Introduction

B 1 Introduction

I. On the distinction between pure and empirical cognition

There is no doubt at all that all our cognition begins with experience. For what else could awaken our cognitive faculty to activity if not objects that affect our senses and partly produce representations of themselves, partly set our understanding into motion to compare these, connect or separate them, and thus work up the raw material of sensible impressions into a cognition of objects called experience? In the order of time, then, no cognition in us precedes experience, and with experience all cognition begins.

But although all our cognition starts with experience, it does not follow that all of it arises from experience. For it could well be that even our cognition through experience is a composite of what we receive through impressions and what our own cognitive faculty, merely prompted by sensible impressions, supplies from itself.

B 2 We do not distinguish this addition from that basic material until long practice has made us attentive to it and skilled at separating it out.

It is therefore at least a question still requiring closer investigation, and not one to be dismissed at first sight, whether there is any such cognition independent of experience and even of all impressions of the senses. Such cognitions are called a priori, and are distinguished from empirical cognitions, whose sources are a posteriori, namely in experience.

That expression, however, is not yet definite enough to convey the full meaning appropriate to the question before us. For it is customary to say of some cognition derived from experiential sources that we are capable of it or possess it a priori, because we derive it not immediately from experience but from a general rule that we have nevertheless ourselves borrowed from experience. Thus one says of someone who undermined the foundation of his house: he could have known a priori that it would collapse; that is, he did not need to wait for the experience of its actual collapse. Yet he could not have known this wholly a priori. For he first had to learn through experience that bodies are heavy and therefore fall when their support is taken away.

In what follows, then, we will understand by a priori cognitions not those that occur independently of this or that experience.

B 3 We mean, rather, those that occur absolutely independently of all experience. Opposed to them are empirical cognitions, or those possible only a posteriori, that is, through experience. Among a priori cognitions, however, those are called pure in which nothing empirical is mixed. Thus, for example, the proposition “Every alteration has its cause” is an a priori proposition, but not a pure one, because alteration is a concept that can be drawn only from experience.

II. We possess certain a priori cognitions, and even ordinary understanding is never without them

What matters here is a mark by which we can securely distinguish a pure cognition from an empirical one. Experience indeed teaches us that something is constituted in this or that way, but not that it cannot be otherwise. First, then, if we find a proposition that is thought together with its necessity, it is an a priori judgment; if, moreover, it is derived from no proposition except one that is itself in turn valid as a necessary proposition, it is absolutely a priori. Second, experience never gives its judgments true or strict universality, but only assumed and comparative universality through induction.

B 4 Properly speaking, it must therefore be said: so far as we have yet perceived, no exception is found to this or that rule. If, then, a judgment is thought with strict universality, that is, in such a way that no exception at all is allowed as possible, it is not derived from experience but is valid absolutely a priori. Empirical universality is therefore only an arbitrary extension of validity from what holds in most cases to what holds in all, as, for example, in the proposition “All bodies are heavy.” Where strict universality belongs essentially to a judgment, by contrast, it points to a special source of its cognition, namely a faculty of a priori cognition. Necessity and strict universality are thus secure marks of an a priori cognition, and also belong inseparably together. Yet in applying them it is sometimes easier to show the empirical limitation of judgments than their contingency, and sometimes more evident to show the unrestricted universality we ascribe to a judgment than its necessity. It is therefore advisable to use these two criteria, each of which is infallible on its own, separately.

It is easy to show that such necessary judgments, universal in the strictest sense and hence pure a priori judgments, actually occur in human cognition. If an example from the sciences is wanted, we need only look to all the propositions of mathematics.

B 5 If one is wanted from the most ordinary use of the understanding, the proposition that every alteration must have a cause will serve. Indeed, in the latter case the very concept of a cause so plainly contains the concept of a necessary connection with an effect and of a strict universality of the rule that it would be entirely lost if we tried, as Hume did, to derive it from a repeated association of what happens with what precedes it, and from a resulting habit—and thus a merely subjective necessity—of connecting representations. Even without needing such examples to prove the actuality of pure a priori principles in our cognition, we could demonstrate their indispensability for the possibility of experience itself, and thus demonstrate it a priori. For where could experience itself obtain its certainty if all the rules according to which it proceeds were always in turn empirical, hence contingent? We could hardly allow these to count as first principles. Here, however, we can be content to have established the pure use of our cognitive faculty as a fact, together with its distinguishing marks. But an a priori origin reveals itself not only in judgments, but even in some concepts. Gradually remove from your experiential concept of a body everything empirical in it: color, hardness or softness, weight, even impenetrability. There still remains the space that the body, now entirely vanished, occupied, and you cannot remove that.

B 6 Likewise, if you remove from your empirical concept of any object, corporeal or incorporeal, all the properties experience teaches you, you still cannot take away the property through which you think it as a substance or as inhering in a substance, although this concept contains more determination than that of an object in general. Convinced by the necessity with which this concept forces itself upon you, you must therefore admit that it has its seat a priori in your cognitive faculty.

III. Philosophy needs a science that determines the possibility, principles, and scope of all a priori cognitions

What signifies far more than everything said so far is this: certain cognitions even leave the field of all possible experiences and seem to enlarge the scope of our judgments beyond all its boundaries through concepts for which no corresponding object can be given anywhere in experience.

Precisely in these latter cognitions, which go beyond the sensible world, where experience can provide neither guidance nor correction, lie the inquiries of our reason.

B 7 We consider these far superior in importance, and their ultimate purpose far more exalted, than anything the understanding can learn in the field of appearances. Here, even at the risk of error, we would sooner venture everything than abandon such important investigations on any grounds of hesitation, or out of contempt and indifference. These unavoidable problems of pure reason itself are God, freedom, and immortality. The science whose ultimate purpose, with all its preparations, is directed properly only toward solving them is called metaphysics. Its procedure is initially dogmatic: that is, without first examining reason’s capacity or incapacity for so great an undertaking, it confidently sets about carrying it out.

Now it does indeed seem natural that, once we have left the ground of experience, we should not immediately erect a building with cognitions we possess without knowing their origin, and on the credit of principles whose source we do not know, without first assuring ourselves of its foundation through careful investigations. It seems, then, that we should long ago have raised the question of how the understanding could arrive at all these a priori cognitions, and what scope, validity, and worth they might have. In fact, nothing is more natural, if by “natural” we understand what ought reasonably and rightly to happen.

B 8 But if we understand by it what ordinarily happens, then nothing is more natural and comprehensible than that this investigation should long have been neglected. For some of these cognitions, mathematical ones, have long possessed reliability, and thus create favorable expectations for others, even though these may be of an entirely different nature. Moreover, once we are beyond the sphere of experience, we are sure not to be refuted by experience. The allure of enlarging our cognitions is so great that only a clear contradiction we encounter can halt our progress. But this can be avoided if we make our inventions cautiously, without their ceasing on that account to be inventions. Mathematics gives us a brilliant example of how far we can go in a priori cognition independently of experience. It does, admittedly, concern itself with objects and cognitions only insofar as these can be presented in intuition. But this circumstance is easily overlooked, because the intuition in question can itself be given a priori and is thus scarcely distinguished from a mere pure concept. Captivated by such a proof of reason’s power, the drive for enlargement sees no boundaries. The light dove, cleaving the air in free flight and feeling its resistance, might imagine that it would fare much better still in airless space.

B 9 Likewise, Plato left the sensible world because it sets such narrow limits to the understanding, and ventured beyond it on the wings of ideas into the empty space of the pure understanding. He did not notice that his efforts made no headway, for he had no resistance, no supporting ground as it were, against which he could brace himself and apply his powers to move the understanding forward. But it is the usual fate of human reason in speculation to finish its building as early as possible and only afterward investigate whether its foundation has been well laid. Then all sorts of embellishments are sought out to reassure us about its soundness, or rather to dismiss such a belated and dangerous examination altogether. What frees us from all anxiety and suspicion while we build, and flatters us with an apparent thoroughness, is this. A great part, perhaps the greatest, of our reason’s business consists in analyzing the concepts we already have of objects. This supplies us with a multitude of cognitions that, although they are nothing more than clarifications or elucidations of what was already thought in our concepts, albeit still confusedly, are nevertheless esteemed, at least in form, as equal to new insights. Yet in matter or content they do not enlarge the concepts we have, but only unfold them. Since this procedure yields an actual a priori cognition that makes secure and useful progress, reason, without itself noticing it, slips in under this pretense assertions of an entirely different kind.

B 10 Here reason adds quite alien concepts to given ones, and does so a priori, without our knowing how it arrives at them, or even letting such a question enter our thoughts. I will therefore deal at the outset with the distinction between these two kinds of cognition.

IV. On the distinction between analytic and synthetic judgments

In all judgments in which the relation of a subject to a predicate is thought—considering only affirmative judgments, since the application to negative ones is easy afterward—this relation is possible in two ways. Either the predicate B belongs to the subject A as something contained (covertly) in this concept A; or B lies entirely outside the concept A, although it stands in connection with it. In the first case I call the judgment analytic, in the second synthetic. Analytic judgments, affirmative ones, are therefore those in which the connection of predicate and subject is thought through identity; those in which this connection is thought without identity are to be called synthetic judgments.

B 11 The former could also be called elucidatory judgments, the latter ampliative judgments. For the former add nothing through the predicate to the concept of the subject, but merely break it up by analysis into its component concepts, which were already thought in it, though confusedly. The latter, by contrast, add to the concept of the subject a predicate not thought in it at all, which could not have been extracted through any analysis of it. For example, if I say, “All bodies are extended,” this is an analytic judgment. For I need not go beyond the concept I combine with body to find extension connected with it; I need only analyze that concept, that is, become conscious of the manifold I always think in it, to encounter this predicate there. It is therefore an analytic judgment. By contrast, if I say, “All bodies are heavy,” the predicate is something quite different from what I think in the mere concept of a body in general. The addition of such a predicate therefore yields a synthetic judgment.

Judgments of experience, as such, are all synthetic. For it would be absurd to found an analytic judgment on experience, since I need not go beyond my concept at all to make the judgment, and thus require no testimony from experience. That a body is extended is a proposition established a priori, not a judgment of experience.

B 12 For before I turn to experience, I already have all the conditions for my judgment in the concept, from which I need only extract the predicate according to the principle of contradiction. In doing so I can at the same time become conscious of the judgment’s necessity, which experience could not even teach me. By contrast, although I do not include the predicate of weight in the concept of a body in general, that concept nevertheless designates an object of experience through one part of experience, to which I can therefore add other parts of that same experience as belonging with the first. I can first cognize the concept of body analytically through the marks of extension, impenetrability, shape, and so on, all of which are thought in this concept. But now I enlarge my cognition: looking back to the experience from which I abstracted this concept of body, I find weight always connected with the marks mentioned above, and thus add it synthetically as a predicate to that concept. It is therefore experience on which the possibility of the synthesis of the predicate of weight with the concept of body is grounded. For although neither concept is contained in the other, the two nevertheless belong together, albeit only contingently, as parts of a whole, namely experience, which is itself a synthetic combination of intuitions.

But in synthetic a priori judgments this aid is entirely lacking.

B 13 If I am to go beyond the concept A to cognize another concept B as combined with it, what is it that I rely on, and through which the synthesis becomes possible? For here I do not have the advantage of looking around for it in the field of experience. Take the proposition “Everything that happens has its cause.” In the concept of something that happens I do indeed think an existence preceded by a time, and so on, and analytic judgments can be drawn from this. But the concept of a cause lies entirely outside that concept and indicates something different from what happens; it is therefore not contained at all in this latter representation. How, then, do I come to say of what happens in general something entirely different from it, and to cognize the concept of cause, although not contained in it, as nevertheless belonging to it, and indeed necessarily? What is here the unknown = X on which the understanding relies when it believes it has found, outside the concept of A, a predicate B alien to it that it nevertheless regards as connected with it? It cannot be experience, because the principle cited adds this second representation to the first not only with greater universality but also with the expression of necessity, hence wholly a priori and from mere concepts. Now the entire ultimate purpose of our speculative a priori cognition rests on such synthetic, that is, ampliative principles.

B 14 For analytic principles are indeed supremely important and necessary, but only to attain that distinctness of concepts required for a secure and extensive synthesis as a genuinely new acquisition.

V. All theoretical sciences of reason contain synthetic a priori judgments as principles

1 Mathematical judgments are all synthetic. This proposition seems hitherto to have escaped the notice of those who analyze human reason, indeed to run directly counter to all their conjectures, although it is indisputably certain and very important in its consequences. For since it was found that mathematicians’ inferences all proceed according to the principle of contradiction, as the nature of every apodictic certainty requires, people persuaded themselves that the principles too were cognized from the principle of contradiction. In this they were mistaken; for a synthetic proposition can certainly be understood in accordance with the principle of contradiction, but only by presupposing another synthetic proposition from which it can be inferred, never in itself.

First of all, it must be noted that properly mathematical propositions are always a priori judgments, not empirical ones, because they carry necessity with them, which cannot be drawn from experience.

B 15 But if this is not conceded, then let me restrict my proposition to pure mathematics, whose very concept entails that it contains not empirical but solely pure a priori cognition.

At first one might indeed think that the proposition 7 + 5 = 12 is merely analytic, following from the concept of a sum of seven and five according to the principle of contradiction. But on closer examination we find that the concept of the sum of 7 and 5 contains nothing more than the union of the two numbers into a single one, which does not at all determine what this single number comprising them both is. The concept of twelve is by no means already thought merely by my thinking that union of seven and five; and however long I analyze my concept of such a possible sum, I will never find twelve in it. We must go beyond these concepts by calling on the intuition that corresponds to one of the two—say, our five fingers, or, as Segner does in his Arithmetic, five points—and thus gradually add the units of the five given in intuition to the concept of seven. For I first take the number 7 and, for the concept of 5, call on the fingers of my hand as an intuition.

B 16 The units that I previously took together to constitute the number 5 I now add, one by one in that image of mine, to the number 7, and so see the number 12 arise. That 7 was to be added to 5 I did indeed think in the concept of a sum = 7 + 5, but not that this sum was equal to the number 12. The arithmetical proposition is therefore always synthetic. We become all the more clearly aware of this when we take somewhat larger numbers; for then it is plainly evident that, however we turn and twist our concepts, we could never find the sum merely by analyzing them without calling on intuition.

Nor is any principle of pure geometry analytic. That the straight line between two points is the shortest is a synthetic proposition. For my concept of straightness contains nothing of magnitude, but only a quality. The concept of the shortest is therefore wholly added to it and cannot be drawn by any analysis from the concept of a straight line. Here, then, intuition must be called on, through which alone the synthesis is possible.

A few principles presupposed by geometers are indeed genuinely analytic and rest on the principle of contradiction.

B 17 But, like identical propositions, they serve only to link the steps of the method, not as principles: for example, a = a, the whole is equal to itself, or (a + b) > a, that is, the whole is greater than its part. Yet even these, although valid through mere concepts, are admitted in mathematics only because they can be presented in intuition. What commonly leads us here to believe that the predicate of such apodictic judgments already lies in our concept, and that the judgment is therefore analytic, is merely the ambiguity of the expression. We are required to think a certain predicate in addition to a given concept, and this necessity already attaches to the concepts. But the question is not what we are required to think in addition to the given concept, but what we actually think in it, though only obscurely. It then becomes clear that the predicate does indeed attach necessarily to those concepts, but not as thought in the concept itself: rather, through an intuition that must be added to the concept.

2 Natural science (Physica) contains synthetic a priori judgments as principles. I will cite only a couple of propositions as examples: that in all alterations of the corporeal world the quantity of matter remains unchanged; or that in every communication of motion, action and reaction must always be equal to one another. In both it is clear not only that they are necessary, hence have an a priori origin, but also that they are synthetic propositions.

B 18 For in the concept of matter I do not think persistence, but merely its presence in space through filling it. I therefore actually go beyond the concept of matter to think something a priori in addition to it that I did not think in it. The proposition is thus not analytic but synthetic, and yet thought a priori; and so it is with the other propositions of the pure part of natural science.

3 Metaphysics, even if we regard it as a science hitherto merely attempted, yet indispensable through the nature of human reason, is to contain synthetic a priori cognitions. Its concern is by no means merely to analyze concepts we form a priori of things and thereby elucidate them analytically. Rather, we wish to enlarge our a priori cognition. For this we must employ principles that add to the given concept something not contained in it, and through synthetic a priori judgments go perhaps so far beyond it that experience itself cannot follow us that far: for example, in the proposition “The world must have a first beginning,” and other such propositions. Thus metaphysics consists, at least in its purpose, entirely of synthetic a priori propositions.

B 19 VI. The general problem of pure reason

Much is already gained if we can bring a multitude of investigations under the formula of a single problem. For we thereby not only lighten our own work by determining it precisely, but also make it easier for anyone who wishes to examine it to judge whether we have satisfied our intention or not. The proper problem of pure reason is now contained in the question: How are synthetic a priori judgments possible?

That metaphysics has hitherto remained in so wavering a condition of uncertainty and contradictions is attributable solely to the fact that this problem, and perhaps even the distinction between analytic and synthetic judgments, was not thought of earlier. The standing or falling of metaphysics now rests on the solution of this problem, or on a satisfactory proof that the possibility it asks to have explained does not in fact exist at all. David Hume, who among all philosophers came closest to this problem, but thought it neither with sufficient precision nor in its universality, stopping instead at the synthetic proposition of the connection of an effect with its causes (Principium causalitatis), believed he had established that such an a priori proposition was entirely impossible.

B 20 According to his conclusions, everything we call metaphysics would amount to a mere delusion of supposed rational insight into what is in fact merely borrowed from experience and has acquired the illusion of necessity through habit. He would never have arrived at this assertion, destructive of all pure philosophy, had he kept our problem in view in its universality. For he would then have seen that, according to his argument, pure mathematics too could not exist, since it certainly contains synthetic a priori propositions; and his good understanding would surely have preserved him from such an assertion.

The solution of the above problem also comprehends the possibility of the pure use of reason in founding and developing all sciences that contain a theoretical a priori cognition of objects; that is, it includes the answers to the questions:

How is pure mathematics possible? How is pure natural science possible?

Since these sciences are actually given, it is entirely fitting to ask how they are possible; for their actuality proves that they must be possible*.

B 21 As for metaphysics, however, its poor progress hitherto, and the fact that of no metaphysics yet presented can it be said, as regards its essential purpose, that it actually exists, must give everyone grounds for doubting its possibility.

* Some might still doubt this last point concerning pure natural science. But one need only look at the various propositions found at the beginning of physics proper (empirical physics)—such as those concerning the persistence of the same quantity of matter, inertia, the equality of action and reaction, and so on—to become convinced that they constitute a physicam puram (or rationalem) that well deserves to be set out separately as a science of its own, in its full scope, whether narrow or wide.

Now in a certain sense this kind of cognition must nevertheless also be regarded as given, and metaphysics is actual, if not as science, then as a natural predisposition (metaphysica naturalis). For human reason advances irresistibly, driven by its own need and not merely moved by the vanity of knowing much, to questions that cannot be answered by any experiential use of reason or by principles borrowed from it. Thus in all human beings, as soon as reason extends in them to speculation, some metaphysics has always actually existed, and will always remain. Of this too, then, the question is:

B 22 How is metaphysics possible as a natural predisposition?

That is, how do the questions pure reason raises for itself, and which its own need drives it to answer as well as it can, arise from the nature of universal human reason?

But since all previous attempts to answer these natural questions—for example, whether the world has a beginning or has existed from eternity, and so on—have always produced unavoidable contradictions, we cannot rest content with the mere natural predisposition to metaphysics, that is, the pure faculty of reason itself, from which some metaphysics, whatever it may be, always grows. Rather, it must be possible to attain certainty with it, either in knowing or in not knowing its objects: that is, to decide either about the objects of its questions or about reason’s capacity or incapacity to judge anything concerning them, and thus either to enlarge our pure reason reliably or to set it definite and secure limits. This last question, which flows from the general problem above, would rightly be: How is metaphysics possible as science?

The critique of reason therefore leads in the end necessarily to science.

B 23 Its dogmatic use without critique, by contrast, leads to groundless assertions against which others equally plausible can be set, and thus to skepticism.

Nor can this science be of a dauntingly great extent, since it deals not with the objects of reason, whose diversity is infinite, but only with reason itself and with problems that arise entirely from its own midst. These are set before it not by the nature of things distinct from it, but by its own nature. Once reason has first become fully acquainted with its own capacity concerning the objects it may encounter in experience, it must therefore be easy to determine fully and securely the scope and boundaries of its attempted use beyond all boundaries of experience.

We can and must therefore regard all attempts hitherto made to bring about a metaphysics dogmatically as if they had never occurred. For whatever is analytic in one or another of them, namely a mere analysis of concepts residing a priori in our reason, is not yet the goal at all, but only a preparation for metaphysics proper: the synthetic enlargement of our a priori cognition. Such analysis is unsuited to this goal, because it shows only what is contained in these concepts, not how we arrive at such concepts a priori, so as then to determine their valid use with regard to the objects of all cognition in general.

B 24 Nor does it take much self-denial to abandon all these claims, since reason’s undeniable contradictions with itself, which are also unavoidable in the dogmatic procedure, have long since deprived every previous metaphysics of its authority. More steadfastness will be needed to keep inward difficulty and outward resistance from deterring us, through a different treatment wholly opposed to the previous one, from at last bringing to healthy and fruitful growth a science indispensable to human reason, of which we may cut off every stem that has shot up, but cannot uproot the root.

VII. The idea and division of a special science called the critique of pure reason

From this alone there now emerges the idea of a special science that can be called the critique of pure reason. For reason is the faculty that supplies the principles of a priori cognition. Pure reason is therefore that which contains the principles for cognizing something absolutely a priori. An organon of pure reason would be the sum total of certain principles.

B 25 According to these principles, all pure a priori cognitions can be acquired and actually brought about. The full application of such an organon would yield a system of pure reason. But since this is a great deal to ask, and it remains unsettled whether an enlargement of our cognition is possible here at all, and in which cases, we can regard a science that merely judges pure reason, its sources and boundaries, as the propaedeutic to the system of pure reason. Such a science would have to be called not a doctrine but only a critique of pure reason. Its benefit with respect to speculation would really be merely negative: it would serve not to enlarge our reason but only to purify it and keep it free from errors, which is already a considerable gain. I call all cognition transcendental that concerns itself not so much with objects as with our way of cognizing objects in general, insofar as this is to be possible a priori. A system of such concepts would be called transcendental philosophy. But this, in turn, is still too much for a beginning. For since such a science would have to contain both analytic and synthetic a priori cognition completely, its scope is too wide for our intention, since we need carry the analysis only so far as is indispensably necessary for insight into the principles of a priori synthesis in their full scope, which alone is our concern.

B 26 This investigation is what now occupies us. We can properly call it not doctrine but only transcendental critique, because its aim is not the enlargement of cognitions themselves but only their correction, and it is to provide the touchstone of the worth or worthlessness of all a priori cognitions. Such a critique is accordingly a preparation, if possible, for an organon, and, should this fail, at least for a canon of these cognitions, according to which the complete system of the philosophy of pure reason could one day be presented both analytically and synthetically, whether it consists in enlarging reason’s cognition or merely in delimiting it. For that this is possible, indeed that such a system need not be too extensive for us to hope to complete it entirely, can already be judged beforehand from the fact that the object here is not the inexhaustible nature of things, but the understanding that judges the nature of things, and this, in turn, only with regard to its a priori cognition. Since we need not seek the understanding’s stock outside ourselves, it cannot remain hidden from us; and it is presumably small enough to be surveyed completely, judged as to its worth or worthlessness, and correctly appraised.

B 27 Still less should one expect here a critique of books and systems of pure reason, rather than of the pure faculty of reason itself. Only when this is laid at the foundation do we have a secure touchstone for assessing the philosophical content of old and new works in this field. Otherwise the unauthorized historian and judge assesses others’ groundless assertions by his own, which are equally groundless.

Transcendental philosophy is the idea of a science for which the critique of pure reason is to draw up the entire plan architectonically, that is, from principles, fully guaranteeing the completeness and security of all the parts that constitute this building. It is the system of all principles of pure reason. That this critique is not itself already called transcendental philosophy rests solely on the fact that, to be a complete system, it would also have to contain a full analysis of the whole of human a priori cognition. Our critique must indeed place before us a complete enumeration of all the fundamental concepts constituting the pure cognition in question. But it rightly refrains from a full analysis of these concepts themselves, as also from a complete survey of those derived from them.

B 28 This is partly because such an analysis would not serve its purpose, since it does not involve the difficulty encountered in synthesis, for whose sake the entire critique properly exists; and partly because it would run counter to the unity of the plan to assume responsibility for the completeness of an analysis and derivation from which its intention could dispense us. This completeness, both of analysis and of derivation from the a priori concepts to be supplied later, is nevertheless easy to add, once they are first present as fully set-out principles of synthesis and nothing is lacking with regard to this essential intention.

Everything that constitutes transcendental philosophy thus belongs to the critique of pure reason, and it is the complete idea of transcendental philosophy, but not yet that science itself, because it carries the analysis only so far as is required for the complete assessment of synthetic a priori cognition.

The chief consideration in dividing such a science is this: no concepts containing anything empirical must enter into it; in other words, the a priori cognition must be wholly pure. Thus, although the supreme principles of morality and its fundamental concepts are a priori cognitions, they nevertheless do not belong to transcendental philosophy.

B 29 For although they do not themselves base their precepts on the concepts of pleasure and displeasure, desires and inclinations, and so on, all of which are of empirical origin, they must nevertheless, in the concept of duty, necessarily bring them into the composition of the system of pure morality, either as an obstacle to be overcome or as an inducement that must not be made a motive. Transcendental philosophy is therefore a philosophy of pure, merely speculative reason. For everything practical, insofar as it contains incentives, relates to feelings, which belong to empirical sources of cognition.

If we now wish to divide this science from the general standpoint of a system as such, the science we are presenting must contain, first, a doctrine of elements and, second, a doctrine of method of pure reason. Each of these main parts would have its subdivisions, the grounds of which, however, cannot yet be set out here. Only this much seems necessary by way of introduction or preliminary reminder: there are two stems of human cognition, which perhaps arise from a common but to us unknown root, namely sensibility and understanding. Through the former objects are given to us; through the latter they are thought. Now insofar as sensibility may contain a priori representations constituting the condition under which objects are given to us, it would belong to transcendental philosophy.

B 30 The transcendental doctrine of the senses would have to belong to the first part of the science of elements, because the conditions under which alone the objects of human cognition are given precede those under which they are thought.

B 1 Introduction

I. How pure and empirical cognition differ

That all our cognition begins with experience is beyond any doubt. What else would wake our faculty of cognition into action, if not objects that stir our senses? In part these objects produce representations on their own. In part they set our activity of understanding in motion, so that it compares those representations, connects or separates them, and so processes the raw stuff of sense impressions into a cognition of objects, which goes by the name of experience. In time, then, no cognition in us comes before experience, and all of it begins with experience.

But even though all our cognition begins with experience, it doesn’t follow that it all arises out of experience. After all, it may well be that even our cognition from experience is a compound of two things. One is what we receive through impressions. The other is what our own faculty of cognition supplies from itself, merely prompted by sensible impressions.

B 2 We can’t tell this addition from the raw stuff until long practice has made us notice it and taught us to separate it out.

So at least this much is a question that needs closer investigation, and can’t be brushed aside at first glance: is there any cognition that does not depend on experience, or even on any sense impressions? Such cognitions are called a priori. They are distinguished from empirical cognitions, which have their sources a posteriori, that is, in experience.

That expression, though, isn’t yet precise enough to cover the full sense of the question before us. We commonly say of some cognition derived from sources in experience that we are capable of it, or have a share in it, a priori. We say so because we derive it not directly from experience but from a general rule, which we nevertheless took from experience ourselves. We say of someone who dug away the foundation of their house that they could have known a priori it would collapse. That is, they didn’t have to wait for the experience of it actually collapsing. Still, they couldn’t have known this entirely a priori. They had to learn through experience beforehand that bodies are heavy, and so fall when their support is taken away.

From here on, then, by a priori cognitions we won’t mean cognitions that are independent of this or that experience.

B 3 We will mean cognitions that occur absolutely independently of all experience. The opposite of these are empirical cognitions, or those that are possible only a posteriori, that is, only through experience. Among a priori cognitions, those are called pure into which nothing empirical is mixed. For example, “every change has its cause” is a proposition a priori, though not a pure one, since the concept of change is one that can only be taken from experience.

II. We possess certain cognitions a priori, and even ordinary understanding is never without them

What we need here is a mark that lets us reliably tell pure cognition from empirical. Experience teaches us that something is such and such, but not that it couldn’t be otherwise. So, first: suppose a proposition turns up that is thought together with its necessity. Then it is a judgment a priori. If, besides, it is derived only from a proposition that itself holds as necessary, it is absolutely a priori. Second: experience never lends its judgments true or strict universality. It lends them only supposed, relative universality (by way of induction). So what it really amounts to saying is this.

B 4 As far as we have observed so far, no exception turns up to this or that rule. Now take a judgment that is thought as strictly universal, which means one that allows no exception at all as even possible. It isn’t derived from experience. It is valid absolutely a priori. Empirical universality is thus only an arbitrary raising of validity, from the validity that holds in most cases to the one that holds in all, as in the proposition “all bodies are heavy.” But where strict universality is an essential part of a judgment, it points to a special source of cognition for that judgment, namely a faculty of cognition a priori. Necessity and strict universality are therefore sure marks of a priori cognition, and they belong together inseparably. In practice, though, it is sometimes easier to show how limited a judgment is in an empirical way than to show its contingency. And sometimes it is more evident to show the unlimited universality that we attribute to a judgment than its necessity. So it’s advisable to use these two criteria separately, since each of them is infallible by itself.

It is easy to show that human cognition really does contain such necessary and strictly universal, and therefore pure, a priori judgments. If you want an example from the sciences, you only have to look at all the propositions of mathematics.

B 5 If you want one from the commonest use of the understanding, the proposition that every change must have a cause will do. In fact, in the latter case the concept of a cause itself includes, so unmistakably, the idea of an effect tied to it by necessity and of a rule that is strictly universal, that the concept would be lost entirely if we tried to derive it, as Hume did, from the frequent pairing of what happens with what comes before it, and from the habit that grows out of that (a necessity that is merely subjective) of connecting representations. We could even do without such examples as proof that pure a priori principles actually exist in our cognition. We could show that these principles are indispensable for the possibility of experience itself, and so show it a priori. For where would experience itself get its certainty, if all the rules by which it proceeds were themselves empirical, and so contingent? So these rules can hardly be allowed to count as first principles. Here, though, we can be content to have set out the pure use of our faculty of cognition as a fact, together with its marks. But it isn’t only in judgments that an a priori origin of some of them shows up. It shows up in concepts too. Take away from your experiential concept of a body, step by step, everything empirical in it: color, hardness or softness, weight, even impenetrability. The space the body took up still remains (the body itself has now vanished entirely).

B 6 You can’t take that space away. In the same way, take away from your empirical concept of any object, bodily or not, all the properties that experience teaches you. You still can’t remove what makes you think of it as a substance, or as clinging to a substance (even though this concept packs in more determination than the concept of an object in general). Convinced by the necessity with which this concept presses itself on you, you have to admit that it has its seat in your faculty of cognition a priori.

III. Philosophy needs a science to determine the possibility, the principles and the range of all a priori cognitions

Something that says far more than all the above is this. Some cognitions even leave the whole field of possible experience. They seem to widen the range of our judgments beyond all its boundaries, by means of concepts for which no corresponding object can ever be given in experience.

And it is exactly in these latter cognitions that the inquiries of our reason lie. They go beyond the world of sense, into territory where experience can give neither guidance nor correction.

B 7 In importance we rank these inquiries far higher, and their final aim far more sublime, than anything the understanding can pick up on the territory of appearances. For their sake we would risk anything, even the danger of error, before we would give up such pressing inquiries from any scruple, or from contempt and indifference. The problems pure reason cannot avoid are God, freedom and immortality. The science whose final aim, with all its preparations, is really directed only at solving them is called metaphysics. Its procedure at the start is dogmatic. That is, it confidently takes on the job without first examining whether reason is able or unable to carry out so great an undertaking.

It does seem natural that, having left the ground of experience, we would not go and put up a building at once with cognitions we possess without knowing where from, and on the credit of principles whose origin we don’t know. It seems natural that we would first have made sure of the building’s foundation by careful investigation. We would surely have asked long ago how the understanding can come by all these a priori cognitions, and what range, validity and worth they may have. And really, nothing is more natural—if “natural” means what ought to happen, going by fairness and good sense.

B 8 But if you mean what usually happens, then nothing is more natural and understandable than that this investigation had to be put off for so long. For one part of these cognitions, the mathematical ones, has long been in possession of reliability, and so raises favorable expectations for the others as well, although they may be of a quite different nature. Besides, once you’re beyond the circle of experience, you’re safe from being refuted by experience. The pull of widening one’s cognitions is so strong that only running into a plain contradiction can stop one’s progress. And that can be avoided, if one is careful in making up one’s fictions. They remain fictions all the same. Mathematics offers a splendid example of how far we can get in a priori cognition without any help from experience. Now mathematics does deal with objects and cognitions only so far as they can be presented in intuition. But this circumstance is easily overlooked, because that intuition itself can be given a priori, and so is hardly distinguished from a mere pure concept. Taken in by such a proof of the power of reason, the drive to extend knowledge sees no boundaries. The light dove, as it cleaves the air in free flight and feels the air’s resistance, could form the idea that it would do much better in empty space.

B 9 In the same way, Plato left the world of sense because it sets such narrow limits on the understanding. He dared to go past it, carried on the wings of ideas, out into the empty space of pure understanding. He didn’t notice that he was making no headway by his efforts. That was because he had nothing pushing back against him, nothing like a support on which he could brace himself and put his strength to use to get the understanding moving. It is a usual fate of human reason, when it speculates, to get its building finished as soon as it can, and only then to ask whether the foundation was well laid. Then all sorts of excuses are sought to comfort us about its soundness, or even to turn away such a late and dangerous examination. While we are building, what keeps us untroubled and unsuspicious, and gives us a flattering air of thoroughness, is this. A large part of the business of our reason, perhaps the largest, consists in analyses of the concepts we already have of objects. This supplies us with a mass of cognitions. They are nothing more than clarifications or explanations of what our concepts already contained in thought (though still in a confused way). Yet they are at least valued, in form, as equal to new insights. In matter or content, though, they do not extend the concepts we have. They only spread them out. Since this procedure gives real a priori cognition, which moves ahead securely and usefully, reason slips in assertions of a quite different kind under this pretense, without even noticing it.

B 10 In these, reason adds to given concepts something wholly foreign, and does so a priori. We don’t know how reason arrives at this, and the question doesn’t even enter our minds. So I’ll deal right at the start with the difference between these two kinds of cognition.

IV. How analytic and synthetic judgments differ

In every judgment where a subject’s relation to a predicate is thought (I’m considering only the affirmative ones, since applying this to negative ones is easy afterward), that relation can come about in two ways. Either predicate B belongs to subject A as something already contained in the concept A, though hidden there. Or B lies wholly outside the concept A, although it is connected with it. I call the judgment analytic in the first case, synthetic in the second. So affirmative analytic judgments are the ones in which the predicate’s connection with the subject is thought through identity. Judgments in which that connection is thought without identity are what I mean by synthetic judgments.

B 11 The first kind could also be called judgments of clarification, and the others judgments of extension. The reason is that the first kind use the predicate to add nothing to the subject’s concept. They only split it up, by analysis, into the partial concepts that were already thought in it, if only confusedly. The second kind, by contrast, attach to the subject’s concept a predicate that wasn’t thought in it at all, and couldn’t have been drawn out of it by any analysis. Take “all bodies are extended.” That is an analytic judgment. I don’t have to go beyond the concept I combine with body to find extension as connected with it. I need only dissect that concept, which is to say, become aware of whatever manifold I think in it each time, to find this predicate there. So it is an analytic judgment. But take “all bodies are heavy.” Here the predicate is something altogether different from what I am thinking when I have the bare concept of body in general. Adding such a predicate therefore gives a synthetic judgment.

Any judgment of experience, taken as such, is synthetic. It would make no sense to base an analytic judgment on experience. To form an analytic judgment I never have to step outside my concept, so I don’t need any testimony from experience. Take the statement that a body is extended. It stands firm a priori.

B 12 It is no judgment of experience. Before I go to experience at all, every condition for my judgment is already in the concept. All I have to do is pull the predicate out of it by the principle of contradiction. In doing so I also become aware that the judgment is necessary, which experience would not even have taught me. It’s different with the predicate of weight. When I think of a body in general, I don’t count weight as part of the concept. Still, that concept designates an object of experience by means of one part of it, and to that part I can add other parts of the same experience, as belonging with the first. To begin with, I can know the concept of body analytically. That happens through the marks of extension, impenetrability and shape, among others, which are all thought in the concept. Then I broaden my cognition. I look back at the experience from which I had drawn this concept of body, and I find weight always connected with those marks as well. So I add weight to the concept as a predicate, and I do it synthetically. It is experience, then, that makes it possible to join weight, as a predicate, synthetically to the concept of body. Neither concept is contained in the other. Even so, the two go together, though only contingently, as parts of one whole. That whole is experience, and experience in turn is a synthetic combination of intuitions.

For synthetic a priori judgments this help is missing altogether.

B 13 Say I have to step outside concept A and recognize some other concept, B, as joined to it. What do I stand on? What makes that synthesis possible? I have no chance here to look around in the field of experience. Take the statement “Everything that happens has its cause.” When I think of something that happens, I do think of an existence with a stretch of time before it, and so on. Analytic judgments can be drawn from that. But the concept of a cause lies wholly outside that concept. It signals something different from what happens, so the representation of what happens doesn’t contain it at all. How, then, do I get to say something quite different about whatever happens? How do I get to recognize the concept of cause as belonging to it, and even necessarily, when it is not contained in it? What is the unknown = X that the understanding leans on, when it thinks it has found, beyond the concept of A, a foreign predicate B that it still takes to be tied to A? It can’t be experience, because the principle in question adds the second representation to the first with greater universality, and it also states necessity. So it works entirely a priori, from mere concepts. Now everything our speculative a priori cognition ultimately aims at depends on synthetic principles like this one, the ones that extend. Analytic principles are of course very important and necessary.

B 14 But they only serve to make concepts clear enough for a secure and far-reaching synthesis, which is what counts as the real new gain.

V. Every theoretical science of reason contains synthetic a priori judgments among its principles

1 Mathematical judgments are all synthetic. The people who dissect human reason seem to have missed this so far. It even seems to contradict everything they have supposed. Still, it is beyond dispute, and it will matter a great deal later on. Here is how they went wrong. They saw that mathematicians’ inferences all proceed by the principle of contradiction, which any apodictic certainty requires by its very nature. From that they persuaded themselves that the basic principles, too, are known by the principle of contradiction. They were mistaken. A synthetic proposition can be seen to be true by the principle of contradiction, but only when another synthetic proposition is assumed from which it can be inferred. It can never be seen that way by itself.

First, a point to note. Mathematical propositions in the proper sense are always a priori judgments, never empirical ones, since they bring necessity with them, and experience can’t yield necessity.

B 15 If someone won’t grant that, well then, I limit my claim to pure mathematics. By its very concept, pure mathematics contains no empirical cognition at all, only pure a priori cognition.

At first you would think that 7 + 5 = 12 is a merely analytic proposition. It would follow by the principle of contradiction from the concept of a sum made of seven and five. On a closer look, the concept “sum of 7 and 5” turns out to hold only the union of those two numbers in one single number. It says nothing at all about which single number takes in both. Merely thinking of seven and five joined together does not yet give me the concept of twelve. I can keep taking apart my concept of such a possible sum for as long as I like. I will never come upon twelve in it. To get there, we have to go beyond these concepts and use an intuition that matches one of them, for instance our five fingers, or five points, as Segner does in his Arithmetic. So we take the five that intuition gives us, and add its units, one after another, to the concept of seven. I start with the number 7. For the concept of 5 I use the fingers of my hand as the intuition.

B 16 The units I earlier put together to make the number 5, I now add one at a time to the number 7 in that image of mine, and I watch the number 12 come out. The concept of the sum 7 + 5 did include the thought of adding 7 to 5. But I did not think that the sum equals 12. So an arithmetical proposition is always synthetic. You see this more clearly with somewhat larger numbers. Then it is obvious that we could turn our concepts this way and that, and still never find the sum by merely taking them apart, unless intuition came to our aid.

No principle of pure geometry is analytic either. Take this claim: between two points, the straight line is the shortest. That is a synthetic proposition. My concept of the straight contains nothing about magnitude. It contains only a quality. So the concept of the shortest is a complete addition, and no analysis can pull it out of the concept of a straight line. Intuition has to be brought in to help here, and only through it is the synthesis possible.

Geometers do presuppose a few principles that really are analytic, and these rest on the principle of contradiction. But like identical propositions, they only serve as links in the chain of method.

B 17 They don’t serve as principles. Take a = a, which says that the whole equals itself. Or take (a + b) > a, which says that the whole is greater than its part. And yet even these are let into mathematics only because intuition can display them, even though they hold by concepts alone. We tend to think that, in judgments of this apodictic kind, the predicate already lies in our concept, so that the judgment is analytic. The only thing that makes us think so is an ambiguity in how we put it. We are supposed to add a certain predicate in thought to a given concept, and this necessity is already attached to the concepts. But the question isn’t what we are supposed to add in thought to the given concept. The question is what we actually think in it, even if only obscurely. That is where we find that the predicate does go with those concepts necessarily, though it is not thought within the concept itself. It attaches by means of an intuition that has to come in addition to the concept.

2 Natural science (Physica) has synthetic a priori judgments inside it, as its principles. I’ll cite just a couple of propositions as examples. One is that in all changes of the bodily world the quantity of matter stays unchanged. The other says that whenever motion is passed on, action and reaction must always be equal. In both, the necessity is clear, and with it their a priori origin. It is also clear that they are synthetic propositions.

B 18 For in the concept of matter I don’t think permanence. I think only its presence in space, by its filling of space. So I really do go beyond the concept of matter, in order to think in addition to it, a priori, something I did not think in it. The proposition is therefore not analytic but synthetic, and still thought a priori. The remaining propositions in the pure part of natural science work the same way.

3 Metaphysics, even if we see it only as a science that has so far merely been attempted, but that human reason’s nature makes indispensable, is meant to contain synthetic a priori cognitions. Its business isn’t at all just to take apart the concepts we make for ourselves a priori of things, and so to clarify them analytically. We want to extend our a priori cognition. For that we need principles that put something into the given concept which it did not hold before. And through synthetic a priori judgments we may even go so far beyond it that experience itself can’t follow us there. An example is the proposition that the world must have a first beginning, along with others of that kind. So metaphysics, at least in its aim, consists of nothing but synthetic a priori propositions.

B 19 VI. The general problem of pure reason

We gain a lot when we can sum up a whole series of investigations in the formula of one problem. It makes our own task easier, because we define it exactly. And it makes it easier for anyone else who wants to examine our work to judge whether we have done justice to our aim or not. The real problem of pure reason is contained in the question: How are synthetic a priori judgments possible?

The reason metaphysics has stayed so long in a shaky state of uncertainty and contradiction is simply that nobody thought of this problem earlier, and perhaps not even of the difference between analytic and synthetic judgments. Whether metaphysics stands or falls depends on solving this problem, or on giving a satisfying proof that the possibility it wants explained does not exist at all. Of all philosophers, David Hume came closest to this problem. But he was far from stating it precisely enough, or in its full generality. Instead he merely stopped at one synthetic proposition, the one about how an effect is connected with its causes (Principium causalitatis).

B 20 He believed he had worked out that such a proposition is completely impossible a priori. By his reasoning, everything we call metaphysics would come down to a delusion. We would think we had rational insight into something that is really just borrowed from experience, and that habit has dressed up with the illusion of necessity. He would never have come out with this claim, which would destroy all pure philosophy, if he had kept our problem in its full generality in view. He would then have noticed that his argument rules out pure mathematics too, because pure mathematics undoubtedly holds synthetic a priori propositions. His good sense would surely have kept him from that claim.

When we solve the problem above, we settle at the same time how reason can be used purely, in setting up and carrying out every science that includes theoretical a priori cognition of objects. In other words, it answers these questions:

How is pure mathematics possible? How is pure natural science possible?

Since these sciences actually exist, it is perfectly fitting to ask how they are possible. That they must be possible is proved by their being actual*. Metaphysics is another matter.

B 21 Its poor progress so far gives everyone good reason to doubt that it is possible. And of no metaphysics presented to date can we say, as far as its essential purpose goes, that it truly exists.

* Some might still doubt this last point about pure natural science. But all one has to do is look through the various propositions that appear at the start of physics proper (empirical physics). Among them are the permanence of the same amount of matter, inertia, equal action and reaction, and so forth. That will quickly persuade you that together they form a physicam puram (or rationalem), meaning a pure or rational physics. It well deserves to be set up on its own as a separate science, in its whole extent, whether narrow or wide.

Still, this kind of cognition must also be regarded, in a certain sense, as given. Metaphysics is real, if not as a science, then as a natural disposition (metaphysica naturalis). For human reason is driven by a need of its own, not by mere vanity about knowing a lot. It presses on, unstoppably, to questions that no use of reason in experience can answer, and no principles borrowed from experience either. So in all human beings, as soon as their reason broadens out into speculation, some metaphysics has always existed, and it will always remain there. And so the question arises about this metaphysics too:

B 22 How is metaphysics possible as a natural disposition?

In other words, what in the nature of universal human reason gives rise to the questions that pure reason puts to itself? Its own need drives it to answer them as well as it can.

Every attempt so far to answer these natural questions has landed in contradictions that couldn’t be avoided. Such questions include whether the world had a beginning or has always been there, and others of the sort. So we can’t stop at the bare natural disposition toward metaphysics. That disposition is just the pure faculty of reason itself, out of which some metaphysics or other, whichever it may be, always grows. It must be possible to use that disposition to reach certainty, either in knowing or in not knowing the objects. That is, we must be able either to decide about the objects of its questions, or to decide about reason’s ability or inability to judge anything about them. So we must either extend our pure reason reliably, or set definite and secure limits to it. The last question, which follows from the general problem stated above, would properly read: How is metaphysics possible as a science?

So the critique of reason ends up, necessarily, in science. Its dogmatic use without critique, on the other hand, ends up in groundless assertions.

B 23 Equally plausible assertions can be set against them. That leads to skepticism.

Nor can this science be so sprawling that it scares people off. Its business is not with objects of reason, whose variety is endless. Its business is only with reason itself. The problems it deals with arise entirely from within reason. They are not set for it by the nature of things that differ from it, but by reason’s own nature. Suppose reason has first come to know its own power completely, as regards the objects that may come up for it in experience. Then it has to be easy to settle fully and securely how far reason’s use extends, and where its boundaries lie, when it tries to venture past every boundary of experience.

That means we can and should treat every dogmatic attempt so far to set up a metaphysics as if it had never been made. Whatever is analytic in one attempt or another, namely the mere taking apart of concepts that live in our reason a priori, is not yet the goal at all. It is only preparation for metaphysics proper, whose goal is to extend one’s cognition a priori, synthetically. And it is useless for that goal. All it does is display what these concepts already contain. It never explains how we get hold of such concepts a priori in the first place.

B 24 Knowing that would let us go on to settle how they may validly be used on the objects of cognition in general. It takes little self-denial to give up all these claims. The contradictions of reason with itself cannot be denied, and in the dogmatic procedure they cannot be avoided either, and they have long since cost every metaphysics so far its standing. It will take more steadfastness not to let difficulty from within and resistance from outside hold us back. The task is to bring a science that human reason cannot do without to healthy, fruitful growth at last, by a treatment quite opposite to the previous one. One can chop off every shoot that science sends up, but one cannot pull out its root.

VII. Idea and division of a particular science, to be known as the critique of pure reason

This alone already gives us the idea of a distinct science. It can be named the critique of pure reason. Reason, after all, is the faculty that hands us the principles of a priori cognition. Pure reason, then, is the kind that holds the principles for cognizing anything wholly a priori. An organon of pure reason would be the sum total of those principles.

B 25 With them, all pure a priori cognitions could be acquired and actually produced. Applying such an organon in full detail would give us a system of pure reason. But that is asking a great deal. It is still open whether we can widen our cognition at all in this area, and in what cases it could be done. So we can regard a science that does nothing but assess pure reason, its sources and its boundaries, as the preliminary study, the propaedeutic, for the system of pure reason. It would have to be called critique of pure reason, not a doctrine. Its usefulness, as far as speculation goes, would really be only negative. It would not widen our reason. It would only cleanse it and keep it clear of mistakes, and that is already a lot to gain. Here is what I call transcendental: any cognition that deals less with objects than with how we can cognize objects, so far as that is meant to be possible a priori. A system built of such concepts would go by the name transcendental philosophy. But for a start even that is too much. Such a science would have to contain analytic cognition in full, and synthetic a priori cognition in full. So, for our purpose, it is too wide in scope. We may push the analysis only as far as we must to survey every principle of a priori synthesis, in its full range. That is our only concern.

B 26 We can’t properly call the investigation we are now engaged in a doctrine, only a transcendental critique. It doesn’t try to widen cognitions themselves. It tries only to set them right, and it is to be the test that shows whether an a priori cognition has any worth or none. So the critique prepares the way for an organon, if that can be done. If it can’t, it prepares at least for a canon of pure reason. A canon like that might one day let the full system of the philosophy of pure reason be laid out, both analytically and synthetically. That system could consist in extending its cognition, or merely in setting its boundaries. We can already judge in advance that this is possible, and that such a system need not be so large that we have to give up hope of completing it. The reason is that the subject matter here is not the nature of things, which is inexhaustible. The subject matter is the understanding, the faculty that judges about the nature of things, and only its a priori cognition at that. We are not to look for its stock outside, so it cannot stay hidden from us. In all likelihood it is small enough to be taken in completely, judged for its worth or worthlessness, and given its proper valuation.

B 27 Still less should anyone expect here a critique of the books and systems of pure reason. What we offer is the critique of the pure faculty of reason itself. Once that is in place, and not before, we have a trustworthy test for appraising the philosophical value of works in this field, old and new. Otherwise an unqualified historian and judge assesses the groundless assertions of others by means of his own, which are just as groundless.

Transcendental philosophy is the idea of a science. The critique of pure reason is to sketch its whole plan architectonically, that is, from principles, with full guarantee of the completeness and certainty of every part that makes up this building. It is the system of all the principles of pure reason. This critique isn’t itself called transcendental philosophy for one reason only. It would have to be a complete system, and for that it would also need a thorough analysis of everything in human cognition that is a priori. Of course our critique must also set out a complete list of all the basic concepts that make up the pure cognition in question. But it rightly refrains from a detailed analysis of these concepts themselves, and from a full review of the concepts derived from them. There are two reasons. First, such an analysis would not serve the purpose.

B 28 It lacks the cause for concern that comes with synthesis, and it is for the sake of that concern that the whole critique exists. Second, it would clash with the unity of the plan to be answerable for the completeness of such an analysis and derivation. Given our aim, we could be excused from that duty anyway. That completeness can easily be supplied later, both for the analysis and for the derivation from the a priori concepts still to be delivered. The one requirement is that those concepts first be there as full-fledged principles of synthesis, and that nothing is missing for this essential aim.

So everything that makes up transcendental philosophy belongs to the critique of pure reason. The critique is the complete idea of transcendental philosophy. It is not that science itself yet, since its analysis goes only as far as a full assessment of synthetic a priori cognition demands.

The main concern in dividing such a science is this: no concepts may enter it that contain anything empirical. The a priori cognition, in short, has to be wholly pure. So the supreme principles of morality and their basic concepts are indeed a priori cognitions, but they do not belong in transcendental philosophy. The reason is this.

B 29 They don’t base their prescriptions on the concepts of pleasure and displeasure, or on those of desires and inclinations, all of which are empirical in origin. Still, the concept of duty forces them to bring these concepts into the construction of a system of pure morality. There they show up as a hindrance to be conquered, or as an inducement that must not become the motive. That makes transcendental philosophy a philosophy of reason that is pure and merely speculative. Anything practical that involves incentives relates to feelings, and feelings are among the empirical sources of cognition.

Say we want to lay out the divisions of this science the way one would for any system whatever. The division we offer here then needs two parts. One is a doctrine of elements for pure reason. The other is a doctrine of method for it. Each part would split further, though the reasons for those splits can’t be laid out yet. For the introduction, or preliminary remark, only this much seems necessary. Human cognition has two stems, namely sensibility and understanding. Perhaps they grow from one common root that we don’t know. Through the first, objects are given to us. Through the second, they are thought. Now suppose sensibility does contain a priori representations. They form the condition for objects being given to us.

B 30 To that extent it would belong to transcendental philosophy. That makes the transcendental doctrine of the senses part of the first division of the science of elements. It has to come first, since the conditions under which objects of human cognition are given precede the conditions under which they are thought.