so essentially different from every other use, that without the cautionary negative teaching of a discipline specifically directed to it, we cannot prevent the errors that must necessarily arise from inappropriately following methods otherwise suited to reason, but not here.

Chapter One Section One The Discipline of Pure Reason in Its Dogmatic Use

Mathematics provides the most brilliant example of pure reason successfully extending itself by its own powers without assistance from experience. Examples are contagious, especially for the same faculty, which naturally flatters itself that it will have the same good fortune in other cases as it has enjoyed in one.

B 741 Pure reason therefore hopes to extend itself just as successfully and thoroughly in its transcendental use as it has in its mathematical use, especially if it applies there the same method that has proved so evidently useful here. It therefore matters greatly to us to know whether the method of attaining apodictic certainty called mathematical in the latter science is identical with the method through which the very same certainty is sought in philosophy, where it would have to be called dogmatic.

Philosophical cognition is rational cognition from concepts; mathematical cognition is rational cognition from the construction of concepts. To construct a concept means to exhibit a priori the intuition corresponding to it. Constructing a concept thus requires a nonempirical intuition which, as intuition, is consequently an individual object, yet, as the construction of a concept (a universal representation), must nevertheless express in the representation universal validity for all possible intuitions falling under the same concept. Thus I construct a triangle by exhibiting the object corresponding to this concept either through mere imagination in pure intuition or, following it, on paper in empirical intuition as well. In both cases I do so entirely a priori, without borrowing the model from any experience.

B 742 The individual drawn figure is empirical, yet serves to express the concept without impairing its universality. For in this empirical intuition we attend only to the act of constructing the concept, to which many determinations, such as size, sides, and angles, are entirely indifferent. We thus abstract from these differences, which do not alter the concept of the triangle.

Philosophical cognition thus considers the particular only in the universal; mathematical cognition considers the universal in the particular, indeed even in the individual, yet a priori and through reason. Just as this individual is determined under certain universal conditions of construction, so the object of the concept, to which this individual corresponds only as its schema, must be thought as universally determined.

The essential difference between these two kinds of rational cognition thus lies in this form, not in a difference of their matter or objects. Those who thought to distinguish philosophy from mathematics by saying that the former has only quality as its object and the latter only quantity have mistaken the effect for the cause. The form of mathematical cognition is the cause that it can concern only quanta. For only the concept of magnitudes can be constructed, that is, presented a priori in intuition.

B 743 Qualities, by contrast, can be exhibited only in empirical intuition. Rational cognition of qualities can therefore be possible only through concepts. Thus no one can obtain an intuition corresponding to the concept of reality from anywhere but experience, never from himself a priori and before empirical consciousness of it. We can make a conical shape intuitive without any empirical assistance, merely according to the concept, but the color of this cone must first have been given in some experience. I cannot exhibit the concept of a cause in general in intuition in any way except through an example supplied by experience, and so on. Moreover, philosophy deals with magnitudes just as mathematics does—for example, with totality, infinity, and so on. Mathematics also concerns itself with differences among lines and surfaces as spaces of different quality, and with continuity of extension as a quality of it. But although they have a common object in such cases, the way reason treats it is entirely different in philosophical and mathematical consideration. The former adheres solely to universal concepts. The latter can accomplish nothing with the mere concept, but immediately hastens to intuition, in which it considers the concept in concreto; yet not empirically, but solely in an intuition that it has exhibited a priori, that is, constructed.

B 744 In this intuition, whatever follows from the universal conditions of construction must also hold universally of the object of the constructed concept.

Give a philosopher the concept of a triangle and let him discover in his own way how the sum of its angles may relate to a right angle. He has nothing but the concept of a figure enclosed by three straight lines and, in it, the concept of as many angles. He may reflect on this concept as long as he likes; he will bring nothing new out of it. He can analyze and clarify the concept of a straight line, an angle, or the number three, but cannot arrive at other properties that do not lie in these concepts at all. Now let the geometer take up this question. He immediately begins by constructing a triangle. Knowing that two right angles together equal all the adjacent angles that can be drawn from a point on a straight line, he extends one side of his triangle and obtains two adjacent angles together equal to two right angles. He then divides the exterior of these angles by drawing a line parallel to the opposite side of the triangle, and sees that an exterior adjacent angle arises here that equals an interior one, and so on.

B 745 In this way, through a chain of inferences always guided by intuition, he arrives at a fully evident and at the same time universal solution to the question.

But mathematics constructs not only magnitudes (quanta), as in geometry, but also mere magnitude (quantitatem), as in algebra, where it abstracts entirely from the constitution of the object to be thought according to such a concept of magnitude. It then chooses a certain notation for all constructions of magnitudes in general (numbers, as in addition, subtraction, and so on) and for extracting roots. Having also designated the universal concept of magnitudes according to their different relations, it exhibits in intuition, according to certain universal rules, every operation that is generated and altered through magnitude. Where one magnitude is to be divided by another, it puts together their symbols according to the notation for division, and so on. Through a symbolic construction it thus reaches, just as geometry does through an ostensive or geometrical construction (of the objects themselves), a point that discursive cognition through mere concepts could never reach.

What can account for the very different situations of these two practitioners of reason, one proceeding by concepts, the other by intuitions that he exhibits a priori in accordance with concepts?

B 746 The transcendental fundamental doctrines presented above make the cause clear. We are concerned here not with analytic propositions, which can be produced by mere analysis of concepts (in this the philosopher would undoubtedly have the advantage over his rival), but with synthetic propositions, specifically those to be cognized a priori. For I am not to consider what I actually think in my concept of the triangle (this is nothing more than the mere definition); rather, I am to go beyond it to properties that do not lie in this concept but nevertheless belong to it. This is possible only if I determine my object according to the conditions either of empirical or of pure intuition. The first would yield only an empirical proposition (by measuring its angles) containing no universality, still less necessity, and nothing of that kind is at issue. The second procedure, however, is mathematical—in this case geometrical—construction. Through it, in a pure intuition just as in an empirical one, I add the manifold belonging to the schema of a triangle in general, and thus to its concept; in this way universal synthetic propositions must certainly be constructed.

I would therefore philosophize about the triangle, that is, reflect discursively on it, in vain.

B 747 I would get not the least bit further than its mere definition, from which I would rightly have to begin. There is indeed a transcendental synthesis from concepts alone, which in turn only the philosopher achieves. But it never concerns more than a thing in general and the conditions under which its perception can belong to possible experience. Mathematical problems, however, are not concerned with this or with existence at all, but with the properties of objects in themselves, solely insofar as these are combined with their concept.

In the example cited, we have sought only to clarify the great difference between the discursive use of reason according to concepts and its intuitive use through the construction of concepts. The question now naturally arises: what makes this twofold use of reason necessary, and by what conditions can we recognize whether only the first or also the second has a place?

All our cognition ultimately relates to possible intuitions, for through these alone is an object given. Now a concept a priori (a nonempirical concept) either already contains a pure intuition, in which case it can be constructed, or contains nothing but the synthesis of possible intuitions not given a priori.

B 748 In the latter case we can indeed judge synthetically and a priori through it, but only discursively, according to concepts, never intuitively through construction of the concept.

Of all intuition, only the mere form of appearances, space and time, is given a priori. A concept of these, as quantis, can be exhibited a priori in intuition, that is, constructed, either together with their quality (their shape), or merely their quantity (the mere synthesis of the homogeneous manifold), through number. But the matter of appearances, through which things in space and time are given to us, can be represented only in perception and thus a posteriori. The sole concept that represents this empirical content of appearances a priori is the concept of a thing in general. Synthetic cognition of it a priori can supply nothing beyond the mere rule for synthesizing what perception may give a posteriori, never the intuition of the real object a priori, because this must necessarily be empirical.

Synthetic propositions concerning things in general, whose intuition cannot be given a priori at all, are transcendental. Thus transcendental propositions can never be given through construction of concepts, but only according to concepts a priori. They contain merely the rule according to which a certain synthetic unity of what cannot be represented intuitively a priori (of perceptions) is to be sought empirically.

B 749 But they cannot exhibit a single one of their concepts a priori in any case; they do this only a posteriori, through experience, which first becomes possible according to those synthetic principles.

If we are to judge synthetically about a concept, we must go beyond it, specifically to the intuition in which it is given. For if we remained with what the concept contains, the judgment would be merely analytic, an elucidation of the thought according to what is actually contained in it. But I can pass from the concept to the corresponding pure or empirical intuition, to consider it there in concreto and cognize a priori or a posteriori what belongs to its object. The former is rational and mathematical cognition through construction of the concept; the latter is merely empirical (mechanical) cognition, which can never yield necessary and apodictic propositions. Thus I could analyze my empirical concept of gold without gaining anything beyond the ability to enumerate everything I actually think with this word. My cognition would thereby undergo a logical improvement, but acquire no increase or addition. I instead take the matter bearing this name and make observations of it, which will supply me with various synthetic but empirical propositions.

B 750 I would construct the mathematical concept of a triangle, that is, give it a priori in intuition, and thereby obtain synthetic but rational cognition. But if I am given the transcendental concept of a reality, substance, force, and so on, it designates neither an empirical nor a pure intuition, but only the synthesis of empirical intuitions (which therefore cannot be given a priori). Since the synthesis cannot go out a priori to its corresponding intuition, no determining synthetic proposition can arise from it, but only a principle of the synthesis* of possible empirical intuitions. Thus a transcendental proposition is synthetic rational cognition according to mere concepts, and hence discursive: it first makes possible all synthetic unity of empirical cognition, but gives no intuition a priori.

* Through the concept of cause I do indeed go beyond the empirical concept of an event (where something happens), but not to the intuition that exhibits the concept of cause in concreto. Rather, I go to the conditions of time in general that might be found in experience in conformity with the concept of cause. I therefore proceed merely according to concepts, and cannot proceed through their construction, because the concept is a rule for the synthesis of perceptions, which are not pure intuitions and thus cannot be given a priori.

B 751 There is, then, a twofold use of reason. Despite the universality of its cognition and its production a priori, which both uses share, they proceed very differently. This is because appearance, through which all objects are given to us, has two components: the form of intuition (space and time), which can be cognized and determined entirely a priori; and matter (the physical), or content, which signifies a something found in space and time and thus contains an existence and corresponds to sensation. With regard to the latter, which can never be given determinately except empirically, we can have nothing a priori but indeterminate concepts of the synthesis of possible sensations insofar as they belong to the unity of apperception (in a possible experience). With regard to the former, we can determine our concepts a priori in intuition by producing the objects themselves in space and time through uniform synthesis, considering them merely as quanta. The first is called reason’s use according to concepts, since we can do no more than bring appearances, as regards their real content, under concepts; these appearances can then be determined only empirically, that is, a posteriori (but in conformity with those concepts as rules of an empirical synthesis). The second is reason’s use through construction of concepts.

B 752 Since these already relate to an intuition a priori, they can for that very reason also be given determinately a priori in pure intuition, without any empirical data. To consider everything that exists (a thing in space or time), as to whether and how far it is a quantum or not; whether existence or its absence must be represented in it; how far this something (which fills space or time) is a first substratum or a mere determination; whether its existence bears a relation to something else as cause or effect; and finally whether in its existence it stands isolated or in reciprocal dependence with others; to consider the possibility, actuality, and necessity of this existence, or their opposites—all this belongs to rational cognition from concepts, which is called philosophical. But to determine an intuition a priori in space (shape), to divide time (duration), or merely to cognize the universal character of the synthesis of one and the same thing in time and space, and the resulting magnitude of an intuition in general (number)—this is reason’s work through construction of concepts, and is called mathematical.

Reason’s great success through mathematics quite naturally produces the supposition that, if not reason itself, at least its method will also succeed outside the field of magnitudes.

B 753 For it brings all its concepts to intuitions that it can give a priori, thereby becoming, so to speak, master over nature; pure philosophy, by contrast, fumbles about in nature with discursive concepts a priori, unable to make their reality intuitive a priori and thereby authenticate them. The masters of this art seem to lack neither this confidence in themselves nor the public’s great expectations of their skill, should they once undertake such a task. For since they have scarcely ever philosophized about their mathematics (a difficult undertaking!), the specific difference between the two uses of reason never enters their minds. Familiar rules employed empirically, borrowed from common reason, then serve them as axioms. They care nothing about the possible origin of the concepts of space and time with which they deal (as the only original quantis). Likewise, they seem to regard investigating the origin of pure concepts of the understanding, and thereby the extent of their validity, as useless; they want only to employ them. In all this they are quite right, provided they do not cross their assigned boundary, that of nature. But in this way they pass unnoticed from the field of sensibility onto the uncertain ground of pure and even transcendental concepts, where the ground (instabilis tellus, innabilis unda) permits them neither to stand nor to swim.

B 754 Only fleeting steps can be taken there, of which time preserves not the slightest trace, whereas their course in mathematics makes a highway that even the most distant posterity can confidently follow.

We have made it our duty to determine the boundaries of pure reason in its transcendental use precisely and with certainty. But this kind of endeavor has the peculiarity that, despite the most emphatic and clearest warnings, it still allows itself to be put off by hope before entirely abandoning the plan of passing beyond the boundaries of experience into the enticing regions of the intellectual. We must therefore remove, as it were, the last anchor of a hope rich in fantasy and show that following the mathematical method in this kind of cognition can offer not the slightest advantage, unless it were this: to expose its own weaknesses all the more clearly, namely that geometry and philosophy are two entirely different things, although they join hands in natural science, and hence that the procedure of one can never be imitated by the other.

The thoroughness of mathematics rests on definitions, axioms, and demonstrations. I shall content myself with showing that none of these, in the sense in which the mathematician takes them, can be accomplished or imitated by philosophy.

B 755 I shall show also that the geometer, following his method, produces nothing in philosophy but houses of cards, and that the philosopher, following his, can stir up only chatter in the domain of mathematics, although philosophy consists precisely in knowing one’s boundaries, and even the mathematician, unless nature has already bounded his talent and restricted it to his specialty, cannot reject philosophy’s warnings or set himself above them.

1 On Definitions. To define, as the expression itself indicates, should properly mean only to present originally the complete concept of a thing within its boundaries*. By this requirement, an empirical concept cannot be defined at all, but only explicated. For since in it we have only some marks of a certain kind of sensible object, it is never certain whether, under the word designating the same object, we think more of its marks at one time and fewer at another.

B 756 Thus, in the concept of gold, one person may think, besides its weight, color, and ductility, of its property of not rusting, while another may know nothing of this. We employ certain marks only so long as they suffice for distinguishing; new observations remove some and add others, so the concept never stands within secure boundaries. What purpose would defining such a concept serve, anyway? When discussing water and its properties, for example, we do not linger over what we think with the word water, but proceed to experiments. The word, with the few marks attached to it, is meant to constitute only a designation, not a concept of the thing; the purported definition is thus nothing but a determination of a word. Second, strictly speaking, no concept given a priori can be defined either—for example, substance, cause, right, equity, and so on. For I can never be sure that the clear representation of a concept given (still confusedly) has been completely developed unless I know that it is adequate to the object. But as given, the concept of the object may contain many obscure representations that we pass over in analysis, although we always employ them in application. The completeness of my concept’s analysis is therefore always doubtful.

B 757 It can be made probable only through many fitting examples, never apodictically certain. Instead of definition, I would prefer the expression exposition, which remains cautious and allows the critic to accept it to a certain degree while still having reservations about its completeness. Since neither empirical concepts nor concepts given a priori can be defined, only concepts thought at will remain on which to attempt this feat. In such a case I can always define my concept: I must know what I have intended to think, since I have deliberately made it myself and it was given to me neither by the nature of the understanding nor by experience. But I cannot say that I have thereby defined a true object. For if the concept rests on empirical conditions, as with a marine chronometer, the object and its possibility are not yet given through this freely devised concept. I do not even know from it whether it has an object at all, and my explanation may better be called a declaration (of my project) than a definition of an object. Thus the only concepts left suitable for definition are those containing an arbitrary synthesis that can be constructed a priori; consequently, only mathematics has definitions. For the object it thinks it also exhibits a priori in intuition, and this certainly can contain neither more nor less than the concept.

B 758 For through the definition the concept of the object was given originally, that is, without deriving the definition from anywhere else. German has only the one word Erklärung for exposition, explication, declaration, and definition. We must therefore relax somewhat the strictness of our demand in denying philosophical explanations the honorary name of definition, and shall restrict this entire observation to the following: philosophical definitions arise only as expositions of given concepts, mathematical definitions as constructions of originally made concepts. The former arise only analytically through analysis (whose completeness is not apodictically certain); the latter arise synthetically, and thus make the concept itself, whereas the former merely explain it. From this it follows:

* Completeness means the clarity and sufficiency of the marks; boundaries mean precision, that there are no more marks than belong to the complete concept; originally means that this determination of boundaries is not derived from elsewhere and so does not still need proof, since that would make the supposed definition unfit to stand at the head of all judgments about an object.

a) That in philosophy we must not imitate mathematics by placing the definition first, except perhaps as a mere trial. For since definitions are analyses of given concepts, these concepts precede them, though still confusedly; and incomplete exposition precedes complete exposition. Thus, from some marks drawn from an as yet unfinished analysis, we can infer much before arriving at complete exposition, that is, definition.

B 759 In a word, in philosophy the definition, as measured distinctness, should conclude the work rather than begin it*. In mathematics, by contrast, we have no concept at all before the definition, through which the concept is first given; mathematics must therefore, and always can, begin with it.

* Philosophy teems with faulty definitions, especially those that genuinely contain elements of a definition but not yet all of them. If we could do nothing with a concept before defining it, all philosophizing would fare very poorly. But since we can always make good and secure use of the elements (of the analysis) as far as they reach, even deficient definitions—that is, propositions not yet properly definitions, but otherwise true and thus approximations to them—can be used very profitably. In mathematics a definition belongs ad esse; in philosophy, ad melius esse. Reaching it is desirable, but often very difficult. Jurists are still seeking a definition for their concept of right.

b) Mathematical definitions can never err. For since the concept is first given through the definition, it contains precisely what the definition intends to be thought through it. But although nothing incorrect can occur in its content, there can sometimes, though rarely, be a fault in its form (the wording), namely with regard to precision. Thus the common definition of a circle is that it is a curved line all of whose points are equally distant from a single point (the center).

B 760 This has the fault of unnecessarily introducing the determination curved. For there must be a separate theorem, inferred from the definition and easily proved: every line whose points are all equally distant from a single point is curved (no part of it straight). Analytic definitions, by contrast, can err in many ways, either by introducing marks not actually contained in the concept or by lacking the completeness essential to a definition, since we cannot be so entirely certain of the completeness of our analysis. For this reason, mathematics’ method of definition cannot be imitated in philosophy.

2 On Axioms. These are synthetic principles a priori insofar as they are immediately certain. Now one concept cannot be combined with another synthetically yet immediately, because a third, mediating cognition is needed for us to go beyond a concept. Since philosophy is rational cognition merely according to concepts, no principle deserving the name of an axiom will be found in it. Mathematics, by contrast, is capable of axioms because, through construction of concepts, it can connect the object’s predicates a priori and immediately in its intuition: for example, that three points always lie in a plane.

B 761 A synthetic principle merely from concepts, by contrast, can never be immediately certain. Take the proposition that everything that happens has its cause: here I must look for a third element, namely the condition of temporal determination in an experience, and could not cognize such a principle directly and immediately from the concepts alone. Discursive principles are thus entirely different from intuitive ones, that is, axioms. The former always still require a deduction, with which the latter can entirely dispense. Since the latter are evident for this very reason, something philosophical principles can never claim despite all their certainty, it is infinitely far from true that any synthetic proposition of pure and transcendental reason is as obvious (as people defiantly like to put it) as the proposition that twice two is four. In the Analytic, under the table of principles of the pure understanding, I did indeed mention certain axioms of intuition. But the principle cited there was not itself an axiom; it served only to state the principle of the possibility of axioms in general, and was itself only a principle from concepts. For even the possibility of mathematics must be shown in transcendental philosophy. Philosophy therefore has no axioms and may never simply command acceptance of its principles a priori.

B 762 It must submit to justifying its entitlement to them through a thorough deduction.

3 On Demonstrations. Only an apodictic proof, insofar as it is intuitive, can be called a demonstration. Experience does teach us what exists, but not that it cannot possibly be otherwise. Empirical grounds of proof can therefore yield no apodictic proof. Nor can intuitive certainty, that is, evidence, ever arise from concepts a priori (in discursive cognition), however apodictically certain the judgment may otherwise be. Only mathematics, then, contains demonstrations, because it derives its cognition not from concepts but from their construction, that is, from the intuition that can be given a priori corresponding to the concepts. Even algebra’s procedure with its equations, from which it produces truth together with its proof by reduction, is a construction—not geometrical, but characteristic. In it, concepts, especially those of the relations of magnitudes, are presented in intuition through signs. Even apart from its heuristic aspect, it secures every inference against error by placing each before our eyes. Philosophical cognition, by contrast, must forgo this advantage, since it must always consider the universal in abstracto (through concepts), whereas mathematics can consider the universal in concreto (in the individual intuition), yet through pure representation a priori, in which every false step becomes visible.

B 763 I would therefore prefer to call the former acroamatic (discursive) proofs, because they can be conducted only through words (the object in thought), rather than demonstrations, which, as the expression itself indicates, proceed in intuition of the object.

From all this it follows that it is wholly inappropriate to the nature of philosophy, especially in the field of pure reason, to swagger along dogmatically and adorn itself with the titles and ribbons of mathematics, to whose order it does not belong, although it has every reason to hope for a sisterly union with it. These are vain pretensions that can never succeed. Rather, they must frustrate philosophy’s intention of uncovering the delusions of a reason that mistakes its boundaries and, through sufficient clarification of our concepts, leading speculation’s conceit back to modest but thorough self-cognition. In its transcendental attempts, reason will therefore be unable to look ahead so confidently, as though the path already traveled led straight to its goal. Nor can it rely so boldly on the premises laid down as to make it unnecessary to look back often and attend to whether errors emerge in the progress of its inferences that were overlooked in the principles.

B 764 Such errors would make it necessary either to determine the principles further or to alter them entirely.

I divide all apodictic propositions (whether they be demonstrable or also immediately certain) into dogmata and mathemata. A directly synthetic proposition from concepts is a dogma; a proposition of this kind through construction of concepts is a mathema. Analytic judgments properly teach us no more about the object than the concept we have of it already contains, because they do not extend cognition beyond the concept of the subject but merely elucidate it. They cannot therefore appropriately be called dogmas (a word one might perhaps translate as doctrinal pronouncements). But among the two kinds of synthetic propositions a priori mentioned, only those belonging to philosophical cognition can bear this name according to ordinary usage; we would scarcely call propositions of arithmetic or geometry dogmata. This usage therefore confirms our explanation that only judgments from concepts, not those from construction of concepts, can be called dogmatic.

Now the whole of pure reason in its merely speculative use contains not a single directly synthetic judgment from concepts. For through ideas it is, as we have shown, incapable of any synthetic judgments with objective validity.

B 765 Through concepts of the understanding it does indeed establish secure principles, but not directly from concepts; always only indirectly, through the relation of these concepts to something entirely contingent, namely possible experience. When this (something as an object of possible experiences) is presupposed, the principles are certainly apodictically certain; in themselves, however, they cannot even be cognized (directly) a priori. Thus no one can gain thorough insight into the proposition that everything that happens has its cause from these given concepts alone. It is therefore no dogma, although from another standpoint, namely the sole field of its possible use, experience, it can quite well be proved apodictically. But although it must be proved, it is called a principle, not a theorem, because it has the special property of itself first making possible its ground of proof, experience, in which it must always be presupposed.

If, then, pure reason in its speculative use contains no dogmas even in content, every dogmatic method, whether borrowed from the mathematician or intended as a distinctive manner of its own, is intrinsically inappropriate. For it merely conceals faults and errors and deceives philosophy, whose true aim is to let us see every step of reason in the clearest light. Nevertheless, the method can always be systematic.

B 766 For our reason (subjectively) is itself a system; but in its pure use through mere concepts it is only a system of inquiry according to principles of unity, for which experience alone can supply the material. Nothing can be said here about the distinctive method of a transcendental philosophy, since we are concerned only with a critique of our resources: whether we can build at all, and how high we may raise our building from the material we have (the pure concepts a priori).

Chapter One Section Two The Discipline of Pure Reason with Regard to Its Polemical Use

Reason must submit to critique in all its undertakings and cannot impair critique’s freedom by any prohibition without harming itself and drawing an unfavorable suspicion upon itself. Nothing is so important in its usefulness, nothing so sacred, that it may withdraw from this scrutinizing, inspecting examination, which respects no person. The very existence of reason rests on this freedom. Reason has no dictatorial authority, and its verdict is always nothing but the agreement of free citizens.

B 767 Each of them must be able to express his reservations, even his veto, without restraint.

But although reason can never refuse critique, it does not always have grounds to fear it. Pure reason in its dogmatic (not mathematical) use, however, is not so conscious of having observed its highest laws most exactly that it would not have to appear, timidly and with complete abandonment of every assumed dogmatic authority, before the critical eye of a higher, judging reason.

The situation is quite different when it faces not the judge’s censure but the claims of a fellow citizen and is merely to defend itself against them. For since these claims seek to be just as dogmatic in denial as the others in affirmation, a justification kat’ anthropon takes place, securing against every encroachment and providing a titled possession that need fear no foreign pretensions, although it cannot itself be sufficiently proved kat’ aletheian.

By the polemical use of pure reason I understand the defense of its propositions against dogmatic denials of them. What matters here is not whether its assertions might themselves be false, but only that no one can ever assert their opposite with apodictic certainty (indeed even merely with greater illusion).

B 768 For then our possession does not depend on another’s grace: we have a title to it before us, though not a sufficient one, and it is entirely certain that no one can ever prove this possession illegitimate.

There is something troubling and dispiriting in the thought that there should be an antithetic of pure reason at all, and that this highest court of all disputes should fall into conflict with itself. Above, we did indeed face such an apparent antithetic. But it proved to rest on a misunderstanding: following a common prejudice, people took appearances for things in themselves and then demanded an absolute completeness of their synthesis in one way or another (which was, however, equally impossible in either way), which cannot be expected of appearances at all. There was therefore no actual contradiction of reason with itself in the propositions that the series of appearances given in themselves has an absolutely first beginning, and that this series is absolutely and in itself without any beginning. Both propositions coexist quite well, because appearances, in respect of their existence (as appearances), are in themselves nothing at all—that is, something contradictory—and assuming them as such must naturally entail contradictory consequences.

B 769 But such a misunderstanding cannot be invoked to settle reason’s dispute if, for example, it is asserted theistically that there is a highest being and atheistically that there is no highest being; or, in psychology, that everything that thinks possesses absolute enduring unity and is thus distinct from every transitory material unity, while another opposes this by saying that the soul is not an immaterial unity and cannot be exempted from transience. For here the object of the question is free of anything foreign that contradicts its nature, and the understanding deals only with things in themselves, not appearances. There would therefore certainly be a true conflict here if only pure reason on the negative side had anything to say approaching a ground for an assertion. As for critique of the dogmatic affirmer’s grounds of proof, we may readily concede it without thereby surrendering these propositions, which at least have reason’s interest on their side, something to which the opponent cannot appeal at all.

I do not share the opinion so often expressed by excellent and reflective men (for example, Sulzer) when they felt the weakness of previous proofs: that we may hope one day to discover evident demonstrations of the two cardinal propositions of our pure reason, “There is a God” and “There is a future life.”

B 770 Rather, I am certain this will never happen. For where is reason to obtain grounds for such synthetic assertions, which do not relate to objects of experience and their inner possibility? But it is also apodictically certain that no human being will ever appear who can assert the opposite with the slightest illusion, still less dogmatically. Since he could establish this only through pure reason, he would have to undertake to prove that a highest being, and the thinking subject in us as a pure intelligence, are impossible. But where is he to obtain the knowledge entitling him to judge so synthetically about things beyond all possible experience? We can therefore be entirely unconcerned that anyone will ever prove the opposite to us. For that very reason, we need not devise scholastic proofs, but can always accept those propositions that accord quite well with our reason’s speculative interest in its empirical use and are, moreover, the only means of uniting it with its practical interest. For the opponent (who must here be considered not merely as a critic) we have our non liquet ready, which must unfailingly confound him. We do not refuse its being turned back upon ourselves.

B 771 For we always have in reserve reason’s subjective maxim, which the opponent necessarily lacks, and under whose protection we can regard all his blows at the air calmly and indifferently.

In this way there is properly no antithetic of pure reason at all. Its only battlefield would have to be sought in the field of pure theology and psychology; but this ground supports no combatant in full armor, with weapons to be feared. He can appear only with mockery or boasting, which can be laughed at as child’s play. This is a comforting observation that restores reason’s courage. For what else could it rely on if it, whose sole vocation is to settle all errors, were internally torn apart, unable to hope for peace and quiet possession?

Everything nature itself arranges serves some good purpose. Even poisons serve to overcome other poisons generated in our own fluids and therefore must not be absent from a complete collection of remedies (dispensary). The objections to the persuasions and conceit of our merely speculative reason are themselves assigned to us by the nature of that reason, and must therefore have a good vocation and purpose that should not be disregarded. Why has providence placed some objects, although bound up with our highest interest, so high?

B 772 Hardly more than an indistinct and self-doubted perception of them is granted us, which stimulates searching glances more than it satisfies them. Whether it is useful to venture bold determinations with regard to such prospects is at least doubtful, perhaps even harmful. But it is always and beyond doubt useful to set both inquiring and examining reason in complete freedom, so that it can attend unhindered to its own interest. This is furthered just as much by reason’s limiting its insights as by extending them, and always suffers when foreign hands interfere to direct it, contrary to its natural course, toward imposed aims.

Let your opponent, then, speak only reason, and combat him only with the weapons of reason. Otherwise, have no anxiety for the good cause (the practical interest), for it never enters the play of a merely speculative dispute. Such a dispute then reveals only a certain antinomy of reason which, since it rests on reason’s nature, must necessarily be heard and examined. It cultivates reason by considering its object from two sides, and corrects its judgment by restricting it. What becomes disputed here is not the matter but the tone.

B 773 For enough remains to let you speak the language of firm faith, justified before the most searching reason, even if you have had to abandon the language of knowledge.

If one were to ask the coolheaded David Hume, formed precisely for balance of judgment, “What moved you, through laboriously devised doubts, to undermine the conviction, so comforting and useful to humanity, that rational insight suffices to assert and form a determinate concept of a highest being?” he would answer, “Nothing but the intention of advancing reason’s self-cognition, and at the same time a certain indignation at the constraint people want to impose on reason, boasting about it while preventing it from frankly admitting the weaknesses that become apparent when it examines itself.” If, by contrast, you ask Priestley, devoted solely to principles of reason’s empirical use and averse to all transcendent speculation, what motives he had for tearing down freedom and immortality of our soul (his hope of a future life being only the expectation of a miracle of resurrection), two such fundamental pillars of all religion, when he is himself a pious and zealous teacher of religion, he could give no other answer than, “The interest of reason, which loses when people try to exempt certain objects from the laws of material nature, the only laws we can know and determine precisely.”

B 774 It would seem unfair to denounce the latter, who knows how to reconcile his paradoxical assertion with a religious aim, and to hurt a well-intentioned man because he cannot find his way once he has strayed from the field of natural science. But this favor must equally benefit Hume, no less well disposed and irreproachable in moral character, who cannot abandon his abstract speculation because he rightly holds that its object lies entirely outside the boundaries of natural science, in the field of pure ideas.

What, then, is to be done here, especially with regard to the danger that seems to threaten the common good? Nothing is more natural or fair than the decision you must make. Just let these people proceed. If they display talent, if they offer deep and new inquiry—in a word, if only they display reason—reason always gains. If you resort to means other than those of unconstrained reason, if you cry high treason and summon the public, which understands nothing of such subtle investigations, as though to put out a fire, you make yourselves ridiculous. For the question is not at all what in this is advantageous or harmful to the common good, but only how far reason can get in speculation that abstracts from every interest.

B 775 It is also a question whether we can count on this speculation at all or should rather abandon it entirely in favor of the practical. Instead of striking in with the sword, calmly watch this contest from the secure seat of critique. It must prove laborious for the combatants, entertaining for you, and, with an outcome certain to be bloodless, fruitful for your insights. For it is very absurd to expect enlightenment from reason while prescribing in advance the side on which it must necessarily come down. Moreover, reason is already so well restrained and kept within limits by reason itself that you have no need to call out patrols to offer civil resistance to the party whose feared superiority seems dangerous to you. In this dialectic there is no victory about which you have cause for concern.

Reason also greatly needs such a dispute, and one could wish it had been conducted earlier and with unrestricted public permission. A mature critique would then have come about all the sooner; on its appearance all these quarrels must fall away of themselves, as the disputants learn to recognize the delusion and prejudices that divided them.

There is a certain impurity in human nature.

B 776 It must ultimately, like everything coming from nature, contain a predisposition toward good ends: a tendency to conceal one’s true sentiments and display certain assumed ones considered good and praiseworthy. Through this tendency both to conceal themselves and to assume an advantageous illusion, human beings have certainly not merely civilized themselves but gradually, to a degree, moralized themselves as well. For no one could see through the veneer of propriety, respectability, and modesty, and thus each found a school for his own improvement in the supposedly genuine examples of goodness he saw around him. But this predisposition to present oneself as better than one is and express sentiments one does not have serves only provisionally, as it were, to bring humanity out of its uncultivated state and initially make it assume at least the manner of the good it knows. Later, once genuine principles have developed and become part of one’s way of thinking, that falsity must gradually be vigorously combated; otherwise it corrupts the heart and prevents good sentiments from growing under the rampant weed of fair illusion.

I am sorry to perceive this same impurity, dissimulation, and hypocrisy even in expressions of speculative thought, where people have far fewer obstacles to declaring their thoughts openly and frankly, as they rightly should, and no advantage at all in concealment.

B 777 For what can be more harmful to insight than communicating even mere thoughts to one another in falsified form, concealing doubts we feel about our own assertions, or giving grounds of proof that do not satisfy us ourselves a veneer of evidence? So long, however, as private vanity alone instigates these secret intrigues (which is commonly the case in speculative judgments that have no particular interest and are not readily capable of apodictic certainty), the vanity of others opposes it with public approval. Matters finally arrive where the purest disposition and sincerity would have brought them, though much earlier. But where the public believes that subtle reasoners intend nothing less than to shake the foundations of public welfare, it seems not only prudent but permissible and even praiseworthy to aid the good cause with specious grounds rather than grant its supposed opponents even the advantage of moderating our tone to that of a merely practical conviction and forcing us to admit the lack of speculative and apodictic certainty. Yet I should think that nothing in the world could be less compatible with defending a good cause than cunning, dissimulation, and deceit.

B 778 That everything must proceed honestly in weighing the rational grounds of mere speculation is surely the least one can demand. If we could securely count on even this little, speculative reason’s dispute over the important questions of God, immortality (of the soul), and freedom would either have been settled long ago or would very soon be brought to an end. As things stand, purity of disposition often varies inversely with the goodness of the cause itself, which perhaps has more sincere and upright opponents than defenders.

I therefore presuppose readers who do not want a just cause defended unjustly. For them it is now settled that, according to our principles of critique, if we consider not what happens but what rightly should happen, there must properly be no polemic of pure reason at all. For how can two people dispute about a thing whose reality neither can exhibit in an actual or even possible experience, brooding over its idea alone in order to bring out of it something more than an idea, namely the actuality of the object itself? By what means will they emerge from the dispute, when neither can directly make his own case comprehensible and certain, but can only attack and refute his opponent’s?

B 779 For this is the fate of all assertions of pure reason: they go beyond the conditions of all possible experience, outside which no evidence of truth can be found anywhere, yet they must employ laws of the understanding intended solely for empirical use, without which not a step in synthetic thinking can be taken. They therefore always expose weaknesses to the opponent, and each can exploit the other’s weakness.

The critique of pure reason can be regarded as the true court of all reason’s disputes; for it is not itself involved in these disputes, which concern objects immediately, but is appointed to determine and judge reason’s rights in general according to the principles of its original institution.

Without it, reason is, as it were, in a state of nature and can assert or secure its claims and assertions only through war. Critique, by contrast, takes all its decisions from the fundamental rules of its own institution, whose authority no one can doubt. It provides us with the peace of a lawful condition in which we are to conduct our disputes only through legal proceedings. What ends quarrels in the first condition is a victory of which both sides boast, usually followed by only an insecure peace established by the authority that intervenes.

B 780 In the second, it is a judgment which, because it strikes here at the very source of the disputes, must secure an eternal peace. The endless disputes of a merely dogmatic reason also finally compel us to seek peace in some critique of reason itself and in legislation founded upon it, just as Hobbes maintains that the state of nature is a state of injustice and violence, which we must necessarily leave in order to submit to the lawful constraint that alone restricts our freedom so that it can coexist with everyone else’s freedom and thereby with the common good.

This freedom also includes submitting one’s thoughts, one’s doubts that one cannot oneself resolve, to public judgment, without being denounced on that account as a restless and dangerous citizen. This already lies in the original right of human reason, which recognizes no other judge than universal human reason itself, in which everyone has a voice. Since every improvement of which our condition is capable must come from this, such a right is sacred and must not be curtailed. It is also very unwise to denounce as dangerous certain daring assertions or presumptuous attacks on assertions that already have the assent of the largest and best part of the public: for this gives them an importance they should not have at all.

B 781 When I hear that an uncommon mind is supposed to have demonstrated away the freedom of the human will, the hope of a future life, and the existence of God, I am eager to read the book, for I expect his talent to advance my insights. I already know beforehand with complete certainty that he will have accomplished none of this—not because I believe myself already in possession of invincible proofs of these important propositions, but because the transcendental critique, which revealed to me the whole stock of our pure reason, has fully convinced me that, just as reason is wholly inadequate for affirmative assertions in this field, it will know just as little, and still less, for making any negative assertion about these questions. For where will the supposed freethinker obtain his knowledge that, for example, there is no highest being? This proposition lies outside the field of possible experience, and therefore also outside the boundaries of all human insight. I would not read the dogmatic defender of the good cause against this enemy at all, because I know beforehand that he will attack the other’s specious grounds only to gain admission for his own. Besides, an everyday illusion provides less material for new observations than an unfamiliar and ingeniously devised one.

B 782 The opponent of religion, dogmatic in his own way as well, would by contrast provide my critique with welcome occupation and an opportunity to correct its principles further, without there being the least to fear on his account.

But should not the young, entrusted to academic instruction, at least be warned against such writings and kept from early acquaintance with such dangerous propositions before their power of judgment has matured—or rather, before the doctrine one wants to establish in them has taken firm root—so that they can vigorously resist every persuasion to the contrary, wherever it may come from?

If dogmatic procedure had to remain in matters of pure reason, and opponents had to be dealt with properly polemically—that is, by entering combat and arming ourselves with grounds of proof for opposing assertions—then nothing would admittedly be more advisable for the moment, but at the same time more futile and fruitless in the long run, than placing the reason of the young under guardianship for a time and protecting it at least that long from seduction. But if curiosity or the fashionable tone of the age later puts such writings into their hands, will that youthful persuasion still hold firm? Someone equipped only with dogmatic weapons to withstand his opponent’s attacks is unable to unfold the hidden dialectic that lies no less in his own breast than in his adversary’s.

B 783 He sees specious grounds with the advantage of novelty confronting specious grounds that no longer possess it, but instead arouse suspicion that youthful credulity has been abused. He believes he can give no better proof of having outgrown childhood discipline than by disregarding those well-meant warnings. Habituated to dogmatism, he drinks in long drafts the poison that dogmatically corrupts his principles.

Academic instruction must do precisely the opposite of what is advised here, though only on the presupposition of thorough instruction in the critique of pure reason. For, to put its principles into practice as early as possible and show their sufficiency against the greatest dialectical illusion, it is absolutely necessary to direct the attacks so terrifying to the dogmatist against his still weak but critically enlightened reason, and let him try examining the opponent’s unfounded assertions one by one against those principles. It cannot be at all difficult for him to dissolve them into mere vapor. He thus feels his own strength early on, fully securing himself against such harmful delusions, which must finally lose all illusion for him.

B 784 Although the very same blows that strike down the enemy’s building must also be equally destructive to his own speculative structure, should he intend to erect one, he is entirely unconcerned. He has no need to live in it, but still has before him a prospect into the practical field, where he has grounds to hope for firmer soil on which to erect his rational and beneficial system.

Thus there is no proper polemic in the field of pure reason. Both parties are fighting the air, grappling with their own shadows, for they go beyond nature, where there is nothing their dogmatic grasp can seize and hold. They can fight at their leisure: the shadows they hew apart grow together again in a moment, like the heroes in Valhalla, to amuse themselves anew in bloodless battles.

But there is also no permissible skeptical use of pure reason that could be called the principle of neutrality in all its disputes. Inciting reason against itself, supplying it with weapons on both sides, and then calmly and mockingly watching its fiercest combat does not look well from a dogmatic standpoint; it has the appearance of a malicious disposition delighting in harm.

B 785 Yet when we consider the invincible delusion and boasting of reasoners who will not let any critique moderate them, there is really no other recourse than to oppose boasting on one side with boasting on the other, resting on precisely the same rights, so that resistance from an enemy may at least startle reason into some doubt about its pretensions and make it listen to critique. But to leave matters entirely at these doubts and make it one’s aim to recommend conviction and confession of one’s ignorance not merely as a remedy for dogmatic conceit but also as the way of ending reason’s conflict with itself is an entirely futile plan. It cannot possibly bring reason to rest, but is at most a means of awakening it from its sweet dogmatic dream to examine its condition more carefully. Since this skeptical manner of extricating oneself from a vexing affair of reason seems, as it were, the shortcut to enduring philosophical repose—or at least the highway readily taken by those who think to acquire philosophical standing through a mocking contempt for all inquiries of this kind—I find it necessary to present this way of thinking in its proper light.

B 786 On the Impossibility of Skeptically Satisfying Pure Reason in Conflict with Itself

Consciousness of my ignorance (unless this ignorance is also cognized as necessary), far from ending my inquiries, is rather what properly awakens them. All ignorance concerns either things or the determination and boundaries of my cognition. If ignorance is contingent, it must impel me in the first case to investigate things (objects) dogmatically, and in the second to investigate the boundaries of my possible cognition critically. But that my ignorance is absolutely necessary, and thus releases me from all further inquiry, cannot be established empirically through observation, but only critically, by exploring the first sources of our cognition. Thus the determination of reason’s boundaries can occur only on grounds a priori. Its restriction, however, which is a cognition, though only indeterminate, of an ignorance never wholly removable, can also be cognized a posteriori, through what always remains for us to know despite all our knowledge. The former cognition of one’s ignorance, possible only through critique of reason itself, is therefore science; the latter is nothing but perception, from which we cannot say how far an inference may reach.

B 787 If I represent the earth’s surface (in accordance with sensible illusion) as a plate, I cannot know how far it extends. But experience teaches me that wherever I go I always see around me a space into which I could proceed further. I thus cognize limits of my actual geographical knowledge at any given time, but not the boundaries of all possible geography. But if I have come so far as to know that the earth is a sphere and its surface spherical, then even from a small part of it, such as the size of one degree, I can cognize the diameter and, through it, the earth’s complete boundary, that is, its surface, determinately and according to principles a priori. Although I am ignorant of the objects this surface may contain, I am not ignorant of the extent containing them, its magnitude and limits.

The sum of all possible objects of our cognition seems to us a level surface with its apparent horizon: that which encompasses its entire extent and which we have called the concept of reason of unconditioned totality. Reaching this horizon empirically is impossible, and every attempt to determine it a priori according to a certain principle has been futile.

B 788 Yet all the questions of our pure reason concern what may lie outside this horizon, or perhaps on its boundary line.

The celebrated David Hume was one of these geographers of human reason. He thought he had adequately disposed of all those questions by relegating them beyond reason’s horizon, although he could not determine that horizon. He dwelt chiefly on the principle of causality and quite rightly observed that its truth (indeed not even the objective validity of the concept of an efficient cause in general) is not grounded on any insight, that is, cognition a priori, and that hence the entire authority of this law consists not in the least in its necessity, but in its mere general usefulness in the course of experience and a resulting subjective necessity, which he calls habit. From our reason’s inability to make a use of this principle extending beyond all experience, he inferred the nullity of all reason’s pretensions to go beyond the empirical in general.

Such a procedure of submitting the facts of reason to examination and, where appropriate, to blame may be called the censure of reason. It is beyond doubt that this censure inevitably leads to doubt concerning every transcendent use of principles.

B 789 But this is only the second step, far from completing the work. The first step in matters of pure reason, marking its childhood, is dogmatic. The second, mentioned above, is skeptical and testifies to the caution of a power of judgment made wise by experience. But a third step is still needed, belonging only to a mature and fully developed power of judgment grounded on firm maxims whose universality has been established: to assess not the facts of reason but reason itself in its entire capacity and aptitude for pure cognitions a priori. This is not the censure but the critique of reason. Through it, not merely reason’s limits but its determinate boundaries, not merely ignorance on one point or another but ignorance regarding all possible questions of a certain kind, is not merely conjectured but proved from principles. Skepticism is thus a resting place for human reason, where it can reflect on its dogmatic journey and sketch the region in which it finds itself, so as to choose its further path with greater security; but it is not a dwelling for permanent residence. For such a dwelling can be found only in complete certainty, whether of cognition of the objects themselves or of the boundaries.

B 790 Within these boundaries all our cognition of objects is enclosed.

Our reason is not a plain extending indefinitely far whose limits we cognize only in a general way. It must rather be compared with a sphere whose radius can be found from the curvature of an arc on its surface (the nature of synthetic propositions a priori), and from which its content and boundary can then also be determined with certainty. Outside this sphere (field of experience) nothing is an object for reason. Even questions about such supposed objects concern only subjective principles for thoroughly determining the relations that can occur among concepts of the understanding within this sphere.

We actually possess synthetic cognition a priori, as the principles of the understanding that anticipate experience demonstrate. If someone cannot comprehend its possibility at all, he may initially doubt whether we actually possess it a priori. But he cannot yet declare that it is impossible through the understanding’s powers alone, or that every step reason takes under its guidance is null. He can only say: if we understood its origin and authenticity, we could determine our reason’s extent and boundaries; until this is done, however, all reason’s assertions are blindly ventured.

B 791 In this way a thoroughgoing doubt concerning all dogmatic philosophy that proceeds without critique of reason itself would be quite well founded. Yet reason could not on that account be denied all such progress if it were prepared and secured by a better foundation. For all the concepts, indeed all the questions, pure reason presents to us lie not in experience but again only in reason itself; they must therefore be capable of solution and of being understood as valid or null. Nor are we entitled to dismiss these problems on the pretext of our inability and refuse further inquiry into them, as though their solution really lay in the nature of things, since reason alone has generated these ideas within itself and is therefore bound to account for their validity or dialectical illusion.

All skeptical polemic is properly directed only against the dogmatist who solemnly continues on his way without any mistrust of his original objective principles, that is, without critique. It is meant only to unsettle his plan and bring him to self-cognition. In itself it settles absolutely nothing about what we know and what, on the other hand, we cannot know.

B 792 All reason’s failed dogmatic attempts are facts that it is always useful to submit to censure. But this can decide nothing about reason’s expectations of hoping for and claiming a better outcome from its future efforts. Mere censure can therefore never end the dispute over the rights of human reason.

Since Hume is perhaps the most ingenious of all skeptics, and indisputably the foremost with regard to the influence skeptical procedure can exert in awakening a thorough examination of reason, it is well worth the effort to present the course of his inferences and the errors of so discerning and estimable a man, which nevertheless began on the trail of truth, as far as suits my purpose.

Hume perhaps had in mind, though he never fully developed it, that in judgments of a certain kind we go beyond our concept of the object. I have called judgments of this kind synthetic. How I can go beyond my existing concept through experience presents no difficulty. Experience is itself a synthesis of perceptions that augments the concept I have through one perception by adding others. But we also believe we can go beyond our concept a priori and extend our cognition.

B 793 We attempt this either through the pure understanding, regarding what can at least be an object of experience, or even through pure reason, regarding properties of things or even the existence of objects that can never occur in experience. Our skeptic did not distinguish these two kinds of judgment as he should have done. He simply regarded this self-augmentation of concepts—this self-generation, so to speak, of our understanding (together with reason), without impregnation by experience—as impossible. He consequently regarded all its supposed principles a priori as imaginary, and found them to be nothing but a habit arising from experience and its laws: merely empirical, that is, in themselves contingent, rules to which we ascribe a supposed necessity and universality. To support this surprising proposition, he appealed to the universally acknowledged principle of the relation of cause to effect. For since no faculty of understanding can lead us from the concept of one thing to the existence of something else universally and necessarily given through it, he believed he could infer that without experience we have nothing that could augment our concept and entitle us to such a judgment that extends itself a priori.

B 794 That the sunlight illuminating wax also melts it while it hardens clay, no understanding could guess from concepts we previously had of these things, still less infer according to a law; experience alone could teach us such a law. In transcendental logic, however, we have seen that, although we can never go immediately beyond the content of the concept given to us, we can nevertheless cognize the law of its connection with other things entirely a priori, though in relation to a third, namely possible experience, and thus still a priori. If wax previously solid melts, I can therefore cognize a priori that something must have preceded (for example, the sun’s heat), upon which this followed according to a constant law; yet without experience I could not cognize either the cause from the effect or the effect from the cause determinately, a priori and without instruction from experience. He thus falsely inferred from the contingency of our determination according to the law the contingency of the law itself. He confused going beyond the concept of a thing to possible experience (which occurs a priori and constitutes its objective reality) with the synthesis of objects of actual experience, which is admittedly always empirical. He thereby turned a principle of affinity, seated in the understanding and expressing necessary connection, into a rule of association.

B 795 This rule is found only in the reproductive imagination, which can represent only contingent and by no means objective combinations.

The skeptical errors of this otherwise extraordinarily acute man arose chiefly from a deficiency he shared with all dogmatists: he did not systematically survey all kinds of the understanding’s synthesis a priori. Had he done so, he would have found, to mention no others here, the principle of persistence, for example, to be one that anticipates experience just as much as the principle of causality. This would also have enabled him to trace determinate boundaries for the understanding that extends itself a priori and for pure reason. But he merely restricts our understanding without bounding it, producing a general mistrust but no determinate knowledge of the ignorance unavoidable for us. He subjects some principles of the understanding to censure without placing the understanding’s entire capacity on the testing scales of critique. In denying it what it actually cannot accomplish, he goes further and disputes every capacity it has to extend itself a priori, although he has not assessed that entire capacity. Thus he suffers what always overthrows skepticism: he himself is doubted.

B 796 For his objections rest only on contingent facts, not on principles that could bring about a necessary renunciation of the right to dogmatic assertions.

Since he also recognizes no distinction between the well-founded claims of the understanding and the dialectical pretensions of reason, against which his attacks are principally directed, reason feels that the space for its expansion has not been closed. Its own characteristic soaring has not been disturbed in the least, only hindered, and, despite being pinched here and there, it can never be entirely dissuaded from its attempts. For against attacks we arm ourselves in defense and insist all the more stubbornly on enforcing our demands. But a complete assessment of our entire capacity, and the resulting conviction of the certainty of a small possession alongside the futility of higher claims, ends every dispute and induces us to be peacefully content with a restricted but undisputed property.

Against the uncritical dogmatist, who has not measured the sphere of his understanding and therefore has not determined from principles the boundaries of his possible cognition, who thus does not already know beforehand how much he can do but thinks to discover it through mere attempts, these skeptical attacks are not only dangerous but ruinous.

B 797 For if he is caught out in a single assertion that he cannot justify, yet whose illusion he also cannot unfold from principles, suspicion falls on all his assertions, however persuasive they may otherwise be.

Thus the skeptic is the dogmatic reasoner’s disciplinarian, leading him toward a sound critique of understanding and reason itself. Once he has reached this, he need fear no further challenge. For he then distinguishes his possession from what lies entirely outside it, to which he makes no claims and over which he cannot be drawn into disputes. Skeptical procedure is thus not in itself satisfactory for reason’s questions, but it is preparatory: it awakens reason’s caution and points to thoroughgoing means of securing it in its rightful possessions.

Chapter One Section Three The Discipline of Pure Reason with Regard to Hypotheses

Since through critique of our reason we finally know this much—that in its pure and speculative use we can in fact know nothing at all—should it not open a still wider field for hypotheses, since we are at least permitted to invent and opine, even if not to assert?

B 798 If imagination is not to indulge in fantasy but to invent under reason’s strict supervision, something must always first be completely certain, not invented or mere opinion: the possibility of the object itself. We may then indeed take refuge in opinion regarding its actuality. But if this opinion is not to be unfounded, it must be connected as a ground of explanation with what is actually given and thus certain; it is then called a hypothesis.

Now we cannot form the slightest concept a priori of the possibility of dynamical connection, and the category of the pure understanding serves not to devise such connection but only to understand it where it is encountered in experience. We therefore cannot originally invent a single object with a new constitution that cannot be indicated empirically, in conformity with these categories, and lay it down as the basis of a permissible hypothesis. That would mean supplying reason with empty fantasies instead of concepts of things. Thus we are not permitted to devise new original forces: for example, an understanding capable of intuiting its object without senses; an attractive force without any contact; or a new kind of substance, such as one present in space without impenetrability.

B 799 Nor, consequently, may we devise a community of substances different from any supplied by experience, a presence anywhere but in space, or a duration anywhere but in time. In a word, our reason can use only the conditions of possible experience as conditions of the possibility of things. It cannot, entirely independently of these, create such conditions for itself, as it were, because such concepts, though without contradiction, would nevertheless also be without an object.

As stated, concepts of reason are mere ideas and admittedly have no object in any experience. But they do not therefore designate invented objects assumed at the same time to be possible. They are thought merely problematically, so that, in relation to them (as heuristic fictions), regulative principles of the systematic use of the understanding in the field of experience may be grounded. If we depart from this, they are mere thought-entities whose possibility cannot be proved and which therefore cannot be laid down as the ground of the explanation of actual appearances through a hypothesis. To think the soul as simple is quite permitted, in order, according to this idea, to make a complete and necessary unity of all powers of the mind the principle for judging its inner appearances, even though we cannot grasp that unity in concreto.

B 800 But assuming the soul as a simple substance (a transcendent concept) would be a proposition not merely unprovable (as many physical hypotheses are) but also entirely arbitrary and blindly ventured. For the simple cannot occur in any experience whatever, and if substance here means the enduring object of sensible intuition, the possibility of a simple appearance cannot be understood at all. Neither merely intelligible beings nor merely intelligible properties of things in the sensible world can be assumed as opinion with any well-founded entitlement of reason; although (since we have no concepts of their possibility or impossibility) neither can they be dogmatically denied through any supposedly superior insight.

To explain given appearances, we can adduce only things and grounds of explanation connected with what is given according to already known laws of appearances. A transcendental hypothesis using a mere idea of reason to explain natural things would therefore be no explanation at all: what is not sufficiently understood from known empirical principles would be explained through something of which we understand nothing. The principle of such a hypothesis would also serve properly only to satisfy reason, not to advance the use of the understanding with regard to objects. Order and purposiveness in nature must in turn be explained from natural grounds and according to natural laws.

B 801 Here even the wildest hypotheses, provided they are physical, are more tolerable than a hyperphysical one, that is, an appeal to a divine author presupposed for this purpose. For that would be a principle of lazy reason (ignava ratio): to bypass at once all the causes whose objective reality, at least as to their possibility, we can still come to know through continued experience, in order to rest in a mere idea very comfortable for reason. As for the absolute totality of grounds of explanation in their series, this can create no obstacle regarding objects in the world, because, since they are nothing but appearances, we can never hope to find in them anything complete in the synthesis of the series of conditions.

Transcendental hypotheses in reason’s speculative use, and a freedom to resort to hyperphysical grounds whenever physical grounds of explanation are lacking, cannot be permitted at all. For one thing, they do not advance reason in the least but rather cut off all progress in its use. For another, this license must finally deprive reason of all the fruits of cultivating its own proper soil, experience. For whenever explaining nature becomes difficult here or there, we have a transcendent ground of explanation constantly at hand that relieves us of the inquiry.

B 802 Our investigation then ends not with insight but with the complete incomprehensibility of a principle devised in advance to contain the concept of the absolutely first.

The second requirement for the acceptability of a hypothesis is its sufficiency for determining a priori from it the consequences that are given. If we are forced to summon auxiliary hypotheses for this purpose, they arouse suspicion of mere invention, because each in itself needs the same justification required by the underlying thought, and therefore cannot provide a competent witness. If, on the presupposition of an unlimitedly perfect cause, there is no lack of grounds for explaining all the purposiveness, order, and greatness found in the world, that presupposition still needs new hypotheses to save it from the deviations and evils that appear, at least according to our concepts, as objections. If the simple self-subsistence of the human soul, laid down as the ground of its appearances, is challenged by the difficulties posed by phenomena resembling changes of matter (growth and decline), new hypotheses must be summoned.

B 803 These are not without illusion, but have no authentication except what is given them by the opinion assumed as the principal ground, which they are nevertheless meant to support.

If the assertions of reason cited here as examples (the soul’s incorporeal unity and the existence of a highest being) are meant to count not as hypotheses but as dogmas proved a priori, they are not under discussion at all. In that case, however, one must be careful that the proof has the apodictic certainty of a demonstration. For seeking merely to make the actuality of such ideas probable is an absurd intention, just as if one meant to prove a geometrical proposition merely probably. Reason separated from all experience can cognize anything only a priori and as necessary, or not at all. Its judgment is therefore never opinion, but either abstention from all judgment or apodictic certainty. Opinions and probable judgments about what belongs to things can occur only as grounds of explanation for what is actually given, or as consequences according to empirical laws of what is laid down as actual, and thus only in the series of objects of experience. Outside this field, opining amounts to playing with thoughts, unless it is merely an opinion about an uncertain path of judgment, that we might perhaps find truth along it.

B 804 Although in merely speculative questions of pure reason hypotheses have no place as foundations for propositions, they are nevertheless quite permissible only for defending those propositions if necessary, that is, not in dogmatic but in polemical use. By defense I understand not an increase in the grounds of proof for one’s assertion, but merely the frustration of an opponent’s specious insights intended to impair our asserted proposition. Now all synthetic propositions from pure reason have this peculiarity: although the person who asserts the reality of certain ideas never knows enough to make his proposition certain, his opponent likewise cannot know enough to assert the contrary. This equality in human reason’s lot favors neither side in speculative cognition, and here is indeed the proper battlefield of feuds that can never be settled. It will emerge later, however, that with regard to practical use reason has a right to assume something it would in no way be entitled to presuppose in the field of mere speculation without sufficient grounds of proof. For all such presuppositions impair the perfection of speculation, about which the practical interest is wholly unconcerned. In the practical domain, then, reason is in possession and need not prove the legitimacy of that possession; indeed, it could not furnish the proof.

B 805 The opponent is therefore to prove. But since he knows as little about the doubted object for establishing its nonexistence as the other, who asserts its actuality, an advantage appears here on the side of the person asserting something as a practically necessary presupposition (melior est conditio possidentis). He is free, as though in self-defense, to employ for his good cause the very same means the opponent employs against it, that is, hypotheses. These are not meant at all to strengthen its proof, but only to show that the opponent understands far too little of the disputed object to flatter himself with any advantage over us in speculative insight.

Hypotheses are therefore permitted in the field of pure reason only as weapons of war, not to found a right upon them but merely to defend it. Yet here we must always seek the opponent within ourselves. For speculative reason in its transcendental use is in itself dialectical. The objections we might fear lie within ourselves. We must seek them out, like old claims that never lapse, in order to found an eternal peace on their annulment. Outward peace is only apparent. The seed of challenges, lying in the nature of human reason, must be uprooted.

B 806 But how can we uproot it unless we give it freedom, even nourishment, to send up shoots and thereby reveal itself, so that we can afterward destroy it root and all? Devise objections yourselves, then, that no opponent has yet thought of, and even lend him weapons or grant him the most favorable position he could wish for. There is nothing to fear here, but indeed something to hope for: that you will secure a possession never again to be challenged in all the future.

Your complete armament also includes hypotheses of pure reason. Although only leaden weapons (since they are not tempered by any law of experience), they nevertheless always accomplish as much as those any opponent may use against you. Suppose, then, that against the (in some other, nonspeculative respect) assumed immaterial nature of the soul, subject to no bodily transformation, you encounter the difficulty that experience seems to prove both the elevation and disruption of our mental powers to be merely different modifications of our organs. You can weaken the force of this proof by assuming that our body is nothing but the fundamental appearance to which, as its condition, the whole faculty of sensibility, and thus all thinking, relates in our present state (in life). Separation from the body would be the end of this sensible use of your cognitive power and the beginning of its intellectual use.

B 807 The body would therefore be not the cause of thinking but a merely restrictive condition of it, and thus to be regarded as furthering sensible and animal life, but all the more as hindering pure and spiritual life. The dependence of the former on bodily constitution would prove nothing about the dependence of life as a whole on the condition of our organs. You can go still further and even discover new doubts, either not yet raised or not pursued far enough.

The contingency of procreation, which in human beings as in nonrational creatures depends on opportunity, but often also on means of support, government and its whims and fancies, and often even on vice, creates a great difficulty for the opinion that the continued existence of a creature, whose life first began under circumstances so insignificant and so entirely left to our freedom, extends into eternity. As regards the continued existence of the whole species (here on earth), this difficulty has little force, because chance in the individual case is nevertheless subject to a rule in the whole. But with regard to each individual, expecting so mighty an effect from such trivial causes certainly seems questionable.

B 808 Against this, however, you can deploy a transcendental hypothesis: that all life is properly only intelligible, not subject to temporal changes at all, and neither began through birth nor ends through death; that this life is nothing but a mere appearance, that is, a sensible representation of pure spiritual life, and the entire sensible world a mere image hovering before our present mode of cognition and, like a dream, without objective reality in itself; that, if we were to intuit things and ourselves as they are, we should see ourselves in a world of spiritual natures, our sole true community with which neither began through birth nor will cease through bodily death (as mere appearances), and so on.

Although we know not the slightest thing about any of this that we hypothetically put forward against the attack, nor seriously assert it—indeed, none of it is even an idea of reason, but merely a concept devised for defense—we nevertheless proceed quite rationally. We merely show the opponent, who thinks he has exhausted all possibility by falsely presenting the absence of its empirical conditions as proof of the complete impossibility of what we believe, that he can no more encompass the whole field of possible things in themselves through mere laws of experience than we can acquire anything well founded for our reason outside experience.

B 809 Whoever employs such hypothetical countermeasures against the pretensions of a boldly denying opponent must not be taken as wishing to adopt them as his true opinions. He abandons them as soon as he has disposed of his opponent’s dogmatic conceit. For however modest and moderate it may seem when someone merely refuses and denies the assertions of others, as soon as he wants these objections to count as proofs of the opposite, his claim is always no less proud and conceited than if he had taken up the affirmative side and its assertion.

We see, then, that in reason’s speculative use hypotheses have no validity as opinions in themselves, but only in relation to opposing transcendent pretensions. For extending the principles of possible experience to the possibility of things in general is just as transcendent as asserting the objective reality of concepts whose objects can be found nowhere but outside the boundary of all possible experience. What pure reason judges assertorically must (like everything reason cognizes) be necessary, or it is nothing at all. Thus pure reason in fact contains no opinions. The hypotheses in question, however, are only problematic judgments that at least cannot be refuted, though admittedly they cannot be proved by anything either.

B 810 They are therefore not private opinions, yet we cannot readily dispense with them (even for inward reassurance) against arising scruples. But we must preserve them in this capacity and carefully prevent their appearing as authenticated in themselves and possessed of any absolute validity, drowning reason in inventions and delusions.

Chapter One Section Four The Discipline of Pure Reason with Regard to Its Proofs

Among all proofs of synthetic cognition a priori, proofs of transcendental and synthetic propositions have this peculiarity: through its concepts, reason may not turn directly to the object, but must first establish the objective validity of the concepts and the possibility of their synthesis a priori. This is not merely a necessary rule of caution; it concerns the essence and possibility of the proofs themselves. If I am to go beyond the concept of an object a priori, this is impossible without a particular guiding thread lying outside that concept. In mathematics, intuition a priori guides my synthesis, and all inferences there can be drawn immediately from pure intuition.

B 811 In transcendental cognition, so long as it deals merely with concepts of the understanding, possible experience is this guide. The proof does not show that the given concept (for example, of what happens) leads directly to another concept (that of a cause); for such a transition would be an entirely unjustifiable leap. Rather, it shows that experience itself, and thus the object of experience, would be impossible without such a connection. The proof therefore also had to indicate the possibility of arriving synthetically and a priori at a certain cognition of things not contained in their concept. Without this attention, proofs run wild and cross-country, like waters breaking their banks, wherever the inclination of hidden association happens to lead them. The illusion of conviction resting on subjective causes of association and mistaken for insight into a natural affinity cannot counterbalance the misgivings that must rightly arise over such daring steps. Hence all attempts to prove the principle of sufficient ground have, by the general admission of experts, been futile. Before transcendental critique appeared, since people could not abandon this principle, they preferred to appeal defiantly to common sense.

B 812 (This is a refuge that always proves reason’s cause desperate.) They preferred it to attempting new dogmatic proofs.

But if the proposition to be proved is an assertion of pure reason, and I even intend through mere ideas to go beyond my concepts of experience, the proof would all the more have to contain the justification of such a step of synthesis (if it were possible at all) as a necessary condition of its probative force. Thus, however plausible the supposed proof of the simple nature of our thinking substance from the unity of apperception may be, it faces an unavoidable objection. Absolute simplicity is not a concept immediately relatable to a perception but must merely be inferred as an idea. It is therefore impossible to see how mere consciousness, which is or at least can be contained in all thinking, though in that respect a simple representation, should lead me to consciousness and knowledge of a thing in which alone thinking can be contained. For when I represent the force of my body in motion, the body is to that extent an absolute unity for me, and my representation of it is simple. I can therefore also express it through the motion of a point, because its volume does not matter here and can be thought as small as one likes without diminishing the force, and thus also as located in a point.

B 813 Yet I shall not infer from this that, if nothing is given me but a body’s moving force, the body can be thought as a simple substance because its representation abstracts from every magnitude of spatial content and is therefore simple. I discover a paralogism through the fact that the simple in abstraction is entirely different from the simple in the object, and that the I, which in the first sense contains no manifold at all, may in the second, where it signifies the soul itself, be a very complex concept, containing and designating very much under itself. But to anticipate this (for without such a preliminary suspicion one would suspect nothing about the proof) it is absolutely necessary to have at hand a standing criterion of the possibility of such synthetic propositions, which are meant to prove more than experience can give. This criterion consists in conducting the proof not directly toward the predicate sought, but only through a principle of the possibility of extending our given concept a priori to ideas and realizing them. Suppose this caution is always employed, and that before the proof is even attempted we first wisely consider how, and with what grounds for hope, we can expect such an extension through pure reason.

B 814 Suppose we also consider where, in such a case, we mean to obtain these insights, which cannot be developed from concepts or anticipated in relation to possible experience. Then we can spare ourselves much arduous yet fruitless effort. In this way we demand of reason nothing manifestly beyond its capacity, or rather subject it to the discipline of restraint, since in its fits of craving speculative expansion it does not readily accept restriction.

The first rule is therefore this: attempt no transcendental proofs without first considering and justifying where you intend to obtain the principles on which you plan to build them, and by what right you can expect successful inferences from them. If they are principles of the understanding (for example, of causality), it is futile to reach ideas of pure reason through them, for they hold only for objects of possible experience. If they are to be principles from pure reason, all effort is again futile. For reason does indeed have such principles, but as objective principles they are all dialectical and can at most be valid only as regulative principles of the systematically coherent use of experience. If such supposed proofs are already available, oppose to their deceptive conviction the non liquet of your mature power of judgment.

B 815 Even if you cannot yet penetrate their delusion, you have every right to demand a deduction of the principles employed in them, which can never be supplied if those principles are supposed to have arisen from mere reason. Thus you need not even occupy yourselves with unfolding and refuting every unfounded illusion, but can dismiss at once, in whole masses, all dialectic, inexhaustible in artifices, at the court of a critical reason that demands laws.

The second peculiarity of transcendental proofs is this: only a single proof can be found for each transcendental proposition. If I am to infer not from concepts but from the intuition corresponding to a concept, whether a pure intuition as in mathematics or an empirical one as in natural science, the underlying intuition gives me manifold material for synthetic propositions. I can connect this material in more than one way and, since I may start from more than one point, reach the same proposition by different paths.

But every transcendental proposition proceeds solely from one concept and states the synthetic condition of the object’s possibility according to that concept. There can therefore be only a single ground of proof, because apart from this concept there is nothing else through which the object could be determined.

B 816 The proof can thus contain nothing beyond the determination of an object in general according to this concept, which is itself only one. For example, in the Transcendental Analytic we drew the principle that everything that happens has a cause from the sole condition of the objective possibility of a concept of what happens in general: that the determination of an event in time, and thus this (event) as belonging to experience, would be impossible unless it stood under such a dynamical rule. This is also the only possible ground of proof. For only through an object’s being determined for the concept by the law of causality does the represented event have objective validity, that is, truth. Other proofs of this principle have indeed been attempted, from contingency, for example. But examined in the light, this yields no mark of contingency except happening, that is, an existence preceded by the object’s nonexistence, so we always return to the same ground of proof. If the proposition that everything that thinks is simple is to be proved, we do not dwell on the manifold of thinking but remain solely with the concept of the I, which is simple and to which all thinking is related.

B 817 The same holds of the transcendental proof of God’s existence, which rests solely on the convertibility of the concepts of the most real being and the necessary being, and can be sought nowhere else.

This cautionary observation greatly reduces the critique of reason’s assertions. Where reason conducts its business through mere concepts, only a single proof is possible, if any proof is possible at all. Hence, if we see the dogmatist appearing with ten proofs, we can safely believe he has none. For if he had one that (as must be the case in matters of pure reason) proved apodictically, why would he need the others? His intention is merely like that of the parliamentary advocate: one argument is for this person, another for that one. He means to exploit the weakness of his judges, who, without entering deeply into the matter and eager to be rid of it, seize the first thing that strikes them and decide accordingly.

The third distinctive rule of pure reason when subjected to a discipline regarding transcendental proofs is that its proofs must never be apagogic, but always ostensive. In every kind of cognition, a direct or ostensive proof combines conviction of the truth with insight into its sources. An apagogic proof, by contrast, can indeed produce certainty, but not comprehension of truth in its coherence with the grounds of its possibility.

B 818 The latter are therefore more an emergency expedient than a procedure satisfying all reason’s aims. Yet they have an advantage in evidence over direct proofs: contradiction always carries greater clarity in representation than the best connection does, and thereby comes closer to the intuitive character of a demonstration.

The actual cause for using apagogic proofs in various sciences is probably this. If the grounds from which a certain cognition is to be derived are too manifold or too deeply concealed, we try to reach it through its consequences. Now the modus ponens of inferring the truth of a cognition from the truth of its consequences would be permissible only if all possible consequences of it were true. For then only a single ground would be possible for them, which would therefore also be the true one. But this procedure is impracticable, because understanding all possible consequences of any assumed proposition exceeds our powers. Yet we employ this manner of inference, admittedly with a certain indulgence, when we seek to prove something merely as a hypothesis. We allow the inference by analogy that, if as many consequences as we have ever tested agree well with an assumed ground, all the other possible ones will agree with it too.

B 819 For this reason, a hypothesis can never be transformed into demonstrated truth along this path. The modus tollens of the inferences of reason that conclude from consequences to grounds proves not only with complete rigor but also with extraordinary ease. For if even a single false consequence can be drawn from a proposition, that proposition is false. Instead of running through the whole series of grounds in an ostensive proof, which can lead to the truth of a cognition through complete insight into its possibility, we need only find a single false consequence flowing from its opposite. That opposite is then also false, and thus the cognition we had to prove is true.

But the apagogic mode of proof can be permitted only in sciences where it is impossible to substitute the subjective element of our representations for the objective, namely for cognition of what belongs to the object. Where such substitution prevails, however, it must frequently happen that the opposite of a certain proposition contradicts merely the subjective conditions of thinking, not the object; or that both propositions contradict one another only under a subjective condition falsely taken as objective. Since the condition is false, both can then be false, without our being able to infer the truth of one from the falsity of the other.

B 820 In mathematics this subreption is impossible; such proofs therefore have their proper place there. In natural science, since everything rests on empirical intuitions, this illicit substitution can usually be prevented through many compared observations; yet this mode of proof is mostly of little importance there. But the transcendental attempts of pure reason are all undertaken within the very medium of dialectical illusion, that is, the subjective, which presents or even forces itself upon reason in its premises as objective. Here, then, with regard to synthetic propositions, we cannot be permitted to justify our assertions by refuting their opposite. For either this refutation merely presents the conflict of the opposed opinion with the subjective conditions of comprehensibility through our reason, which does nothing to warrant rejecting the thing itself (just as, for example, unconditioned necessity in the existence of a being cannot be comprehended by us at all, and therefore subjectively opposes, rightly, every speculative proof of a necessary highest being, but wrongly opposes the possibility of such an original being in itself). Or both the affirming and the denying party, deceived by transcendental illusion, take an impossible concept of the object as their basis.

B 821 The rule then holds: non entis nulla sunt praedicata, that is, both what is affirmed and what is denied of the object are incorrect, and we cannot arrive at cognition of the truth apagogically through refutation of the opposite. For example, if the sensible world is presupposed as given in itself in its totality, it is false that it must be either spatially infinite or finite and bounded, because both are false. For appearances (as mere representations) that were nevertheless given in themselves (as objects) are something impossible. The infinity of this imagined whole would admittedly be unconditioned, but would conflict (since everything in appearances is conditioned) with the unconditioned determination of magnitude nevertheless presupposed in the concept.

The apagogic mode of proof is also the very delusion with which admirers of our dogmatic reasoners’ thoroughness have always been put off. It is, as it were, the champion who seeks to prove the honor and indisputable right of his chosen party by undertaking to fight anyone who doubts it. Yet by such boasting nothing is settled about the matter itself, but only the relative strength of the opponents, and even this only on the side of the one who takes the attacking part.

B 822 Seeing that each in his turn is now victorious, now defeated, spectators often take occasion to doubt skeptically the very object of the dispute. But they have no grounds for this; it is enough to call out to them: non defensoribus istis tempus eget. Each must conduct his case through a lawful proof furnished by transcendental deduction of the grounds of proof, that is, directly, so that we may see what his rational claims can offer on their own behalf. For if his opponent rests on subjective grounds, he is certainly easy to refute, but without advantage to the dogmatist, who commonly adheres just as much to subjective causes of judgment and can likewise be driven into a corner by his opponent. If both parties proceed only directly, however, they will either themselves notice the difficulty, indeed impossibility, of finding a title for their assertions and finally be able to appeal only to prescription; or critique will easily discover the dogmatic illusion and compel pure reason to abandon its excessive pretensions in speculative use and retreat within the boundaries of its own proper ground, namely practical principles.

B 823 Transcendental Doctrine of Method Chapter Two The Canon of Pure Reason

It is humiliating for human reason that it accomplishes nothing in its pure use and even needs a discipline to curb its excesses and prevent the delusions arising from them. Yet on the other hand it is elevated again and given confidence in itself by being able and obliged to exercise this discipline itself, without permitting another censure above it, and likewise by the fact that the boundaries it is forced to set to its speculative use also restrict every opponent’s sophistical pretensions and can therefore secure against all attacks whatever remains of its formerly excessive demands. The greatest and perhaps only benefit of all philosophy of pure reason is thus probably only negative; since it serves, namely, not as an organon for extension but as a discipline for determining boundaries, and instead of discovering truth has only the quiet merit of preventing errors.

Yet somewhere there must be a source of positive cognitions belonging to the domain of pure reason, which perhaps occasion errors only through misunderstanding, but in fact constitute the goal of reason’s zeal.

B 824 For to what other cause could we ascribe the irrepressible desire to gain a firm foothold somewhere entirely beyond the boundary of experience? Reason anticipates objects of great interest to it. It takes the path of mere speculation to approach them, but they flee before it. Better fortune may presumably be hoped for on the only path still open to it, that of practical use.

By a canon I understand the sum of principles a priori for the correct use of certain cognitive faculties in general. Thus general logic in its analytic part is a canon for understanding and reason in general, but only as to form, since it abstracts from all content. Thus the Transcendental Analytic was the canon of the pure understanding, for this alone is capable of true synthetic cognitions a priori. But where no correct use of a cognitive power is possible, there is no canon. Now, according to all the proofs conducted so far, every synthetic cognition of pure reason in its speculative use is entirely impossible. There is therefore no canon at all of its speculative use (for this is thoroughly dialectical), but all transcendental logic in this respect is nothing but discipline.

B 825 Consequently, if there is any correct use of pure reason, in which case it must also have a canon, this will concern not speculative but practical use of reason, which we shall now investigate.

The Canon of Pure Reason Section One On the Ultimate End of the Pure Use of Our Reason

A tendency of its nature drives reason beyond its use in experience, to venture in a pure use, through mere ideas, to the furthest boundaries of all cognition, and to find rest only in the completion of its circle, in a self-subsistent systematic whole. Is this striving grounded merely in its speculative interest, or rather solely in its practical interest?

I shall now set aside the success of pure reason in its speculative aim and ask only about the problems whose solution constitutes its ultimate end, whether it attains that end or not, and in relation to which all the others have merely the value of means.

B 826 According to reason’s nature, these highest ends must in turn possess unity, so as jointly to further that interest of humanity which is subordinate to no higher one.

The final aim toward which reason’s speculation in its transcendental use ultimately runs concerns three objects: freedom of the will, immortality of the soul, and the existence of God. Regarding all three, reason’s merely speculative interest is very slight. For its sake, the exhausting labor of transcendental inquiry, struggling with unceasing obstacles, would scarcely be undertaken, because no use could be made of any discoveries about these matters that would prove beneficial in concreto, that is, in the investigation of nature. Even if the will is free, this can concern only the intelligible cause of our willing. For as regards the phenomena in which it manifests itself, that is, its actions, an inviolable fundamental maxim, without which we cannot exercise reason in empirical use, requires us always to explain them just like all other appearances of nature, according to its unchangeable laws. Second, even if the spiritual nature of the soul (and with it its immortality) could be understood, we could rely on this neither as a ground for explaining the appearances of this life nor for determining the particular constitution of a future state.

B 827 For our concept of an incorporeal nature is merely negative; it does not extend our cognition in the least or offer any suitable material for inferences except perhaps such as can count only as inventions, which philosophy does not permit. Third, even if the existence of a highest intelligence were proved, we would indeed thereby make the purposiveness in the world’s arrangement and order generally comprehensible, but would be in no way entitled to derive any particular arrangement or order from it, or boldly infer such an order where it is not perceived. For a necessary rule of reason’s speculative use forbids bypassing natural causes and abandoning what experience can teach us in order to derive something we know from what entirely surpasses all our knowledge. In a word, these three propositions always remain transcendent for speculative reason. They have no immanent use, that is, no use permissible for objects of experience and thus useful to us in any way; considered in themselves, they are entirely idle and, moreover, extremely difficult exertions of our reason.

These three cardinal propositions are not at all necessary for our knowledge, and yet our reason urgently recommends them to us.

B 828 Their importance must therefore properly concern only the practical.

Everything possible through freedom is practical. But if the conditions for exercising our free power of choice are empirical, reason can have only a regulative use here, serving merely to bring about unity of empirical laws. In the doctrine of prudence, for example, reason’s whole task is to unite all ends assigned to us by our inclinations into the single end of happiness and bring into agreement the means of attaining it. For this reason it can supply only pragmatic laws of free conduct for attaining the ends recommended to us by the senses, not pure laws determined entirely a priori. Pure practical laws, by contrast, whose end is given by reason entirely a priori, and which command absolutely rather than under empirical conditions, would be products of pure reason. Moral laws are of this kind; they alone, therefore, belong to the practical use of pure reason and permit a canon.

Thus the entire preparation of reason in the undertaking we may call pure philosophy is in fact directed solely toward the three problems mentioned. These themselves, however, have a further aim: what is to be done if the will is free, if there is a God and a future world.

B 829 Since this concerns our conduct in relation to the highest end, the ultimate intention of nature, which wisely provides for us, in the arrangement of our reason is properly directed only toward the moral.

Caution is needed, however, now that we turn our attention to an object foreign* to transcendental philosophy, lest we stray into digressions and violate the system’s unity; on the other hand, we must also avoid saying so little about our new material that clarity or conviction suffers. I hope to accomplish both by staying as close as possible to the transcendental and setting aside entirely whatever here might be psychological, that is, empirical.

* All practical concepts relate to objects of liking or disliking, that is, of pleasure or displeasure, and thus at least indirectly to objects of our feeling. But feeling is no power of representing things; it lies outside our entire cognitive power. Hence the elements of our judgments insofar as they relate to pleasure or displeasure, and thus of practical judgments, do not belong to the sum of transcendental philosophy, which is concerned solely with pure cognitions a priori.

We must first note, then, that for the present I shall employ the concept of freedom only in its practical sense.

B 830 Freedom in its transcendental meaning, which cannot be empirically presupposed as a ground for explaining appearances but is itself a problem for reason, I set aside here as dealt with above. A power of choice is merely animal (arbitrium brutum) if it can be determined only through sensible impulses, that is, pathologically. But a power of choice that can be determined independently of sensible impulses, and thus by motives represented only by reason, is called the free power of choice (arbitrium liberum); everything connected with it, whether as ground or consequence, is called practical. Practical freedom can be proved through experience. For the human power of choice is determined not merely by what stimulates, that is, immediately affects the senses. We have a power to overcome impressions on our sensible faculty of desire through representations of what is useful or harmful even in a more remote way. But these reflections on what is desirable, that is, good and useful, with regard to our whole condition rest on reason. Reason therefore also gives laws that are imperatives, that is, objective laws of freedom, which say what ought to happen, although perhaps it never does happen. In this they differ from laws of nature, which deal only with what happens; hence they are also called practical laws.

B 831 But whether reason itself, in these acts through which it prescribes laws, is not in turn determined by other influences, and whether what is called freedom with regard to sensible impulses might not in turn be nature with regard to higher and more remote efficient causes, does not concern us in the practical sphere, where we initially ask reason only for a prescription of conduct. It is a merely speculative question, which we can set aside so long as our intention is directed toward action or inaction. We therefore cognize practical freedom through experience as one of the natural causes, namely a causality of reason in determining the will. Transcendental freedom, by contrast, requires this reason itself to be independent (with regard to its causality of beginning a series of appearances) of all determining causes of the sensible world. To that extent it seems contrary to the law of nature, and thus to all possible experience, and therefore remains a problem. But this problem does not belong before reason in its practical use. In a canon of pure reason, then, we are concerned only with two questions involving pure reason’s practical interest, regarding which a canon of its use must be possible: Is there a God? Is there a future life? The question of transcendental freedom concerns speculative knowledge alone.

B 832 We can set it aside as entirely indifferent when the practical is at issue, and a sufficient discussion of it is already to be found in the Antinomy of Pure Reason.

The Canon of Pure Reason Section Two On the Ideal of the Highest Good as a Determining Ground of the Ultimate End of Pure Reason

In its speculative use, reason led us through the field of experiences and, because it can never find complete satisfaction there, onward to speculative ideas. These, however, ultimately led us back to experience, thus fulfilling reason’s intention in a useful way, but one entirely at odds with our expectation. One attempt remains: to see whether pure reason is also to be found in practical use; whether in this use it leads to the ideas that attain the highest ends of pure reason just cited; and whether, from the standpoint of its practical interest, it thus could not grant what it entirely refuses us with regard to its speculative interest.

Every interest of my reason (the speculative as well as the practical) unites in the following three questions:

1 B 833 What can I know?2. What ought I to do?3. What may I hope?

The first question is merely speculative. We have (as I flatter myself) exhausted all possible answers to it and finally found the one with which reason must indeed be satisfied and, if it does not look to the practical, also has grounds to be content. But we have remained just as far from the two great ends toward which this whole striving of pure reason was properly directed as if, for our own comfort, we had refused this labor from the outset. Thus, where knowledge is concerned, at least this much is certain and settled: with regard to those two problems, we can never attain it.

The second question is merely practical. As such it can indeed belong to pure reason, but it is then not transcendental but moral, and thus cannot in itself occupy our critique.

The third question—if I now do what I ought, what may I then hope?—is at once practical and theoretical. The practical serves merely as a guiding thread for answering the theoretical and, when pursued far, speculative question. For all hope concerns happiness, and in relation to the practical and the moral law it is precisely what knowledge and the law of nature are in relation to theoretical cognition of things.

B 834 The former ultimately issues in the inference that something is (which determines the ultimate possible end) because something ought to happen; the latter, that something is (which acts as the highest cause) because something happens.

Happiness is the satisfaction of all our inclinations (extensively in their manifoldness, intensively in their degree, and protensively in their duration). I call a practical law motivated by happiness pragmatic (rule of prudence); but a law, if there is such a law, whose motive is nothing but worthiness to be happy, I call moral (moral law). The first advises what to do if we want to attain happiness; the second commands how we ought to conduct ourselves merely to become worthy of happiness. The first rests on empirical principles, for only through experience can I know either what inclinations seek satisfaction or what natural causes can bring about their satisfaction. The second abstracts from inclinations and the natural means of satisfying them, considering only the freedom of a rational being in general and the necessary conditions under which alone it accords with the distribution of happiness according to principles. It can therefore at least rest on mere ideas of pure reason and be cognized a priori.

B 835 I assume that there actually are pure moral laws determining entirely a priori (without regard to empirical motives, that is, happiness) what a rational being in general does or refrains from doing, that is, its use of freedom; and that these laws command absolutely (not merely hypothetically on the presupposition of other empirical ends), and are thus necessary in every respect. I can rightly presuppose this proposition by appealing not only to the proofs of the most enlightened moralists, but to every human being’s moral judgment, if he wishes to think such a law distinctly.

Pure reason therefore contains, though not in its speculative use, in a certain practical use, namely the moral, principles of the possibility of experience: of actions that might be found in human history in accordance with moral precepts. For since it commands that such actions ought to happen, they must also be able to happen. A particular kind of systematic unity, the moral, must therefore be possible. By contrast, systematic unity of nature could not be proved according to speculative principles of reason, because reason has causality with regard to freedom in general, but not with regard to the whole of nature; moral principles of reason can produce free actions, but not laws of nature.

B 836 Accordingly, the principles of pure reason in its practical, specifically moral, use have objective reality.

I call the world, insofar as it would conform to all moral laws (as indeed it can be, according to the freedom of rational beings, and, according to the necessary laws of morality, ought to be), a moral world. To this extent it is thought merely as an intelligible world, because in it we abstract from all conditions (ends) and even from all obstacles to morality (weakness or impurity of human nature). To this extent it is thus a mere but nevertheless practical idea, which really can and ought to influence the sensible world so as to make it conform to this idea as far as possible. The idea of a moral world therefore has objective reality, not as relating to an object of an intelligible intuition (of which kind we cannot think at all), but to the sensible world as an object of pure reason in its practical use, and to a corpus mysticum of rational beings in it, insofar as their free choice under moral laws has thoroughgoing systematic unity both with itself and with the freedom of everyone else.

That answered the first of the two questions of pure reason concerning its practical interest: do what makes you worthy to be happy.

B 837 The second now asks: if I conduct myself so as not to be unworthy of happiness, may I also hope thereby to attain it? The answer depends on whether the principles of pure reason that prescribe the law a priori also necessarily connect this hope with it.

I therefore say: just as moral principles are necessary according to reason in its practical use, it is equally necessary according to reason in its theoretical use to assume that everyone has grounds to hope for happiness in the same measure as he has made himself worthy of it in his conduct, and that thus the system of morality is inseparably, but only in the idea of pure reason, combined with that of happiness.

Now in an intelligible, that is, moral world, in whose concept we abstract from all obstacles to morality (the inclinations), such a system of happiness proportioned to and combined with morality can also be thought as necessary. For freedom, partly moved and partly restricted by moral laws, would itself be the cause of universal happiness. Rational beings themselves, guided by such principles, would thus be authors of their own enduring welfare and that of others.

B 838 But this system of self-rewarding morality is only an idea whose execution rests on the condition that everyone does what he ought: that all actions of rational beings occur as if they sprang from one highest will encompassing every private choice within or under itself. Yet obligation under the moral law remains valid for each particular use of freedom even if others do not conform to this law. Neither the nature of things in the world nor the causality of the actions themselves and their relation to morality therefore determines how their consequences will relate to happiness. The necessary connection mentioned between the hope of being happy and the unceasing effort to make oneself worthy of happiness cannot be cognized by reason if nature alone is laid down as the basis. It may be hoped for only if a highest reason commanding according to moral laws is also laid down as the cause of nature.

I call the idea of such an intelligence—in which the morally most perfect will, combined with the highest blessedness, is the cause of all happiness in the world insofar as this stands in exact proportion to morality (as worthiness to be happy)—the ideal of the highest good. Thus only in the ideal of the highest original good can pure reason find the ground of the practically necessary connection of both elements of the highest derived good, namely an intelligible, that is, moral world.

B 839 Now, since we must necessarily represent ourselves through reason as belonging to such a world, although the senses exhibit nothing to us but a world of appearances, and since this sensible world does not present such a connection to us, we must therefore assume the moral world as a consequence of our conduct in the sensible world, as a world future for us. God and a future life are thus two presuppositions inseparable, according to principles of that same reason, from the obligation pure reason imposes on us.

Morality in itself constitutes a system, but happiness does not, except insofar as it is distributed in exact conformity with morality. This, however, is possible only in the intelligible world under a wise author and ruler. Reason finds itself compelled to assume such a being, together with life in such a world, which we must regard as future, or else to regard moral laws as empty fantasies. For without that presupposition their necessary consequence, which the same reason connects with them, would have to disappear. Hence everyone also regards moral laws as commands. But they could not be commands unless they connected appropriate consequences a priori with their rule, and thus carried promises and threats with them.

B 840 Nor can they do this unless they lie in a necessary being as the highest good, which alone can make such purposive unity possible.

Leibniz called the world, insofar as we attend in it only to rational beings and their coherence according to moral laws under the government of the highest good, the kingdom of grace. He distinguished it from the kingdom of nature, where rational beings indeed stand under moral laws but expect no consequences of their conduct other than those following the course of nature in our sensible world. To see ourselves in the kingdom of grace, where all happiness awaits us except insofar as we ourselves restrict our share through unworthiness to be happy, is therefore a practically necessary idea of reason.

Practical laws, insofar as they also become subjective grounds of actions, that is, subjective principles, are called maxims. We judge morality in its purity and consequences according to ideas; we follow its laws according to maxims.

Our entire conduct of life must necessarily be subordinated to moral maxims. Yet it is at the same time impossible for this to happen unless reason connects with the moral law, which is a mere idea, an efficient cause determining for conduct according to that law an outcome exactly corresponding to our highest ends, whether in this life or another.

B 841 Thus without a God and a world presently invisible to us but hoped for, the glorious ideas of morality are indeed objects of approval and admiration, but not incentives to resolution and practice. For they do not fulfill the entire end that is natural to every rational being and is determined a priori and made necessary by that very same pure reason.

Happiness alone is far from being the complete good for our reason. Reason does not approve it (however much inclination may desire it) unless it is united with worthiness to be happy, that is, moral good conduct. Yet morality alone, and with it mere worthiness to be happy, is also far from being the complete good. To complete it, someone whose conduct has not been unworthy of happiness must be able to hope to attain it. Even reason free of every private aim, if it put itself without considering any interest of its own in the place of a being required to distribute all happiness to others, could judge no differently. For in the practical idea both elements are essentially combined, though in such a way that moral disposition, as the condition, first makes a share in happiness possible, not, conversely, the prospect of happiness the moral disposition.

B 842 In the latter case the disposition would not be moral and thus would not be worthy of complete happiness, which before reason recognizes no restriction except that arising from our own immoral conduct.

Thus happiness in exact proportion to the morality of rational beings, through which they are worthy of it, alone constitutes the highest good of a world into which we must absolutely place ourselves according to the precepts of pure but practical reason. This is admittedly only an intelligible world, since the sensible world promises us no such systematic unity of ends from the nature of things. Its reality can be grounded on nothing but the presupposition of a highest original good, in which self-subsistent reason, equipped with all the sufficiency of a highest cause, establishes, preserves, and carries out, according to the most perfect purposiveness, the universal order of things, though this order is deeply concealed from us in the sensible world.

This moral theology has a distinctive advantage over speculative theology: it inevitably leads to the concept of a single, most perfect, rational original being, toward which speculative theology does not even point us on objective grounds, much less could it convince us of it. For neither in transcendental nor in natural theology, however far reason may lead us there, do we find any substantial ground for assuming only a single being.

B 843 It would be a being that we set above all natural causes, and on which we would have sufficient reason to make them depend in every respect. By contrast, if from the standpoint of moral unity as a necessary law of the world we consider the cause that alone can give it the appropriate effect, and thus binding force for us, this must be a single highest will encompassing all these laws. For how could we find perfect unity of ends among different wills? This will must be almighty, so that all nature and its relation to morality in the world may be subject to it; omniscient, so that it may cognize the innermost dispositions and their moral worth; omnipresent, so that it may be immediately close to every need required by the highest good of the world; eternal, so that at no time may this agreement of nature and freedom fail; and so on.

But this systematic unity of ends in this world of intelligences—which as mere nature is only a sensible world, but as a system of freedom can be called an intelligible, that is, moral world (regnum gratiae)—inevitably also leads to the purposive unity of all things making up this great whole according to universal laws of nature, just as the former does according to universal and necessary moral laws, and unites practical with speculative reason.

B 844 The world must be represented as having sprung from an idea if it is to agree with that use of reason without which we would regard ourselves as unworthy of reason itself: the moral use, which rests entirely on the idea of the highest good. All investigation of nature thereby receives a direction according to the form of a system of ends, and in its greatest extension becomes physicotheology. Yet because this began from moral order as a unity grounded in the essence of freedom, not contingently established through external commands, it traces nature’s purposiveness to grounds that must be inseparably connected a priori with the inner possibility of things. It thereby leads to a transcendental theology that takes the ideal of the highest ontological perfection as a principle of systematic unity, connecting all things according to universal and necessary laws of nature, because all originate in the absolute necessity of one single original being.

What use can we make of our understanding, even with regard to experience, unless we set ourselves ends? But the highest ends are those of morality, and only pure reason can make these known to us. Equipped with them and guided by them, we can make no purposive use of the knowledge of nature itself with regard to cognition unless nature has itself placed purposive unity there.

B 845 Without this we would not even possess reason, since we would have no school for it and no cultivation through objects offering material for such concepts. But the former purposive unity is necessary and grounded in the essence of the power of choice itself. The latter, therefore, which contains the condition for applying the former in concreto, must be necessary too. Thus the transcendental elevation of our rational cognition would be not the cause but merely the effect of the practical purposiveness pure reason imposes on us.

We therefore also find in the history of human reason that, before moral concepts had been sufficiently purified and determined, and the systematic unity of ends according to them had been understood from necessary principles, knowledge of nature and even a considerable degree of reason’s cultivation in other sciences could produce only crude and wandering concepts of the deity, or else left behind a remarkable indifference to the question altogether. A fuller development of moral ideas, made necessary by the supremely pure moral law of our religion, sharpened reason’s attention to the object through the interest it compelled reason to take in it. Neither extended knowledge of nature nor correct and reliable transcendental insights (of which kind have at all times been lacking) contributed to this.

B 846 Yet these ideas produced a concept of the divine being that we now regard as correct—not because speculative reason convinces us of its correctness, but because it agrees perfectly with moral principles of reason. Thus, in the end, pure reason alone, but only in its practical use, always deserves the credit for connecting with our highest interest a cognition that mere speculation can only suppose, not establish, thereby making it not a demonstrated dogma but an absolutely necessary presupposition for reason’s most essential ends.

But once practical reason has reached this high point, the concept of a single original being as the highest good, it must not presume to start from this concept and derive the moral laws themselves from it, as though it had risen above all empirical conditions of its application and soared to immediate knowledge of new objects. For it was precisely these laws whose inner practical necessity led us to presuppose a self-subsistent cause or wise ruler of the world in order to give them effect. We cannot therefore in turn, according to this, regard them as contingent and derived from mere will, especially a will of which we would have no concept at all had we not formed it in accordance with those laws.

B 847 As far as practical reason has the right to lead us, we shall regard actions as obligatory not because they are God’s commands, but as divine commands because we are inwardly bound to them. We shall study freedom under purposive unity according to principles of reason, and believe ourselves in conformity with the divine will only insofar as we hold sacred the moral law that reason teaches us from the nature of the actions themselves. We shall believe that we serve him solely by promoting the good of the world in ourselves and others. Moral theology therefore has only an immanent use: to fulfill our vocation here in the world by fitting into the system of all ends, and not fanatically or even impiously to abandon the guiding thread of morally legislative reason in good conduct in order to connect it immediately with the idea of the highest being. That would be a transcendent use which, like the use of mere speculation, must distort and frustrate reason’s ultimate ends.

B 848 The Canon of Pure Reason Section Three On Opinion, Knowledge, and Faith

Holding something true is an occurrence in our understanding that may rest on objective grounds, but also requires subjective causes in the mind of the person judging. If it is valid for everyone so long as he has reason, its ground is objectively sufficient, and holding true is then called conviction. If its ground lies only in the subject’s particular constitution, it is called persuasion.

Persuasion is a mere illusion, because the ground of the judgment, lying solely in the subject, is taken as objective. Such a judgment therefore also has only private validity, and the holding true cannot be communicated. Truth, however, rests on agreement with the object, with regard to which the judgments of every understanding must consequently agree (consentientia uni tertio, consentiunt inter se). The outward touchstone of holding true, whether it is conviction or mere persuasion, is therefore the possibility of communicating it and finding it valid for every human being’s reason.

B 849 For then we at least presume that the ground of agreement among all judgments, despite the differences among subjects, will rest on their common ground, the object, with which they therefore all agree, thereby proving the judgment’s truth.

Persuasion cannot, then, be distinguished subjectively from conviction if the subject regards his holding true merely as an appearance of his own mind. But testing its grounds, valid for us, on the understanding of others, to see whether they have precisely the same effect on another’s reason as on ours, is nevertheless a means, though only subjective, not of producing conviction but of discovering the judgment’s merely private validity, that is, something in it that is mere persuasion.

If, moreover, we can unfold the subjective causes of the judgment that we take for its objective grounds, and thus explain the deceptive holding true as an occurrence in our mind without needing the object’s constitution, we expose the illusion and are no longer deceived by it, though still tempted to a degree if the subjective cause of the illusion is inherent in our nature.

I can assert nothing—that is, pronounce it as a judgment necessarily valid for everyone—except what produces conviction.

B 850 I may keep persuasion to myself if I feel comfortable with it, but I cannot and ought not seek to make it valid beyond myself.

Holding true, or the subjective validity of judgment, has the following three degrees in relation to conviction (which is at the same time objectively valid): opinion, faith, and knowledge. Opinion is holding true with consciousness of its subjective as well as objective insufficiency. If holding true is only subjectively sufficient and is at the same time regarded as objectively insufficient, it is called faith. Finally, holding true that is both subjectively and objectively sufficient is called knowledge. Subjective sufficiency is called conviction (for myself); objective sufficiency, certainty (for everyone). I shall not linger over the elucidation of such readily comprehensible concepts.

I must never venture to opine without knowing at least something through which the judgment, in itself merely problematic, acquires a connection with truth that, though incomplete, is more than an arbitrary invention. The law of such a connection must, moreover, be certain. For if regarding it too I have nothing but opinion, everything is merely a play of imagination without the slightest relation to truth. In judgments from pure reason, opining is not permissible at all.

B 851 For they are not supported by grounds of experience, but everything is to be cognized a priori, where everything is necessary. The principle of connection therefore requires universality and necessity, and thus complete certainty; otherwise no guidance toward truth is found at all. It is therefore absurd to opine in pure mathematics: we must know or refrain from all judgment. The same holds of moral principles, where we may not risk an action on the mere opinion that it is permissible, but must know this.

In reason’s transcendental use, by contrast, opinion is admittedly too little, but knowledge is also too much. In a merely speculative respect we can therefore make no judgment here at all. For subjective grounds of holding true, such as those capable of producing faith, deserve no assent in speculative questions, since they cannot sustain themselves free of all empirical assistance or be communicated equally to others.

But holding true that is theoretically insufficient can be called faith only in a practical relation. This practical aim concerns either skill or morality: the first for freely chosen and contingent ends, the second for absolutely necessary ends.

Once an end is set, the conditions of attaining it are hypothetically necessary.

B 852 This necessity is subjectively but only comparatively sufficient if I know no other conditions under which the end could be attained. It is absolutely sufficient and sufficient for everyone if I know with certainty that no one can know other conditions leading to the end set. In the first case my presupposition and holding true of certain conditions is merely contingent faith; in the second, necessary faith. A physician must do something for a patient in danger, but does not know the illness. He considers the appearances and, knowing nothing better, judges it to be consumption. Even in his own judgment his faith is merely contingent; another might perhaps hit upon something better. I call such contingent faith, which nevertheless underlies the actual use of means for certain actions, pragmatic faith.

The usual touchstone of whether what someone asserts is mere persuasion or at least subjective conviction, that is, firm faith, is a wager. Someone often pronounces his propositions with such confident and unbending defiance that he seems to have entirely cast off all fear of error. A wager gives him pause. Sometimes it turns out that he possesses enough persuasion to be valued at one ducat, but not at ten.

B 853 He will still risk the first, but at ten he first becomes aware of what he had not noticed before: that he might after all be mistaken. If we imagine having to stake the happiness of our entire life on something, our triumphant judgment dwindles greatly; we become extremely timid and only then discover that our faith does not reach so far. Pragmatic faith thus has only a degree, which may be great or small according to the different interest at stake.

But although we can undertake nothing in relation to an object, so that holding it true is merely theoretical, in many cases we can nevertheless conceive and imagine an undertaking for which we believe we have sufficient grounds, if there were a means of establishing the matter’s certainty. Thus in merely theoretical judgments there is an analogue of practical judgments to whose holding true the word faith applies, and which we can call doctrinal faith. If it were possible to settle the matter through some experience, I would readily wager all I possess that at least one of the planets we see has inhabitants. Hence I say that it is not mere opinion but a strong faith (on whose correctness I would already risk many advantages of life) that there are also inhabitants of other worlds.

B 854 Now we must admit that the doctrine of God’s existence belongs to doctrinal faith. For although in theoretical knowledge of the world I have nothing at my disposal that necessarily presupposes this thought as a condition of my explanations of the world’s appearances—rather, I am bound to use my reason as if everything were mere nature—purposive unity is nevertheless so great a condition of applying reason to nature that, since experience also abundantly offers examples of it, I cannot disregard it. But I know no other condition for this unity that would make it a guiding thread for investigating nature than to presuppose that a highest intelligence has ordered everything thus according to the wisest ends. Consequently, presupposing a wise author of the world is a condition of an aim that, though contingent, is not insignificant: having guidance in investigating nature. The outcome of my attempts so often confirms the usefulness of this presupposition, and nothing decisive can be brought against it, that I say far too little if I call my holding true a mere opinion. Even in this theoretical relation, I can say that I firmly believe in a God. Yet this faith is still not practical in the strict sense, but must be called doctrinal faith, which the theology of nature (physicotheology) must necessarily produce everywhere.

B 855 In view of this same wisdom, considering the excellent endowment of human nature and the brevity of life so ill suited to it, we can likewise find sufficient ground for doctrinal faith in a future life of the human soul.

In such cases, the expression of faith is an expression of modesty in an objective respect, but at the same time of firmness of confidence in a subjective one. If I were to call this merely theoretical holding true even a hypothesis I was entitled to assume, I would already be pledging myself to possess more of a concept of the constitution of a world-cause and another world than I can actually show. For even of what I assume only as a hypothesis, I must know at least enough of its properties to be permitted to invent not its concept but only its existence. The word faith, however, refers only to the guidance an idea gives me and its subjective influence in furthering my reason’s activity, which keeps me attached to it although I cannot account for it in a speculative respect.

But merely doctrinal faith has something unstable about it.

B 856 Difficulties encountered in speculation often unsettle it, although we invariably return to it again.

Moral faith is entirely different. Here something must happen with absolute necessity: I must follow the moral law in every respect. The end is inescapably fixed, and according to all my insight only one condition is possible under which this end coheres with all ends together and thereby has practical validity: that there is a God and a future world. I also know with complete certainty that no one knows other conditions leading to the same unity of ends under the moral law. Since the moral precept is thus also my maxim (as indeed reason commands that it ought to be), I shall inevitably believe in the existence of God and a future life. I am certain that nothing could shake this faith, because my moral principles themselves would thereby be overthrown, and I cannot renounce them without becoming detestable in my own eyes.

In this way, after all the ambitious aims of a reason roaming beyond the boundaries of all experience have been frustrated, enough remains to give us grounds for satisfaction in a practical respect. Admittedly, no one can boast that he knows there is a God and a future life.

B 857 For if he knows this, he is precisely the man I have long sought. All knowledge (if it concerns an object of mere reason) can be communicated, and I could therefore hope through his instruction to see my knowledge extended to so admirable a degree. No: the conviction is not logical but moral certainty. Since it rests on subjective grounds (of the moral disposition), I must not even say, “It is morally certain that there is a God,” and so on, but rather, “I am morally certain,” and so on. That is, faith in a God and another world is so interwoven with my moral disposition that, just as I run no danger of losing the latter, I have equally little fear that the former could ever be torn from me.

The only reservation here is that this rational faith rests on the presupposition of moral dispositions. If we depart from this and consider someone entirely indifferent to moral laws, the question reason raises becomes merely a problem for speculation. It can then still be supported by strong grounds from analogy, but not by grounds to which the most stubborn doubt would have to yield*. Yet no human being is free of all interest in these questions.

B 858 For although a lack of good dispositions might separate him from the moral interest, even then enough remains to make him fear a divine existence and a future. For this requires nothing more than that he at least cannot claim certainty that no such being and no future life are to be found. Since this would have to be proved through mere reason, and thus apodictically, he would have to establish the impossibility of both, something no rational person can undertake. This would be a negative faith which, though it could produce neither morality nor good dispositions, could nevertheless produce their analogue: powerfully restraining the outbreak of evil dispositions.

* The human mind takes (as I believe necessarily happens with every rational being) a natural interest in morality, although this interest is neither undivided nor practically predominant. Strengthen and enlarge this interest, and you will find reason very teachable, and even more enlightened, in uniting its speculative with its practical interest. But unless you first take care to make people good, at least halfway, you will never make sincerely believing people of them either!

But is that all, someone will say, that pure reason accomplishes by opening prospects beyond the boundaries of experience—nothing more than two articles of faith?

B 859 Common understanding could surely have accomplished as much without consulting philosophers!

I shall not extol here philosophy’s service to human reason through the laborious striving of its critique, even if the outcome should prove merely negative; something more will be said of that in the following section. But do you demand that a cognition concerning all human beings should exceed common understanding and be discovered for you only by philosophers? Precisely what you criticize is the best confirmation of the correctness of the foregoing assertions. It reveals what could not have been foreseen at the outset: that in matters concerning all human beings without distinction, nature cannot be accused of distributing its gifts partially, and that, regarding the essential ends of human nature, the highest philosophy can get no further than the guidance nature has also granted the most ordinary understanding.

B 860 Transcendental Doctrine of Method Chapter Three The Architectonic of Pure Reason

By an architectonic I understand the art of systems. Since systematic unity is what first makes ordinary cognition into science, that is, turns a mere aggregate of cognitions into a system, architectonic is the doctrine of the scientific in our cognition in general, and therefore necessarily belongs to the doctrine of method.

Under reason’s government, our cognitions in general must not constitute a rhapsody but a system, in which alone they can support and further reason’s essential ends. By a system I understand the unity of manifold cognitions under an idea. This is reason’s concept of the form of a whole, insofar as through it both the extent of the manifold and the position of the parts relative to one another are determined a priori. The scientific concept of reason thus contains the end and the form of the whole congruent with it. The unity of the end, to which all parts relate, and in its idea also to one another, makes it possible to notice the absence of any part when the others are known.

B 861 It excludes any accidental addition or indeterminate magnitude of perfection without boundaries determined a priori. The whole is thus articulated (articulatio) and not heaped together (coacervatio). It can indeed grow inwardly (per intus susceptionem), but not outwardly (per appositionem), like an animal body whose growth adds no member but makes each stronger and more capable for its ends without changing the proportions.

To be carried out, the idea needs a schema: an essential manifold and order of parts determined a priori from the principle of the end. A schema devised not according to an idea, that is, from reason’s principal end, but empirically according to aims that happen to present themselves (whose number cannot be known in advance), yields technical unity. A schema arising only in accordance with an idea (where reason prescribes the ends a priori instead of awaiting them empirically) grounds architectonic unity. What we call science can arise not technically, because of the similarity of the manifold or the contingent use of cognition in concreto for various freely chosen external ends, but architectonically, because of kinship and derivation from a single highest and inner end that first makes the whole possible.

B 862 Its schema must contain the outline (monogramma) and the division of the whole into members in accordance with the idea, that is, a priori, and must distinguish this whole securely and according to principles from every other.

No one attempts to establish a science without an underlying idea. But in working it out, the schema, and even the definition he gives of his science at the outset, very rarely corresponds to his idea. For the idea lies like a seed in reason, in which all the parts lie hidden, still tightly enfolded and scarcely recognizable even under microscopic observation. Since all sciences are devised from the standpoint of a certain general interest, we must therefore explain and determine them not according to the description their author gives, but according to the idea we find grounded in reason itself through the natural unity of the parts he has brought together. For we shall find that the author, and often even his latest successors, wander around an idea they have not been able to make clear to themselves, and thus cannot determine the science’s distinctive content, articulation (systematic unity), and boundaries.

It is unfortunate that it first becomes possible for us to see the idea in a clearer light, and to design a whole architectonically according to reason’s ends, only after we have long collected, rhapsodically and under the guidance of an idea hidden within us, many cognitions relating to it as building material, and have even assembled them technically over long periods.

B 863 Systems seem to have formed like worms through a generatio aequivoca from the mere confluence of collected concepts, initially mutilated, complete in time. Yet they all had their schema as an original seed in reason merely unfolding itself. Hence not only is each articulated in itself according to an idea, but all are also purposively united with one another in a system of human cognition as members of one whole. They permit an architectonic of all human knowledge which today, when so much material has already been collected or can be taken from the ruins of collapsed ancient buildings, would be not only possible but not even difficult. Here we content ourselves with completing our own task: merely to design the architectonic of all cognition from pure reason. We begin only at the point where the common root of our cognitive power divides and puts out two stems, one of which is reason. But by reason here I understand the entire higher cognitive faculty, and thus oppose the rational to the empirical.

If I abstract from all the content of cognition considered objectively, all cognition is, subjectively, either historical or rational.

B 864 Historical cognition is cognitio ex datis, the rational, however, cognitio ex principiis. Wherever a cognition may originally be given, for its possessor it is nevertheless historical if he cognizes only to the degree and extent that it has been given to him from elsewhere, whether through immediate experience, through an account, or through instruction (in general cognitions). Hence someone who has properly learned a system of philosophy, the Wolfian system, for example, possesses nothing but complete historical cognition of Wolfian philosophy, even if he has all its principles, definitions, and proofs, together with the division of the entire doctrinal structure, in his head and can count them all off on his fingers. He knows and judges only as much as was given to him. Challenge a definition, and he does not know where to obtain another. He has formed himself according to another’s reason, but the imitative faculty is not the productive one. His cognition did not arise in him from reason; although objectively it was certainly rational cognition, subjectively it is merely historical. He has grasped and retained it well, that is, learned it, and is a plaster cast of a living human being. Cognitions that are objectively rational (that is, can originally arise only from a human being’s own reason) may bear that name subjectively as well only then.

B 865 They do so when they have been drawn from the universal sources of reason, from which critique, and even rejection of what has been learned, can also arise: that is, from principles.

Now all rational cognition proceeds either from concepts or from the construction of concepts. The former is called philosophical, the latter mathematical. I have already discussed their inner difference in the first chapter. A cognition can therefore be objectively philosophical yet subjectively historical, as with most learners and everyone who never goes beyond the school and remains a learner all his life. Yet it is remarkable that mathematical cognition, as one has learned it, can also count subjectively as rational cognition, and that this distinction does not occur in it as in philosophical cognition. The reason is that the sources of cognition from which alone the teacher can draw lie nowhere but in reason’s essential and genuine principles, and thus can neither be obtained elsewhere by the learner nor disputed. This is because reason’s use here occurs only in concreto, though still a priori, in pure intuition, which for that very reason is free from error and excludes all deception and mistake. Thus among all rational sciences (a priori), mathematics alone can be learned, never philosophy (except historically); as far as reason is concerned, we can at most learn to philosophize.

B 866 Now the system of all philosophical cognition is philosophy. We must take it objectively when by it we understand the archetype for judging all attempts to philosophize, which is to serve in judging every subjective philosophy, whose structure is often so manifold and changeable. In this way philosophy is a mere idea of a possible science, nowhere given in concreto, which we seek to approach by various paths until the one footpath, much overgrown by sensibility, is discovered, and the copy, which has so far failed, is made to match the archetype as far as human beings are permitted. Until then, no philosophy can be learned. For where is it, who possesses it, and how can it be recognized? We can learn only to philosophize: to exercise reason’s talent in following its universal principles through certain existing attempts, yet always reserving reason’s right to investigate these principles themselves in their sources and confirm or reject them.

So far, however, the concept of philosophy is only a scholastic concept: that of a system of cognition sought only as science, with no further end than the systematic unity of this knowledge, and thus the logical perfection of cognition. But there is also a cosmopolitan concept (conceptus cosmicus) that has always underlain this name, especially when it was, as it were, personified and represented as an archetype in the ideal of the philosopher.

B 867 In this respect philosophy is the science of the relation of all cognition to the essential ends of human reason (teleologia rationis humanae); and the philosopher is not a practitioner of reason but the legislator of human reason. In this sense it would be very boastful to call oneself a philosopher and presume to have equaled the archetype that lies only in the idea.

The mathematician, the natural scientist, and the logician, however excellently the former may have advanced in rational cognition generally and the latter especially in philosophical cognition, are nevertheless only practitioners of reason. There is also a teacher in the ideal who sets all these to work, using them as instruments to further the essential ends of human reason. Him alone we would have to call the philosopher. But since he himself is nowhere to be found, while the idea of his legislation is found everywhere in every human reason, we shall adhere solely to the latter.

B 868 We shall determine more closely what systematic unity philosophy, according to this cosmopolitan concept*, prescribes from the standpoint of ends.

* Cosmopolitan concept here means one concerning what necessarily interests everyone. I therefore determine a science’s aim according to scholastic concepts when it is regarded merely as one skill among others for certain freely chosen ends.

Essential ends are not on that account the highest ends, of which (in a perfect systematic unity of reason) there can be only one. They are therefore either the final end or subordinate ends necessarily belonging to it as means. The former is nothing but the entire vocation of the human being, and philosophy concerning it is called morals. Because of this priority of moral philosophy over every other pursuit of reason, the ancients always understood by the name philosopher at the same time, and above all, the moralist. Even today the outward illusion of self-mastery through reason causes someone to be called a philosopher by a certain analogy, despite his limited knowledge.

The legislation of human reason (philosophy) has two objects, nature and freedom, and therefore contains both the law of nature and the moral law, initially in two separate philosophical systems, but ultimately in a single one. The philosophy of nature concerns everything that is; the philosophy of morals concerns only what ought to be.

All philosophy, however, is either cognition from pure reason or rational cognition from empirical principles. The former is called pure, the latter empirical philosophy.

B 869 The philosophy of pure reason is either a propaedeutic (preliminary exercise), investigating reason’s capacity with regard to all pure cognition a priori, and is called critique; or, second, the system of pure reason (science), the whole (true as well as apparent) philosophical cognition from pure reason in systematic coherence, and is called metaphysics. Yet this name can also be given to the whole of pure philosophy, including critique, to comprise both the investigation of everything that can ever be cognized a priori and the exhibition of what constitutes a system of pure philosophical cognitions of this kind, distinguished from every empirical and likewise from mathematical use of reason.

Metaphysics divides into that of the speculative and that of the practical use of pure reason, and is thus either metaphysics of nature or metaphysics of morals. The former contains all pure rational principles from mere concepts (thus with the exclusion of mathematics) of theoretical cognition of all things; the latter contains the principles that determine action and inaction a priori and make them necessary. Now morality is the only lawfulness of actions that can be derived entirely a priori from principles. Metaphysics of morals is therefore properly pure morals, in which no anthropology (no empirical condition) is laid down as a basis.

B 870 Metaphysics of speculative reason is what is customarily called metaphysics in the narrower sense. Yet since pure moral doctrine also belongs to the distinctive stem of human, specifically philosophical, cognition from pure reason, we shall retain that name for it, although we set it aside here as not belonging to our present purpose.

It is of the utmost importance to isolate cognitions differing from others in kind and origin, and carefully prevent their flowing into a mixture with others with which they are commonly combined in use. What chemists do in separating materials, what mathematicians do in their pure theory of magnitudes, is still more incumbent on the philosopher, so that he can securely determine the contribution a particular kind of cognition makes to the understanding’s roaming use, its own value and influence. Hence human reason, ever since it has thought, or rather reflected, has never been able to dispense with a metaphysics, yet has never been able to exhibit it sufficiently purified of everything foreign. The idea of such a science is as old as speculative human reason—and what reason does not speculate, whether scholastically or popularly?

B 871 Yet we must admit that the distinction between the two elements of our cognition, one wholly within our power a priori, the other obtainable only a posteriori from experience, remained very indistinct even among professional thinkers. It could therefore never yield a determination of the boundaries of a particular kind of cognition, and thus not the genuine idea of a science that has occupied human reason so long and so intensely. Saying that metaphysics is the science of the first principles of human cognition marked out not an entirely distinctive kind but only a rank in universality, which therefore could not distinguish it recognizably from the empirical. For among empirical principles too, some are more general and thus higher than others. In the series of such a subordination (since one does not distinguish what is cognized entirely a priori from what is cognized only a posteriori), where should one make the cut separating the first part and highest members from the last and subordinate ones? What would one say if chronology could mark the epochs of the world only by dividing them into the first centuries and those following? Does the fifth century, the tenth, and so on also belong to the first? one would ask. In the same way I ask: does the concept of the extended belong to metaphysics? You answer yes! But also that of body?

B 872 Yes! And that of fluid body? You hesitate, for if this continues, everything will belong to metaphysics. This shows that the mere degree of subordination (the particular under the universal) cannot determine the boundaries of a science; in our case it is rather the complete heterogeneity and difference of origin. But another factor obscuring the fundamental idea of metaphysics was that, as cognition a priori, it shows a certain homogeneity with mathematics. Their origin a priori indeed makes them related; yet the manner of cognition from concepts in the former, compared with judging merely through construction of concepts a priori in the latter—the difference between philosophical and mathematical cognition—shows so decisive a heterogeneity that people always, as it were, felt it but could never formulate clear criteria for it. Thus, because philosophers themselves failed to develop the idea of their sciences, their work could have no determinate end and no secure guide. With so arbitrarily made a design, ignorant of the path they should take and always disputing among themselves about the discoveries each claimed to have made on his own path, they brought their science into contempt first among others and finally even among themselves.

B 873 All pure cognition a priori thus constitutes a distinctive unity by virtue of the particular cognitive faculty in which alone it can have its seat; metaphysics is the philosophy meant to exhibit that cognition in this systematic unity. Its speculative part, which has especially appropriated this name—what we call metaphysics of nature, considering everything insofar as it is (not what ought to be) from concepts a priori—is divided as follows.

Metaphysics so called in the narrower sense consists of transcendental philosophy and the physiology of pure reason. The former considers only understanding and reason themselves in a system of all concepts and principles relating to objects in general, without assuming objects that are given (Ontologia). The latter considers nature, that is, the sum of given objects (whether they be given to the senses or, if one wishes, to another kind of intuition), and is thus physiology (although only rationalis). Now reason’s use in this rational consideration of nature is either physical or hyperphysical, or better, either immanent or transcendent. The former concerns nature insofar as its cognition can be applied in experience (in concreto); the latter concerns a connection of objects of experience that exceeds all experience.

B 874 This transcendent physiology therefore has as its object either an inner or an outer connection, both going beyond possible experience. The former is the physiology of nature as a whole, transcendental cognition of the world; the latter concerns the coherence of the whole of nature with a being above nature, transcendental cognition of God.

Immanent physiology, by contrast, considers nature as the sum of all objects of the senses, thus as it is given to us, but only according to conditions a priori under which it can be given to us at all. Its objects are of only two kinds. 1. Those of the outer senses, whose sum is corporeal nature. 2. The object of inner sense, the soul, and, according to its fundamental concepts in general, thinking nature. The metaphysics of corporeal nature is called physics, but since it is to contain only the principles of its cognition a priori, rational physics. The metaphysics of thinking nature is called psychology, and for the reason just given only rational cognition of it is to be understood here.

Accordingly, the entire system of metaphysics consists of four main parts: 1. Ontology. 2. Rational physiology. 3. Rational cosmology. 4. Rational theology.

B 875 The second part, the doctrine of nature of pure reason, contains two divisions, the physica rationalis* and psychologia rationalis.

* Do not suppose that by this I mean what is commonly called physica generalis, which is more mathematics than philosophy of nature. Metaphysics of nature separates itself entirely from mathematics and has far fewer insights to offer that extend cognition than mathematics. Yet it is very important for the critique of pure cognition of the understanding as applied to nature in general. Without such a critique, even mathematicians, adhering to certain ordinary yet in fact metaphysical concepts, have unwittingly burdened the doctrine of nature with hypotheses that disappear under a critique of these principles, without in the least impairing the use of mathematics in this field (which is wholly indispensable).

The original idea of a philosophy of pure reason itself prescribes this division. It is therefore architectonic, conforming to its essential ends, not merely technical, arranged according to contingently perceived kinships and, as it were, at random. For that very reason it is also unchangeable and legislative. Yet some points here raise reservations and might weaken conviction of its lawfulness.

First, how can I expect cognition a priori, and thus metaphysics, of objects insofar as they are given to our senses, and thus a posteriori? How is it possible to cognize the nature of things according to principles a priori and arrive at a rational physiology?

B 876 The answer is that we take from experience no more than is needed to give us an object, in one case of outer sense, in the other of inner sense. The former occurs through the mere concept of matter (impenetrable lifeless extension); the latter through the concept of a thinking being (in the empirical inner representation: “I think”). Beyond this, in the entire metaphysics of these objects we would have to refrain completely from all empirical principles that might add any further experience to the concept in order to judge something about these objects from it.

Second, where does this leave empirical psychology, which has always maintained its place in metaphysics and from which in our time such great things have been expected for illuminating metaphysics, after hope was abandoned of accomplishing anything useful a priori? I answer: it belongs where the proper (empirical) doctrine of nature must be placed, on the side of applied philosophy, for which pure philosophy contains the principles a priori. Pure philosophy must therefore indeed be combined with applied philosophy, but not mixed with it. Empirical psychology must thus be banished entirely from metaphysics and is already entirely excluded by its very idea.

B 877 Nevertheless, according to scholastic custom we must still allow it a small place there (though only as an episode), for reasons of economy. It is not yet rich enough to constitute a subject of study on its own, yet is too important to be cast out altogether or attached elsewhere, where it would probably find still less kinship than in metaphysics. It is thus merely a foreigner taken in for a time, allowed to stay until it can move into its own dwelling in a comprehensive anthropology (the counterpart of the empirical doctrine of nature).

This, then, is the general idea of metaphysics. Initially more was demanded of it than could fairly be required, and people delighted for a time in pleasant expectations; finally, finding themselves deceived in their hopes, they brought it into general contempt. The entire course of our critique will have sufficiently convinced us that, although metaphysics cannot be the foundation of religion, it must always remain its bulwark. Human reason, already dialectical through the direction of its nature, could never dispense with a science that restrains it and, through scientific and fully evident self-cognition, prevents the devastation that a lawless speculative reason would otherwise inevitably wreak in morals as well as religion.

B 878 We can therefore be certain that, however aloof or dismissive those may act who know how to judge a science not by its nature but only by its contingent effects, they will always return to it as to a beloved from whom they have become estranged. For since essential ends are at issue here, reason must work restlessly either toward thorough insight or toward the destruction of good insights already possessed.

Metaphysics of both nature and morals, and especially the critique of reason venturing on its own wings, which precedes as a preliminary exercise (propaedeutically), thus alone properly constitute what we can call philosophy in the genuine sense. Philosophy relates everything to wisdom, but by the path of science, the only path which, once opened, never becomes overgrown and permits no straying. Mathematics, natural science, even empirical knowledge of the human being, have great value as means, mostly for contingent ends, but ultimately for necessary and essential ends of humanity. They serve the latter, however, only through the mediation of rational cognition from mere concepts, which, whatever name we give it, is properly nothing but metaphysics.

For this very reason, metaphysics is also the completion of all cultivation of human reason.

B 879 It is indispensable even if we set aside its influence as a science on certain determinate ends. For it considers reason according to its elements and highest maxims, which must themselves underlie the possibility of some sciences and the use of all. That as mere speculation it serves more to ward off errors than to extend cognition does not diminish its value. Rather, it gives it dignity and authority through the office of censor, which secures the general order and concord, indeed the welfare, of the scientific commonwealth, and prevents its bold and fruitful labors from departing from the principal end, universal happiness.

B 880 Transcendental Doctrine of Method Chapter Four The History of Pure Reason

This title stands here only to mark a place remaining in the system that must be filled in the future. I content myself with casting, from a merely transcendental standpoint, that of the nature of pure reason, a fleeting glance over the whole of its previous labors, which admittedly present buildings to my eye, but only in ruins.

It is remarkable enough, although naturally it could not have happened otherwise, that in philosophy’s childhood human beings began where we would now prefer to end: by studying first the cognition of God and the hope, or even the constitution, of another world. Whatever crude religious concepts may have been introduced by ancient customs surviving from the uncultivated state of peoples, these did not prevent the more enlightened from devoting themselves to free inquiry into this object. It was easily understood that there could be no more thorough and reliable way of pleasing the invisible power that rules the world, so as to be happy at least in another world, than good conduct.

B 881 Theology and morals were therefore the two incentives, or better, reference points, for all the abstract rational inquiries to which people have since devoted themselves. Yet it was properly the former that gradually drew merely speculative reason into the undertaking that subsequently became so famous under the name of metaphysics.

I shall not now distinguish the times at which this or that change in metaphysics occurred, but present only a brief outline of the differences in the idea that occasioned the principal revolutions. I find three respects in which the most notable changes on this stage of conflict have been brought about.

1 With regard to the object of all our rational cognitions, some were merely philosophers of sense, others merely philosophers of intellect. Epicurus can be called the foremost philosopher of sensibility, Plato of the intellectual. This difference between schools, subtle though it is, had already begun in the earliest times and long continued uninterrupted. Those of the first school asserted that reality is found only in objects of the senses, everything else being imagination.

B 882 Those of the second said, by contrast, that the senses contain nothing but illusion, and only the understanding cognizes what is true. The former did not thereby deny reality to concepts of the understanding, but for them it was only logical, while for the others it was mystical. The former admitted intellectual concepts but assumed only sensible objects. The latter required true objects to be merely intelligible and asserted an intuition through the pure understanding, unaccompanied by any senses, which in their opinion only confused it.

2 With regard to the origin of pure rational cognitions: whether they are derived from experience or have their source in reason independently of it. Aristotle can be regarded as the head of the empiricists, Plato of the noologists. Locke, who in more recent times followed the former, and Leibniz, who followed the latter (though at a sufficient distance from the latter’s mystical system), have nevertheless not yet been able to settle this dispute. At least Epicurus, for his part, proceeded much more consistently according to his system of sense (for his inferences never went beyond the boundary of experience), than Aristotle and Locke (but especially the latter). Locke, having derived all concepts and principles from experience, goes so far in their use that he asserts God’s existence and the soul’s immortality can be proved as evidently as any mathematical theorem.

B 883 (Yet both objects lie entirely outside the boundaries of possible experience.)

3 With regard to method. If something is to be called a method, it must be a procedure according to principles. Now the method currently prevailing in this branch of the investigation of nature can be divided into naturalistic and scientific. The naturalist of pure reason makes it his principle that common reason without science (which he calls sound reason) can accomplish more regarding the most sublime questions constituting metaphysics’ task than speculation can. He thus asserts that the moon’s size and distance can be determined more securely by eye than through mathematical detours. This is mere misology elevated into principles; and, most absurd of all, neglect of every artful means is praised as a method of its own for extending cognition. For as for naturalists from lack of further insight, nothing can rightly be held against them. They follow common reason without boasting of their ignorance as a method supposedly containing the secret of drawing truth from Democritus’s deep well. Quod sapio, satis est mihi; non ego curo, esse quod Arcesilas aerumnosique Solones, Pers. is their motto, with which they can live contentedly.

B 884 They can live praiseworthily with it, too, without troubling themselves about science or disrupting its business.

As for those who follow a scientific method, they have the choice here of proceeding either dogmatically or skeptically, but in every case the obligation to proceed systematically. If I name the celebrated Wolf for the former and David Hume for the latter, I can leave the rest unnamed for my present purpose. The critical path alone remains open. If the reader has had the kindness and patience to travel it in my company, he may now judge whether, should he care to contribute his part toward making this footpath a highway, what many centuries could not accomplish might not yet be attained before the present one ends: to bring human reason to complete satisfaction in what has always, but until now fruitlessly, occupied its thirst for knowledge.

B 733 II. Transcendental Doctrine of Method

B 735 Suppose I look at the sum of all cognition that pure, speculative reason can have as one building, one that we at least carry the idea of within us. In the Transcendental Doctrine of Elements, I’d say, we added up the building materials and worked out what building they would be enough for, and how tall and how sturdy it could be. It turned out, of course, that we had a tower in mind, one that was to reach the sky, but the supply of materials was enough only for a dwelling. That dwelling was roomy enough for what we do down on the plain of experience, and tall enough to look out over that plain. The bold project had to fail for lack of material. And that leaves out the confusion of languages, which was bound to split the workers over the plan and scatter them across the world, each going off to build alone to their own design. Now the plan matters to us more than the materials. We have been warned not to gamble on some arbitrary, blind design that might be beyond all our powers. Still, we can hardly give up on putting up a solid place to live. So what we need is an estimate for a building that fits the supply we actually have and also suits our needs.

So the Transcendental Doctrine of Method, as I use the term, settles what the formal conditions are.

B 736 It settles them for a complete system of pure reason. To that end our subjects will be a discipline, a canon, an architectonic and, last of all, a history of pure reason. In the transcendental setting we will accomplish what the schools look for, and do badly, under the name of a practical logic for the use of the understanding in general. The reason they do it badly is that general logic isn’t restricted to any special kind of cognition by the understanding (the pure kind, for example), or to certain objects. If it borrows nothing from other sciences, all it can do is set out headings for possible methods, along with the technical terms that all sorts of sciences use for systematic matters. These give the beginner a first acquaintance with names, whose meaning and use the beginner has yet to learn.

Transcendental Doctrine of Method First Chapter Pure Reason’s Discipline

Take negative judgments, the ones that are negative in content and not just in logical form. People hungry for knowledge don’t hold them in much regard. Some even see them as jealous enemies of our restless drive to widen our cognition.

B 737 It takes almost an apology just to get them tolerated, and even more to win them favor and respect.

Logically, you can put any proposition you like in negative form. But look at the content of our cognition in general, and ask whether a judgment widens it or narrows it. Then denying judgments have one job of their own, which is simply to keep error out. That is why negative propositions meant to block a false cognition, where no error is possible anyway, are perfectly true but empty. They don’t suit their purpose at all, and for that very reason they are often silly. Take the claim of a certain school orator that Alexander couldn’t have conquered countries without an army.

But take a case where the limits on our possible cognition are very narrow, the urge to judge is strong, the illusion on offer is very deceptive, and the harm from error is serious. In that case the negative side of instruction, which does nothing except guard us against errors, matters even more than a good deal of positive teaching that might add to our cognition. We call discipline the constraint that holds back, and in the end wipes out, a constant tendency to stray from certain rules. Discipline differs from culture. Culture is meant only to give a skill, without abolishing another skill that is already there. So take the shaping of a talent.

B 738 A talent already has a drive of its own to show itself. In its case discipline will make a negative* contribution, while culture and doctrine make a positive one.

* I know that in the language of the schools “discipline” is usually treated as if it meant the same as “instruction.” But in many other cases the first word, in the sense of training, is carefully kept apart from the second, in the sense of teaching. The nature of things also calls for keeping the only fitting words for this difference. So I wish that no one would ever permit the word “discipline” to be used in anything but a negative sense.

Everyone will readily grant that temperament needs discipline in some respects. So do talents that like to allow themselves free and unlimited movement, such as imagination and wit. That reason should need it too may well seem strange. After all, reason is the very faculty whose business is to lay down discipline for all other efforts. And in fact reason has escaped such a humbling until now, for just this reason: it comes on with such solemnity and such a thorough air of dignity that no one could easily suspect it of a frivolous game, played with fancies instead of concepts and with words instead of things.

Reason needs no critique in its empirical use, since its principles are put to the test again and again on the touchstone.

B 739 That touchstone is experience. It needs none in mathematics either, where its concepts must be shown at once in pure intuition, in concreto, so that anything baseless or arbitrary comes to light immediately. But there is a use where neither empirical nor pure intuition holds reason to a visible track. That is its transcendental use, working from bare concepts. There it needs discipline so badly, to tame its urge to expand past the tight boundaries of possible experience and to keep it from excess and error, that the entire philosophy of pure reason deals only with this negative benefit. Individual lapses can be put right by censure, and their causes by critique. But when we meet, as in pure reason, a whole system of deceptions and delusions, closely tied together and joined under shared principles, a legislation all of its own seems to be called for, and a negative one. Under the name of discipline it would set up, out of the nature of reason and of the objects of its pure use, a kind of system of caution and self-examination. No false, quibbling illusion could survive before it. Whatever reasons it offered to dress itself up, it would give itself away at once.

B 740 But note this well. Here in the second main division of the transcendental critique, I aim the discipline of pure reason not at content but only at the method of cognition from pure reason. The content was already dealt with in the Doctrine of Elements. Now, the way reason is used has a lot in common, no matter what object it is applied to. Yet to the extent that it is to be transcendental, it also differs so essentially from every other use that errors can’t be prevented without the warning, negative teaching of a discipline set up especially for it. Those errors must unavoidably come from applying, in the wrong way, methods that suit reason elsewhere but just don’t fit here.

First Chapter Section One Pure Reason’s Discipline in Its Dogmatic Use

Mathematics gives the most brilliant example of pure reason expanding happily by its own power, with no help from experience. Examples are catching, above all for a faculty that naturally flatters itself it will have in other cases the very same luck it had in one. So pure reason hopes for the same luck when it is used transcendentally.

B 741 It hopes to expand there as happily and as soundly as it did in mathematics, most of all by using there the same method that has been of such plain benefit here. For us it is therefore a big question whether the method for reaching apodictic certainty, which in mathematics is called mathematical, is the same as the one by which philosophy seeks that very same certainty, and which there would have to be called dogmatic.

Philosophical cognition is cognition by reason from concepts. Mathematical cognition is cognition by reason from the construction of concepts. To construct a concept means to present a priori the intuition that corresponds to it. So constructing a concept requires a non-empirical intuition. As an intuition, that is a single object. But it is also the construction of a concept, which is a general representation, so it has to express in the representation a universal validity for all possible intuitions that come under the same concept. Here is how I construct a triangle. I present the object that matches this concept, either through imagination alone, in pure intuition, or afterward on paper, in empirical intuition. Either way it is done wholly a priori, with no model borrowed from any experience. The figure I draw is one single figure.

B 742 It is empirical, and yet it serves to express the concept without harming the concept’s generality. For in this empirical intuition we look only at the act of constructing the concept. Many determinations, size, sides and angles among them, make no difference to the concept. So we set aside these differences, which leave the concept of the triangle unchanged.

So philosophical cognition looks at the particular only in the universal. Mathematical cognition looks at the universal in the particular, even in the single case, and yet it does so a priori and by means of reason. This single case is fixed by certain universal conditions of construction. In the same way the object of the concept, which the single case matches only as its schema, has to be thought of as universally determined.

These two kinds of rational cognition differ essentially in this form. The difference doesn’t rest on their matter, or objects. Some people thought they could tell philosophy from mathematics by saying that philosophy has only quality as its object and mathematics only quantity. They took the effect for the cause. The form of mathematical cognition is the reason it can deal only with quanta. Magnitudes are the only things whose concept can be constructed, meaning laid out in intuition a priori.

B 743 Qualities can be presented in no intuition other than an empirical one. So a rational cognition of them can be possible only through concepts. In the same way, an intuition for the concept of reality can come from experience only. Nobody can ever come to have one a priori, out of themselves, before they have empirical consciousness of it. We can make the shape of a cone intuitable, with no empirical help, by the concept alone. But the color of this cone will have to have been given beforehand in one experience or another. Take cause in general. The only way I can show that concept in intuition is by an example that experience happens to put in my hands, and so on. Besides, philosophy is concerned with magnitudes no less than mathematics is, for instance with totality and infinity. Mathematics also concerns itself with the difference between lines and planes, which are spaces of different quality, and with the continuity of extension, which counts as one of its qualities. In such cases they have a shared object. Even so, the way reason handles that object is entirely different in philosophical and in mathematical study. Philosophy keeps strictly to general concepts. Mathematics can do nothing with the bare concept. It hurries at once to intuition, where it considers the concept in concreto, but not empirically.

B 744 It does so only in an intuition it has presented, that is constructed, a priori. There, whatever follows from the general conditions of the construction must hold universally for the object of the constructed concept too.

Say a philosopher is given the concept of a triangle. The job is to find out, in the way philosophers work, how the total of its angles relates to a right angle. Their whole stock is the concept of a figure bounded by three straight lines, and, within that, the concept of as many angles. They can ponder this concept as long as they like and will produce nothing new. They can take apart the concept of a straight line, or an angle, or the number three, and make it clear. But they can’t arrive at other properties that don’t lie in these concepts at all. Now let the geometer take up the same question. The geometer begins at once by constructing a triangle. They know that two right angles together amount to exactly as much as the sum of all adjacent angles that can be drawn at one point on a straight line. So they extend one side of the triangle and get two adjacent angles that together equal two right angles. Next the outer one of these angles is divided, by a line drawn parallel with the side opposite. The geometer now sees that an outer adjacent angle arises here that equals an inner one, and so on. They go on in this way.

B 745 Guided by intuition at every step, a chain of inferences brings them to a solution of the question that is perfectly clear and universal at once.

Mathematics doesn’t only construct magnitudes (quanta), as in geometry. It also constructs bare magnitude (quantitatem), as in algebra, and there it sets aside entirely the nature of the object that is to be thought through such a concept of magnitude. It then picks a notation for all constructions of magnitude in general (numbers, for addition, subtraction and so on, and extraction of roots). Once it has also given signs for the general concept of magnitudes in all their various relations, it displays in intuition, by certain general rules, every operation that magnitude produces and alters. To divide one magnitude by another, it writes the signs of both together in the form that stands for division, and so on. In this way a symbolic construction takes mathematics, just as well as an ostensive or geometric construction (of the objects themselves) does in geometry, to a place that discursive cognition by bare concepts could never reach.

Why do two craftsmen of reason find themselves in such different positions, when one goes by concepts and the other by intuitions that they present a priori to match those concepts?

B 746 The transcendental first principles laid out above make the answer clear. What matters here is not analytic propositions, which can be produced just by taking concepts apart. (There the philosopher would no doubt have the edge over a rival.) What matters is synthetic propositions, and in particular ones that are to be cognized a priori. I am not supposed to attend to what I really think when I think my concept of a triangle, which is nothing more than the bare definition. I am meant to go beyond the concept to properties that aren’t in it but still belong to it. That can be done in only one way, by determining my object under the conditions of either empirical or pure intuition. The first way would give only an empirical proposition, obtained by measuring the angles. It would contain no universality, let alone necessity, and we aren’t talking about anything of that sort. The second way is mathematical construction, in this case geometrical construction. Working in a pure intuition, as I would in an empirical one, I add whatever manifold belongs to the general schema for triangles, and so to the triangle’s concept. And that is how universal synthetic propositions have to be constructed.

So I would philosophize about the triangle in vain, that is, think it over discursively.

B 747 I would get not an inch further than the bare definition, which is where I would have to start anyway. There is, it is true, a transcendental synthesis made of nothing but concepts, and again only the philosopher can manage it. But all it ever concerns is a thing in general, namely under what conditions perception of such a thing could belong to possible experience. Mathematical problems don’t ask this, and they don’t ask about existence at all. They ask what properties the objects have in themselves, solely so far as these are bound up with their concept.

In the example we gave, we tried only to bring out how large a difference there is between two uses of reason. One is the discursive use, by concepts. The other is the intuitive use, through the construction of concepts. The natural question now is what makes it necessary to use reason in two ways, and by what conditions we can tell whether only the first is at work or the second as well.

All our cognition does relate in the end to possible intuitions, since an object is given only through these. Now a concept a priori (a non-empirical concept) either has a pure intuition already in it, and then it can be constructed. Or it has nothing but the synthesis of possible intuitions that are not given a priori. In that case we can indeed judge by means of it.

B 748 The judgments are synthetic and a priori, but they can only be discursive, made by concepts, and never intuitive, made by constructing the concept.

Of all intuition, the only part given a priori is the mere form of appearances, namely space and time. Treating these as quanta, we can present a concept of them a priori in intuition, that is, construct it. We can do this together with their quality, their shape, or for their quantity alone, by number. That quantity is the bare synthesis of the homogeneous manifold. Appearances also have matter, and that is what gives us things in space and time. It can be represented only in perception, so a posteriori. Just one concept stands for this empirical content of appearances a priori, the concept of a thing in general. Synthetic cognition of a thing in general, a priori, gives nothing beyond the bare rule for synthesizing whatever perception may deliver a posteriori. It never delivers an intuition of the real object a priori, since that intuition has to be empirical.

A synthetic proposition is transcendental when it is about things in general and their intuition can’t be given a priori at all. So transcendental propositions can never be given by constructing concepts, only by concepts a priori. They contain nothing but the rule for looking, through experience, for a certain synthetic unity in what can’t be presented in intuition a priori.

B 749 I mean perceptions. And in no case can they present even one of their concepts a priori. They do that only a posteriori, by way of the experience that first becomes possible under those synthetic principles.

Suppose we want to make a synthetic judgment about a concept. Then we have to move outside it, to the intuition where it is given. Staying with what the concept contains would give a merely analytic judgment, which only explains the thought by what is actually in it. But I can move from the concept to the pure or empirical intuition that matches it. In that intuition I look at the concept in concreto and find out, either a priori or a posteriori, what applies to its object. The first is rational, mathematical cognition, obtained by constructing the concept. The second is merely empirical, or mechanical, cognition, and it can never yield necessary, apodictic propositions. Here is an example. Say I break down my empirical concept of gold. All I would gain is the ability to list everything I actually think when I say the word. That improves my cognition logically, but adds nothing to it. Now suppose I take the matter that goes by this name and make observations with it.

B 750 They will hand me various synthetic but empirical propositions. Or take the mathematical concept of a triangle. I would construct it, meaning give it a priori in intuition, and that yields synthetic but rational cognition. A transcendental concept is different: say reality, substance, force and so on. Once I am given one, it points to neither an empirical nor a pure intuition, only to the synthesis of empirical intuitions, and those can’t be given a priori. The synthesis can’t reach out a priori to an intuition matching the concept. So no determining synthetic proposition can come from it, only a principle governing the synthesis* of possible empirical intuitions. A transcendental proposition is therefore synthetic rational cognition from bare concepts, so a discursive one. It first makes all synthetic unity of empirical cognition possible, yet gives no intuition a priori.

* With the concept of cause I do really step outside the empirical concept of an event (something happening). But I don’t step to an intuition that presents the concept of cause in concreto. I step to the conditions of time in general, which might be found in experience to fit the concept of cause. So I proceed by concepts alone, and can’t proceed by constructing concepts. That is because a concept of this kind is a rule for combining perceptions into a synthesis, and perceptions are not pure intuitions, so they can’t be given a priori.

B 751 So reason is used in two ways. In what they share they are alike, since the cognition is universal and is produced a priori. In how they proceed they differ widely. The reason is that every appearance, which is the way all objects reach us, has two parts. One is the form of intuition, space and time, and that can be fully known and fixed a priori. The other is the matter, the physical element or content. It means something that turns up in space and time, so it carries existence and answers to sensation. The matter can never be given in a determinate way except empirically. About it we can have nothing a priori except indefinite concepts of how possible sensations are synthesized, provided they belong to the unity of apperception (within a possible experience). About the form we can fix our concepts a priori in intuition. By a uniform synthesis we generate the objects themselves, in space and time, simply by treating them as quanta. The first of these is called the use of reason by concepts. There we can do nothing except bring appearances, as far as their real content goes, under concepts. Afterward those concepts can be fixed only empirically, a posteriori, though following the concepts as rules of an empirical synthesis. The second is the use of reason by the construction of concepts.

B 752 These concepts already go to an intuition a priori, and for that very reason they can be given in a fixed way a priori, in pure intuition, with no empirical data at all. Take whatever there is, some thing in space or time. We can ask whether it is a quantum, and how far. We can ask whether existence, or a lack of it, must be represented in it. Is the something that fills space or time a first substratum, or only a determination? Does its existence stand in relation to something else, as cause or as effect? Finally, does it stand alone, or in mutual dependence with other things where existence is concerned? We can weigh whether this existence is possible, actual or necessary, or the opposite of these. All this is the business of rational cognition from concepts, and that is what we call philosophical. But fixing an intuition a priori in space (shape), dividing time (duration), or knowing only the general element in synthesizing the same item in time and in space, plus the magnitude of an intuition in general that follows from it (number): that is a task for reason through the construction of concepts, and it is called mathematical.

Reason has had great luck through mathematics. Quite naturally that luck suggests that its success will carry over outside the field of magnitudes too, if not for reason itself then at least for its method.

B 753 In mathematics, after all, reason turns every one of its concepts into intuitions it can supply a priori, and that makes it master of nature, so to speak. Pure philosophy, in contrast, fumbles around in nature with a priori concepts that work discursively. It can’t show the reality of those concepts a priori in intuition, and so it can’t make them trustworthy either. The masters of this art also seem to lack neither confidence in themselves nor the public’s great hopes of their skill, should they ever take this matter on. They have hardly ever philosophized about their mathematics (a hard job!). So the specific difference between one use of reason and the other never occurs to them. Rules that are in common circulation and used empirically, borrowed from ordinary reason, count for them as axioms. Where the concepts of space and time come from, which they work with as the only original quanta, is of no concern to them. In the same way it seems pointless to them to look into where the pure concepts of the understanding come from, and with that how far they hold. They just want to use them. In all this they are quite right, as long as they don’t cross the boundary assigned to them, which is the boundary of nature. But in fact they slip without noticing from the field of sensibility onto the unsteady ground of pure and even transcendental concepts. There the footing (instabilis tellus, innabilis unda) won’t let them stand.

B 754 Nor will it let them swim. They can take only fleeting steps, of which time keeps not the slightest trace. In mathematics, by contrast, their course makes a highway that even the latest descendants can walk with confidence.

We have made it our duty to mark out exactly, and with certainty, where the boundaries of pure reason lie when it is used transcendentally. But this kind of striving has a peculiar feature. Despite the most emphatic and clearest warnings, people still let hope string them along before they give up the plan of getting beyond the boundaries of experience into the charming regions of the intellectual. So it is necessary to pull up, so to speak, the final anchor of an imaginative hope. We have to show that bringing the mathematical method into this kind of cognition can bring no advantage at all. The only thing it can do is show all the more plainly its own weak spots, namely that the art of measuring and philosophy are two entirely different things. They do join hands in natural science, but neither can copy the other’s way of working.

Mathematics gets its thoroughness from definitions, axioms and demonstrations. I will be content to show this: none of these three, as the mathematician understands them, can be supplied by philosophy.

B 755 Nor can philosophy imitate them. And I will show that a geometer working by their method can build only card houses in philosophy, and that a philosopher working by theirs can stir up only chatter in mathematics’ share, even though knowing its boundaries is exactly what philosophy consists in. I will also show that even the mathematician, unless nature has already limited their talent and confined it to their own field, can’t brush aside the warnings of philosophy or set themselves above them.

1 On definitions. To define, as the word itself suggests, really means no more than this: originally to present, inside its boundaries, the complete concept of a thing*. By that standard an empirical concept can’t be defined at all. It can only be explicated. In such a concept we hold just a few marks of a certain kind of object of the senses. So we can never be sure that a word naming the same object doesn’t make us think of more of its marks one time and fewer another time.

B 756 One person might think of gold as having weight, color and toughness, and also the property of not rusting. Another person might know nothing of that last one. We use certain marks only as long as they are enough for telling things apart. New observations drop some marks and bring in others. A concept like this therefore never sits between firm boundaries. And what would be the point of defining it anyway? Suppose we are talking about water and its properties. We won’t stop at what we think when we hear the word “water.” We go on to experiments. Water, with the handful of marks that cling to the word, is supposed to be only a label for the thing, not a concept of it. So the so-called definition is nothing more than a fixing of what a word means. Strictly speaking, concepts given a priori can’t be defined either. That is the second point. Take substance, cause, right, equity and so on. Only if I know that a distinct representation of a concept (a concept given, as yet, only confusedly) is adequate to its object can I be sure it has been developed completely. A concept, in the shape in which it is given, may carry many obscure representations that we leave out when we analyze it, even though we depend on them every time we use it. So whether my analysis of the concept is complete is always doubtful.

B 757 It can be made probable by many fitting examples, but never apodictically certain. In place of the word “definition” I would rather use “exposition.” That word stays cautious, and a critic can accept an exposition up to a point and still have doubts about its completeness. Since neither empirical nor a priori concepts can be defined, the only ones left for this trick are concepts that someone has made up at will. In that case I can always define my concept. After all, I must know what I meant to think, since I made the concept myself on purpose. Neither the nature of the understanding nor experience handed it to me. But I can’t claim that I have defined a true object by doing so. If the concept depends on empirical conditions (a ship’s clock, for example), this made-up concept still doesn’t give the object or its possibility. From it I don’t even know whether there is any object at all. My explanation deserves the name of a declaration (of my project) more than that of a definition of an object. So the only concepts left that suit defining are those that hold a self-chosen synthesis, one that can be constructed a priori. Therefore only mathematics has definitions. Mathematics presents the object it thinks a priori in intuition.

B 758 That object can’t contain more or less than the concept does, because the explanation gave the concept of the object originally, that is, without deriving it from anything else. German has only one word, “Erklärung” (explanation), for “exposition,” “explication,” “declaration” and “definition.” So we must relax our strict demand a little, since we denied philosophical explanations the honorable name of definition. We’ll limit this remark to the following. In philosophy, definitions come about only as expositions of concepts already given. In mathematics they come about as constructions of concepts made originally. The first kind arises only analytically, by taking the concept apart (and the completeness of that is not apodictically certain). The second arises synthetically, and so it makes the concept itself, while the first only explains it. From this it follows:

* Completeness means that the marks are clear and sufficient. Boundaries means precision, that is, having no more marks than the complete concept calls for. And original means that this setting of boundaries isn’t derived from anywhere else. If it were, it would still need a proof, and that would disqualify the supposed explanation from coming first among all judgments about an object.

a) Philosophy shouldn’t copy mathematics by sending the definition ahead of everything else, apart from perhaps a rough try. Philosophical definitions are analyses of given concepts. So those concepts come first, though still confused, and the incomplete exposition comes before the complete one. From a few marks drawn out of an analysis that isn’t finished yet, we can infer a good deal in advance, before we arrive at the complete exposition, which is the definition.

B 759 To put it briefly, in philosophy a definition, being exactly measured distinctness, should close the work and not open it*. Mathematics is different. Before the definition we have no concept whatever, because the definition is what first provides one. So mathematics must begin with it, and always can.

* Philosophy teems with faulty definitions, above all ones that hold real elements of a definition but not the full set. If we could do nothing at all with a concept until we had defined it, all philosophizing would be in bad shape. But as far as the elements (of the analysis) reach, we can always make good and safe use of them. So even defective definitions can be used to great benefit. By these I mean propositions that are not yet really definitions but are otherwise true, and so come close to being definitions. In mathematics the definition belongs ad esse, to the thing’s being. In philosophy it belongs ad melius esse, to its being better. It is fine to reach one, but often very hard. Jurists are still looking for a definition of their concept of right.

b) Mathematical definitions can never be wrong. Since the concept is first given by the definition, it contains exactly what the definition wants thought through it. Nothing incorrect can turn up in the content. Still, there can occasionally be a mistake in the form (the dress), though only rarely, and the mistake is one of precision. Take the common explanation of the circle. It says the circle is a curved line.

B 760 All the points on it are the same distance from a single point (the center). The fault here is that the word “curved” has slipped in without need. There has to be a separate theorem, which follows from the definition and is easy to prove: any line whose points are all the same distance from one point is curved (no part of it is straight). Analytic definitions, by contrast, can go wrong in many ways. They can bring in marks that really weren’t in the concept. Or they can lack the completeness that is the essential point of a definition, since we can’t be fully certain that our analysis is complete. That is why the mathematical way of defining can’t be copied in philosophy.

2 On axioms. These are synthetic principles a priori, in so far as they are immediately certain. Now one concept can’t be connected with another both synthetically and immediately. That is because, to go beyond a concept, we need a third, mediating cognition. Now philosophy is nothing but rational cognition by concepts, so no principle will be found in it that deserves the name of an axiom. Mathematics, however, is capable of axioms, because by constructing concepts in the intuition of the object it can link the object’s predicates a priori and immediately. For example, three points always lie in one plane.

B 761 A synthetic principle from concepts alone, by contrast, can never be immediately certain. Consider this proposition: whatever happens has a cause. Here I have to look around for a third thing, namely the condition of determining time in an experience. The concepts alone could never have shown me such a principle, immediately and directly. So discursive principles are quite different from intuitive ones, that is, axioms. Discursive principles always require a deduction as well, while axioms can do without one entirely. Axioms are evident for that very reason, and philosophical principles, certain as they may be, can never claim that. So no synthetic proposition of pure, transcendental reason comes anywhere near being as plainly evident (to use the defiant phrase) as the statement that two times two gives four. In the Analytic, where I set out the principles of pure understanding in a table, I did speak of certain axioms of intuition. But the principle given there was itself no axiom. It was meant only to name the underlying principle that makes axioms possible at all, and it was itself just a principle from concepts. For even the possibility of mathematics has to be shown in transcendental philosophy. So philosophy has no axioms, and it may never simply command its principles a priori.

B 762 It has to bring itself to justify its right to them by a thorough deduction.

3 On demonstrations. Only an apodictic proof that is also intuitive deserves the name demonstration. Experience does teach us what is there, but not that it couldn’t be otherwise. So empirical grounds of proof can never yield an apodictic proof. And from concepts a priori (in discursive cognition), intuitive certainty, that is, evidence, can never arise, no matter how apodictically certain the judgment itself may be. That is why only mathematics has demonstrations. It draws its cognition not from concepts but from constructing them, which means from an intuition that can be supplied a priori to fit them. Even the method algebra uses with its equations is a construction, though not a geometrical one. From the equations it produces the truth together with the proof by reduction. It is a construction by symbols, in which we lay out the concepts in intuition by means of signs, above all concepts of the relation of magnitudes. It secures every inference against errors by putting each one before our eyes, quite apart from any use in discovery. Philosophical cognition has to do without this advantage, because it must always look at what is universal abstractly, in abstracto, by means of concepts. Mathematics looks at what is universal in concreto, in a single intuition.

B 763 And it still works a priori with pure representation, where every misstep shows. That is why I would rather call the philosophical ones acroamatic (discursive) proofs than demonstrations. They can be carried on only through words alone (the object in thought), whereas demonstrations, as the word itself indicates, proceed in the intuition of the object.

All this shows that it simply doesn’t suit philosophy’s nature, above all in the realm of pure reason, to strut around in a dogmatic manner and dress itself up in the titles and ribbons of mathematics. Philosophy isn’t a member of that order, though it has good cause to hope for a sisterly alliance with it. Such claims are empty conceit, and they can never work. They can only reverse philosophy’s own aim, which is to uncover the delusions of a reason that misjudges its boundaries and, by clearing up our concepts enough, to bring the self-conceit of speculation back to modest but thorough self-knowledge. So in its transcendental attempts reason can’t look straight ahead with such confidence, as if the road it has traveled led so directly to the goal. And it can’t count so boldly on the premises it started from that it never needs to look back and watch for errors. Such errors may turn up as the inferences go on, and may have been overlooked in the principles.

B 764 They would make it necessary either to define the principles more closely or to change them altogether.

I divide all apodictic propositions (whether provable or immediately certain) into dogmata and mathemata. A dogma is a synthetic proposition drawn directly from concepts. A mathema is a proposition of that sort that comes through the construction of concepts. Analytic judgments teach us nothing more about the object than what is already in the concept we have of it. They don’t widen cognition past the concept of the subject. They only make it clearer. So they can hardly be named dogmas (a word we might render as “doctrinal sayings”). Of those two sorts of a priori synthetic propositions, ordinary speech lets only the ones in philosophical cognition wear this name. Hardly anyone would call the propositions of arithmetic or geometry dogmata. So this usage confirms the explanation we gave: only judgments from concepts, and not those from the construction of concepts, can be called dogmatic.

Taken in its purely speculative use, pure reason as a whole holds no directly synthetic judgment from concepts at all, not even one. As we have shown, it can make no synthetic judgments through ideas that carry objective validity.

B 765 Through concepts of the understanding it does set up secure principles, but never directly from concepts. It does so only indirectly, by tying those concepts to something completely contingent, namely possible experience. Once that is presupposed (something as an object of possible experiences), the principles are indeed apodictically certain. But in themselves they can’t be cognized (directly) a priori at all. No one can see the truth of the proposition that whatever happens has a cause, in a thorough way, from those given concepts alone. That is why it is not a dogma, even though from another point of view it can be proved quite well and apodictically. That point of view is the single field of its possible use, experience. It is called a principle and not a theorem, even though it has to be proved, because it has a special property: it first makes possible its own ground of proof, namely experience, and must always be presupposed in that experience.

Suppose there are no dogmata at all in the speculative use of pure reason, not even as to content. Then every dogmatic method is unsuitable in itself, whether it is borrowed from the mathematician or is meant to become a manner of its own. All it does is hide faults and errors, and it deceives philosophy, whose real aim is to let every step of reason be seen in the clearest light. Still, the method can always be systematic.

B 766 Our reason, taken subjectively, is itself a system, but when it works in its pure use, with bare concepts alone, it amounts to just a system of searching for principles of unity, and only experience can supply the material for that unity. A transcendental philosophy has a method peculiar to itself, but there is nothing to say about it here. We are dealing only with a critique of our resources. The questions are whether any building can go up at all, and how tall a structure we might put up using the materials on hand, namely pure concepts a priori.

First Chapter Section Two Pure Reason’s Discipline with Regard to Its Polemical Use

In all its undertakings reason must submit to critique. No ban can cut into critique’s freedom without hurting reason itself and bringing on it a suspicion that does it harm. Nothing is so important for its usefulness, and nothing so sacred, that it may slip away from this testing and inspecting search, which pays no regard to persons. Reason’s very existence rests on this freedom. Reason has no dictatorial authority. Its verdict is always only the agreement of free citizens.

B 767 Each of them has to be able to voice their reservations, even their veto, without holding back.

Reason can never refuse critique, but that doesn’t mean it always has cause to fear it. When pure reason works dogmatically (not mathematically), it isn’t so conscious of having kept its supreme laws with perfect care. So it would have to stand under the scrutiny of a higher reason sitting as judge. It would do so timidly, with every claim to dogmatic authority laid aside.

Things are quite different when reason isn’t up against a judge’s censure but is answering what a fellow citizen claims, and only has to defend itself. The fellow citizen’s claims want to be dogmatic too, though in denying, just as reason’s own claims are dogmatic in affirming. So a justification kat’ anthropon is available. It protects against every encroachment and secures a titled possession that need not fear anyone else’s pretensions, even though the possession itself can’t be proved sufficiently kat’ aletheian.

I call it the polemical use of pure reason when it defends its propositions against dogmatic denials of them. The issue here isn’t whether reason’s claims could be false after all. The issue is only that nobody can ever claim the opposite with apodictic certainty.

B 768 Nobody can claim it even with greater plausibility. For we don’t hold our possession as a favor granted on request when we have a title to it, even an insufficient one, and when it is completely certain that nobody can ever prove the possession unlawful.

It is saddening and dispiriting that pure reason should have an antithetic at all. Pure reason stands as the highest court over all disputes, and yet it is supposed to fall into conflict with itself. Above, to be sure, we did have such an apparent antithetic of reason before us. But it turned out to rest on a misunderstanding. Going along with a widespread prejudice, people treated appearances as things in themselves. Then they demanded an absolute completeness of the synthesis of appearances, in one way or another (and either way was equally impossible). That can’t be expected of appearances at all. So at that time there was no real contradiction of reason with itself between two propositions. One was that the series made up of appearances given in themselves has a first beginning that is absolute. The other was that the same series, taken purely in itself, has no beginning at all. The two go together quite well. For appearances, as far as their existence goes (as appearances), are nothing in themselves, that is, something self-contradictory, and so assuming them naturally has to draw contradictory conclusions after it.

B 769 But a misunderstanding of this kind can’t be pleaded, and the dispute of reason can’t be settled that way, in the following cases. Suppose one side claimed, as a theist, that a highest being exists, and the other claimed, as an atheist, that none does. Or take psychology. One claim there is that everything that thinks is of absolute, permanent unity, and so is distinct from all perishable material unity. The opposite claim is that the soul isn’t a unity free of matter, and so can’t escape perishing. For the subject of the question here is free of anything alien that conflicts with its nature, and the understanding is concerned only with things in themselves, not appearances. So a true conflict would indeed turn up here, if only pure reason had something to say on the denying side that came close to the ground of an assertion. As for criticism of the grounds of proof offered by the dogmatic affirmer, that can be granted to them quite readily without giving up these propositions. These propositions do at least have the interest of reason behind them, which the opponent can’t invoke at all.

I do not share the opinion that excellent, thoughtful men (Sulzer, for example) have so often voiced when they felt the weakness of the proofs so far. They hoped that someday we might prove, with demonstrations that are plain to see, our pure reason’s two cardinal propositions: there is a God, there is a future life.

B 770 I am rather certain that this will never happen. For where could reason get the ground for such synthetic assertions, which have nothing to do with objects of experience or with their inner possibility? It is just as apodictically certain, though, that nobody will ever step forward who can maintain the opposite with the slightest plausibility, let alone dogmatically. They could demonstrate it only through pure reason. So they would have to try proving that a highest being cannot exist, and likewise the thinking subject in us as pure intelligence. But where would they get the knowledge that entitled them to judge synthetically in this way about things beyond all possible experience? So we can be quite unconcerned about anyone someday proving the opposite to us. That means we have no need to devise textbook-style proofs either. We can go on adopting those propositions that fit well with the speculative interest of our reason in its empirical use, and that are, besides, the only means of uniting it with the practical interest. Against the opponent (who must not be regarded here as a mere critic) we hold our non liquet (“it is not clear”) ready, and it is bound to confuse them. We don’t refuse their retort against us, since we always keep in reserve the subjective maxim of reason.

B 771 The opponent necessarily lacks it, and under its protection we can watch all their blows at the air with calm and indifference.

In this way there really is no antithetic of pure reason at all. The only battlefield for it would have to be sought in pure theology and psychology. But that ground bears no fighter in full armor, armed with weapons to be feared. The opponent can show up only with mockery or bragging, and these can be laughed off as child’s play. This is a comforting remark, and it gives reason courage again. For what else could reason rely on if it, the only faculty called to do away with all errors, were itself in disarray, with no hope of peace and quiet possession?

Everything nature itself arranges is good for some purpose. Even poisons serve to overpower other poisons that form in our own bodily fluids, and so they must not be missing from a complete stock of remedies (an apothecary’s shop). The objections against the persuasions and self-conceit of our merely speculative reason are themselves set for us by the nature of this reason. So they must have their good purpose and aim, which should not be thrown to the wind. Why has providence set certain objects so high, though they connect with our highest interest?

B 772 We are almost only permitted to come upon them in a perception that is vague, and that we ourselves doubt. Searching glances are provoked by this more than satisfied. Whether it does any good to venture bold claims about such views is open to doubt at the least, and may even do harm. But it is always, and beyond all doubt, useful to give reason, both as inquirer and as examiner, complete freedom, so that it can look after its own interest unhindered. That interest is served just as much by setting limits to its insights as by widening them. And it always suffers when outside hands interfere to steer reason against its natural course toward forced aims.

So let your opponent speak only in terms of reason, and fight them only with the weapons of reason. As for the good cause (the practical interest), put your worries aside, because it never comes into play in a merely speculative dispute. All the dispute reveals is a certain antinomy of reason. Since it rests on reason’s nature, it must necessarily be heard and examined. The dispute cultivates reason by viewing its object from two sides, and it corrects reason’s judgment by restricting it. The quarrel in all this concerns not the subject itself but the tone. For you still have enough left to speak the language of a firm belief.

B 773 That language is justified before the sharpest reason, even though you have had to give up the language of knowledge.

Suppose we were to ask David Hume, that cool-headed man, truly made for balance in judgment: what moved you, with laboriously brooded scruples, to undermine the persuasion, so comforting and useful to human beings, that their rational insight is enough to claim, and to frame a definite concept of, a highest being? He would answer that it was nothing but the aim of carrying reason further in its self-knowledge. At the same time he felt a measure of resentment over the pressure people try to place on reason, by making a great show of it while stopping it from freely confessing the weaknesses that show up when it examines itself. Now ask Priestley, who is devoted to the principles of the empirical use of reason alone and averse to all transcendent speculation. What motives did he have for tearing down the freedom and immortality of our soul, two such pillars of all religion? (For him the hope of a future life is just the expectation of a miraculous resurrection.) And this from a man who is himself a devout, eager teacher of religion. He could answer nothing other than this: the interest of reason. Reason loses out when people want to put certain objects out of the reach of the laws of material nature, which are the only laws we can know and fix with precision.

B 774 It would seem unfair to decry Priestley, who knows how to unite his paradoxical claim with his religious purpose, and to hurt a well-meaning man because he is lost the moment he has wandered out of natural science. But the same favor has to be granted to Hume, who is no less well-meaning and whose moral character is beyond reproach. Hume can’t give up his abstract speculation, since he is right to hold that its object lies entirely beyond natural science’s boundaries, in the field of pure ideas.

What should be done about this, especially when the common good seems to be in danger from it? Nothing is more natural, nothing fairer, than the decision you should take. Just let these people go on. If they show talent, if they show profound new research, in short, if they simply display reason, reason always gains. Suppose you use means other than those of free, unforced reason. Suppose you shout “treason!” and summon the public to the scene as if for a fire, though it has no understanding of such subtle work. Then you make yourselves ridiculous. The question is not what helps or harms the common good here. The only questions are these. How far can reason get in speculation cut off from every interest?

B 775 And can we count on such speculation at all, or would we rather give it up entirely in favor of the practical? So instead of striking out with the sword, watch this dispute calmly from the safe seat of critique. It must turn out tiring for the fighters, entertaining for you, and, since the outcome is sure to be bloodless, useful for your insights. It is quite absurd to expect enlightenment from reason and yet tell it beforehand which side it has to come down on. Besides, reason is already tamed and held within limits by reason itself so well that you needn’t summon the guard to set civil resistance against the side whose worrying superior power seems dangerous to you. In this dialectic there is no victory you would have cause to worry about.

Reason also badly needs such a dispute, and it would have been desirable for it to have been fought earlier, with unrestricted public permission. That would have brought a ripe critique that much earlier. When it appeared, all these quarrels would have to drop away of themselves, because the disputants would learn to see the blindness and prejudices that had set them at odds.

There is a certain insincerity in human nature.

B 776 Like everything that comes from nature, it must in the end contain a predisposition to good purposes. This is an inclination to hide one’s true convictions and to display certain adopted ones that one considers good and honorable. Certainly through this tendency, both to hide themselves and to put on a show that flatters them, human beings have not only become civilized but gradually, to a certain degree, moralized. No one could see through the rouge of decency, respectability and modesty. So each person found, in the supposedly genuine examples of good that they saw around them, a school of improvement for themselves. But this knack for looking better than one really is, and for voicing convictions one lacks, serves only provisionally, as it were. It is there to bring human beings out of crudeness and let them at first at least take on the manner of the good that they know. Later, once genuine principles have been developed and have passed into their way of thinking, that falseness has to be fought vigorously, bit by bit. Otherwise it corrupts the heart, and it lets good convictions find no room to grow under the rank weeds of a fine-looking show.

I’m sorry to see the same insincerity, pretense and hypocrisy even in speculative thinking. Here people have far less to stop them from confessing their thoughts openly and frankly, as they fairly should.

B 777 And they have nothing at all to gain by hiding them. For what could be worse for insight than passing on even our bare thoughts to each other in a falsified form, hiding the doubts we feel about our own claims, or giving proofs that don’t satisfy even us a look of clear certainty? As long as private vanity alone stirs up these secret schemes, other people’s vanity pushes back, with the public’s approval. (That is usually how it goes with speculative judgments, which hold no special interest and can’t easily reach apodictic certainty.) In the end things arrive where the purest intentions and honesty would have brought them, only much sooner. But suppose the community believes that hair-splitting reasoners are out to shake the very foundations of public welfare. Then it seems not just prudent but allowed, even admirable, to help the good cause with sham arguments. That beats handing its supposed opponents even this small win: getting us to lower our voice to the modest level of a conviction that is only practical, and making us confess that we lack speculative, apodictic certainty. Still, I’d think that nothing in the world goes worse with the aim of defending a good cause than trickery, pretense and fraud.

B 778 That everything should be honest when we weigh reasons in a mere speculation is surely the least anyone can ask. But if we could count on even that little, the dispute of speculative reason over the weighty questions of God, the immortality of the soul and freedom would have been settled long ago, or would be over very soon. As it is, purity of intention often runs in inverse proportion to the goodness of the cause itself. The good cause perhaps has more sincere and honest opponents than defenders.

So I assume readers who don’t want a just cause defended by unjust means. For them the principles of our critique settle it: if we look at what ought to happen rather than at what does happen, strictly speaking there shouldn’t be any polemic of pure reason at all. How can two people argue over something when neither can show its reality in any actual experience, or even any possible one? All either of them does is brood over its idea, hoping to squeeze something more than an idea out of it, namely the actuality of the object itself. How do they plan to get out of the quarrel, when neither can make their own side directly understandable and certain, and each can only attack and refute the other’s? This is the fate of every claim of pure reason.

B 779 They reach past the conditions that make any experience possible, and outside those conditions no documentary proof of truth turns up anywhere. Yet they still have to use the laws of the understanding, which are meant only for empirical use, and without which we can’t take one step in synthetic thinking. So they always leave themselves open to the opponent, and each side can take advantage of the other’s exposed weak spots.

We can see the critique of pure reason as the true court for all of pure reason’s disputes. It isn’t tangled up in those disputes, which deal directly with objects. It was set up to fix and judge the rights of reason in general, according to the principles of reason’s original founding.

Without critique, reason is in a kind of state of nature. It can make its claims and demands count, or protect them, only by war. Critique, on the other hand, takes all its decisions from the basic rules of reason’s own establishment, and no one can doubt their authority. It brings us the calm of life under law, where we are to carry on our dispute only through a trial. In the first state, what ends the quarrels is a victory, and both sides boast of it. Mostly only an uncertain peace follows, one that the authorities set up. They step in between the parties.

B 780 In the second state, what ends them is a verdict, and since it reaches the source of the quarrels themselves, it has to bring an everlasting peace. The endless quarrels of a merely dogmatic reason also force us, in the end, to look for peace in some critique of that reason itself, and in a legislation based on it. Hobbes says the same about the state of nature: it is a state of injustice and violence, and we must leave it and submit to the constraint of law. Only that constraint limits our freedom so that it can exist alongside everyone else’s freedom, and by that very fact alongside the common good.

Part of this freedom is the freedom to put our thoughts and our doubts, the ones we can’t settle ourselves, before the public for judgment, without being shouted down as a restless and dangerous citizen. This is already contained in the original right of human reason. Reason accepts no judge except the general reason of all people, where each person has a say. Since every improvement our condition allows has to come from there, this right is sacred and must not be cut back. It’s also very unwise to raise an alarm over certain daring claims or arrogant attacks on views that already have the backing of the biggest and best share of the community. That only gives them an importance they shouldn’t have.

B 781 Suppose I hear that a man of no ordinary mind has supposedly proved that the human will isn’t free, that there’s no hope of a life to come, and that God doesn’t exist. I’m eager to read his book. I expect his talent to take my insights further. But I know beforehand, with complete certainty, that he won’t have achieved any of this. That isn’t because I think I already hold unbeatable proofs of these important propositions. It’s because transcendental critique showed me everything our pure reason has in stock, and it has left me completely convinced of this: reason is quite inadequate to make positive claims in this field, and it knows just as little, or even less, that would let it claim anything negative about these questions. Where would the so-called freethinker get his knowledge that there is, say, no supreme being? That claim lies beyond the field of possible experience, and therefore beyond the boundaries of all human insight. As for the dogmatic champion who defends the good cause against this enemy, I wouldn’t read him at all. I know in advance that he’ll attack the other man’s sham arguments only to win a hearing for his own. Besides, an everyday illusion doesn’t give as much material for new observations as a strange and cleverly devised one.

B 782 An opponent of religion, on the other hand, who is dogmatic too in his own way, would give my critique welcome work and a reason to correct its principles further. And there would be nothing at all to fear from him.

But shouldn’t young people who are entrusted to academic teaching at least be warned against writings like these? Shouldn’t they also be kept from early knowledge of such dangerous propositions, until their power of judgment has ripened? Or rather, until the doctrine we want to plant in them has taken root so firmly that it can strongly resist any persuasion to the opposite, whatever its source?

Suppose dogmatic procedure had to stay in place in matters of pure reason. Suppose dealing with opponents had to be properly polemical, that is, such that we’d go into battle and arm ourselves with proofs for the opposite claims. Then nothing would be more advisable for the moment. But in the long run nothing would be emptier or more fruitless than to put the reason of the young under a guardian for a while and shield it from seduction at least that long. Suppose, though, that later on, through curiosity or the fashion of the times, they come across such writings. Will that youthful persuasion still stand up? Take someone who brings only dogmatic weapons to fend off his opponent’s attacks. He doesn’t know how to bring out the hidden dialectic.

B 783 It lies no less in his own heart than in his opponent’s. He sees sham arguments with the pull of novelty line up against sham arguments that no longer have it, and that instead stir up the suspicion that young people’s gullibility was abused. He thinks the best way to show that he’s outgrown the discipline of childhood is to brush aside those well-meant warnings. Dogmatic by habit, he drinks in great gulps of the poison that dogmatically ruins his principles.

In university teaching we have to do exactly the reverse of what’s advised here, though only if students have first been thoroughly taught the critique of pure reason. To put its principles to work as early as possible, and to show that they hold up even against the greatest dialectical illusion, it’s absolutely necessary to aim the attacks that frighten the dogmatist so much at his own reason. That reason is still weak, but critique has enlightened it. We have to let him try testing the opponent’s groundless claims, piece by piece, against those principles. It can’t be hard for him to dissolve them into plain smoke. In this way he feels early on how strong he is, strong enough to make himself fully safe against such harmful deceptions, which in the end must lose all their illusion for him.

B 784 Of course, the very same blows that knock down the enemy’s building must be just as ruinous to his own speculative structure, if he ever thought of putting one up. But this doesn’t trouble him in the least. He has no need of living in it. He still has a view ahead into the practical field, where he can hope with good reason for firmer ground on which to build his own sound and wholesome system.

So there is no real polemic in the field of pure reason. Both sides are fencing with the air and grappling with their own shadows. They have gone beyond nature, and there is nothing there for their dogmatic holds to grab and keep. They can fight all they like. Like the heroes of Valhalla, the shadows they hack in two join up again in an instant, so that the fun of bloodless fighting can start over.

Nor does pure reason have any acceptable skeptical use, which we might call the principle of staying neutral in all its disputes. To set reason against itself, to hand it weapons on both sides, and then to watch its fiercest fight with calm and mockery, doesn’t look good from a dogmatic point of view. It has the air of a spiteful, gloating temper. Still, look at the unbeatable blindness and bragging of those reasoners.

B 785 They refuse to be moderated by any critique. In that case there really is no other course than to set against the bragging on one side another that stands on exactly the same rights. Then the resistance of an enemy will at least stop reason short, make it doubt its pretensions a little, and get it to listen to critique. But to leave things entirely at these doubts is a wholly futile plan. The same goes for urging people to be convinced of their ignorance, and to confess it, as something more than a cure for dogmatic self-conceit, namely as the way to end reason’s conflict with itself. It can’t possibly bring reason to rest. At most it is a means of waking reason from its sweet dogmatic dream, so that it examines its condition more carefully. This skeptical manner of getting out of an irritating business of reason seems to be the short road to lasting philosophical calm. At least it is the highway that people like to take when they think a mocking contempt for every inquiry of this kind gives them philosophical standing. So I find it necessary to show this way of thinking in its own proper light.

B 786 On the Impossibility of a Skeptical Satisfaction for a Pure Reason at Odds with Itself

Awareness of my ignorance (unless that ignorance is also recognized as necessary) is not what ends my inquiries, though it may seem it should. It is rather the real cause that stirs them up. All ignorance is either ignorance of things, or ignorance of the determination and boundaries of my cognition. If the ignorance is accidental, it has to drive me to look into the things (the objects) dogmatically in the first case, and into the boundaries of my possible cognition critically in the second. Whether my ignorance is absolutely necessary, and so lets me off all further inquiry, can’t be decided empirically, by observing. Only a critical test can decide it, by probing the first sources of our cognition. So the setting of our reason’s boundary can happen only on grounds a priori. Its restriction, on the other hand, is a cognition, though only an indefinite one, of an ignorance that can never be fully removed. That can also be recognized a posteriori, from what is always still left to know in spite of all our knowing. The first kind of knowledge of one’s ignorance, which only a critique of reason itself makes possible, is therefore science, while the second is nothing but perception.

B 787 About that, no one can say how far an inference from it might reach. Suppose I picture the earth’s surface as a plate, as the illusion of the senses suggests. Then I can’t know how far it extends. But experience does teach me this: wherever I get to, I always see space around me that I could go on into. So I do see limits to the earth-knowledge I actually have each time, but not the boundaries of any possible description of the earth. Now suppose I’ve got as far as knowing that the earth is a ball and that its surface is spherical. Then from a small piece of it, say the length of one degree, I can work out the diameter, and through the diameter the complete boundary of the earth, that is, its surface. I can know this definitely and by principles a priori. And although I’m ignorant about the objects this surface may hold, I’m not ignorant about the extent that holds them, about its size and limits.

Everything that could possibly be an object of our cognition seems to us a flat surface with an apparent horizon. That horizon is whatever takes in the whole extent of the surface, and we have called it the concept of reason of unconditioned totality. We can’t reach it empirically. All the attempts to fix it a priori by some principle have failed.

B 788 Yet every question our pure reason asks is about something that may lie beyond this horizon, or at most right on its boundary line.

One of these geographers of human reason was the famous David Hume. He thought he had dealt with those questions well enough by sending them all outside the horizon, though he could not fix where the horizon was. He dwelt mainly on the principle of causality. About it he saw, quite rightly, that its truth rests on no insight, meaning no cognition a priori. The same goes for the notion of an efficient cause as such: not even its objective validity rests on insight. So the necessity of this law has no part at all in giving it its standing. What gives it its whole standing is only that it can be used everywhere as experience goes on, together with a subjective necessity that arises from this, which he calls habit. Our reason can’t use this principle beyond all experience. From that inability he concluded that all the pretensions of reason to go beyond the empirical in general are void.

A procedure like this, which puts the facts of reason to the test and, where it finds fault, blames them, can be called the censure of reason. Beyond question, a censure like this must lead to doubts about every transcendent use of the principles.

B 789 But this is only the second step, and it is far from finishing the job. In dealing with pure reason, the first step, the one that characterizes its childhood, is dogmatic. The second step, named above, is skeptical. It shows the carefulness of a power of judgment that experience has made wiser. A third step is still needed, and it belongs only to a mature, adult power of judgment, one that rests on firm maxims proven in their universality. That step is to assess reason itself rather than the facts it produces: its whole capacity, and how well suited it is to pure cognitions a priori. That isn’t censure but critique of reason. It shows not just limits but the definite boundaries of reason. It shows ignorance not just in this or that area, but about every possible question of a certain type. And this isn’t merely suspected but proved from principles. So skepticism gives human reason a place to rest. There it can reflect on its dogmatic wandering and draw a sketch of the region where it stands, so that it can pick its path with more confidence from then on. But it is not a place to live permanently. A permanent home exists only where certainty is complete, whether it is certainty about the objects themselves or about the boundaries.

B 790 All our cognition of objects lies enclosed inside those boundaries.

Our reason is not a plane that spreads out without any determinable end, one whose limits we know only in a general way. We should compare it instead to a sphere. We can work out its radius from the bend of an arc on its surface (which is the nature of synthetic propositions a priori). From the radius we can also give, with certainty, its content and its boundary. Beyond this sphere (which is the field of experience) reason has no object at all. Even questions about such alleged objects touch only subjective principles. These are principles for fully determining the relations that can occur among the concepts of the understanding inside this sphere.

We really do possess synthetic cognition a priori. Those principles of the understanding that anticipate experience prove it. Now suppose someone can’t make its possibility understandable to himself. At first he may doubt whether we really have such cognition a priori. But he can’t yet declare it impossible through the mere forces of the understanding, or declare worthless every step reason takes by that guideline. All he can say is this: if we saw where these cognitions come from and whether they’re genuine, we could fix the extent and the boundaries of our reason.

B 791 Until that is done, all the claims of reason are ventured blindly. In that case a thoroughgoing doubt about all dogmatic philosophy that goes its way without a critique of reason itself would be well founded. Even so, reason could not be denied such progress altogether, if better groundwork prepared and secured it. For one thing, all the concepts, indeed all the questions, that pure reason puts to us do not lie in experience. They lie in reason itself. So they must be capable of being solved, and of being understood as either valid or void. Nor may we dismiss these tasks by claiming we’re not up to them, as if the answer really did lie in how things are, or refuse to investigate any further. Reason alone, in its own womb, produced these very ideas. So it is bound to give an account of their validity, or of their dialectical illusion.

All skeptical polemic is really aimed at one target, the dogmatist. He goes solemnly on his way without ever doubting the objective principles he began with, which means without critique. The skeptic only wants to upset his plans and bring him to self-knowledge. Taken by itself, such polemic decides nothing at all about what we are able to know and what we aren’t.

B 792 Reason’s failed dogmatic attempts are all facts, and it’s always useful to put them to censure. But censure can decide nothing about what reason may expect. It can’t say whether reason may hope for better success in its future efforts, or lay claim to it. That is why censure alone can never finish the dispute about what human reason is entitled to.

Hume may well be the cleverest of all skeptics. Beyond dispute he is the foremost, in the influence that the skeptical procedure can have in stirring up a thorough examination of reason. So it is worth the effort to lay out how his reasoning ran, and where such a perceptive and valuable man went astray, since his errors began on the trail of truth. I’ll do this only as far as my purpose requires.

Perhaps Hume sensed, without ever working it out fully, that certain judgments take us past the concept we have of the object. I have called this kind of judgment synthetic. There is no difficulty about how I can go beyond the concept I have so far by means of experience. Experience is itself a synthesis of perceptions of this sort. It takes the concept I have by means of one perception and enlarges it with other perceptions that come in. But we also believe we can go out beyond our concept a priori and widen our cognition that way.

B 793 We try this in one of two ways: through the pure understanding, concerning whatever may at least become an object in experience, or through pure reason, which covers features of things, and even the existence of objects, that experience can never present. Our skeptic didn’t tell these two kinds of judgment apart, though he should have. He simply held it impossible for our understanding (together with reason) to enlarge its concepts out of itself and, so to speak, to give birth to itself, without being made pregnant by experience. So he took all its supposed principles a priori to be imagined. What he found was that they amount to nothing more than a habit that grows out of experience and its laws. They are therefore merely empirical rules, that is, rules accidental in themselves, and we credit them with a supposed necessity and universality. To back up this odd claim, he appealed to the generally accepted principle about the relation of cause to effect. No power of the understanding can lead us from a thing’s concept to the existence of something else, something that would be given by that concept universally and necessarily. From that he thought he could infer that apart from experience we have nothing to widen our concept, nothing that would justify a judgment that expands itself a priori like this. Sunlight shines on wax.

B 794 That it melts the wax while it hardens clay, he said, no understanding could guess from the concepts we had of these things beforehand, let alone infer according to a law. Only experience could teach us such a law. But in the transcendental logic we saw otherwise. We can never go directly beyond what is contained in the concept we are given. Yet we can know the law of connection with other things completely a priori, in relation to a third thing, namely possible experience. So the knowledge is still a priori. When wax that was solid melts, then, I can know a priori that something must have come before (the sun’s warmth, say), and that the melting followed it according to a constant law. Still, without experience I couldn’t work out a definite cause from the effect, or a definite effect from the cause, a priori and without being taught by experience. So he wrongly inferred, from the accidental character of our determination according to the law, that the law itself is accidental. And he confused two things. One is stepping out of a thing’s concept toward possible experience. That happens a priori, and it constitutes the concept’s objective reality. The other is the synthesis of the objects that real experience gives, and that is of course always empirical. In this way he turned a principle of affinity, which has its seat in the understanding and states a necessary connection, into a rule of association.

B 795 It is found only in the reproductive imagination, and it can present only accidental combinations, not objective ones at all.

The skeptical errors of this man, who was otherwise extremely sharp, came mainly from a shortcoming that he shared with all dogmatists. He did not survey, systematically, all the kinds of synthesis of the understanding a priori. If he had, he would have found (to leave the rest aside here) that the principle of persistence, for one, anticipates experience exactly as the principle of causality does. That would have let him mark out definite boundaries both for the understanding as it expands itself a priori and for pure reason. As it was, he only restricts our understanding without bounding it. He produces a general distrust, but no definite knowledge of the ignorance we cannot escape. He puts some principles of the understanding under censure, without weighing the understanding itself, in its whole capacity, on the testing scales of critique. And in denying it what it really cannot do, he goes further and disputes its whole capacity to extend itself a priori, even though he never put that whole capacity to the test. So the same thing happens to him that always brings skepticism down: he himself is doubted. His objections rest only on facts, which are accidental.

B 796 They do not rest on principles that could make giving up the right to dogmatic claims a matter of necessity.

He also fails to tell apart what the understanding can rightly claim from the dialectical pretensions of reason, though his attacks are mostly aimed at the latter. So reason feels that the room for its expansion has not been shut off. Its very own momentum isn’t disturbed at all, only held back. It may be nipped at now and then, but it can never be argued out of its attempts completely. For people arm themselves against attacks, and dig in their heels all the harder to get their demands through. A complete survey of one’s whole capacity is different. From it comes the conviction that one’s possession is certain though small, and that higher claims are vanity. That ends all quarrel, and moves one to be peacefully content with a limited property that nobody disputes.

Skeptical attacks are not just dangerous to the uncritical dogmatist. They are ruinous to him. He hasn’t measured the sphere of his understanding, and so hasn’t fixed by principles the boundaries of his possible cognition. He doesn’t know beforehand how much he can do, and thinks he’ll find out by trying. Suppose he is caught out on a single claim.

B 797 He can’t justify it, and he can’t develop its illusion from principles either. Then suspicion falls on all of his claims, however persuasive they may otherwise be.

And so the skeptic is the taskmaster who drives the dogmatic reasoner toward a sound critique of the understanding and of reason itself. Once the dogmatist has got that far, he has no further challenge to fear. For he then tells his own possession apart from what lies entirely outside it. He makes no claims on that, and so can’t be drawn into disputes about it. So the skeptical procedure, though it does not satisfy us about the questions of reason in itself, is still a useful preliminary exercise. It wakes reason’s caution, and it points to thorough means by which reason can secure its rightful possessions.

First Chapter Section Three Pure Reason’s Discipline with Regard to Hypotheses

At long last the critique of our reason has taught us this much: when we use it purely and speculatively, we really can know nothing whatever. So shouldn’t reason now have all the wider a field open to hypotheses? After all, we’re at least allowed to invent and to hold opinions, even if we can’t assert anything.

B 798 Where imagination isn’t to run wild but to invent under the strict supervision of reason, something must always come first that is completely certain, neither invented nor mere opinion. That something is the possibility of the object itself. Only then is it allowed to fall back on opinion about the object’s actuality. But to avoid being groundless, that opinion has to be connected, as an explanatory ground, with what is actually given and therefore certain. It is then called a hypothesis.

We can’t form the faintest concept of how dynamic connection could be possible a priori. And the category of the pure understanding isn’t there to invent such things. It serves only to understand them where they turn up in experience. So we can’t originally think up even one object with a new quality, one that experience can’t show us, in line with these categories, and then lay it down as the basis of an allowed hypothesis. That would mean giving reason empty fantasies in place of concepts of things. In the same way, we may not think up any new original forces. One example would be an understanding able to intuit its object without senses. Another would be a force of attraction without any contact. A third would be a new kind of substance, say one that would be present in space without impenetrability. It follows that we may not think up a community of substances either.

B 799 It must not differ from any that experience offers: no presence except in space, no duration except in time. To sum up: the only thing our reason can do is take what makes experience possible and treat it as what makes things possible. It can’t, quite independently of those conditions, create some of its own, so to speak. Concepts like that, though free of contradiction, would still have no object.

As I said, concepts of reason are mere ideas. They have no object in any experience. Still, that doesn’t mean they stand for objects that are made up and, at the same time, taken to be possible. They are thought only problematically. Their purpose is to serve (as heuristic fictions) as the basis for regulative principles that guide how the understanding is used systematically within experience. Take that away and they are mere thought-things. Their possibility can’t be proved, so they can’t be used as the basis of a hypothesis that explains actual appearances. It’s perfectly allowed to think of the soul as simple. Guided by this idea, we can adopt a complete and necessary unity of all the mind’s forces as our principle for judging its inner appearances, though we can’t see that unity concretely. But to accept the soul as a simple substance, which is a transcendent concept, is another matter.

B 800 That would be a proposition that can’t be proved, as with many physical hypotheses, and in addition is entirely arbitrary and risked blindly. For the simple can’t turn up in any experience at all. And if by substance here we mean the persisting object of sensible intuition, we can’t see at all how a simple appearance could be possible. Merely intelligible beings, or merely intelligible properties of the things of the world of sense, can’t be adopted even as an opinion on any well-grounded authority of reason. We have no concept of whether they are possible or impossible. So we can’t flatly deny them, dogmatically, on the strength of some supposedly better insight either.

To explain given appearances, we can bring in only those things and grounds of explanation that have been connected with the given appearances according to already known laws of appearances. A transcendental hypothesis, in which a mere idea of reason was used to explain things in nature, would therefore explain nothing. What we don’t sufficiently understand from known empirical principles would be explained by something we understand nothing about at all. Such a hypothesis would really just give reason some satisfaction. It would do nothing to help the understanding in dealing with its objects. Order and purposiveness in nature, in turn, have to be explained from natural grounds and by natural laws.

B 801 Here even the wildest hypothesis is easier to put up with, provided it is physical, than a hyperphysical one, which would mean appealing to a divine author assumed for the occasion. For that is the principle of lazy reason (ignava ratio): to walk past, in one stroke, every cause whose objective reality we could still learn, at least as something possible, through more experience, just so that we can settle down with a bare idea that suits reason very well. As for the absolute totality of the ground of explanation in the series of such grounds, it can’t be an obstacle for the objects of the world. They are nothing but appearances, so we can never hope to see the synthesis of a series of conditions for them completed.

Transcendental hypotheses for the speculative use of reason can’t be allowed at all. Neither can a freedom to make up for a lack of physical grounds of explanation by turning, when need be, to hyperphysical ones. One reason is that this gets reason no further. It cuts off the whole progress of its use. The other is that this license would in the end cost reason all the fruits of working its own proper soil, namely experience. For whenever explaining nature gets hard for us here or there, we would always have a transcendent ground of explanation at hand to excuse us from that investigation.

B 802 Our inquiry then ends not in insight but in the total incomprehensibility of some principle, one that was designed beforehand so that it had to include the concept of what is absolutely first.

The second requirement for a hypothesis to deserve acceptance is that it be sufficient to determine a priori the consequences that are given. If we’re forced to call in helper hypotheses for this purpose, they raise the suspicion of mere invention. Each of them needs, in itself, the same justification that the underlying thought needed, and so none can serve as a reliable witness. Suppose we assume an unlimitedly perfect cause. Then we are never short of grounds to account for the purposiveness, order and size we find in the world. But that cause still needs new hypotheses to rescue it from the deviations and evils that show up, at least by our concepts, as objections to it. Suppose the soul has been laid down as a simple thing that stands on its own, at the base of its appearances. And suppose this is challenged by difficulties in its phenomena, which resemble the changes of a material (growth and decline). Then new hypotheses must be called in to help. They have a certain look of plausibility, but no warrant at all.

B 803 The only warrant they have is the one that the opinion taken as the main ground gives them, and they’re supposed to speak up for that very opinion.

Take the claims of reason used here as examples: the incorporeal unity of the soul and the existence of a highest being. Suppose they are meant to be taken not as hypotheses but as dogmas that have been proved a priori. Then they don’t come up here at all. In that case we have to make sure the proof is as apodictically certain as a demonstration. To want to make the actuality of such ideas merely probable is an absurd undertaking, as if someone planned to prove a proposition of geometry only as probable. When reason is cut off from all experience, it can know things only a priori, and only as necessary, or it can’t know them at all. So its judgment is never opinion. It is either withholding of all judgment or apodictic certainty. Opinions, and judgments that are merely probable, about what pertains to things have a place only in two roles: as grounds that explain something actually given, or as consequences, by empirical laws, of something actual lying at the base. So they can occur only within the series of objects of experience. Outside this field, to hold an opinion is as good as playing with thoughts. The one exception would be if someone held, as an opinion only, that an uncertain way of judging might perhaps lead him to the truth.

B 804 When the questions are purely speculative questions of pure reason, hypotheses can’t serve as the basis for any proposition. Still, they are perfectly fine for defending such propositions where needed. That means using them polemically, not dogmatically. By defense I don’t mean adding to the proofs of one’s own claim. I mean only foiling the sham insights of the opponent, which are meant to damage our asserted proposition. All synthetic propositions that come from pure reason share one peculiarity. Whoever asserts that certain ideas are real never knows enough to make that claim certain. But on the other side, the opponent can know just as little in order to assert the opposite. In speculative cognition this equal lot of human reason favors neither of them. And that is the real battlefield of feuds that never get settled. We’ll see later, however, that in practical use reason does have a right to assume things that it could never presuppose in mere speculation without adequate proofs. Every such presupposition damages the perfection of speculation, and practical interest doesn’t care about that at all. There reason is in possession. It doesn’t have to prove that its possession is lawful, and in fact it couldn’t supply the proof anyway.

B 805 So the opponent is the one who has to prove. But the opponent knows just as little about the doubted object as the first person, who asserts that it is real. He knows too little to show that it doesn’t exist. So the advantage here goes to whoever asserts something as a presupposition that practice requires (melior est conditio possidentis). As a kind of self-defense, he is free to use hypotheses, the same tools his opponent uses against his good cause. They’re not meant to strengthen the proof of his case. Their only job is to show that the opponent knows so little about what the quarrel is over that he can’t boast of any gain in speculative insight over us.

So in the field of pure reason hypotheses are allowed only as weapons of war. They’re not for founding a right on, but only for defending one. We have to look for the opponent here always in ourselves. Speculative reason in its transcendental use is dialectical in itself. The objections we might have to fear lie within us. We have to dig them out, like old claims that never expire, in order to found an everlasting peace on their annulment. Outer calm is only apparent. The seed of these challenges is planted in the nature of human reason, and it has to be rooted out.

B 806 But how can we root it out unless we give it freedom, even food, to shoot up its weeds so that it shows itself, and then destroy it root and all? So think up objections yourselves, ones no opponent has yet hit on, and even lend him weapons, or give him the most favorable ground he could wish for. There is nothing to fear in this, but there is something to hope for: that you’ll win a possession that will never again be challenged, for all time to come.

Your full armor now includes the hypotheses of pure reason too. They are only lead weapons, since no law of experience has tempered them into steel. Still, they are always as strong as the ones any opponent may use against you. Suppose you run into a difficulty against the nature of the soul, which you have assumed (on some other, non-speculative ground) to be immaterial and not subject to bodily change. Experience seems to prove that the raising up and the breakdown of our mental forces are just different modifications of our organs. You can weaken that proof if you suppose our body to be only the fundamental appearance. In our present state (in life) the whole capacity of sensibility, and with it all thinking, relates to it as its condition. Leaving the body behind would end this sensory use of your cognitive power and begin its intellectual use.

B 807 So the body would not be the cause of thinking but only a restricting condition of it. We’d therefore have to regard the body as something that promotes the life of the senses and the animal side of us, and even more as something that holds back the pure, spiritual life. The sensory life’s dependence on the body’s condition would prove nothing about whether our whole life depends on the state of our organs. You can go further still, and even find new doubts that haven’t been raised or haven’t been pushed far enough.

Procreation is a matter of chance. In human beings, as in creatures without reason, it depends on opportunity. It also often depends on means of support, on the government and its moods and whims, and often even on vice. This is a big difficulty for the opinion that a creature goes on existing for eternities, when its life first began under such trivial circumstances, circumstances left entirely to our freedom. As for the species as a whole continuing here on earth, this difficulty matters little, since chance in single cases is still ruled by a law in the whole. But to expect such a mighty effect from such trivial causes for each individual does seem questionable. Against this you can bring forward a transcendental hypothesis. Its claim is that all life is really only intelligible.

B 808 Such life is not subject to changes in time at all, and it neither began with birth nor ends with death. The hypothesis adds that this life is just an appearance, in other words a sensory representation of the pure spiritual life, and that the whole world of sense is a mere picture that floats before our present way of knowing and, like a dream, has no objective reality in itself. It adds that, were we to intuit things, and ourselves, as they really are, we would find ourselves in a world made up of spiritual natures, and that our one true community with that world neither began with birth nor will stop with bodily death (these being mere appearances), and so on.

We know nothing at all of what we put forward here, as hypotheses, against the attack, and we don’t seriously assert any of it. It isn’t even an idea of reason. It is only a concept thought up for defense. Even so, we are acting entirely in line with reason. The opponent thinks he has used up every possibility. He falsely passes off the lack of their empirical conditions as proof that what we believe is wholly impossible. All we do is show him this: he can no more reach all possible things in themselves with laws of experience alone than we can obtain anything for our reason, outside experience, on firm ground.

B 809 If someone turns such hypothetical antidotes against the arrogance of an opponent who denies things boldly, nobody should think he is adopting them as opinions he truly holds. He drops them as soon as he has dealt with the opponent’s dogmatic self-conceit. It can look modest and restrained when someone just declines and says no to other people’s claims. But once he wants his objections to pass as proofs of the contrary, his pretension is just as proud and conceited as if he had taken the affirmative side and its assertion.

This shows that when reason is used speculatively, hypotheses don’t count as valid opinions in their own right. They are valid only relative to opposing transcendent presumptions. It is every bit as transcendent to carry the principles of possible experience over to the possibility of things in general as it is to claim objective reality for concepts whose objects can only be found beyond the boundary of any possible experience. What pure reason judges assertorically has to be necessary (as does everything reason cognizes), or it is nothing. So reason in fact holds no opinions at all. The hypotheses we have in mind are only problematic judgments. They at least cannot be refuted, though of course nothing can prove them.

B 810 So they aren’t private opinions. Still, we can’t well do without them, even for our own inner reassurance, against scruples that stir. But we have to keep them in that character. We must be careful that they don’t show up as vouched for in themselves, or as having some absolute validity, and so drown reason in inventions and deceptions.

First Chapter Section Four Pure Reason’s Discipline with Regard to Its Proofs

Of all the proofs we give for synthetic cognition a priori, those for transcendental, synthetic propositions are special. When reason proves one of these through its concepts, it isn’t allowed to go straight at the object. First it has to show that the concepts are objectively valid, and that they can be put together a priori. This is not just a rule of caution we happen to need. It goes to the nature of proofs themselves, and to whether they are possible. If I’m to go a priori beyond my concept of an object, I can’t do it without a special guide that lies outside the concept. In mathematics, the guide is intuition a priori, which steers my synthesis, and there every inference can be drawn straight from pure intuition.

B 811 In transcendental cognition, as long as it deals only with concepts of the understanding, this guideline is possible experience. The proof doesn’t show that a given concept (of what happens, say) leads straight to another (that of a cause). A crossing like that would be a leap that couldn’t be defended at all. What it shows instead is that without such a connection there could be no experience at all, and so no object of experience. So the proof had to show at the same time how we can reach, by synthesis and a priori, some cognition of things that their concept didn’t contain. Without this attention, proofs run like water that has broken its banks. They go wild, straight across country, to wherever the slope of hidden association happens to lead them. The illusion of conviction that rests on subjective causes of association, and is taken for insight into a natural affinity, can’t hold its own against the misgiving that such risky steps rightly ought to raise. That is also why every attempt to prove the principle of sufficient reason has failed, as the experts all admit. Before transcendental critique appeared, people could not abandon this principle. They would sooner fall back stubbornly on common sense than attempt new dogmatic proofs.

B 812 (That refuge always shows that the cause of reason is desperate.)

Now suppose the proposition we want to prove is a claim of pure reason, and that I’m trying to get past my concepts of experience by using nothing but ideas. Then the proposition would need, all the more, to contain a justification for such a synthetic step, if the step is possible at all. That justification would be a necessary condition for the proposition to prove anything. There is a supposed proof, from the unity of apperception, that our thinking substance is simple by nature. It may look as plausible as you like. Still, an unavoidable misgiving stands against it. Absolute simplicity is not a concept that can be related directly to a perception. As an idea it can only be inferred. So it’s impossible to see how bare consciousness could carry me across to awareness and knowledge of a thing that can hold thinking and nothing else. True, that consciousness is present in all thinking, or at least can be, and so far it is a simple representation. For suppose I picture the force of my body in motion. So far as that goes, the body counts for me as an absolute unity, and the representation I have of it is simple. So I can also express that representation through the motion of a point. The body’s volume plays no part here. Without any loss of force it can be made as small as I like.

B 813 So it can also be thought of as sitting in one point. Even so, I would not infer that the body may be thought of as a simple substance, merely because its representation abstracts from all size of spatial content and so is simple, in a case where nothing is given to me but a body’s moving force. Here I find a paralogism. It is this: the simple in abstraction and the simple in the object are two quite different things. In the first sense the I contains no manifold at all. In the second sense, where it means the soul itself, it can be a very complex concept, since it contains and designates a great deal under itself. But to sense such a paralogism ahead of time (without a preliminary suspicion like that, we would never grow suspicious of the proof), we absolutely need a standing criterion at hand for the possibility of synthetic propositions that are supposed to prove more than experience can give. The criterion is this: the proof must not go straight to the predicate that is wanted. It must rely only on a principle that makes it possible to extend the concept we are given, a priori, out to ideas, and to make those ideas real. Suppose we always took this care. Suppose we first asked ourselves, wisely, before trying a proof, how and on what ground of hope we could expect such an extension from pure reason. And suppose we asked where, in a case like that, we would get these insights from.

B 814 They can’t be developed out of concepts, and they can’t be anticipated in relation to possible experience either. Then we could spare ourselves a lot of hard but fruitless work. We would ask nothing of reason that plainly goes beyond its capacity. Or rather, we would put reason under the discipline of abstinence, since in its fits of speculative craving to expand it doesn’t like to be restricted.

The first rule, then, is this: don’t attempt any transcendental proofs without first thinking it over, and justifying to yourself, where you mean to get the principles you plan to build them on, and by what right you can expect the inferences to succeed. If they are principles of the understanding (causality, say), it is pointless to use them to arrive at ideas of pure reason. They apply only to objects of possible experience. If they’re to be principles from pure reason, all the effort is again pointless. Reason does have such principles. Taken as objective principles, though, they are all dialectical. At most they can be valid as regulative principles of the systematically connected use of experience. If proofs of this kind are already on the table, set against their deceptive conviction the non liquet (“it is not clear”) that your mature power of judgment pronounces.

B 815 You may not yet see through their deception. Still, you have every right to demand the deduction of the principles they use. If those principles are supposed to spring from mere reason, that deduction can never be supplied to you. So you needn’t even trouble yourselves with unraveling and refuting every groundless illusion. You can dismiss, in whole heaps at once, all that dialectic with its endless supply of tricks, before the tribunal of a critical reason that insists on laws.

Transcendental proofs have a second peculiarity: for any transcendental proposition, only one proof can be found. Suppose my inference doesn’t start from concepts at all but from the intuition that matches a concept. The intuition may be pure, as in mathematics, or empirical, as in natural science. Then the intuition I start from gives me varied material for synthetic propositions. I can connect that material in several ways, and because I’m free to start from more than one point, I can arrive at the same proposition by different paths.

Every transcendental proposition, though, starts from a single concept and says what the synthetic condition is for an object to be possible under that concept. So the ground of proof can be only one. There is nothing else besides this concept.

B 816 Nothing else could determine the object. So the proof can contain nothing more than the determination of an object in general by this concept, which is itself only one. In the transcendental analytic, for example, we had the principle that whatever happens has a cause. It was drawn from one single condition for a concept of what happens at all to be objectively possible: an event could not be determined in time, and so could not belong to experience, unless it stood under a dynamical rule of this sort. This is, in fact, the only ground of proof that is possible. Only because an object is determined for the concept through the law of causality does the event we represent have objective validity, that is, truth. People have tried other proofs of this principle too, for example from contingency. But look at contingency closely and the only sign of it we can find is happening, which is existence preceded by the object’s non-existence. So we always come back to the same ground of proof. To prove the proposition “everything that thinks is simple,” we don’t stop at the manifold in thinking. We hold only to the concept of the I, since that is simple and all thinking refers back to it. The same holds for the transcendental proof of God’s existence.

B 817 It rests solely on the fact that the concept of the most real being and the concept of the necessary being can be swapped for each other, and it can’t be looked for anywhere else.

This warning remark shrinks the critique of the claims of reason down to a very small job. Where reason does its work through mere concepts, only one proof is possible, if any is possible at all. So when you see a dogmatist step forward with ten proofs, you can safely believe he has none. If he had a single proof that was apodictic (and in pure reason it has to be), what would he want the others for? His aim is the same as that of the lawyer who pleads before a high court: one argument is for this judge, another for that one. His plan is to play on the weakness of his judges, who don’t look into the case deeply. They want the business over with fast, so they grab whatever happens to catch their eye first and rule on that.

The third special rule of pure reason, when it is disciplined with regard to transcendental proofs, is this: its proofs must never be apagogic. They must always be ostensive. In every sort of cognition, the direct (ostensive) proof is the kind that gives us conviction that something is true together with insight into where that truth comes from. The apagogic proof, on the other hand, can produce certainty, but it can’t produce comprehensibility of the truth in its connection with the grounds of its possibility.

B 818 So the latter are more of an emergency help than a procedure that satisfies all the aims of reason. Still, they have one advantage over direct proofs in clearness of evidence. A contradiction always brings more clarity to the representation than the best connection does, and so comes closer to the intuitive quality of a demonstration.

The real reason apagogic proofs are used in various sciences is probably this. Sometimes the grounds that a given cognition is supposed to be derived from are too varied or too deeply buried. Then people try to get at them through the consequences. Now the modus ponens, which concludes that a cognition is true because its consequences are true, would be allowed only if all the possible consequences of it are true. Then only one ground is possible for them, and that one is therefore the true one. But this procedure is not workable, because it’s beyond our powers to see all the possible consequences of any assumed proposition. Still, people do use this kind of inference, though with a certain indulgence, when the aim is to prove something merely as a hypothesis. They accept an inference by analogy: suppose every consequence anyone has tried agrees nicely with an assumed ground. Then all the remaining possible consequences will agree with it as well.

B 819 For that reason no hypothesis can ever be turned into demonstrated truth by this route. The modus tollens, among the inferences of reason that run from consequences back to grounds, proves things with complete strictness and also with great ease. If a proposition yields even one false consequence, that proposition is false. In an ostensive proof we would have to go through the whole series of grounds that could bring us to a cognition’s truth by fully seeing how it is possible. Instead, we need only find a single one of the consequences that flow from its opposite to be false. Then the opposite is false, and the cognition we were supposed to prove is therefore true.

The apagogic kind of proof is allowed only in sciences where it’s impossible to slip what is subjective in our representations in place of what is objective, that is, cognition of what belongs to the object. Where the subjective does rule, it must often happen that the opposite of a given proposition contradicts only the subjective conditions of thinking and not the object. Or it can happen that the two propositions contradict each other only under a subjective condition, one wrongly taken to be objective. The condition is false, so both can be false, and then the falsity of one tells us nothing about the truth of the other.

B 820 In mathematics this subreption cannot happen, which is why these proofs have their proper home there. In natural science everything rests on empirical intuitions. So that sneaking-in can mostly be prevented there by many compared observations. But even there this kind of proof is mostly of little importance. The transcendental attempts of pure reason, however, are all carried out within the proper medium of dialectical illusion. That is, they are carried out within the subjective, which offers itself to reason in its premises as objective, or even forces itself on it. Here, as far as synthetic propositions go, it can’t be allowed at all to justify one’s claims by refuting the opposite. For either this refutation is nothing other than showing that the opposing view conflicts with the subjective conditions under which our reason can grasp things. That does nothing to throw out the thing itself. (For example, an unconditioned necessity in a being’s existence is something we simply cannot grasp. For that reason, subjectively, it rightly stands in the way of every speculative proof of a necessary supreme being. But it wrongly stands in the way of the possibility, in itself, of such a primal being.) Or both parties, the asserting and the denying, are deceived by transcendental illusion and lay an impossible concept of the object at the base.

B 821 Then the rule applies: non entis nulla sunt praedicata. That is, whatever one asserted of the object, whether affirming or denying, is wrong in both cases, and one can’t reach cognition of the truth apagogically by refuting the opposite. For example, suppose it is assumed that the world of sense is given in itself in its totality. Then it’s wrong to say it must be either infinite in space or finite and bounded, since each is false. For appearances (being mere representations) that would still be given in themselves (as objects) are an impossibility. And the infinity of this imagined whole would indeed be unconditioned. But, since everything in appearances is conditioned, it would contradict the unconditioned determination of magnitude that is presupposed in the concept.

The apagogic kind of proof is also the real deception by which admirers of the thoroughness of our dogmatic reasoners have always been kept in suspense. It is like a champion who tries to establish the honor and undisputed right of the side he has chosen by offering to fight anyone who cares to doubt it. Yet such bragging settles nothing about the matter itself. It decides only how strong the opponents are relative to each other, and even that only in favor of whoever goes on the attack.

B 822 The spectators see that each one wins in his turn and loses in his turn too, and this often leads them to become skeptical about what the dispute is over in the first place. But they have no reason to. It’s enough to call out to them: non defensoribus istis tempus eget (the time doesn’t need defenders like these). Everyone must argue his case by a proof of right, one built on a transcendental deduction of the grounds of proof. That means going directly, so that we can see what his claims of reason have to say for themselves. If his opponent relies on subjective grounds, it’s certainly easy to refute him. But the dogmatist gains nothing, since he usually clings to subjective causes of judgment too and can be cornered the same way. But if both parties proceed only directly, one of two things will happen. Either they’ll notice on their own how hard, indeed impossible, it is to find a title for their claims, and end up able to appeal only to long possession. Or else critique will easily expose the dogmatic illusion and make pure reason give up its overstretched pretensions in speculative use. Reason will then pull back inside the boundaries of its own ground, which is practical principles.

B 823 Transcendental Doctrine of Method Second Chapter Pure Reason’s Canon

It is humbling for human reason that in its pure use it accomplishes nothing, and even needs a discipline to hold its excesses in check and prevent the deceptions that come from them. On the other hand, it lifts reason up again and gives it confidence in itself that it can and must exercise this discipline itself, without allowing any other censure over it. It is also uplifting that the boundaries reason is forced to set for its speculative use at the same time restrict the sophistical pretensions of any opponent. So whatever is still left of its earlier exaggerated demands can be made safe against all attacks. The greatest and perhaps the only use of all philosophy of pure reason is therefore only negative. It serves not as an organon for extending knowledge but as a discipline for fixing boundaries. It discovers no truth. Its only merit is the quiet one of keeping errors from happening.

Still, there must be a source somewhere for positive cognitions that belong to the territory of pure reason.

B 824 Perhaps only a misunderstanding makes them lead to errors. In fact they are the goal of reason’s zeal. What else could we blame for the unstoppable urge to get a firm foothold somewhere beyond the boundary of experience? Reason has a sense of objects that hold great interest for it. It sets out on the path of mere speculation to get near them, but they flee from it. Probably better luck can be hoped for on the one path that is still left to it, namely that of practical use.

By a canon I mean all the a priori principles, taken together, for using certain powers of cognition correctly, in general. General logic works this way too. In its analytic part it is a canon for the understanding and for reason as such, but only a canon of form, because it sets aside all content. The transcendental analytic was likewise the canon for the pure understanding, since only the understanding is capable of genuine synthetic cognitions a priori. Where no correct use of a power of cognition is possible, there is no canon. But by every proof given so far, no synthetic cognition at all is possible for pure reason when it is used speculatively. So there is no canon at all for its speculative use (since that use is dialectical through and through). In this respect all transcendental logic is nothing but discipline.

B 825 So suppose pure reason has some correct use after all. Then it must also have a canon, and that canon will deal not with speculative use but with practical use. That is what we now want to investigate.

Pure Reason’s Canon Section One The Final Purpose of the Pure Use of Our Reason

A natural tendency in reason pushes it past its use in experience. Working purely, with nothing but ideas, it dares to go out to the farthest boundaries of all cognition. And it finds rest only once it has completed its circle, in a systematic whole that stands on its own. Is this striving grounded merely in reason’s speculative interest, or rather solely and entirely in its practical interest?

For now I’ll set aside whatever success pure reason has with a speculative aim. I ask only about the tasks whose solution makes up its final purpose, whether it reaches that purpose or not. Next to that purpose, all its other aims have only the value of means.

B 826 By the nature of reason, these highest purposes will in turn have to form a unity, so that together they can advance the interest of humanity that is subordinate to no higher one.

The final aim that the speculation of reason in its transcendental use ultimately comes down to concerns three objects: the freedom of the will, the soul’s immortality, and God’s existence. In all three cases the interest that reason has in merely speculative terms is very small. For the sake of that interest alone, hardly anyone would take on the wearying labor of transcendental inquiry, which struggles with endless obstacles. Whatever might be discovered about these three, we could make no use of it that would prove its worth in concreto, that is, in the study of nature. First, the will may be free. Even so, that could bear only on the intelligible cause behind our willing. As for the phenomena of its expressions, that is, our actions, we must, by an inviolable basic maxim without which we can’t exercise reason in its empirical use at all, explain them in no other way than all other appearances of nature, namely by nature’s unchanging laws. Second, perhaps we could gain insight into the soul’s spiritual nature (and with it its immortality). Even so, we couldn’t count on it as an explanation for the appearances of this life.

B 827 Nor could we count on it for the particular character of the future state. The reason is that the concept we have of a nature without a body is purely negative. It doesn’t extend our cognition in the least. It offers no usable material for conclusions, except perhaps ones that can pass only for inventions, and philosophy doesn’t allow those. Third, suppose the existence of a supreme intelligence were proved. We could then understand the purposiveness in how the world is arranged, and its order in general. But we would have no right at all to derive from it any particular arrangement or order, or to boldly infer one where none is perceived. For speculative reason has a necessary rule: don’t skip natural causes, and don’t abandon what experience can teach us, merely to explain something we know by appeal to what is wholly beyond our knowledge. To put it briefly, for speculative reason these three propositions stay transcendent, always. None of them has an immanent use, meaning a use that is allowed for objects of experience and so is in some way useful to us. Considered in themselves they are quite idle, and yet extremely hard, labors of our reason.

Suppose we don’t need these three cardinal propositions for knowledge at all, and still our reason strongly urges them on us.

B 828 Then their importance must really concern only what is practical.

Practical means everything that is possible through freedom. But suppose that what is needed for our free power of choice to act is empirical in nature. Then reason can have only a regulative use there, and serves only to bring about unity among empirical laws. Take the doctrine of prudence. There the whole business of reason is to unite all the ends that our inclinations set for us into the one end, happiness, and to bring the means for reaching it into agreement. So all reason can offer are pragmatic laws for free conduct, laws for reaching the ends that the senses urge on us. It can’t supply pure laws, determined completely a priori. Pure practical laws would be different. Their end is given completely a priori by reason, and they command absolutely, not conditioned by anything empirical. They would be products of pure reason. The moral laws are of this kind. That is why only the moral laws fall under the practical use of pure reason, and only they allow a canon.

All the equipment of reason, in the work that can be called pure philosophy, is in fact aimed only at the three problems just named. They in turn have a more distant aim: what we ought to do should the will be free, should there be a God, and should there be a world to come.

B 829 This has to do with how we act in relation to the highest end. So nature, which looks after us wisely when it sets up our reason, really aims in the end only at the moral.

We need to be careful, though. We are now turning our attention to a subject that is foreign* to transcendental philosophy. On the one hand, we must not wander off into side episodes and break the unity of the system. On the other, we must not say too little about this new material and so leave it lacking in clearness or conviction. I hope to do both by staying as close to the transcendental as I can, and by leaving out entirely anything that might be psychological here, in other words empirical.

* Every practical concept is about objects that please or displease us, that is, objects of pleasure or displeasure. So they are directed, at least indirectly, at objects of our feeling. Feeling, though, is not a power of representing things. It lies outside the whole power of cognition. So the elements of our judgments that refer to pleasure or displeasure, and therefore the practical elements, don’t belong in the sum total of transcendental philosophy, which is concerned only with pure cognitions a priori.

A note to start with: for the present I will use the concept of freedom in its practical meaning alone. The concept in its transcendental meaning I put aside here, as settled above.

B 830 That meaning can’t be assumed empirically as an explanation of appearances, and is itself a problem for reason. Whatever power of choice is determinable only by sensory impulses, which is to say pathologically, is merely animal (arbitrium brutum). The power of choice that can be determined without depending on sensory impulses, and so by motives which only reason puts before us, is known as the free power of choice (arbitrium liberum). Whatever is tied to it, as a ground or as a consequence, gets the name practical. Practical freedom can be proved by experience. For what determines the human power of choice is not merely what stimulates, that is, what directly affects the senses. We have a power to overcome the impressions on our sensory faculty of desire. We do so by conceiving of what is advantageous or damaging, even if only at a further remove. These deliberations about what is desirable with regard to our whole condition, that is, what is good and useful, rest on reason. So reason also gives laws, namely imperatives, which are objective laws of freedom. They say what ought to happen, even if it perhaps never does. That is where they differ from laws of nature, which are only about what happens. That’s why they are also called practical laws.

B 831 Whether reason itself, in the very acts by which it lays down laws, is again determined by other influences is no concern of ours in practical matters. The same goes for whether what we call freedom, as against sensible impulses, might turn out to be nature once more when we look at higher and more distant efficient causes. In practice we only ask reason, first of all, for the rule of conduct. These questions are purely speculative, and we can put them aside as long as our aim is to act or to refrain. So we know practical freedom from experience. It is one of the natural causes: reason acting as a cause when it determines the will. Transcendental freedom is another matter. It requires reason itself to be independent of every determining cause in the world of sense, in respect of its causality in starting a series of appearances. To that extent it seems to conflict with the law of nature, and so with all possible experience, and it remains a problem. But this problem has no place in reason’s practical use. So in a canon of pure reason we have to deal with only two questions. They concern the practical interest of pure reason, and a canon of how reason is used must be possible for them: Is there a God? Is there a future life? The question of transcendental freedom touches only speculative knowledge. We can treat it as a matter of complete indifference and leave it aside.

B 832 That holds whenever the practical is what matters. The Antinomy of Pure Reason has already discussed it enough.

Pure Reason’s Canon Section Two The Ideal of the Highest Good as What Determines the Final Purpose of Pure Reason

When reason worked in its speculative way, it took us across the field of experience. It can never find full satisfaction there, so from there it took us on to speculative ideas. In the end those ideas brought us back to experience. So they did serve their purpose, in a way that is useful but nothing like what we had expected. One attempt is still left to us. Can pure reason also be found at work in practical use? Does it lead us there to the ideas that reach the highest purposes of pure reason, the ones we have just named? Looked at from its practical interest, can it give us what it flatly refuses us on the speculative side?

Everything that my reason takes an interest in, speculative and practical alike, comes together in these three questions:

1 B 833 What can I know?2. What should I do?3. What may I hope for?

The first question is purely speculative. We have gone through every possible answer to it, or so I flatter myself, and have finally found the one that reason has to accept. If reason sets the practical aside, it even has cause to be content with it. But we’ve stayed just as far from the two great aims that this whole effort of pure reason was really aimed at as if we had refused the work from the start, out of love of ease. So where knowledge is concerned, this much at least is certain and settled: we can never have it on those two problems.

The second question is purely practical. As such it can belong to pure reason. But then it isn’t transcendental. It’s moral, and so our critique can’t take it up in itself.

The third question is this: if I now do what I should, what may I then hope for? It is practical and theoretical at once. The practical side serves only as a guide toward answering the theoretical question, and, if that goes high enough, the speculative one. All hoping aims at happiness. For the practical and the moral law, hoping is just what knowing and natural law are for theoretical cognition of things.

B 834 The one ends in the inference that something exists (something that fixes the last possible purpose) because something ought to happen. The other ends in the inference that something exists (something that acts as the supreme cause) because something does happen.

Happiness means having all our inclinations satisfied. We can measure it in three ways: extensively, by the variety of inclinations that are met; intensively, by how strongly; and protensively, by how long it lasts. A practical law that takes happiness as its motive I call pragmatic, a rule of prudence. A law that has no motive but being worthy of happiness, if there is such a law, I call moral, the moral law. The pragmatic law gives advice: here is what to do if you want a part in happiness. The moral law gives an order: here is how to behave if all you want is to become worthy of happiness. The pragmatic law is built on empirical principles. Without experience I can’t tell which inclinations exist and ask to be met, or which natural causes might meet them. The moral law pays no attention to inclinations or to the natural ways of meeting them. It looks solely at the freedom of rational beings as such, and at the conditions that are necessary if that freedom is to agree, on principle, with how happiness gets shared out. For that reason it can rest, at the very least, on pure ideas of reason, and we can know it a priori.

B 835 I assume that pure moral laws really exist. They settle what we do and what we refrain from doing, in other words how any rational being uses its freedom. They do this entirely a priori, with no eye to empirical motives, which means happiness. I assume, too, that these laws command without condition, and not merely hypothetically on the basis of some other empirical purpose, so that they are necessary in every way. This is an assumption I may fairly make. I can appeal to what the most enlightened moralists have demonstrated, and also to anyone’s moral judgment, as soon as they try to picture such a law clearly.

So pure reason does contain principles of the possibility of experience. It doesn’t in its speculative use, but it does in one practical use, the moral one. I mean experience of the kind of actions that could turn up in human history in line with moral precepts. Reason commands that such actions are to happen, so they must be able to happen. That means a special kind of systematic unity must be possible, the moral kind. Systematic unity of nature, by contrast, couldn’t be proved from the speculative principles of reason. Reason has causality in regard to freedom in general but not in regard to nature as a whole, and moral principles of reason can bring about free actions but not natural laws.

B 836 So the principles of pure reason have objective reality in their practical use, and above all in their moral use.

A world that fitted every moral law I call a moral world. Such a world can exist, given the freedom of rational beings, and it should exist, given morality’s necessary laws. In this sense we think of it only as an intelligible world, since it leaves out of account all conditions (purposes) and even every obstacle to morality there (the weakness or impurity of human nature). So far it is a mere idea, yet a practical one, since it can and should shape the world of sense, to make that world match it as well as possible. That is why the idea of a moral world has objective reality. It isn’t that the idea aims at an object of intelligible intuition, which we couldn’t even think. It aims at the world of sense, but as an object that pure reason has in its practical use. And it aims at a corpus mysticum (a mystical body) formed by the rational beings in that world, to the degree that each one’s free power of choice, under moral laws, is consistently and systematically unified with itself and with the freedom of every other.

That answered the first of pure reason’s two practical questions: do what makes you worthy of happiness.

B 837 The second question is this. Suppose I conduct myself so that I’m not unworthy of happiness. Can I then hope to receive it? To answer it we have to ask something about the principles of pure reason, the ones that lay down the law a priori: do they also tie that hope to the law by necessity?

My answer, then, is this. The moral principles are necessary for reason in its practical use. By the same token, reason in its theoretical use has to accept that each person has grounds to hope for as much happiness as they have made themselves worthy of by how they act. It follows that the system of morality and the system of happiness can’t be pulled apart. They are joined, however, only in the idea of pure reason.

Think of an intelligible world, a moral one, whose very concept leaves out every obstacle to morality, meaning our inclinations. In that world we can also see it as necessary that happiness is shared out in proportion to morality and joined to it. Freedom there is partly driven and partly held back by moral laws, so freedom itself would produce general happiness. Rational beings, led by such principles, would be the makers of their own lasting well-being and of everyone else’s too. But this system, in which morality pays for itself, is only an idea.

B 838 Making it real depends on a condition: everyone must do what they ought, so that all the actions of rational beings come out as if they flowed from one supreme will that holds all private choice inside it or beneath it. However, the obligation under the moral law stays in force for each person’s own use of freedom, even if others don’t live up to the law. For that reason nothing in the nature of worldly things, and nothing in how actions cause things or how they stand to morality, tells us how the results of actions will line up with happiness. Reason can’t know the necessary connection I mentioned, between hoping to be happy and tirelessly striving to deserve happiness, if it builds on nature alone. We can only hope for the connection, and only if a highest reason that gives commands by moral laws is placed beneath nature as its cause.

The ideal of the highest good is my name for the idea of an intelligence like this: a will that is morally perfect and joined with supreme blessedness, and that causes all the happiness in the world to the extent that this happiness stands in exact proportion to morality, which is worthiness to be happy. The ground of the practically necessary connection between the two elements can be found by pure reason in just one place, the ideal of the highest original good.

B 839 Those two elements make up the highest derived good: an intelligible, that is, moral, world. Reason forces us to represent ourselves as members of such a world, though our senses present nothing but a world of appearances. Since the sensible world offers no such connection, we have to take the moral world to be a result of how we behave here, and to be a world that lies ahead of us. So God and a future life are two things we must presuppose. The principles of this same reason won’t let us separate them from the obligation that pure reason puts on us.

Morality by itself forms a system. Happiness does not, unless it is shared out in exact keeping with morality. That works only in the intelligible world, where a wise creator and governor presides. Reason is driven to assume one: a governor, along with a life in that world, which we have to see as lying in the future. The only alternative is to dismiss the moral laws as idle fantasies. For without that assumption the necessary result that reason itself attaches to the laws would vanish. That’s why everyone treats moral laws as commands. They couldn’t be commands if they didn’t attach suitable consequences to their rule a priori, and so bring promises and threats with them.

B 840 They can’t do that, though, unless they rest on a necessary being that is itself the highest good, since only such a being can make that kind of purposive unity possible.

Leibniz called the world the realm of grace when we attend in it only to the rational beings and how they hang together under moral laws, governed by the highest good, and distinguished it from the realm of nature. In the realm of nature these beings also stand under moral laws, but they expect no results from their conduct other than those that follow the course of nature in our world of sense. To see ourselves in the realm of grace, then, where all happiness waits for us unless we cut down our own share of it by being unworthy to be happy, is a practically necessary idea of reason.

When practical laws also become subjective grounds for acting, they turn into subjective principles, and these are called maxims. Judging morality, in its purity and its consequences, goes by ideas. Following its laws goes by maxims.

Our whole conduct of life must be put under moral maxims. Yet that cannot happen unless reason links the moral law, a mere idea, to an operating cause. This cause has to fix, for conduct in line with the law, an outcome that fits our highest ends exactly, in this life or in some other.

B 841 So without a God and a world to come, one that we can’t see now but hope for, the magnificent ideas of morality earn our approval and admiration but don’t spur us to resolve and act. That’s because they don’t fulfill the entire end that comes naturally to every rational being and that this very same pure reason fixes a priori as necessary.

In the eyes of our reason, happiness alone is nowhere near the complete good. Reason does not give it approval, however strongly inclination wants it, unless it comes together with worthiness to be happy, which is to say, good moral conduct. Yet morality alone is not the complete good either, and neither is the bare worthiness to be happy that goes with it. To make the good complete, whoever has behaved in a way that doesn’t make them unworthy of happiness has to be able to hope for a share in it. A reason free of every private aim would judge no differently, if it imagined itself in the place of a being who has all happiness to give out to others and took no interest of its own into account. In the practical idea, both parts are bound together essentially, but in this order: the moral disposition, as the condition, makes a share in happiness possible. The prospect of happiness does not first make the moral disposition possible. If it did, the disposition wouldn’t be moral.

B 842 And so it wouldn’t deserve the whole of happiness, which in reason’s view is limited only by what comes of our own immoral behavior.

So the highest good of a world is nothing else than happiness that keeps exact step with the morality of rational beings, the morality that makes them worthy of it. Pure but practical reason requires us to see ourselves as living in such a world. Of course it can only be an intelligible world, because the world of sense doesn’t promise that the nature of things will give us any such systematic unity of purposes. What makes that unity real can rest on one thing only: the assumption of a highest original good. There, an independent reason with every power a supreme cause needs sets up, sustains and brings to completion the universal order of things, with perfect purposiveness, though in the world of sense that order stays deeply hidden from us.

Moral theology has one advantage of its own over speculative theology. It leads inevitably to the concept of a single primal being, perfect in every way and rational. Speculative theology doesn’t even hint at that on objective grounds, much less persuade us of it. Neither transcendental theology nor natural theology, however far reason carries us in them, offers any weighty reason for assuming just one being.

B 843 It would have to be a being we could set over all natural causes, with sufficient reason to make them depend on it in every respect. Look at the matter from the side of moral unity instead. That is a necessary law for the world. Ask what cause alone can give this law its fitting effect, and with it binding force for us. Then it has to be one supreme will, which holds all these laws within itself. How else would we find perfect unity of purpose among a variety of wills? That will must be all-powerful, so that all of nature and its bearing on morality in the world is under its rule. It must be all-knowing, so that it can see into the depths of our dispositions and judge their moral worth. It must be present everywhere, so that it is right there for every need that the world’s highest welfare makes. And it must be eternal, so that this harmony of nature and freedom never fails at any time, and so on.

This systematic unity of purposes belongs to the world of intelligences. As mere nature, that world is only the world of sense. As a system of freedom, it can be called an intelligible, that is, a moral, world (regnum gratiae). It also leads without fail to a purposive unity of all the things in this great whole under universal laws of nature, just as the first unity holds under universal and necessary moral laws. So it joins practical reason to speculative reason. The world must be thought of as sprung from an idea.

B 844 Only so can it agree with the moral use of reason, the one use without which we would think ourselves unworthy of reason itself. That moral use rests wholly on the idea of the highest good. That gives all inquiry into nature a direction toward the form of a system of purposes. Carried as far as it can possibly be extended, such inquiry becomes physico-theology. But physico-theology started out from a moral order, which is a unity rooted in the essence of freedom and not set up by accident through commands from outside. So it takes nature’s purposiveness back to grounds that must be bound up, a priori and inseparably, with the inner possibility of things. This brings us in turn to a transcendental theology. It makes the ideal of supreme ontological perfection into a principle of systematic unity, one that links all things by universal and necessary laws of nature, since all of them have their source in the absolute necessity of one primal being.

Without purposes, what use could we make of our understanding, even for experience? The highest purposes are the moral ones, and pure reason alone can bring them to our knowledge. Armed with these and following them as our guide, we still can’t use our knowledge of nature purposively for the sake of cognition, except where nature has itself laid down purposive unity.

B 845 Without it we wouldn’t have reason at all, because there would be no schooling for reason and no cultivation from objects that offer the raw material for such concepts. Now the purposive unity of morals is necessary and is rooted in the very nature of the power of choice. The purposive unity in nature, which contains the condition for applying it to concrete cases, must therefore be necessary too. And then the transcendental raising of our rational cognition would not be what causes the practical purposiveness that pure reason imposes on us. It would be merely an effect of it.

The history of human reason shows the same thing. There was a time when moral concepts hadn’t yet been purified or defined well enough, and the systematic unity of purposes that follows from them hadn’t yet been understood from necessary principles. In that period, knowledge of nature, and even a high level of cultivation of reason in several other sciences, led in some cases to nothing but rough, drifting ideas of the deity. In other cases it left people with a surprising indifference to the whole question. Then came a fuller treatment of moral ideas, which the very pure moral law of our religion made necessary. It sharpened reason’s focus on the subject, because of the interest that reason was forced to take in it. Wider knowledge of nature did nothing to bring this about, and neither did sound, reliable transcendental insight, which has been lacking in every age.

B 846 Yet the moral ideas produced the notion of the divine being that we now consider correct. We don’t consider it correct because speculative reason has satisfied us of its correctness. We do so because it fits perfectly with the moral principles of reason. So when it comes down to it, the credit always belongs to pure reason, in its practical use only. It takes a cognition that mere speculation can only fancy and cannot make valid, and fastens it to our highest interest. That doesn’t make the cognition a demonstrated dogma, but it does make it an absolutely necessary assumption for reason’s most essential purposes.

But there is a limit on practical reason once it has reached this height, the concept of one primal being as the highest good. It must not presume to behave as if it had risen above every empirical condition for applying that concept. It must not behave as if it had swung up into immediate knowledge of new objects, so that it could start from this concept and deduce the moral laws from it. Those laws, after all, are what drove us, by their own inner practical necessity, to assume an independent cause or wise ruler of the world, to make the laws effective. So we can’t now turn around and regard them as accidental and derived from a mere will.

B 847 That goes above all for a will that we couldn’t even conceive if we hadn’t shaped the concept of it to fit those laws. As far as practical reason is entitled to lead us, we will not hold actions to be obligatory because God commands them. Instead we will see them as God’s commands because we are obligated to them from within. We will study freedom under the purposive unity set by principles of reason. We will believe that we match the divine will only to the extent that we hold the moral law sacred, which reason teaches from the nature of actions themselves, and we will think of ourselves as serving God only when we advance the world’s good, in ourselves and in other people. Moral theology is therefore only for immanent use. That is, it helps us live out our calling here in the world, by finding our place in the system of all purposes. It is not to abandon, in a fanatical or even outrageous way, the thread of a morally legislating reason in the course of a good life, in order to attach that life directly to the idea of the highest being. That would be a transcendent use. Like speculation alone, it would have to twist and thwart the final purposes of reason.

B 848 Pure Reason’s Canon Section Three Having an Opinion, Knowing and Having Faith

Taking a thing to be true is something that happens in our understanding. It can rest on objective grounds, but it also calls for subjective causes in the mind of the one judging. If anyone at all with reason would accept it, the ground is objectively sufficient, and then we call it conviction. When its ground lies only in the particular constitution of the subject, we call it persuasion.

Persuasion is just illusion. A ground that lies solely in the subject gets mistaken for an objective one. For that reason a judgment of this kind is valid only privately, and taking it as true cannot be passed on to anyone else. Truth rests on agreement with the object, so the judgments of every understanding have to agree with one another about it (consentientia uni tertio, consentiunt inter se). From outside, then, the test of whether taking something as true is conviction or mere persuasion is whether we can communicate it and find that it holds for every human’s reason. If so, there is at least a presumption.

B 849 It is that the ground of the agreement among all these judgments, in spite of the differences among the people judging, lies in a shared ground, the object. Each of them is in line with the object, and that shows the judgment is true.

From the subject’s own point of view, persuasion can’t be told apart from conviction, as long as the subject sees the taking-as-true only as something appearing in their own mind. But there is a test we can run. We take the grounds that convince us and try them on someone else’s understanding, to see whether they affect another reason as they affect ours. This is a means, though a merely subjective one. It cannot create conviction, but it can bring to light the merely private validity of the judgment, that is, whatever in it is just persuasion.

There is more we can do. Suppose we can lay out the subjective causes that stand behind the judgment, the ones we have been taking for objective grounds, we can explain the misleading taking-as-true as something that happened in our own minds, without needing to know anything about the object. Then we have stripped the illusion bare, and it fools us no longer, although it can still tempt us to some extent when the subjective cause of the illusion belongs to our nature.

The only thing I can assert, that is, declare as a judgment necessarily valid for all, is what produces conviction.

B 850 Persuasion I can keep for myself, if it suits me, but I can’t, and shouldn’t, try to make it count outside myself.

Taking something as true, which is the subjective validity of a judgment, has three levels, related to conviction (which also counts objectively): having an opinion, having faith, and knowing. An opinion is a taking-as-true that you are aware is not enough, either subjectively or objectively. If it is enough subjectively but regarded as not enough objectively, it is called faith. And when it is enough both subjectively and objectively, it is called knowledge. Enough subjectively is conviction (for me myself); enough objectively is certainty (for everybody). I won’t dwell on explaining notions so easy to grasp.

I must never take it on myself to hold an opinion unless I know something, at least, that connects the judgment (which taken alone is merely problematic) with truth. The connection may be incomplete, but it must be more than free invention. And the law of such a connection has to be certain. If I have nothing but opinion about that as well, it is all a play of imagination with no relation to truth at all. In judgments of pure reason, forming opinions is not allowed whatsoever. They are not supported by grounds taken from experience.

B 851 Everything in them is to be known a priori, where all is necessary. So the principle of connection requires universality and necessity, and therefore complete certainty. Otherwise nothing guides us toward truth at all. That’s why it’s absurd to hold opinions in pure mathematics. You must know, or else refrain from judging entirely. The principles of morality are the same. You may not risk an action because you merely suppose it’s allowed. You have to know that.

In the transcendental use of reason, by contrast, an opinion is too little, though knowledge is also too much. So from a purely speculative standpoint we can’t judge at all here. Subjective grounds for taking something as true, like those that can give rise to faith, deserve no approval in speculative questions. They can’t be kept clear of every empirical aid, and they can’t be passed on to others in the same measure.

Only in a practical connection, then, can we call a theoretically inadequate taking-as-true faith. And this practical aim is either skill or morality. Skill is for any chance purposes, whichever we like. Morality is for purposes that are necessary without exception.

Once a purpose is given, the conditions for reaching it are hypothetically necessary. That necessity is subjective.

B 852 It is sufficient only by comparison, and only if there are no other conditions known to me that would let the purpose be reached. It is sufficient absolutely and for everyone if I know for sure that nobody could know other conditions that would lead to the purpose set. In the first case, my assumption and my taking certain conditions as true is an accidental faith. In the second case it is a necessary faith. A doctor with a patient in danger must act, but doesn’t know the illness. The doctor looks at the signs and, knowing nothing better, decides it’s consumption. By the doctor’s own judgment this belief is only accidental; someone else might perhaps hit on it better. The name I give to this kind of accidental faith, when it underlies the actual use of means for particular actions, is pragmatic faith.

The usual test of what lies behind someone’s assertion, mere persuasion or at least subjective conviction (firm faith), is to bet on it. Often a person speaks with such sure, stubborn defiance that every worry about error seems to be gone. A bet makes them hesitate. Now and then it turns out that they have just enough persuasion to be worth one ducat, but not ten. One ducat they will still risk.

B 853 But at ten they realize for the first time what they hadn’t seen before, that they may well be wrong. Suppose you imagine staking your whole life’s happiness on it. Our triumphant judgment then drops sharply, we turn very timid, and we discover for the first time that our faith doesn’t stretch that far. So pragmatic faith comes in degrees, and the degree can be large or small, depending on how much is at stake.

Sometimes we can do nothing at all with an object, so that taking something to be true about it is purely theoretical. Even then, in many cases we can think up an undertaking and picture it, one we believe we have good enough grounds for, if only there were some way to settle the matter with certainty. So in purely theoretical judgments there is something that parallels practical ones, and the word faith suits the way we hold such a judgment true. We can call it doctrinal faith. Suppose some experience could settle the question. I would gladly stake all I own on there being inhabitants on at least one of the planets we can see. That is why I say it is more than an opinion. It is a strong faith, on whose being right I would risk many of life’s advantages, that other worlds have inhabitants too.

B 854 Now we must concede that the teaching about God’s existence is a matter of doctrinal faith. When it comes to explaining the world theoretically, nothing I have to work with requires this thought as a premise for accounting for the appearances. On the contrary, I’m bound to use my reason as though everything were only nature. Still, purposive unity is such an important condition for applying reason to nature, and experience gives me so many examples of it, that I cannot simply pass it by. The only condition I know of that would make this unity a guide for my study of nature is to assume that a supreme intelligence has arranged everything according to the wisest purposes. Supposing there is a wise maker of the world is therefore a condition for reaching an aim that is accidental but not trivial: having guidance as I investigate nature. The results of my attempts confirm, again and again, how useful this assumption is, and nothing decisive can be said against it. I would be saying far too little if I called my holding it true a mere opinion. I can go further and say, even here on the theoretical side, that my belief in God is firm. Yet in the strict sense this faith is still not practical. It has to be called doctrinal faith.

B 855 The theology of nature (physico-theology) is bound to produce this faith everywhere. The same wisdom, together with the excellent equipment of human nature and the shortness of life, which fits that equipment so poorly, can likewise supply sufficient ground for a doctrinal faith in the future life of the human soul.

In cases like these, the word faith expresses modesty from the objective side and yet firm confidence from the subjective side. Suppose I called this merely theoretical holding-true a hypothesis that I was entitled to adopt. Then I would already be committing myself to more of a concept of the cause of the world and of another world than I can really show. Whatever I adopt even as a hypothesis, I have to know enough about its properties that I am free to invent only its existence, not its concept. But the word faith points only to the lead that an idea provides, and to the pull it has within me on how my rational actions go forward. That pull keeps me attached to the idea, though I’m unable to account for it from a speculative standpoint.

Merely doctrinal faith, though, has something unsteady about it. Difficulties that turn up in speculation often knock us out of it.

B 856 We always come back to it again, though, without fail.

Moral faith is a very different matter. Here it is absolutely necessary that something must happen: that I obey the moral law in every respect. The purpose is firmly fixed, with no way around it. As far as I can see, only one condition makes it possible for this purpose to hang together with all purposes taken together, and so to have practical validity: that a God exists and a world to come exists. I also know for certain that nobody knows of any other condition that leads to the same unity of purposes under the moral law. But the moral precept is at the same time my maxim, as reason commands that it should be. So I can’t help believing that God exists and that there is a life to come. And I’m sure nothing could shake this faith, because it would overturn my own moral principles, and I can’t give those up without becoming detestable in my own eyes.

So, with all the ambitious aims of a reason that roams beyond the boundaries of all experience thwarted, enough still remains to give us cause for satisfaction in the practical respect. Of course no one will be able to boast of knowing that a God exists and that a future life exists.

B 857 If they know that, they are exactly the person I have been looking for all this time. All knowledge, when it concerns an object of pure reason alone, can be communicated, so I could hope that their teaching would extend my own knowledge to a wonderful degree. No: the conviction is not logical certainty but moral certainty. It rests on subjective grounds (the moral disposition), so I mustn’t even put it this way: “It is morally certain that God exists,” and so on. The right way is: “I am morally certain,” and so on. What I mean is that my belief in a God and another world is woven into my moral disposition so tightly that I am in no more danger of losing the disposition than I fear this belief could ever be torn from me.

There is only one troubling point here. This faith of reason is founded on the assumption that moral dispositions exist. Drop that, and take someone completely indifferent to moral laws. Then the question that reason raises becomes merely a task for speculation. Strong grounds from analogy can still support the answer, but not grounds that the most stubborn skepticism would have to give in to*.

B 858 Still, nobody is wholly uninterested in these questions. Even if a lack of good dispositions cuts that person off from the moral interest, enough is left to make them fear that there is a divine being and a future. For that, all that is needed is that they can’t pretend to be sure that no such being exists and that there is no future life. They would have to prove that both are impossible, and since that would have to be proved by pure reason, and so apodictically, no reasonable person could take it on. This would be a negative faith. It could not produce morality and good dispositions, but it could produce their analogue: it could powerfully hold back the outbreak of bad dispositions.

* The human mind has a natural interest in morality. I believe this is so, necessarily, in every rational being, even though the interest is neither undivided nor practically dominant. Strengthen and deepen this interest, and reason will turn out to be very ready to learn, and even brighter at joining its speculative interest to its practical one. But if you don’t first see to it that people become good, at least partway, you will never turn them into honest believers either!

“Is that all?” someone will say. “Is that all pure reason achieves by opening up prospects beyond the boundaries of experience? Nothing more than two articles of faith?

B 859 Common understanding could have managed that much without asking any philosophers!”

I won’t praise here what philosophy has done for human reason through the hard work of its critique, though the outcome may prove merely negative. A little more will be said about that in the next section. But do you really demand that a cognition which concerns all human beings should rise above common understanding and be revealed to you only by philosophers? What you complain about is the best confirmation that what I’ve said so far is correct. It reveals something that no one could foresee at the start: that nature can’t be accused of handing out its gifts unfairly in what matters to all people alike, and that the highest philosophy, regarding the essential purposes of human nature, can get no further than the guidance that nature has given even to the most ordinary understanding.

B 860 Transcendental Doctrine of Method Third Chapter Pure Reason’s Architectonic

By architectonic I mean the art of building systems. Ordinary cognition becomes science, that is, a system rather than a mere aggregate, only through systematic unity. So architectonic is the doctrine of the scientific element in our cognition as a whole, and it therefore belongs necessarily to the doctrine of method.

Under reason’s rule, our cognitions must not be a patchwork. They have to form a system, since only in a system can they support and advance reason’s essential purposes. By a system I mean the unity of many different cognitions under one idea. This idea is the concept of reason for the form of a whole. It settles a priori both how far the manifold extends and where the parts stand in relation to one another. The scientific concept of reason therefore contains the purpose and the form of the whole that matches it. All the parts relate to that single purpose, and in the idea of it they relate to one another as well. This unity of purpose means that once we know the other parts, we can tell when any one part is missing.

B 861 No accidental addition can occur, and no amount of perfection that is not fixed within limits a priori. The whole is therefore articulated (articulatio), not piled up (coacervatio). It can grow from within (per intus susceptionem) but not from outside (per appositionem). An animal body is like this: its growth adds no limb, but makes each limb stronger and better fitted for its ends, with no change in proportion.

To be carried out, an idea needs a schema. That is, it needs an essential manifold and an order of the parts, fixed a priori by the principle of the purpose. A schema that is drawn up not from an idea, that is, from the main purpose of reason, but from experience, shaped by whatever aims happen to present themselves (and nobody can know in advance how many), gives technical unity. What arises solely from an idea, where reason sets the purposes a priori and does not wait for them to come from experience, founds architectonic unity. What we call a science cannot arise technically, from the likeness of the manifold or from the accidental use of cognition in concrete cases for all sorts of external purposes of one’s choosing. It arises architectonically, from the affinity of the parts and their derivation from one supreme, inner purpose that first makes the whole possible. The schema of a science has to hold the outline (monogramma) of the whole.

B 862 It also has to hold the division into members, drawn from the idea and so a priori. And it has to set the science apart from every other, securely and by principles.

No one sets out to build a science without an idea underlying it. But as the work proceeds, the schema, and even the definition the person gives of their science right at the start, very seldom matches their idea. The idea lies in reason like a seed, with all the parts still tightly folded up and hidden, barely visible even under a microscope. For this reason, and because every science is thought up from the standpoint of some general interest, we should not explain and define a science by the description its founder gives. We should do it by the idea that we find grounded in reason itself, on the basis of the natural unity of the parts the founder has brought together. We will then find that the founder, and often even the latest followers, wander around an idea they haven’t managed to make clear to themselves. They can’t fix the science’s own content, its articulation (systematic unity) and its limits.

It is unfortunate that for a long while we collect many related cognitions as building material, in patchwork fashion, guided by an idea that lies hidden in us. We even put them together technically over long periods.

B 863 Only then can we catch sight of the idea in clearer light and draw up a whole architectonically, in line with reason’s purposes. Systems seem to have been formed like worms, by generatio aequivoca, out of the mere flowing together of gathered concepts. At first they are mutilated, and with time they become complete. Yet all of them had their schema, as the original seed, in reason as it simply unfolded. For that reason each system is articulated by an idea on its own, and beyond that, all of them are united purposively with one another, as members of a whole, in one system of human cognition. This allows an architectonic of all human knowledge. In our time, when so much material has already been gathered, or can be salvaged from the rubble of old, collapsed buildings, such an architectonic would not only be possible but not even hard. For now we are satisfied to finish our own business, which is only to outline the architectonic for all the cognition that comes from pure reason. Our starting point is where the shared root of our power of cognition splits and sends out two trunks, reason being one of them. By reason here I mean the whole higher power of cognition, and so I set the rational against the empirical.

Set aside everything a cognition contains when we look at it objectively.

B 864 Looked at subjectively, every cognition is then either historical or rational. Historical cognition is cognitio ex datis. Rational cognition is cognitio ex principiis. A cognition may have been given in the first place from anywhere at all. In the person who has it, it is still historical if they know only as much as someone else has handed them, and only to that degree. It makes no difference whether it came through direct experience, through a report, or through teaching of general cognitions. So take someone who has truly learned a system of philosophy, say the Wolfian one. They might carry all the principles, explanations and proofs in their head, along with the layout of the whole teaching structure, and might be able to count it all off on their fingers. Even so, what they have is only a complete historical cognition of the Wolfian philosophy. They know and judge only as much as they were given. If someone disputes one of their definitions, they don’t know where to find another. They were shaped by another person’s reason. But the power to copy is not the power to produce. In other words, their cognition did not spring from reason. Objectively it was indeed a cognition of reason, but subjectively it is merely historical. They took it in well and kept it, that is, they learned it, and they are a plaster cast of a living person. A cognition that counts as rational objectively, one that could at first only have arisen from a person’s own reason, earns that name in the subjective sense as well only if it has been drawn from the general sources of reason.

B 865 Criticism can arise from those sources, and so can the rejection of what was learned. That is, the cognition must be drawn from principles.

Rational cognition always works in one of two ways: from concepts, or by constructing concepts. The first is called philosophical, the second mathematical. I have already dealt with the inner difference between them in the first chapter. A cognition can therefore be philosophical objectively and yet historical subjectively. That is how it is with most apprentices, and with everyone who never gets past the school and stays an apprentice all their life. It is odd, though, that mathematical cognition, learned as it was taught, can still count subjectively as cognition of reason, and that mathematics doesn’t show this kind of difference the way philosophy does. The reason is that the teacher can draw only on sources that lie in nothing but the essential, genuine principles of reason. So the apprentice can’t take them from anywhere else, and they can’t be disputed. In mathematics reason is used only in the concrete, though still a priori: it works on pure intuition. Pure intuition can’t mislead, and so it shuts out every deception and error. So among all the sciences of reason (a priori), only mathematics can be learned. Philosophy never can, unless as history. As far as reason is concerned, the most anyone can do is learn to philosophize.

B 866 Philosophy is the system made up of all philosophical cognition. We have to take philosophy objectively if by it we mean the archetype for judging every attempt to philosophize. That archetype is meant to serve as the standard for judging each subjective philosophy, and the structures of those are often so varied and so changeable. Understood like this, philosophy is nothing but the idea of a science that could exist. It is not given anywhere in the concrete. People try to approach it by many routes, until the one footpath, thickly overgrown with sensibility, is found, and they succeed in making the copy, which has so far failed, match the archetype as closely as human beings are allowed. Until then no one can learn philosophy. Where is it, who has it, and how could we recognize it? All we can learn is to philosophize. That means practicing the talent of reason, in following its general principles, on certain attempts that already exist. This is always done with reason keeping its right to examine those attempts right down to their sources, and to confirm or reject them.

Until that happens, the concept of philosophy remains a school concept. It is the concept of a system of cognition that is sought only as a science, with no aim beyond the systematic unity of this knowledge, and so the logical perfection of the cognition. But there is also a world concept (conceptus cosmicus), which has always underlain this name.

B 867 That holds above all when one, so to speak, personified it and pictured it as an archetype in the ideal philosopher. In this sense philosophy is the science of how all cognition relates to the essential purposes of human reason (teleologia rationis humanae), and the philosopher is not a craftsman of reason but the lawgiver of human reason. It would be quite vain to call yourself a philosopher in that sense, and to claim you have come up to the archetype, which exists only as an idea.

Mathematicians, natural scientists and logicians can be first-rate. The former may make excellent progress in rational cognition in general, and the latter in philosophical cognition in particular. Still, they are only craftsmen of reason. There is another teacher, in the ideal, who sets all of them to work and uses them as tools to advance the essential purposes of human reason. Only this teacher should be called the philosopher. But no such teacher is found anywhere, while the idea of this teacher’s lawgiving is found everywhere in every human reason. So we will keep to that idea alone, and work out more closely what philosophy, according to this world concept*, prescribes.

B 868 What it prescribes is a systematic unity, seen from the standpoint of purposes.

* A world concept here means one that concerns what interests everyone necessarily. So I determine a science’s aim by school concepts when it is looked at only as one skill among others, serving certain purposes anyone happens to choose.

Essential purposes are not for that reason the highest purposes. There can be only one highest purpose, if reason is to have perfect systematic unity. So essential purposes are either the final purpose, or subordinate purposes that necessarily belong to it as means. The final purpose is nothing other than the whole vocation of human beings, and the philosophy about it is called morals. Moral philosophy has this priority over every other pursuit of reason. Because of it, the ancients also always meant by the name of philosopher, above all, the moralist as well. And even now, the outward look of self-command through reason leads us to call someone a philosopher, by a kind of analogy, though their knowledge is limited.

The legislation of human reason, which is philosophy, has two objects: nature and freedom. So it contains the law of nature and also the moral law, at first in two separate philosophical systems and in the end in a single one. The philosophy of nature is about everything that is. The philosophy of morals is only about what ought to be.

Philosophy is of two kinds. One is cognition from pure reason. The other is rational cognition that starts from empirical principles. We call the first pure philosophy and the second empirical philosophy.

B 869 The philosophy of pure reason is one of two things. First, it can be a propaedeutic (a preliminary exercise) that examines the power of reason with respect to all pure cognition a priori. That is called critique. Second, it can be the system of pure reason (a science): the whole of philosophical cognition from pure reason, true and illusory alike, in systematic connection. That is called metaphysics. The name metaphysics can also be applied to pure philosophy as a whole, critique included. Then it takes in, together, the inquiry into whatever we may ever come to cognize a priori, together with the account of what makes up a system of such pure philosophical cognitions. Both are set apart from everything empirical, and also from the mathematical use of reason.

Metaphysics divides into the metaphysics of the speculative use of pure reason and that of its practical use. So it is either the metaphysics of nature or the metaphysics of morals. The first contains all pure principles of reason, drawn from concepts alone (so leaving mathematics out), for the theoretical cognition of all things. The second contains the principles that determine what we do and leave undone, a priori, and make it necessary. Of all the ways actions can conform to law, morality is the only one we can derive wholly a priori from principles. So the metaphysics of morals is really pure morals, with no anthropology (no empirical condition) laid at its base.

B 870 The metaphysics of speculative reason is what people usually mean by metaphysics in the narrower sense. But pure moral doctrine also belongs to that particular stem of human, and indeed philosophical, cognition from pure reason. So we will let it keep that name too, even though we leave it to one side here, since it has no part in our present aim.

It matters enormously to isolate cognitions that differ from others in kind and origin, and to take care that they don’t run together in a mixture with other cognitions they are usually combined with in use. Chemists do this when they separate substances. Mathematicians do it in their pure theory of magnitudes. Philosophers have even more reason to do it, so that they can reliably determine the share a particular kind of cognition has in the free-ranging use of the understanding, along with its own worth and influence. So from the moment people first thought, or rather began to reflect, their reason has needed a metaphysics. But it never managed to present one cleaned of everything alien to it. The idea of this science goes back exactly as far as speculative reason does. And whose reason doesn’t speculate, whether in the schools or in everyday ways? We must admit, however, that thinkers by trade kept one distinction very hazy.

B 871 I mean the distinction between two elements in our cognition. One is wholly at our disposal a priori. The other can be obtained only from experience, a posteriori. Because of that, they could never fix the boundary of a particular kind of cognition, and so could never form the true idea of a science that has kept human reason busy for so long and so intensely. Suppose someone defined it like this: “Metaphysics is the science that deals with the first principles in human cognition.” That points out not a quite particular kind of cognition but only a rank in generality. It couldn’t set metaphysics apart from the empirical in any recognizable way. Even empirical principles come in more and less general ones, and the more general are higher. Where, in a series ordered like that, with no distinction drawn between what is known wholly a priori and what is known only a posteriori, do you make the cut between the first part, with its highest members, and the last part, with the subordinate ones? How would we react if chronology could divide the world’s epochs only into the first centuries and those that came after? Would we ask whether the fifth century belongs among the first ones? And the tenth? And so on? I ask in the same way: is the concept of something extended part of metaphysics? You answer: yes! Well, then, the concept of body too? Yes! And of a liquid body?

B 872 Now you hesitate, because if we go on this way, everything will turn out to belong to metaphysics. From this we can see that no science gets its boundaries from a mere degree of subordination, that is, the particular falling under the general. Here the boundaries come from complete difference of kind and of origin. Something else obscured the basic idea of metaphysics from another side. As cognition a priori, metaphysics shows a certain likeness to mathematics. In origin, that likeness makes the two akin, because both are a priori. But look at the way metaphysics cognizes from concepts, and compare it with the way mathematics judges a priori purely by constructing concepts. That is the difference between philosophical and mathematical cognition. There the two turn out to be completely unlike. People always felt it, in a way, but never managed to state it in clear criteria. The result was this. Philosophers themselves went wrong in developing the idea of their sciences. So the work on those sciences could have no fixed purpose and no reliable guideline. The plan was made arbitrarily. Philosophers did not know which road they ought to take, and they were always quarreling, each boasting of finds made along their own path. In the end they brought their science into contempt, first with others and finally even with themselves.

B 873 All pure cognition a priori forms a unity of its own, thanks to the special power of cognition in which alone it can be seated. The philosophy that is to display this cognition within that systematic unity is metaphysics. The speculative part of it, which has mostly taken the name for itself, is what we call the metaphysics of nature. It weighs everything that exists, and not what ought to be, working from a priori concepts. We divide it as follows.

Metaphysics, as the name is used in the narrower sense, has two parts. One is transcendental philosophy. The other is the physiology of pure reason. Transcendental philosophy looks only at the understanding and at reason itself. It sets out a system of all concepts and principles that apply to objects in general, and it assumes no objects as given (Ontologia). The physiology of pure reason looks at nature, meaning everything given as an object, whether it is given to the senses or, if you prefer, to some other kind of intuition. So it is a physiology, though only a rational one (rationalis). Reason can go about this rational study of nature in a physical way or in a hyperphysical way. Better said, its use is either immanent or transcendent. Immanent use covers nature as far as the cognition of it can be applied in experience (in concreto). Transcendent use covers that connection among the objects of experience which goes beyond all experience.

B 874 This transcendent physiology takes as its subject either an inner or an outer connection, and both of them exceed possible experience. The inner one is the physiology of all of nature taken together, that is, transcendental cognition of the world. The outer one concerns how all nature hangs together with a being above nature, that is, transcendental cognition of God.

Immanent physiology, on the other hand, looks at nature as everything that the senses can take in as objects. It takes nature in the way it is given to us, but looks only at the a priori conditions that must hold for anything to be given to us. It has just two kinds of object. 1. Objects of the outer senses, which together make up corporeal nature. 2. The object of inner sense, which is the soul and, by the basic concepts of the soul in general, thinking nature. The metaphysics of corporeal nature is physics. Since it is to contain only the a priori principles for knowing nature, it is rational physics. The metaphysics of thinking nature is psychology. For the same reason just given, only rational cognition of the soul is meant here.

So the whole system of metaphysics has four main parts. 1. Ontology. 2. Rational physiology. 3. Rational cosmology. 4. Rational theology. The second part is the doctrine of nature drawn from pure reason.

B 875 It has two divisions: physica rationalis* and psychologia rationalis.

* Let no one suppose that I mean by this what is commonly called physica generalis. That is more mathematics than philosophy of nature. The metaphysics of nature is a wholly separate thing from mathematics. It can offer much less in the way of new insights that widen what we cognize. But it is very important for criticizing the pure cognition of the understanding in general, insofar as that is applied to nature. Where that critique is missing, even mathematicians have held on to certain common concepts that are really metaphysical, and have loaded natural science with hypotheses without noticing. A critique of these principles makes such hypotheses vanish. That does no damage whatever to the use of mathematics here, and mathematics can’t be done without.

The very first idea of what a philosophy of pure reason is already lays down this division. It is therefore architectonic: it follows reason’s essential purposes. It is not merely technical, which would mean arranging things by affinities noticed by chance, more or less hit and miss. Because of that, it is also fixed and legislative. But a few points come up here that raise concern and could shake our conviction that the division is lawful.

First, how can I look for a priori cognition, and so for metaphysics, about objects given through our senses, that is, a posteriori? And how is it possible to know the nature of things?

B 876 How can that be done by a priori principles, so that we reach a rational physiology? The answer is that we take nothing from experience except what we need to be given an object, partly of outer sense and partly of inner sense. For outer sense, the bare concept of matter does this (impenetrable, lifeless extension). For inner sense, the concept of a thinking being does it (in the empirical inner representation, I think). For the rest, throughout the metaphysics of these objects, we must abstain from all empirical principles that would add some further experience to the concept in hopes of drawing some judgment about these objects out of it.

Second: where does empirical psychology go? It has always held its place in metaphysics, and in our time people have expected great things from it for enlightening metaphysics, once they gave up hope of getting anything useful done a priori. My answer is that it goes where the properly empirical doctrine of nature has to go: on the side of applied philosophy. Pure philosophy contains the a priori principles for applied philosophy, so the two must be joined but not mixed. Empirical psychology therefore has to be banished from metaphysics altogether, and the very idea of metaphysics already shuts it out. Even so, by the custom of the schools we will still have to allow it a little spot there, as a mere episode.

B 877 We do so for reasons of economy. It isn’t yet rich enough to be a study of its own, and yet it is too important to throw out entirely or to pin on somewhere it would have even less kinship than it has in metaphysics. So it is only a stranger who is taken in for the time being, given a place to stay until its own house is ready in a full anthropology (the counterpart to the empirical doctrine of nature).

That is the general idea of metaphysics. At first people asked more of it than could fairly be demanded, and for a time they amused themselves with pleasant expectations. Then they found their hopes betrayed, and metaphysics finally fell into general contempt. The whole course of our critique should have convinced the reader of this much. Metaphysics cannot be the foundation of religion, but it must always stand as religion’s bulwark. And human reason is dialectical by the very tendency of its nature. It could never do without a science that holds it in check. Through scientific, fully evident self-knowledge, that science keeps away the devastation that lawless speculative reason would otherwise inevitably cause in morals and in religion alike. So we can be sure of one thing.

B 878 However prudish or scornful those people may be who weigh a science by what happens to come of it and not by what it is, people will always come back to metaphysics, like a beloved with whom we have quarreled. Reason cannot rest, because essential purposes are at stake. It must work either toward thorough insight or toward tearing down good insights that already exist.

So metaphysics, of nature and of morals alike, together with above all the critique of a reason that ventures out on its own wings, which comes first as a preparatory exercise (propaedeutic), is all that we can properly call philosophy in the true sense. Philosophy refers everything to wisdom. It goes by way of science, which is the only road that, once cut, doesn’t grow over again and doesn’t let anyone wander off. Mathematics, natural science, and even empirical knowledge of human beings are highly valuable as means. They mostly serve accidental purposes of humanity, but in the end necessary and essential ones too. But they can do this only with the help of a rational cognition from concepts alone. Call it what you like, it is really nothing but metaphysics.

That’s why metaphysics also completes the cultivation of human reason.

B 879 Such completion can’t be dispensed with, even if we leave aside what metaphysics does, as a science, for particular ends. It examines reason in its elements and supreme maxims. Some sciences couldn’t even be possible without them, and no science could be used without them. Metaphysics, as mere speculation, does more to keep errors away than to extend cognition. That takes nothing from its value. It gives metaphysics dignity and authority, through its role as a censor that safeguards general order, harmony and even the prosperity of the scientific commonwealth, and keeps that commonwealth’s bold and fruitful labors from moving away from the chief aim, universal happiness.

B 880 Transcendental Doctrine of Method Fourth Chapter Pure Reason’s History

This title is here only to mark a place that remains open in the system and will have to be filled later. I’ll be content to take a quick look at everything that has been done with pure reason so far. I look at it from a purely transcendental point of view, that is, from the nature of pure reason. To my eye it shows buildings, to be sure, but only in ruins.

It is remarkable enough, though it could hardly have gone any other way, that people in the childhood of philosophy began where we would now rather end. They started by studying the cognition of God, and the hope of another world, or even what that world is like. Whatever crude ideas of religion may have been introduced by the old customs, which were left over from the rough early state of peoples, this did not stop the more enlightened part from devoting itself to free inquiry into the subject. It was easy for them to see how one might please the invisible power that rules the world, and so be happy in another world at the very least.

B 881 No way could be more thorough or more reliable than a good way of life. So theology and morals were the two driving forces, or better, the two points of reference, for all the abstract inquiries of reason that people have devoted themselves to since. Theology, though, was really what drew merely speculative reason, bit by bit, into that business, which was later to win such fame as metaphysics.

I won’t now sort out the periods in which this or that change in metaphysics took place. I only want to sketch quickly the differences in the idea that set off the main revolutions. And here I find three aims behind the most famous changes on this stage of dispute.

1 About the object of all our cognitions of reason: some philosophers were sensualists only, others intellectualists only. Epicurus is the leading philosopher of sensibility, and Plato the leading philosopher of the intellectual. This difference between the schools, subtle as it is, began in the earliest times and has lasted without a break for a long while. The first school held that reality is found only in the objects of the senses and everything else is imagination. The second school said the opposite: in the senses there is nothing but illusion.

B 882 Only the understanding cognizes what is true. Yet the first school did not deny that concepts of the understanding have reality. For them that reality was only logical, whereas for the others it was mystical. The first school admitted intellectual concepts but accepted only sensible objects. The second demanded that true objects be purely intelligible. They claimed there is an intuition through the pure understanding, one that is accompanied by no senses, which in their view would only confuse it.

2 About where pure cognitions of reason come from. Are they taken from experience, or do they originate in reason itself, without depending on experience? Aristotle may be seen as the chief of the empiricists, Plato as the chief of the noologists. In more recent times Locke followed the first, and Leibniz the second (though at a good distance from Plato’s mystical system). Yet neither has been able to bring this dispute to a decision. At least Epicurus, for one, was much more consistent in following the sensualist system than Aristotle and Locke were (above all Locke). Epicurus never took any inference beyond the limit of experience. Locke derived all concepts and principles from experience. Then Locke went so far in using them as to claim that we can prove the existence of God and the immortality of the soul as evidently as any mathematical theorem.

B 883 Both of these objects, though, lie wholly outside the limits of possible experience.

3 About method. To deserve the name of method, something has to be a way of proceeding by principles. The methods now in force in this field of natural inquiry fall into two kinds, the naturalistic and the scientific. The naturalist of pure reason adopts as a principle that common reason without science (which the naturalist calls sound reason) can accomplish more on the loftiest questions that make up the task of metaphysics than speculation can. So they claim that the size and distance of the moon can be determined more reliably by eye than by mathematical detours. This is plain hatred of reasoning (misology) turned into a principle. And, most absurd of all, ignoring every artificial aid gets praised as a distinct way of widening one’s cognition. Naturalists can’t fairly be blamed for simply lacking further insight. They go by common reason and don’t brag that their ignorance is a method with the secret of pulling truth up from the bottom of Democritus’s deep well. Quod sapio, satis est mihi; non ego curo, esse quod Arcesilas aerumnosique Solones, Pers. (“What I know is enough for me; I don’t care to be what Arcesilas and the careworn Solons were”) is their motto.

B 884 With it they can live cheerfully and respectably, without troubling themselves about science or disturbing its work.

Those who adopt a scientific method can choose here between a dogmatic and a skeptical course, but either way they are bound to work systematically. If I name the famous Wolf for the first group and David Hume for the second, I can leave the rest unnamed, given my present aim. Only the critical path is still open. If the reader has been kind and patient enough to walk this path in my company, they may now judge for themselves. Suppose they are willing to do their part toward making this footpath a highway. Might not what many centuries could not achieve then be reached before the present one is over? I mean this: bringing human reason to full satisfaction in what has always occupied its thirst for knowledge, but until now in vain.