V. In all theoretical sciences of reason synthetic a priori judgments are contained as principles

1. Mathematical judgments are one and all synthetic. This proposition appears so far to have escaped the observations of those who dissect human reason, and indeed to stand in flat opposition to all their surmises, even though it is beyond contradiction certain and, for what follows, of great importance. For since it was observed that the reasonings of mathematicians all proceed by way of the principle of contradiction (as the very nature of any apodictic certainty requires), people convinced themselves that the principles too were cognized through that same principle, and here they went astray; for although a synthetic proposition can indeed be apprehended by way of the principle of contradiction, this holds only when a second synthetic proposition is laid down in advance, one out of which the first may be derived, and never on its own account.

First of all it must be remarked: that proper mathematical propositions are at all times judgments a priori and not empirical, since they carry with them a necessity that cannot be gleaned from experience . But should one refuse to grant this, very well, then I restrict my proposition to pure mathematics, whose very concept already implies that it contains not empirical but merely pure cognition a priori.

At the outset one would of course be inclined to think: that the proposition 7+5 = 12 is a purely analytic one, which flows by the principle of contradiction from the concept of seven and five taken as a sum. But upon closer scrutiny it becomes apparent that the concept of the sum of 7 and 5 embraces nothing beyond the union of both numbers into one, through which it is left entirely unthought which single number it is that combines the two. By merely thinking to myself that union of seven and five I have in no way already thought the concept of twelve, and however long I go on dissecting my concept of such a possible sum, the twelve will still not be met with inside it. One is obliged to go beyond these concepts by summoning the aid of an intuition answering to one of the pair, say the five fingers of one's hand or (as Segner in his arithmetic does) five dots, and thus, one by one, to join the units of the five that intuition furnishes to the concept of the seven. For I begin by taking the number 7, and, calling in the fingers of my hand as the intuition belonging to the concept of the 5, I now transfer the units that I had previously put together to make up the number 5, one after another onto that image of mine, adding them to the number 7, and in this way watch the number 12 emerge. Now that 5 ought to be joined to 7 was something I did think within the concept of a sum = 7+5, though not that this sum should be identical with the number 12. The arithmetical proposition, accordingly, is invariably synthetic — a point one appreciates the more clearly on choosing numbers of some size, since it then shines out plainly that, however we might rotate and reshuffle our concepts, we could, apart from the help of intuition, and by the bare dissection of our concepts alone, never arrive at the sum.

No more is any principle of pure geometry an analytic one. The claim that between two points the straight line is the shortest is a synthetic proposition. For in my concept of the straight there lies nothing pertaining to magnitude, but a quality only. The concept of the shortest is therefore something wholly superadded, and no amount of dissection will extract it from the concept of a straight line. Here, then, intuition has to be summoned to our aid, for through it alone is the synthesis rendered possible.

A small number of principles presupposed by geometers are, it is true, really analytic and depend upon the principle of contradiction; but these, like identical propositions, function merely as links binding the method together and not in the capacity of principles, for example a = a, the whole equals itself, or (a + b) > a, i.e. the whole exceeds its part. And even these, notwithstanding that they are valid on the basis of mere concepts, gain admission into mathematics solely on the ground that they permit of presentation in intuition. What ordinarily persuades us in this matter that the predicate of judgments of this apodictic kind is already lodged in our concept, so that the judgment counts as analytic, is nothing but the ambiguity residing in the expression. We are supposed, that is, to think a certain predicate together with a given concept, and this necessity already adheres to the concepts themselves. But what is at issue is not what we ought to think in addition to the given concept, but rather what we actually, obscurely though it be, think within it, and it thereby comes to light that, while the predicate does attach to those concepts necessarily, it does so not as thought within the concept itself, but by way of an intuition that has to be joined to the concept.

2. Natural science (physics) harbors within itself synthetic judgments a priori as principles. Let me put forward just a pair of propositions by way of illustration: the one holding that throughout all changes in the bodily world the quantity of matter stays constant, or else the one that in every transmission of motion action and counteraction must forever balance each other. In each of the two it stands clear not merely that there is necessity, and consequently an a priori origin, but likewise that they are synthetic propositions. For it is not permanence that I think to myself in the concept of matter, but merely matter's presence in space through its filling thereof. Thus I do in fact pass beyond matter's concept, so as to think onto it something a priori that I had not thought within it. The proposition, then, is not analytic but synthetic, and is nonetheless thought a priori — and so it stands with the other propositions belonging to the pure portion of natural science.

3. In metaphysics, granting that one takes it merely for a science attempted up to now yet, by the very nature of human reason, indispensable, synthetic cognitions a priori are supposed to be contained, and its concern is by no means simply to take apart concepts that we frame for ourselves a priori of things and so to elucidate them analytically, but rather our aim is to broaden our cognition a priori, and to that end we have to enlist principles of the sort that lay upon the given concept something it did not already hold, going, through synthetic judgments a priori, so far afield indeed that experience itself is unable to keep pace with us, as in the proposition: the world has to possess a first beginning, and more of the same; and so metaphysics, at least as measured by its aim, is composed of nothing save synthetic propositions a priori.

VI. The general problem of pure reason.

One stands to gain a great deal already if a whole multitude of inquiries can be subsumed under the formula of a single task. For in this way one lightens not only one's own business, by fixing it precisely for oneself, but also, for anyone else who cares to examine it, the verdict on whether or not we have done justice to our undertaking. The genuine task of pure reason is thus comprised in this question: How are synthetic judgments a priori possible?

The reason metaphysics has so far persisted in such a shaky state of uncertainty and contradictions lies solely in this: that no one let this task, and perhaps even the distinction between analytic and synthetic judgments, enter their thoughts sooner. It is on the resolution of this task, or on an adequate proof that the possibility whose clarification it demands does not in fact take place at all, that the standing and falling of metaphysics now depends. David Hume, who among all philosophers approached this task most closely, still thought it through with nowhere near enough precision and never in its full generality, but stopped short at the synthetic proposition linking an effect to its causes (Principium causalitatis), and he took himself to have established that any such proposition is wholly impossible a priori; on his reasoning, all that we term metaphysics would amount to nothing more than a delusion of fancied rational insight into what has really been borrowed from experience alone and has, by force of habit, acquired the semblance of necessity — a claim that demolishes all pure philosophy, one he would never have arrived at had our task in its generality stood before his eyes, for he would then have grasped that, on his own argument, there could be no pure mathematics either, since this assuredly contains synthetic propositions a priori, a claim from which his sound understanding would surely have saved him in that case.

The resolution of the above task also embraces, at one stroke, the possibility of putting pure reason to use in grounding and executing every science that holds a theoretical cognition a priori of objects, in other words the reply to the following questions:

How is pure mathematics possible?

How is pure natural science possible?

Of these sciences, seeing that they are really given, it is surely proper to ask how they are possible; for that they have to be possible their actuality itself proves.⁷ As for metaphysics, however, its poor progress up to now, together with the fact that of no single one presented so far can it be said, as regards its essential purpose, that it really exists, must with good reason make anyone doubt its possibility.

Still, this kind of cognition must in a certain sense be counted as given after all, and metaphysics, even if not as a science, is real as a natural disposition (metaphysica naturalis). For, propelled by a need of its own and not spurred on by any mere vanity of knowing a great deal, human reason advances irresistibly to questions of a kind that no empirical use of reason, and no principles drawn from such use, can ever answer; and so, in every human being, the moment reason widens within them as far as speculation, some metaphysics or other has existed at every period and will forever persist there. And here too the question presents itself: How is metaphysics possible as a natural disposition? in other words, out of the nature of universal human reason, how do the very questions arise that pure reason raises for itself and that its own need compels it to answer as best it can?

Since, however, every attempt made so far to answer these natural questions — for instance, whether the world had a beginning or has existed from all eternity, and the like — has invariably run into inescapable contradictions, one cannot leave things at the bare natural disposition toward metaphysics, that is, at the pure faculty of reason itself, from which indeed some metaphysics or other (be it what it may) always springs, but it must instead be possible to arrive with it at certainty, whether in knowing or in not knowing the objects, that is, either by reaching a decision upon the objects that its questions concern, or upon the power and impotence of reason to pronounce judgment on anything with regard to them, and hence either to extend our pure reason reliably, or to fix determinate and secure bounds upon it. This final question, issuing from the general task set out above, would properly run: How is metaphysics possible as a science?

The critique of reason thus leads in the end, of necessity, to science, whereas the dogmatic use of it without any critique leads instead to baseless assertions, against which equally plausible ones may be set, and so to skepticism.

Nor need this science be of any vast, off-putting length, since it deals not with objects of reason, whose manifold is infinite, but solely with itself, with tasks that spring wholly from its own bosom and are set before it not by the nature of things distinct from it, but by its own nature; for once it has first fully acquainted itself with its own capacity in regard to the objects that may present themselves to it in experience, it must become an easy matter to mark out completely and reliably the compass and the boundaries of its use as ventured beyond every limit of experience.

One can therefore, and indeed must, treat all the attempts hitherto made to establish a metaphysics dogmatically as though they had never occurred; for whatever in the one or the other is analytic — mere analysis, that is, of the concepts residing a priori in our reason — is not yet the goal at all, but only a groundwork for metaphysics properly so called, whose aim is to enlarge one's cognition a priori synthetically, and it is useless for that aim, since it does no more than lay out what already lies in these concepts, and not how we come to have such concepts a priori, so that we might thereafter determine as well their legitimate use in respect of the objects of all cognition whatsoever. Little self-renunciation, moreover, is called for in surrendering all these pretensions, since reason's contradictions with itself — which cannot be denied and are, in the dogmatic procedure, unavoidable as well — long ago robbed every metaphysics to date of its standing. More firmness will be needed here, so as not to be deterred, inwardly by the difficulty and outwardly by the resistance, from at last bringing a science indispensable to human reason, one whose every upshooting stem may indeed be lopped off but whose root cannot be eradicated, through a treatment wholly opposed to the one pursued so far, into a thriving and fruitful growth.

VII. Idea and division of a special science, under the title of a Critique of Pure Reason

All of this yields the idea of a distinct science, one that may bear the title Critique of Pure Reason. For reason is the power that supplies us with the principles of a priori cognition. Pure reason, then, is the reason that holds within it the principles for cognizing something in a wholly a priori manner. An organon of pure reason would amount to the totality of those principles whereby every pure a priori cognition can be gained and genuinely established. Applied in full, such an organon would yield a system of pure reason. Yet because that asks for a great deal, and because it is as yet an open question whether—and, if so, in which cases—our cognition admits of any enlargement here at all: we can treat a science that merely appraises pure reason, together with its sources and its bounds, as the propaedeutic to a system of pure reason. A science of that kind would deserve the name not of a doctrine but only of a critique of pure reason, and, where speculation is concerned, its value would truly be negative alone—not enlarging our reason but merely cleansing it, holding it clear of errors, and that in itself is no small achievement. I give the name transcendental to every cognition that concerns itself less with objects than with the way in which we cognize objects, so far as that way is to be possible a priori. A system built from such concepts would bear the name transcendental philosophy. This, however, is in turn more than a beginning can bear. For inasmuch as a science of that sort would have to hold, in full, both analytic cognition and synthetic cognition a priori, it reaches, as far as our purpose goes, too far—since we are permitted to carry the analysis only to the point where it becomes strictly indispensable for surveying, across their whole range, the principles of synthesis a priori, and it is those alone that we are after. This inquiry—which, strictly speaking, we may term not a doctrine but a transcendental critique, since its purpose is not to enlarge the cognitions themselves but only to set them right, and since it is meant to furnish the touchstone for the worth or worthlessness of every a priori cognition—is what we are engaged upon at present. A critique of this kind is thus a groundwork—for an organon, if that can be managed, and, failing that, at least for a canon belonging to it—on the strength of which the full system of the philosophy of pure reason (be it a matter of enlarging or merely of bounding its cognition) could one day be laid out, along analytic as well as synthetic lines. That it is indeed feasible—and, more than that, that such a system need not be of any very large extent, so that one may reasonably hope to finish it in full—can be judged beforehand from the following: that what forms the subject matter here is not the nature of things, which has no end, but the understanding, which delivers verdicts upon the nature of things, and even this only as regards its a priori cognition; and the stock of that cognition, since we have after all no license to look for it outside ourselves, cannot stay concealed from us, and to all appearances is modest enough to be taken in completely, weighed for its worth or worthlessness, and placed under a just estimate. Still less should one look here for a critique of the books and systems belonging to pure reason; what is meant is a critique of the very faculty of pure reason itself. Only where this serves as the foundation does one possess a reliable touchstone for gauging the philosophical substance of works old and new in this domain; otherwise the unqualified chronicler and judge measures the baseless claims of others against his own, which are no less baseless.

Transcendental philosophy is the idea of a science whose entire plan the critique of pure reason is charged with drafting architectonically—that is, out of principles—while guaranteeing in full the completeness and soundness of every component that goes into this structure. It is the system comprising all the principles of pure reason. The reason this critique does not already itself bear the name of transcendental philosophy lies purely in this: that, to constitute a complete system, it would also need to embrace an exhaustive analysis of the whole of human a priori cognition. Admittedly our critique must indeed set out before us a full census of all the root concepts out of which the pure cognition in question is composed. But it rightly holds back from any exhaustive analysis of these concepts as such, and likewise from a full review of those derived from them—partly because such a breaking-down would serve no purpose , given that it lacks the misgiving one encounters in synthesis, which is precisely what the whole critique exists for, and partly because it would offend against the plan's unity to shoulder the task of vouching for the completeness of an analysis and derivation of that sort, from which, in light of one's purpose, one might in any case be spared. This completeness—of the breaking-down no less than of the derivation from the a priori concepts still to be delivered—is in any event readily supplied, provided only that these are first on hand as fully worked-out principles of synthesis, and that nothing is lacking with regard to this essential purpose.

Everything that constitutes transcendental philosophy therefore falls within the critique of pure reason, and the critique is the complete idea of transcendental philosophy—yet not, as yet, that science itself, since it pushes the analysis only as far as the full appraisal of synthetic a priori cognition demands.

The chief thing to attend to in dividing up such a science is this: that no concept may find its way in that carries anything empirical within it, or, put otherwise, that the a priori cognition be entirely pure. Thus, even though the highest principles of morality, along with its basic concepts, are a priori cognitions, they still have no place within transcendental philosophy, for although they do not themselves ground their precepts upon the concepts of pleasure and displeasure, of appetites and inclinations, and so forth—concepts that one and all arise from an empirical source—they must nonetheless, in framing the concept of duty, unavoidably bring such concepts in when the system of pure morality is drawn up, whether as an obstacle to be surmounted or as a lure that is not to be converted into a motive. Transcendental philosophy is, for this reason, the philosophy of a reason that is pure and merely speculative. For all that is practical, in so far as it carries incentives with it, has to do with feelings, and these count among the empirical sources of cognition.

Should one now set about dividing this science from the general vantage of a system as such, then the division we are here putting forward must comprise, in the first place, a doctrine of elements, and in the second, a doctrine of method of pure reason. Each of these main divisions would carry subdivisions of its own, the grounds for which, however, do not yet admit of being laid out at this point. By way of introduction, or advance remark, only this much appears to be needed: that human cognition has two stems, which spring perhaps from one root that is shared but hidden from us—namely, sensibility and understanding—the first of them giving objects to us, whereas by the second they come to be thought. Now to the extent that sensibility should prove to contain a priori representations that constitute the condition under which objects are given to us, it would fall within transcendental philosophy. The transcendental doctrine of the senses would have to be placed in the opening part of the elementary science, for the conditions that alone allow the objects of human cognition to be given rank ahead of those under which such objects come to be thought.

I. Transcendental Doctrine of Elements.

The Transcendental Doctrine of Elements

First Part. Transcendental Aesthetic

Introduction §1

No matter in what way or by what means a cognition may be referred to objects, intuition is that by which it is referred to them directly, and toward which all thinking, as a means, is directed. Yet intuition occurs only where an object is given to us, and this, at least for us as human beings, is in turn possible only if the object affects the mind in a certain manner. That capacity for receiving representations by means of the manner in which we are affected by objects — a receptivity — we call sensibility. Objects, then, are given to us through sensibility, and it alone yields us intuitions; but they are thought through the understanding, and concepts have their origin in it. All thinking, however, whether it proceeds straightforwardly (directe) or by a roundabout path (indirecte), must in the end, through certain marks, bear upon intuitions and therefore, in us, upon sensibility, since there exists no other way in which an object could be given to us.

Sensation is the effect produced by an object upon the faculty of representation, so far as we are affected by that object. An intuition that bears upon its object by way of sensation is termed empirical. The undetermined object of an empirical intuition is what we call appearance.

Within an appearance, I give the name matter to whatever answers to sensation, whereas whatever allows the manifold of the appearance to be arranged under certain relations I give the name form of the appearance. Because that in which the sensations can alone be arranged and set into a definite form cannot itself once more be a sensation, the matter of every appearance is, to be sure, furnished to us only a posteriori, whereas its form must already lie prepared for them all a priori within the mind, and hence admits of being examined in separation from every sensation.

All representations in which nothing that belongs to sensation is encountered I call pure, taking the term in its transcendental sense. The pure form of sensible intuitions as such will accordingly be met with a priori in the mind, and within it the entire manifold of appearances is intuited under certain relations. This pure form of sensibility will, in its own right, likewise be termed pure intuition. So, for instance, if from my representation of a body I take away all that the understanding thinks in it — substance, force, divisibility, and the like — together with all that belongs in it to sensation — impenetrability, hardness, color, and so forth — there is still left over to me, out of this empirical intuition, something more, namely extension and figure. These latter belong to pure intuition, which has its place a priori in the mind as a mere form of sensibility, even in the absence of any actual object of sense or sensation.

I give the name transcendental aesthetic to a science of all the a priori principles of sensibility.⁸ Such a science, then, must exist, forming the first division of the transcendental doctrine of elements, as opposed to the one that holds the principles of pure thinking and goes under the name of transcendental logic.

Within transcendental aesthetic, accordingly, we shall in the first place set sensibility apart on its own, stripping away all that the understanding contributes there by means of its concepts, so that empirical intuition alone is left behind. In the second place, we shall then remove from this whatever pertains to sensation, so that there is left over nothing save pure intuition together with the bare form of the appearances — the sole item that sensibility is able to furnish a priori. This inquiry will bring to light two pure forms of sensible intuition that serve as principles of a priori cognition, namely space and time, and it is with weighing these that we shall now busy ourselves.

Section 1. On Space

§ 2. Metaphysical exposition of this concept.

Through outer sense — which is a property of our mind — we set before ourselves objects as external to us, and, without exception, as located in space. It is there that their figure, their size, and their mutual relation stand determined, or admit of determination. As for inner sense, through which the mind has intuition of itself, or of its own inner condition, it affords, admittedly, no intuition of the soul as such, taken as an object; and yet a determinate form does exist, one under which alone the intuition of the mind's inner condition becomes possible, with the result that whatever pertains to the inner determinations comes to be represented in temporal relations. Time admits of no outward intuition, just as little as space admits of being intuited as something internal to us. So what, in truth, are space and time? Are they actual beings? Are they nothing more than determinations — or else relations — of things, though determinations that would attach to those things in themselves even were the things never intuited; or do they instead cling solely to the form of intuition, and thereby to the subjective make-up of our mind, apart from which such predicates could be attributed to no thing at all? In order to gain instruction on this matter, we shall begin by expounding the concept of space. Now by exposition (expositio) I mean the clear — though not necessarily complete — representation of that which belongs to a concept; and an exposition counts as metaphysical when what it contains is that which presents the concept as given a priori.

1) The concept of space is no empirical one, got by abstraction from outer experiences. For if certain sensations are to be related to something external to me (namely, to something occupying a place in space distinct from the place where I myself am), and if, moreover, I am to represent them as external to and beside each other — thus not simply as differing, but as situated at different points — then the representation of space must already be presupposed as their ground. It follows that the representation of space can in no way be culled from the relations of outer appearance by means of experience; on the contrary, such outer experience first becomes possible only by way of this very representation.

2) Space is a representation that is necessary and a priori, forming the ground of every outer intuition. One can never form a representation to the effect that there is no space, even though it is entirely possible to conceive that no objects at all are met with in it. Space is therefore taken as the condition that makes appearances possible, not as a determination hanging upon them, and it constitutes an a priori representation that of necessity grounds outer appearances.

3) Space is no discursive concept — no general concept, as the phrase goes, of the relations of things at large — but is rather a pure intuition. For, to begin with, only one single space lets itself be represented, and talk of several spaces refers merely to parts of one and the very same single space. Nor can these parts stand prior to the one all-embracing space, functioning as it were as the components from which it might be assembled; they admit of being thought only within it. In its essence it is single, and the manifold it contains — together with the general concept of spaces at large — depends entirely upon limitations. What follows is that, where space is concerned, an a priori (hence non-empirical) intuition underlies every concept we form of it. For this reason every geometrical principle as well — say, that any two sides of a triangle taken together exceed the remaining one — is drawn never from universal concepts of line and of triangle, but out of intuition, and that a priori, carrying apodictic certainty.

4) Space is represented as an infinite given magnitude. Admittedly, any concept whatever has to be thought as a representation that an infinite plurality of differing possible representations includes beneath it (serving as their shared mark), so that the concept holds these under itself; yet no concept, qua concept, admits of being thought as if it enclosed an infinite plurality of representations within itself. Space, however, is thought precisely thus (since the parts of space, without limit, all coexist). The original representation of space, then, is an a priori intuition, and by no means a concept.

§3. Transcendental exposition of the concept of space.

By the term transcendental exposition I mean the accounting for a concept as a principle by whose means the possibility of further synthetic a priori cognitions may be grasped. To this end two things are demanded: 1) that cognitions of that kind do in fact spring from the given concept, 2) that such cognitions are possible solely on the supposition of one particular way of explaining the concept.

Geometry, now, is that science which fixes the properties of space in a synthetic and yet a priori manner. What character, then, must belong to the representation of space, if a cognition of this kind about it is to be possible? In its origin it has to be intuition; for out of a bare concept there is no drawing of propositions that reach past the concept, and yet just this occurs in geometry (Introduction V). This intuition, however, has to be met with within us a priori — that is, in advance of any perception of an object — and must accordingly be a pure and not an empirical intuition. For the propositions of geometry are without exception apodictic — that is, joined to an awareness of their necessity — as when space is said to possess but three dimensions; and propositions of that kind can be neither empirical nor judgments of experience, nor yet derived from any such (Intro. II).

How, in that case, is it possible for an outer intuition to reside in the mind ahead of the objects themselves, an intuition wherein the concept of those objects admits of a priori determination? Plainly in no way other than this: that it is lodged solely in the subject, as that subject's formal capacity to be affected by objects and so to obtain of them an immediate representation, which is to say an intuition — and therefore merely as the form of outer sense taken generally.

It is thus our explanation, and it alone, that makes intelligible the possibility of geometry as a synthetic a priori cognition. Whatever mode of explanation fails to yield as much — however much, to appearances, it might resemble ours — is by these very tokens most reliably set apart from it.

Conclusions from the above concepts.

a) Space presents no property at all belonging to things in themselves, nor does it present them in their mutual relation — that is, it presents no determination of them clinging to the objects as such, a determination that would persist even were every subjective condition of intuition set aside. For determinations, be they absolute or relative, cannot be intuited in advance of the existence of the things they qualify, and thus cannot be intuited a priori.

b) Space amounts to nothing beyond the form belonging to all appearances of the outer senses, namely the subjective condition of sensibility on which alone outer intuition is, for us, made possible. Given that the subject's receptivity — its being liable to be affected by objects — must of necessity come before any intuition of those objects, it becomes intelligible how the form belonging to all appearances may be present in the mind ahead of every actual perception, that is, a priori, and how this form, being a pure intuition within which all objects have to be determined, may hold within it the principles governing their relations before any experience at all.

Only from the vantage of a human being, then, are we in a position to speak of space, of extended beings, and the like. Should we set aside that subjective condition apart from which no outer intuition can come to us — the condition, namely, of our being susceptible to affection by objects — then the representation of space means nothing whatsoever. This predicate gets attributed to things only to the extent that they make their appearance to us — only, that is, as objects of sensibility. The abiding form of this receptivity — sensibility, as we term it — is a condition necessary to every relation wherein objects are intuited as outside us, and, once these objects are set aside, it is a pure intuition that we designate as space. Because the special conditions of sensibility can be turned by us into conditions not for the possibility of the things but only for that of their appearances, we are certainly entitled to say that space embraces everything liable to appear to us outwardly, yet not the things as they are in themselves, irrespective of whether they be intuited or not, and irrespective of the subject doing the intuiting. For concerning the intuitions of other thinking beings we are wholly unable to judge whether they lie under the very conditions that bound our own intuition and that possess universal validity for us. When the restriction placed on a judgment is folded into the concept of the subject, the judgment thereupon holds without condition. Take the proposition: all things stand side by side in space; it is valid subject to the restriction that these things be regarded as objects of our sensible intuition. But if at this point I incorporate the condition into the concept and state: all things, considered as outer appearances, stand side by side in space, then the rule is valid universally and free of any restriction. What our expositions thus impart is the reality of space (its objective validity, that is) as regards all that can present itself to us outwardly as an object, and at one and the same time the ideality of space as regards things whenever reason weighs them in themselves — that is, leaving the make-up of our sensibility out of account. Hence we maintain the empirical reality of space (as regards every outer experience that is possible), while maintaining at once its transcendental ideality — the point being that space is nothing once we drop the condition making all experience possible and treat it as something underlying the things in themselves.

Apart from space, however, there is likewise no other representation, subjective and directed upon something external, that could bear the title of objective a priori. For not one of them permits the deriving of synthetic propositions a priori, in the way that intuition in space does (§3). For this reason no ideality whatever attaches to them, properly speaking, though they do concur with the representation of space in one respect: that they pertain solely to the subjective make-up of the manner of sense — of sight, say, of hearing, of feeling, by way of the sensations of color, of sound, and of warmth — which, being nothing but sensations rather than intuitions, yield the cognition of no object in itself, and a priori least of all.

The purpose of this remark extends no further than this: to forestall anyone's hitting upon the idea of illustrating the alleged ideality of space through examples that fall far short, seeing that colors, taste, and the like are, quite rightly, viewed not as qualities of things but only as modifications of our subject, modifications that may even vary from one human being to the next. For here what is in its own origin nothing more than appearance — a rose, for instance — passes, in the empirical understanding, for a thing in itself, and this all the same can show itself to each eye differently in point of color. The transcendental concept of appearances in space, on the other hand, stands as a critical reminder that nothing at all which is intuited within space is a thing in itself, and that space is no form belonging to things such as might be their own apart from us — the reminder being, rather, that the objects taken in themselves remain wholly unknown to us, and that the things we name outer objects are but representations of our sensibility and nothing besides, having space for their form, while their genuine correlate — the thing in itself — is by this means neither cognized nor cognizable, and is furthermore something after which, in experience, no inquiry is ever made.

Section 2. On Time

§ 4. Metaphysical Exposition of the Concept of Time.

Time, to begin with, is 1) not any empirical concept drawn in some manner out of an experience. For simultaneity, or a following of one upon another, would itself never enter into perception at all were the representation of time not laid down at its basis a priori. It is solely on the supposition of this representation that we can represent to ourselves: that some things are at one and the same time (simultaneously), or at different times (one after the other).

2) Time is a representation that is necessary and underlies every intuition whatever. One cannot, in respect of appearances generally, cancel time itself, although one may quite well withdraw the appearances out of time. Time, accordingly, is something given a priori. It is in time alone that any actuality of appearances becomes possible. The appearances may collectively drop away, yet time itself — being the universal condition of their possibility — admits of no cancellation.

3) This a priori necessity is likewise the ground for the possibility of apodictic principles about time's relations, that is, of axioms of time as such. Time possesses but a single dimension: distinct times do not coexist but succeed each other (whereas distinct spaces, conversely, do not succeed each other but coexist). Such principles are not to be extracted from experience, for experience could furnish neither rigorous universality nor apodictic certainty. We could say no more than this: ordinary perception instructs us so; and never: thus it must necessarily be. These principles function as rules under which experiences are possible at all, and they teach us in advance of experience rather than by means of it.

4) Time is not a discursive concept — a general one, as it is termed — but rather a pure form belonging to sensible intuition. Distinct times amount to nothing but portions of that very same time. Now a representation that can be furnished only by way of one sole object is, however, an intuition. Furthermore, the proposition that distinct times cannot be simultaneous is one that no general concept would allow us to derive. This proposition is synthetic, and out of mere concepts it can never spring. It is, consequently, something directly comprised within the intuition and the representation of time.

5) The infinitude of time means nothing beyond this, that every determinate magnitude of time proves possible only by way of restrictions placed on a single underlying time. Hence the primordial representation time has to be given as something wholly unrestricted. But in any case where the parts themselves, together with every magnitude of an object, can be represented as determinate only through limitation, there the representation as a whole cannot be supplied by concepts (these, after all, carry only partial representations); rather, an immediate intuition has to underlie them.

§ 5. Transcendental Exposition of the Concept of Time.

I am therefore able to refer back to number 3, where, so as to be concise, I ranked whatever is genuinely transcendental among the items of the metaphysical exposition. To this I would append the following: the concept of alteration, and along with it the concept of motion (understood as alteration of place), can occur only through, and within, the representation of time; and were this representation not an inner intuition given a priori, then no concept of any kind whatsoever would be capable of rendering intelligible how an alteration is possible — an alteration being the uniting of contradictorily opposed predicates (for instance, the being at some place and the non-being of that very thing at the same place) in one and the selfsame object. Only within time is it possible for both contradictorily opposed determinations to be found together in a single thing — that is to say, one following upon another. In this way our concept of time accounts for the possibility of just as much synthetic cognition a priori as the general doctrine of motion — itself far from unfruitful — lays out.

§ 6. Inferences from these Concepts.

a) Time is nothing that could stand on its own account, nor anything clinging to things as an objective determination and so left behind once one has abstracted from every subjective condition under which they are intuited: for on the former alternative it would be a thing that, lacking any actual object, was nevertheless itself actual. With respect to the second alternative, on the other hand, if time were a determination or ordering inhering in the things themselves, it could not run ahead of those objects as the condition of them and be intuited and cognized a priori by means of synthetic propositions. This last, by contrast, comes about perfectly well provided that time is merely the subjective condition whereby any intuiting can occur within us at all. For in such a case this form of inner intuition allows of being represented in advance of the objects, thus a priori.

b) Time is none other than the very form of inner sense — the form, that is, under which we intuit ourselves and our own inner condition. For time can constitute no determination of outer appearances: it has nothing to do with any shape or location and so forth; what it does fix, on the other hand, is the relation among representations within our inner condition. And precisely because this inner intuiting furnishes no shape, we endeavour to compensate for the deficiency by means of analogies, portraying the succession of time as a line prolonged without end, along which the manifold makes up a series of but one dimension, and we reason from that line's features to all the features of time — with a single exception, namely that the parts of the line exist alongside one another, whereas those of time invariably follow in sequence. This too makes plain that the representation of time is itself an intuition, seeing that the whole of its relations admits of being set forth in an outer intuition.

c) Time constitutes the formal condition, a priori, of every appearance whatever. Space, being the pure form of all outer intuition, stands as an a priori condition confined solely to outer appearances. By contrast, since all representations — whether or not they take outer things for their object — do nevertheless, considered in themselves, belong as determinations of the mind to the inner condition, and since this inner condition falls in turn under the formal condition of inner intuition, and thus of time: time is accordingly an a priori condition of every appearance whatsoever, namely the direct condition of inner appearances (of our souls) and, precisely thereby, the indirect condition of outer appearances also. If I am entitled to affirm a priori: all outer appearances are in space and stand determined a priori by the relations of space, then, out of the principle of inner sense, I may affirm quite universally: all appearances whatsoever, i.e. every object of the senses, lie in time and necessarily enter into relations of time.

Should we abstract from our manner of inwardly intuiting ourselves, and — by the mediation of that intuition — of likewise gathering every outer intuition into the faculty of representation, and thus take objects just as they may be in their own right, then time turns out to be nothing at all. Its objective validity extends to appearances alone, for these are already things that we accept as objects of our senses; but it forfeits its objectivity the moment one abstracts from the sensibility proper to our intuiting — that is, from the mode of representation peculiar to us — and speaks instead of things in general. Time is thus no more than a subjective condition of our (human) intuition (an intuition that is invariably sensible, that is, so far as we find ourselves affected by objects), while in itself, taken apart from the subject, it is nothing whatever. For all that, with respect to every appearance — and hence to every thing that might present itself to us in experience — it is of necessity objective. We cannot say: all things are in time, since in the concept of things as such one leaves aside every mode of intuiting them, and yet it is exactly this mode that is the real condition under which time enters into the representation of objects. But once that condition is joined to the concept, so that the statement runs: all things as appearances (objects of sensible intuition) are in time, then the principle possesses its full objective correctness together with a priori universality.

What we maintain, then, establishes the empirical reality of time — its objective validity, that is, in relation to whatever objects may at any time be presented to our senses. And because our intuiting is on every occasion sensible in kind, there can be presented to us in experience no object whatever that would fall outside time's condition. We contest, on the other hand, every claim of time to absolute reality — the claim, that is, that it would belong to things simply as such, as a condition or a property, even where no account is taken of the form of our sensible intuition. Properties of this sort, which pertain to things as they are in themselves, could in any case never reach us by way of the senses. It is in this that the transcendental ideality of time consists: on such a view, once one abstracts from the subjective conditions of sensible intuition, time amounts to nothing whatever and cannot be reckoned to the objects in themselves — apart, that is, from their relation to our intuition — either as something subsisting or as something inhering. Still, this ideality is no more to be set alongside the subreptions of sensation than is that of space, since in the latter case one does presuppose of the appearance itself — the appearance in which those predicates inhere — that it possesses an objective reality, whereas here such reality drops away completely, save insofar as it is merely empirical, that is, regards the object in question simply as appearance: on which point the foregoing remark of the earlier section may be consulted.

§ 7. Elucidation.

Against the present theory — which allows time an empirical reality but denies it any absolute and transcendental one — I have heard from perceptive men an objection voiced with such unanimity that I infer it must present itself, as a matter of course, to every reader for whom these reflections are unfamiliar. It goes as follows: alterations are actual (as is shown by the succession of changes among our own representations, even supposing one wished to deny all outer appearances along with their alterations). But since alterations can take place only in time, it follows that time is something actual. There is no difficulty in answering this. I concede the argument in its entirety. Time is indeed actual — it is, namely, the actual form belonging to inner intuition. It possesses, accordingly, a subjective reality as regards inner experience: that is, I genuinely do have a representation of time and of my determinations within it. It is thus to be viewed as actual not in the character of an object, but as the manner in which I represent myself as an object. Yet if I myself, or else some other being, were able to intuit me without this condition of sensibility, then those selfsame determinations that we now represent to ourselves as alterations would deliver a cognition wherein no representation of time — and consequently none of alteration either — made any appearance whatever. What remains, then, is its empirical reality, standing as the condition of all our experiences. It is only absolute reality that, in light of what was set out above, cannot be granted to it. It amounts to nothing beyond the form belonging to our inner intuition.⁹ Take away from it the particular condition constituting our sensibility, and the concept of time vanishes along with it; time clings not to the objects themselves but purely to the subject that does the intuiting.

The reason, however, why this objection is raised so unanimously — and that by the very people who, for their part, can find nothing cogent to urge against the doctrine of the ideality of space — is the following. They held out no hope of demonstrating the absolute reality of space with apodictic force, for they are met by idealism, on whose showing the actuality of outer objects is susceptible of no rigorous proof: the actuality, by contrast, of the object of our inner sense (of myself and of my state) stands immediately clear through consciousness. The former might be a bare semblance, whereas the latter, on their view, is beyond denial something actual. What they overlooked, though, is that the two of them — however little one may contest their actuality as representations — belong all the same solely to appearance, and appearance always presents two aspects: the one on which the object is regarded in itself (leaving aside the way in which it is intuited, whose constitution for just that reason stays perpetually problematic), the other on which one looks to the form of the intuition of this object, a form to be sought not in the object taken in itself but in the subject to whom that object appears, yet one that genuinely and necessarily attaches to this object's appearance.

Time and space, then, are two wellsprings of cognition out of which a variety of synthetic cognitions can be drawn a priori — as pure mathematics, above all, supplies a shining example in the case of the cognitions concerning space and its relations. For the two of them, taken jointly, are the pure forms of all sensible intuition, and it is on that basis that they render synthetic propositions a priori possible. These a priori sources of cognition, however, mark out their own limits by that very circumstance (that they are nothing but conditions of sensibility), the limit being that they bear only upon objects insofar as these are taken as appearances and do not exhibit things as they are in themselves. That domain alone forms the field within which they hold; step beyond it, and no further objective use of them can be made. This reality of space and of time, for that matter, leaves the reliability of experiential cognition wholly intact: for we remain equally sure of it whether these forms attach of necessity to the things in themselves or merely to our intuiting of those things. By contrast, whoever affirms the absolute reality of space and time — taking them, that is, either as subsisting or merely as inhering — is bound to fall into disagreement with the very principles of experience. For should they come down on the side of the first alternative (usually the camp of the mathematical investigators of nature), they are then obliged to posit two eternal, infinite, self-standing non-things (space and time), which are there (although nothing actual answers to them) with no purpose but to hold within themselves everything that is actual. Take up the second party instead (to which certain metaphysical students of nature belong), on which space and time pass for relations of appearances (side by side or one after the other) abstracted from experience though, once set apart, confusedly represented: in that case they are forced to deny to the mathematical doctrines a priori their validity — or at any rate their apodictic certainty — as concerns actual things (in space, for example), inasmuch as no such certainty is to be had a posteriori, and on this opinion the a priori concepts of space and time are mere fabrications of the imagination, whose source has genuinely to be looked for in experience, out of whose abstracted relations imagination has fashioned something that does contain what is universal in them, yet cannot subsist without the restrictions that nature has tied to them. The first group gains this much, that they clear the field of appearances on behalf of their mathematical claims. Yet by these same conditions they land themselves in great confusion whenever the understanding seeks to pass beyond that field. The second group, for its part, does gain in respect of this last point, namely that the representations of space and time put no obstacle in their path when they mean to judge of objects not as appearances but purely in their relation to the understanding; but they can neither assign any ground for the possibility of mathematical cognitions a priori (lacking, as they do, a genuine and objectively valid intuition a priori) nor bring the propositions of experience into the requisite accord with those assertions. On our own account of the genuine nature of these two primitive forms of sensibility, both difficulties are set to rest.

That, in the end, the transcendental aesthetic can hold no more than these two elements — space and time — becomes evident from the consideration that all the remaining concepts pertaining to sensibility, even the concept of motion, which brings the two of them together, take something empirical for granted. For motion presupposes that something movable be perceived. But within space, regarded on its own, nothing movable is to be met with: hence what is movable has to be a thing discoverable in space only through experience, and so an empirical datum. In the same way the transcendental aesthetic is unable to number the concept of alteration among its data a priori: for it is not time itself that alters, but rather something situated in time. What this calls for, accordingly, is the perception of some existence together with the succession of its determinations — in short, experience.

§ 8. General Remarks on the Transcendental Aesthetic

I. First of all it will be requisite to make plain, with all possible distinctness, what our position is in regard to the basic character of sensible cognition as such, so that no misconstruction of it may arise.

Our intention, then, has been the following: that the whole of our intuition amounts to nothing beyond the representation of appearance; that the things submitted to our intuition are not, as they stand in themselves, what we take them for in intuiting them, and that their relations, too, are not so ordered in themselves as they present themselves to us; and further, that were we to cancel our subject — or even merely the subjective make-up of the senses at large — every characteristic and every relation obtaining among objects throughout space and time, space and time themselves not excepted, would fall away, incapable, qua appearances, of subsisting in their own right and capable of existing only within us. What the bearing of the objects in themselves may be, once abstracted from this entire receptivity of our sensibility, remains for us altogether unknown. We are familiar with nothing beyond the manner in which we ourselves take them up — a manner distinctive of us, which, though it pertains to every human being, need not for all that pertain to every being as such. And this manner alone is what we have to deal with. Its pure forms are space and time, while sensation as such supplies its matter. The first of these we are able to cognize solely a priori — in advance, that is, of any actual perception — for which reason it bears the name of pure intuition; the second, by contrast, is that ingredient of our cognition on whose account the cognition is termed a posteriori, or empirical intuition. The former cling to our sensibility with unqualified necessity, no matter what character our sensations happen to bear; the latter admit of great variety. Even could we heighten this intuition of ours to the utmost pitch of distinctness, no such heightening would bring us one step nearer to how objects are constituted in themselves. For in every case what we would cognize fully is still only our own manner of intuiting — our sensibility, that is — and this invariably under those conditions of space and time that cleave to the subject from the outset; as to what the objects might be in their own right, not even the most fully clarified cognition of their appearance, the only cognition granted us, would ever bring it to our knowledge.

The claim, accordingly, that our sensibility in its entirety is nothing but a confused way of representing things — one that captures solely what pertains to them in themselves, yet does so only beneath a heaped-together mass of marks and partial representations that we never draw apart in consciousness — corrupts the very concept of sensibility and of appearance, and thereby drains the whole doctrine concerning them of use and content. The difference that sets an indistinct representation apart from a distinct one is purely logical and does not touch the content. There is no doubt that the concept of right which sound understanding puts to work holds precisely what the finest speculation is able to draw out of it; the only difference is that, in ordinary and practical dealings, one remains unaware of these manifold representations lodged within the thought. Hence it will not do to call the common concept sensible, or to say it harbors a mere appearance; for right admits of no appearing whatever — its concept resides in the understanding and sets forth a property of actions (the moral property) that pertains to them in themselves. The representation of a body in intuition, on the other hand, holds nothing at all that might pertain to an object taken in itself, but only the appearance of a something, together with the way in which we come to be affected through it; and this receptiveness on the part of our cognitive capacity is what we call sensibility, which stays — however thoroughly one might care to penetrate that appearance (the appearance) to its very base — divided by an immeasurable gulf from cognition of the object in itself.

The philosophy of Leibniz and Wolff has, in consequence, directed every inquiry into the nature and origin of our cognitions along a wholly wrong line of sight, treating the difference between the sensible and the intellectual as a merely logical one, when in truth it is transcendental through and through: it concerns not the form of distinctness or its lack, but rather the very source and content of these cognitions, so that by way of sensibility we come to cognize the character of things in themselves not obscurely but not whatsoever, and, the moment our subjective character is withdrawn, the represented object — bearing the properties that sensible intuition had lent it — is to be found nowhere at all, nor could it be found, since it is just this subjective character that fixes the form of that object as appearance.

In other contexts, to be sure, we mark off, within appearances, that which clings essentially to the intuition of them and obtains for any and every human sense, from that which accrues to them only by accident, being valid not for the relation to sensibility taken generally but merely for some special placement or organization of this or that particular sense. The former kind of cognition is then said to be one that represents the object as it stands in itself, the latter merely the appearance of that object. Yet this distinction is empirical, nothing more. Should one come to rest at this point (as usually happens) and fail to view that empirical intuition, in its turn, as itself mere appearance (as one ought to), so that within it nothing is met with that could bear on any thing in itself, then our transcendental distinction has slipped away, and we go on believing, after all, that we cognize things in themselves, notwithstanding that throughout (in the world of sense), right down to the profoundest inquiry into its objects, we are dealing with nothing except appearances. The rainbow, for instance, we shall readily call a mere appearance attending a rain lit by sun, and this rain we shall call the thing in itself — which is indeed right, so long as we take the latter concept in a merely physical sense, namely as that which, throughout the range of ordinary experience and under every diversity of position relative to the senses, stands determined in intuition thus and never otherwise. But should we take this empirical thing quite generally and inquire — with no regard to its concurrence with each human sense — whether it, too, represents an object in itself (not the raindrops, since these, being appearances, already rank as empirical objects), then the inquiry into how the representation stands related to the object turns transcendental, and now not merely those drops are mere appearances, but their rounded figure as well, indeed the very space through which they descend, are nothing in themselves, being no more than modifications, or foundations, of our sensible intuition — while the transcendental object stays unknown to us.

A second matter of weight for our transcendental aesthetic is that it should not win a measure of favor merely as a specious hypothesis, but should carry as much certainty and freedom from doubt as could ever be asked of any theory meant to function as an organon. To set this certainty in a fully convincing light, let us take up some case or other in which its validity may come plainly into view, one apt as well to lend further clarity to what was brought forward in §3.

Grant, then, that space and time are objective in their own right, conditions for the possibility of things as they are in themselves: the first thing to emerge is that from both there issue, a priori, apodictic and synthetic propositions in great abundance — pre-eminently in the case of space, which for that very reason we shall single out here for examination by way of illustration. Seeing that geometrical propositions are cognized synthetically a priori and carry apodictic certainty, my question runs: whence do you take propositions of this sort, and upon what does our understanding lean in reaching truths so utterly necessary and universally valid? No path lies open save that of concepts or that of intuitions — both, however, taken as given whether a priori or a posteriori. As for the second, namely concepts drawn from experience, and likewise the empirical intuition on which such concepts rest, these can furnish no synthetic proposition beyond one that is itself merely empirical — a proposition of experience — and hence one incapable ever of carrying necessity and absolute universality, the very features that stamp every proposition of geometry. As for what would be the first and sole means — the attaining of cognitions of this kind through bare concepts or through intuitions a priori — it is plain that bare concepts yield no synthetic cognition at all, but analytic cognition only. Take just the proposition that two straight lines shut in no space whatever, so that no figure can arise from them, and attempt its derivation from the concept of straight lines together with the number two; or again the proposition that three straight lines make a figure possible, and attempt the like from these concepts on their own. Every exertion of yours comes to nothing, and you find yourself driven to fall back on intuition, exactly as geometry has always done. So you provide yourself with an object in intuition; but of what kind is this intuition — a pure intuition a priori, or an empirical one? Were it empirical, no proposition of universal validity, and still less an apodictic one, could ever spring from it; for experience is powerless to supply anything of the sort. You are obliged, then, to furnish your object a priori within intuition and to rest your synthetic proposition upon it. Now suppose there were not resident in you a power of intuiting a priori; suppose this subjective condition, as to its form, were not at once the universal a priori condition beneath which alone the object of such (outer) intuition can itself be; suppose the object (the triangle) were a something in itself, standing in no relation to your subject — how then could you claim that whatever is bound up, in your subjective conditions, with constructing a triangle must belong of necessity to the triangle in itself as well? For to your concepts (of three lines) you could add nothing further (the figure) such as would then have to be met with of necessity in the object, given that this object stands there ahead of your cognition and not by means of it. And so, were space (and with it time) not a bare form of your intuition, holding a priori those conditions under which alone things can figure for you as outer objects — things that, apart from these subjective conditions, are in themselves nothing — you would be able to settle nothing synthetic a priori about outer objects at all. It stands therefore beyond all doubt — not as something merely possible, nor even as probable — that space and time, being the conditions required for all experience, outer and inner alike, are no more than subjective conditions attaching to every intuition of ours; and it is with reference to these that all objects rank as sheer appearances rather than as things given, after this fashion, on their own account — objects of which, just on this score, much may be affirmed a priori so far as their form goes, yet never the slightest thing about the thing in itself that may lie at the ground of these appearances.

II. In support of this doctrine of the ideality of both outer and inner sense — hence of all objects of the senses as nothing but appearances — one observation is of particular service: that whatever, in our cognition, belongs to intuition (setting aside, that is, the feeling of pleasure and displeasure, and the will, none of which are cognitions) comprises nothing but mere relations — of positions within an intuition (extension), of the shifting of positions (motion), and of the laws by which such shifting is governed (the forces of motion). As for what is present at the position itself, or what, over and above the change of position, is at work within the things themselves, of that nothing is thereby given. But no thing in itself gets cognized through mere relations; so it is reasonable to conclude that, since outer sense delivers to us nothing but representations of relation, this sense likewise can hold within its representation only how an object stands related to the subject, and not the inner being that belongs to the object in itself. With inner intuition matters stand in just the same way. For not only do the representations of outer senses furnish the genuine stuff with which we stock our mind; the time, too, in which we set these representations — a time preceding our very awareness of them in experience and lying at their ground as the formal condition of the way in which we lodge them in the mind — carries within it, already, relations of succession, of coexistence, and of what endures alongside succession (the abiding). Now whatever, as representation, can go before every act of thinking anything at all is intuition, and, where it holds nothing but relations, it is the form of intuition — which, representing nothing except so far as something comes to be set within the mind, can amount to nothing else than the way in which the mind, through an activity of its own — namely this setting of its representation — and so through itself, comes to be affected, that is, an inner sense as regards its form. Anything that a sense represents is, to that extent, always appearance; and so an inner sense would have either to be denied altogether, or else the subject that forms its object could be represented by it only as appearance, not as that subject would judge of itself if its intuition were pure self-activity, that is, intellectual. The whole of the difficulty here turns solely on how a subject can inwardly intuit its own self; but a difficulty of this kind besets every theory alike. Self-consciousness (apperception) is the simple representation of the I, and were all that is manifold in the subject given, through it alone, in self-active fashion, then inner intuition would be intellectual. In the human being, such consciousness calls for an inner perception of the manifold already furnished within the subject, and the way in which this manifold reaches the mind devoid of spontaneity has, on account of just this difference, to be named sensibility. If the power of becoming conscious is to search out (to apprehend) what lies within the mind, it must affect that mind, and only thus can it bring forth an intuition of its own self — an intuition, however, whose form, resting antecedently at the ground of the mind, fixes within the representation of time the manner in which the manifold lies gathered in the mind; whereupon it intuits itself, not in the way it would, directly and self-actively, represent itself, but according to the manner in which it undergoes affection from within, and thus as it appears to itself, not as it is in fact.

III. If I say that, in space and time, intuition sets before us both the outer objects and the mind's intuition of itself, each just as it affects our senses — that is, as it appears — I do not mean by this that such objects would be a mere semblance. For within the appearance the objects — indeed the very characters we attach to them — are invariably taken as something actually given; only that, in so far as such a character depends purely on the subject's mode of intuition in the relation the given object bears to it, this object, as appearance, comes to be distinguished from that same thing as an object in itself. I therefore do not assert that bodies merely seem to exist outside me, or that my soul merely seems to be given in my self-consciousness, when I hold that the qualitative character of space and time, conformably to which — as a condition of their existence — I place them both, resides in my mode of intuition and not in these objects taken in themselves. It would be a failing all my own, were I to make a bare semblance out of what I ought to reckon as appearance.¹⁰ This, however, does not follow upon our principle of the ideality of all our sensible intuitions; on the contrary, once one lends objective reality to those forms of representation, it becomes impossible to keep everything from being turned thereby into sheer semblance. For if one takes space and time to be characters that, in point of their possibility, would have to be encountered in things themselves, and then weighs the absurdities into which one is thereupon drawn — seeing that two infinite things, which are no substances, and equally nothing that genuinely inheres in substances, yet must for all that be existent, nay the necessary condition for the existence of everything, and must moreover persist even when all existing things have been cancelled — then one can hardly reproach the worthy Berkeley for lowering bodies to bare semblance; indeed our own existence too, made in this manner to hang upon the self-standing reality of such a non-thing as time, would have to be converted, together with it, into nothing but semblance — an absurdity that up to now no one has let himself fall into.

IV. In natural theology, where the object one thinks is not merely, for us, no object of intuition whatever, but is such that it can be no object of sensible intuition even to itself, great care is taken to strip away from the whole of its intuition (for its cognition must throughout be intuition of that sort and not thought, which invariably discloses limits) the conditions of time and of space. Yet with what warrant can this be done, once one has already turned the two of them into forms of things in themselves — and forms, at that, which persist a priori as conditions of the existence of things even where one had cancelled the things in their own right: for, as conditions of all existence as such, they would have to be conditions of God's existence no less. There remains no course, if one is unwilling to make them objective forms of all things, but to make them subjective forms of our mode of intuition, outer as well as inner — a mode termed sensible for the reason that it is not original, that is, not one by which the very existence of the object of intuition is itself given (a kind that, so far as we can discern, can pertain to the primordial being alone), but rather one that hangs upon the existence of the object, and is therefore possible solely in that the subject's capacity for representation is affected by that object.

Nor need we restrict this manner of intuiting, throughout space and time, to human sensibility; it might well hold that every finite thinking being is bound to accord with the human being on this point (a thing we cannot settle), yet for all this universal validity it does not thereby cease to be sensibility, precisely for the reason that it is derivative (intuitus derivativus) and not original (intuitus originarius), and so is not intellectual intuition — the latter, on the ground just given, appearing to belong to the primordial being alone, and never to a being that is dependent both in its existence and in its intuition (an intuition that determines that being's existence in relation to given objects); though this last observation is to be reckoned, within our aesthetic theory, merely as clarification and not as a ground of proof.

Conclusion of the Transcendental Aesthetic

Here we now have one of the requisite pieces for the resolution of the general task of transcendental philosophy: how are synthetic propositions possible a priori?, namely pure intuitions a priori, space and time, in which we, whenever in an a priori judgment we wish to pass beyond the given concept, come upon what can be discovered a priori not in the concept but indeed in the intuition that corresponds to it, and can be connected synthetically with the former, which judgments, however, for this reason never reach further than to objects of the senses and can be valid only for objects of a possible experience.

Second Part. Transcendental Logic

Introduction. Idea of a Transcendental Logic

I. On Logic in General

Our cognition springs from two basic sources of the mind: the first is the reception of representations (the receptivity of impressions), and the second is the power to cognize an object through such representations (the spontaneity of concepts); by way of the former an object gets given to us, while by way of the latter that same object, considered in its bearing on the representation (as nothing more than a determination of the mind), comes to be thought. Intuition and concepts, accordingly, make up the elements of the whole of our cognition, in such a way that concepts deprived of an intuition answering to them in some fashion, and no less intuition deprived of concepts, prove unable to furnish any cognition. Both alike are either pure or else empirical. They count as empirical whenever a sensation (one that presupposes the object's actual presence) is contained in them; as pure, by contrast, whenever nothing of sensation has been mixed into the representation. This latter component one may term the matter belonging to sensible cognition. Pure intuition, on this account, holds nothing but the form under which a thing is intuited, and pure concept holds solely the form for thinking an object as such. Only pure intuitions or concepts are possible a priori, whereas empirical ones are possible merely a posteriori.

Suppose we choose to give the receptivity of our mind — its capacity for receiving representations in so far as it is affected in some way or other — the name sensibility: then, by contrast, the power to bring forth representations of its own accord, the spontaneity of cognition, constitutes the understanding. Our nature is so constituted that intuition can never be anything but sensible, that is, it embraces solely the way objects come to affect us. The power to think the object of a sensible intuition, on the other hand, constitutes the understanding. Neither of these two properties merits being ranked above the other. Absent sensibility, not a single object would be given us; absent understanding, not one would be thought. A thought without any content is empty; an intuition without any concept is blind. Hence it is every bit as necessary to render one's concepts sensible (that is, to attach to them their object in intuition) as it is to render one's intuitions intelligible (that is, subsuming them under concepts). These two faculties, or capacities, are likewise unable to trade their functions. The understanding is capable of intuiting nothing, the senses of thinking nothing. It is solely from this, from their uniting, that cognition can arise. Even so, one may by no means blend their respective shares on that account; on the contrary, there is strong reason to keep each carefully apart from the other and to tell them apart. And so we mark off the science that furnishes the rules of sensibility as such — that is, aesthetics — from the one that furnishes the rules of the understanding as such, namely logic.

Now logic, in its turn, admits of being pursued with two different aims: either as a logic of the general employment of the understanding or as one of its particular employment. The first sort holds those rules of thinking that are unconditionally necessary, rules apart from which the understanding gets no employment whatever, and it thus addresses the understanding without any regard to how the objects it may be trained upon differ among themselves. The logic of the particular employment of the understanding holds the rules for thinking rightly about a determinate kind of object. The first of these may be termed elementary logic, whereas the second is the organon of one science or another. In the schools it is usually placed first, serving as a propaedeutic for the sciences, even though, in the order that human reason actually travels, it is the very last thing reason attains, reached only once a science stands long completed and wants no more than a finishing touch toward its correction and its perfection. For one has to be acquainted with the objects already to a rather high degree if one means to lay down the rules by which a science concerning them might be established.

General logic, for its part, is either pure or applied. Within the first of these we leave out of account every empirical condition under which our understanding is brought into play — for example, the influence of the senses, the play of the imagination, the laws of memory, the force of habit, inclination, and so on — and along with them the sources of our prejudices, indeed, quite generally, all those causes out of which certain cognitions may arise in us or come to be foisted on us, for they touch the understanding only under particular circumstances attending its application, circumstances that can be known only by way of experience. A logic that is both general and pure thus concerns itself exclusively with principles that are a priori, and it amounts to a canon of the understanding and, no less, of reason, though only as regards the formal side of their employment, no matter what the content may happen to be (whether empirical or transcendental). A general logic, by contrast, comes to be called applied once it is aimed at the rules for employing the understanding under conditions of a subjective, empirical kind — the sort that psychology instructs us in. It therefore rests on empirical principles, even though it counts as general in so far as it bears on the employment of the understanding irrespective of any difference among objects. That is likewise why it constitutes no canon of the understanding at large, nor any organon for the particular sciences, but merely a cathartic serving the common understanding.

Within general logic, then, the portion meant to make up reason's pure doctrine has to be set wholly apart from the portion that makes up the applied (yet still general) logic. This first portion is, strictly speaking, the only genuine science here, however terse and dry it may be — as terse and dry as the scholastically correct exposition of an elementary theory of the understanding demands. In dealing with this first portion, accordingly, logicians must at every moment keep two rules in view.

1) Being general logic, it leaves aside all the content of the understanding's cognition together with the differences among its objects, and it is occupied with nothing beyond the sheer form of thinking.

2) Being pure logic, it possesses no empirical principles at all, so that (contrary to what people have now and then talked themselves into) it borrows nothing from psychology, which accordingly exerts no influence of any kind upon the canon of the understanding. It is a demonstrated body of doctrine, and everything within it has to be wholly certain a priori.

What I, for my part, call applied logic (against the ordinary sense of the term, on which it would take in certain exercises for which pure logic supplies the rule) is a representation of the understanding and of the rules for its necessary employment in concreto — that is, under the accidental conditions belonging to the subject, conditions capable of impeding or of aiding that employment, and given, one and all, only empirically. It treats of attention, of what obstructs it and what follows from it, of the origin of error, of the condition of doubt, of misgiving, of conviction, and the like; and to it general and pure logic stands related just as pure morality — which holds nothing but the necessary moral laws of a free will as such — stands related to the doctrine of virtue proper, a doctrine that weighs those laws against the resistance of the feelings, the inclinations, and the passions, to which human beings find themselves subject to a greater or lesser degree, and that is never able to furnish a genuine and demonstrated science, since it, exactly like that applied logic, stands in need of empirical and psychological principles.

II. On Transcendental Logic

As was indicated earlier, general logic sets aside the whole content of a cognition—every bearing it may have upon the object—and attends solely to logical form, namely to how cognitions stand toward one another, which is to say the form of thinking as such. Now because intuitions come in two kinds, pure as well as empirical (as the transcendental aesthetic makes plain), a corresponding difference might well be found between pure and empirical thinking of objects. Were that so, we should have a logic that did not leave every content of cognition out of account; for a logic confined to the rules by which an object is thought purely would shut out any cognition whose content happened to be empirical. Such a logic would moreover reach back to the source from which our cognitions of objects arise, at least so far as that source cannot be charged to the objects, whereas general logic takes no interest whatever in where cognition has its beginning but examines representations—be they lodged in us from the first a priori, or furnished only through experience—purely under the rules by which the understanding sets them to work against one another in the act of thinking, and so busies itself only with that form of the understanding which can be conferred on representations, from whatever quarter they may otherwise have sprung.

At this point I insert an observation whose bearing carries over into every discussion still to come, one that ought to be held firmly before us, namely this: that the term transcendental is owed not to every cognition a priori, but only to the cognition through which we come to know that, and in what fashion, particular representations (whether intuitions or concepts) are put to use or are rendered possible purely a priori (transcendental, in other words, marking the possibility of a cognition, or its employment, a priori). For this reason space itself, and every geometrical specification of it a priori alike, is no transcendental representation; what alone may carry that name is the cognition that these representations arise from no empirical source whatever, together with the possibility of how they are nonetheless able to apply a priori to objects of experience. The employment of space in regard to objects generally would, in the same way, prove transcendental too: restrict it, though, to objects of the senses alone, and it thereby comes to be styled empirical. The line drawn between the transcendental and the empirical thus has its home solely within a critique of cognitions and says nothing about how those cognitions are related to their object.

Anticipating, then, that there might after all exist concepts bearing a priori upon objects—not in the guise of pure or sensible intuitions, but as sheer operations of pure thought, hence concepts, though ones owing their origin to neither experience nor an aesthetic ground—we sketch out for ourselves beforehand the idea of a science of pure understanding and of the cognition yielded by reason, whereby objects come to be thought entirely a priori. Any such science—one that fixed the source, the reach, and the objective validity belonging to cognitions of this kind—would necessarily bear the name transcendental logic, for its business lies purely with the laws governing understanding and reason, yet only to the degree that these laws are brought to bear on objects a priori, and not, in the manner of general logic, on rational cognitions empirical and pure without any distinction being drawn.

III. On the Division of General Logic into Analytic and Dialectic

That old and celebrated question by which people supposed they could back the logicians into a corner, seeking to drive them either into a wretched circular argument or into an admission of their ignorance — and thereby of the emptiness of their whole art — runs as follows: What is truth? As for the nominal definition of truth — that it consists in a cognition's agreement with its object — this is granted at the outset and presupposed; what one wants to know, rather, is the universal and reliable criterion for the truth of any cognition whatsoever.

To know what one can reasonably ask for is already a substantial and necessary proof of prudence or discernment. For if a question is inherently absurd and demands needless answers, then, apart from embarrassing the one who poses it, it sometimes has the added drawback of tempting an incautious listener into equally absurd replies, and of presenting the laughable sight of one person (as the ancients said) milking a he-goat while the other holds a sieve beneath it.

If the truth of a cognition lies in its agreement with the object it concerns, then that object must thereby be marked off from others; for a cognition is false when it does not accord with the object to which it is referred, even if it should contain something that might well hold of other objects. A universal criterion of truth, now, would have to be one valid for all cognitions alike, without regard to any difference among their objects. Yet it is evident that, since with any such criterion one leaves aside the whole content of a cognition (its relation to its object), while truth bears precisely on that content, it is downright impossible, and indeed absurd, to demand a mark of the truth of cognitions as regards this content; and thus that no sufficient and at the same time universal sign of truth can possibly be given. Since we earlier designated a cognition's content as its matter, we shall have to say this: with respect to matter, no universal sign of a cognition's truth can be demanded, since to ask for one is inherently self-contradictory.

But where a cognition is taken merely as to its form (with all content laid aside), it is just as evident: that a logic, insofar as it presents the universal and necessary rules of the understanding, must in these very rules set out criteria of truth. For whatever conflicts with them is false, since in such a case the understanding contravenes its own universal rules of thought, and hence itself. These criteria, however, touch only the form of truth — that is, of thinking as such — and to that degree are wholly correct, though not sufficient. For however completely a cognition might conform to logical form — that is, avoid contradicting itself — it may still, for all that, be at odds with its object. The purely logical criterion of truth, then — namely a cognition's agreement with the universal and formal laws of understanding and reason — is indeed the conditio sine qua non, and so the negative condition of all truth: but here logic reaches its limit, and the error that strikes not the form but the content lies beyond the reach of any logical touchstone.

General logic, then, breaks the entire formal business of the understanding and of reason down into its elements, and presents them as the principles by which all our cognition is to be logically appraised. This part of logic may accordingly be termed analytic, and it is on that very account the at least negative touchstone of truth, inasmuch as one must first check and assess every cognition as to its form against these rules before examining it as to its content, so as to make out whether, in regard to the object, it holds any positive truth. But since the mere form of a cognition, however far it may square with logical laws, comes nowhere near to establishing the material (objective) truth of that cognition, no one may venture, on the strength of logic alone, to pass judgment on objects or to assert anything, without first having gathered well-grounded information about them from a source outside logic — reserving logic merely for the subsequent task of putting that information to use, of linking it into a connected whole by logical laws, or, better yet, of testing it against them. Even so, there is something so seductive in commanding such a plausible art — that of imparting to all our cognitions the form of the understanding, however empty and impoverished one may remain as to their content — that this general logic, a mere canon for appraisal, has been employed as though it were an organon for actually bringing forth objective assertions, or at any rate for putting on a deceptive show of them, and so has in truth been abused in the process. General logic, taken now as a supposed organon, is called dialectic.

However diverse the meanings in which the ancients applied this name to a science or an art, one may still infer with confidence, from the use they actually made of it, that in their hands it was nothing but the logic of illusion. It was an art of sophistry that lent to one's ignorance — indeed to one's willful deceptions — the semblance of truth, aping the method of thoroughness that logic prescribes across the board and turning its topics to the embellishment of every hollow proceeding. Now this may be set down as a sound and useful caution: that general logic, regarded as an organon, is at all times a logic of illusion — that is, dialectical. For since it instructs us in nothing at all concerning the content of a cognition, but only in the formal conditions of accord with the understanding — conditions, moreover, wholly indifferent with respect to the objects — the demand that one wield it as an instrument (organon) so as to broaden and extend one's knowledge, at least in appearance, must come to nothing more than idle talk, whereby one asserts whatever one pleases with a certain show of plausibility, or, if one prefers, contests it at will.

Instruction of that sort is in no way consonant with the dignity of philosophy. On that account, the term dialectic has instead been assigned to logic as a critique of dialectical illusion, and it is in this sense that we too would have it understood here.

IV. On the Division of Transcendental Logic into Transcendental Analytic and Dialectic

Within a transcendental logic we set the understanding apart (just as, above, sensibility was set apart in the transcendental aesthetic), and we extract from our cognition merely that portion of thinking whose origin lies solely in the understanding. Yet the use of this pure cognition rests, as its condition, upon this: that objects be given to us in intuition, to which the former may be applied. For in the absence of intuition all our cognition lacks objects, and then remains wholly empty. That part of transcendental logic, then, which presents the elements of pure understanding-cognition together with the principles without which no object at all can be thought, constitutes the transcendental analytic, and is likewise a logic of truth. For no cognition can conflict with it without at the same time surrendering all its content, that is, all relation to any object whatsoever, and thus all truth. But because it is exceedingly alluring and seductive to make use of these pure cognitions and principles of the understanding on their own, and even beyond the bounds of experience—which alone, after all, can put into our hands the matter (objects) on which those pure concepts of the understanding might be brought to bear: the understanding thereby runs the risk of putting the merely formal principles of pure understanding to a material use by means of empty ratiocinations, and of judging without distinction about objects that are nonetheless not given to us, indeed that perhaps can in no way be given at all. Since it ought properly to be nothing more than a canon for appraising the empirical use, it is abused when one permits it to serve as an organon for a universal and unrestricted use, and when, with the pure understanding alone, one ventures to judge, assert, and decide synthetically about objects in general. The use of the pure understanding would in that case be dialectical. The second part of transcendental logic must accordingly consist in a critique of this dialectical illusion; it bears the name transcendental dialectic—not as an art of arousing such illusion dogmatically (an art unfortunately much in vogue among the manifold conjuring tricks of metaphysics), but as a critique of the understanding and of reason in respect of their hyperphysical use, so as to uncover the false illusion of their baseless pretensions and to bring their claims to discovery and extension—which they fancy themselves able to attain merely through transcendental principles—down to the mere appraisal and safeguarding of the pure understanding against sophistical delusion.

First Division. Transcendental Analytic

This analytic takes the whole of our a priori cognition and breaks it down into the elements that belong to the understanding's pure cognition. Here the matter turns on the following points: 1. That the concepts should be pure ones and not empirical. 2. That they pertain not to intuition and sensibility, but to thinking and the understanding. 3. That they are elementary concepts, and are clearly kept apart from those derived or compounded out of them. 4. That their table is complete, and that they exhaustively occupy the entire domain of pure understanding. Now, the completeness of a science cannot be assumed with any confidence from a rough tally of an aggregate thrown together merely by way of experiments; it is therefore possible solely through an idea of the whole of the understanding's a priori cognition, and through the division—determined by that idea—of the concepts that compose it, hence solely through their connection in a system. The pure understanding cuts itself off entirely, not merely from all that is empirical, but even from sensibility as such. It is thus a unity that subsists on its own, is sufficient unto itself, and is not to be augmented by any additions supervening from outside. For this reason the entire body of its cognition comes to make up a system that can be embraced and determined under one idea, whose completeness and articulation can serve simultaneously as a touchstone of the correctness and genuineness of every piece of cognition that fits within it. This whole part of transcendental logic, however, consists of two books, of which the one contains the concepts, the other the principles of the pure understanding.

First Book. Analytic of Concepts

By the analytic of concepts I understand not their analysis, nor the usual procedure in philosophical inquiries of taking apart concepts as they offer themselves and unfolding their content until they become distinct, but rather the still barely attempted dissection of the faculty of understanding itself, in order thereby to explore the possibility of concepts a priori by tracking them down in the understanding alone, as their birthplace, and analyzing its pure employment as such; for this is the distinctive business of a transcendental philosophy; the remainder is the logical handling of concepts in philosophy at large. Accordingly we shall pursue the pure concepts down to their earliest germs and predispositions in the human understanding, where they lie in readiness until at length, prompted by experience, they are unfolded and, by this very same understanding, freed from the empirical conditions that cling to them, set forth in their purity.

Chapter 1. On the clue to the discovery of all pure concepts of the understanding

Whenever a cognitive faculty is brought into play, various concepts emerge in response to the several occasions that prompt them, concepts that make this faculty recognizable and that can be assembled into a more or less exhaustive essay, once one has observed them over a longer stretch of time or with greater acuteness. On such a quasi-mechanical procedure it can never be settled with certainty just where this inquiry will have reached completion. Moreover, the concepts one merely happens upon in this way, as the occasion offers, disclose themselves in no order and systematic unity, but end up merely paired by resemblance and ranged into series according to how much they contain, running from the simplest up to the more composite ones, series produced in a fashion that is anything but systematic, however methodical it may be in a certain respect.

Transcendental philosophy enjoys the advantage, but also incurs the obligation, of tracking down its concepts by a principle, since they issue pure and unmixed from the understanding as an absolute unity and hence must, in accordance with some concept or idea, cohere among themselves . Such an interconnection, however, puts into our hands a rule by which every pure concept of the understanding can be assigned its place, and all of them together their completeness, a priori — all of which would otherwise be left to preference or to chance.

Section 1. On the logical use of the understanding in general

Above, the understanding was explained in a merely negative fashion: through a nonsensible cognitive faculty. Yet no intuition can fall to our share independently of sensibility. Consequently the understanding is not a power of intuition. Aside from intuition, though, cognition is possible in no other manner than by way of concepts. The cognition belonging to any understanding — the human one at any rate — is thus conceptual cognition, discursive rather than intuitive. Since all intuitions are sensible, they depend upon affections, and concepts accordingly upon functions. By a function I understand here the unity of the act of ordering diverse representations beneath a single shared one. Concepts, then, are grounded in the spontaneity of thought, just as sensible intuitions are grounded in a receptivity to impressions. Of such concepts the understanding is able to make but a single use, namely to form judgments by their means. Because intuition alone bears directly upon its object, while no other representation does, a concept is applied to an object never directly but always through some further representation of that object (be this an intuition or perhaps already a concept in its own right). A judgment, accordingly, is the mediate cognition of an object, and so the representation of a representation of the same. Every judgment contains some concept valid for a plurality, and within that plurality it encompasses a given representation as well — and it is this representation, in the end, that bears directly upon the object. So, for instance, in the judgment: all bodies are divisible, the concept of divisibility bears upon a range of further concepts; out of these, though, it is on this occasion linked especially with the concept of body, and the latter with certain appearances presented to us. By the concept of divisibility, then, these objects come to be represented in a mediate way. Every judgment, on this showing, is a function of unity among our representations, inasmuch as the cognition of the object proceeds not from an immediate representation but from a superior one that embraces both it and several besides, so that a multitude of possible cognitions gets contracted within a single one. Now every operation of the understanding admits of being reduced to judgments, with the result that the understanding as such can be conceived as a capacity to judge. For, as emerged above, it is a capacity to think. And to think is to cognize by means of concepts. Concepts, for their part, function as predicates of possible judgments and so refer to some representation or other of an object not yet determined. The concept of body, for example, stands for something — metal, say — cognizable by means of that very concept. It qualifies as a concept solely because further representations fall under it, and it is through these that it manages to reach objects at all. Hence it serves as the predicate of some possible judgment — for instance, all metal is body. The whole set of the understanding's functions may accordingly be discovered, provided one succeeds in laying out exhaustively the functions of unity at work in judgments. And that this is in fact perfectly feasible the next section will make plain.