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.

Section 2. On the logical function of the understanding in judgments. §9

If we set aside the entire content of a judgment as such and attend solely to the mere form contributed by the understanding, we discover that the function of thought within it can be brought under four titles, each of which harbors three moments under itself. These may fittingly be laid out in the following table.

Since this division seems to diverge, on a few points—though not on essential ones—from the accustomed procedure of the logicians, the following safeguards against a misunderstanding one might worry about will not be superfluous.

1. The logicians are correct in saying that, when judgments are employed in syllogisms, singular judgments may be handled just like universal ones. For on precisely this ground—that they have no extension at all—the predicate of such a judgment cannot be applied to only a part of what the subject-concept comprehends while being denied of another part. It thus applies to that concept without any exception, exactly as though the concept were a commonly valid one endowed with an extension over the whole of whose meaning the predicate is valid. If, on the other hand, we compare a singular judgment with a commonly valid one simply as a cognition, in respect of its magnitude, it then stands toward the latter as a unit stands toward infinity, and is thus, in and of itself, essentially distinct from it. Accordingly, if I estimate a singular judgment (judicium singulare) not only in terms of its inner validity but also as a cognition generally, in terms of the magnitude it has when set beside other cognitions, it is certainly to be distinguished from commonly valid judgments (judicia communia) and merits a distinct place within a full table of the moments of thought in general (though of course not within a logic confined merely to the reciprocal use of judgments among one another).

2. In a transcendental logic, similarly, infinite judgments have still to be kept apart from affirmative ones, notwithstanding that general logic properly reckons them together with the latter and treats them as no distinct member of the division. For general logic leaves out of account the entire content of the predicate (however negative that content may be) and looks solely to whether it is ascribed to the subject or, on the contrary, set against it. Transcendental logic, by contrast, weighs the judgment also in respect of the value or content of this logical affirmation effected through a predicate that is merely negative, and of the gain that such affirmation yields for cognition taken as a whole. Had I declared of the soul, it is not mortal, then through a negative judgment I would at least have averted an error. Now, by the proposition "the soul is non-mortal," I have, as far as logical form goes, actually affirmed something, inasmuch as I place the soul within the unlimited extension of non-mortal beings. Now since, of the whole extension of possible beings, the mortal makes up one part and the non-mortal the other, my proposition says nothing more than that the soul is one among the infinite multitude of things that remain once I remove everything mortal. By that means, though, the infinite sphere of everything possible is restricted only insofar as the mortal is cut away from it, while the soul finds its place in the space that remains within its extension. This space, however, even under such an exception, goes on being infinite, and yet more of its parts can be removed without the concept of the soul growing in the slightest or being determined affirmatively. These infinite judgments, then, with regard to logical extension are in truth merely limiting with regard to the content of cognition as such, and to this extent they may not be omitted from the transcendental table of every moment of thought in judgments, because the function of the understanding exercised in them could well be of importance within the field of its pure a priori cognition.

3. All the relations of thought within judgments are: a) that which the predicate bears to the subject, b) that which the ground bears to the consequence, c) that which the divided cognition and the gathered members of the division bear to one another. In judgments of the first sort only two concepts stand in relation, in those of the second two judgments, and in those of the third a plurality of judgments set over against one another . The hypothetical proposition—"if a perfect justice exists, then the obstinately wicked man is punished"—really holds within it the relation of two propositions: a perfect justice exists, and: the obstinately wicked man is punished. Whether both of these propositions are true in themselves is left undecided here. It is only the consequence that is thought through this judgment. Lastly, the disjunctive judgment holds a relation between two or more propositions set against each other—not, however, a relation of consequence, but one of logical opposition, since the sphere of the one shuts out that of the other, though at the same time a relation of community, since jointly they occupy the sphere of the cognition properly meant—and so a relation among the parts of one cognition's sphere, given that each part's sphere serves to supplement the sphere of the other toward the entire compass of the cognition that has been divided; for example, the world is there either by a blind accident, or by inner necessity, or by some external cause. Each of these propositions takes up a portion of the sphere of possible cognition regarding the existence of a world as such, and all of them jointly take up the entire sphere. To withdraw the cognition out of one of these spheres amounts to setting it in one of the remaining ones, and, conversely, to set it in one sphere amounts to withdrawing it from the rest. In a disjunctive judgment, accordingly, there obtains a certain community among the cognitions, which lies in their reciprocally excluding one another and yet, precisely thereby, determining as a whole the true cognition, since taken together they constitute the whole content of a single given cognition. And this too is all that I find it necessary to note here for the sake of what follows.

4. The modality of judgments is an altogether special function of theirs, marked off by the fact that it adds nothing to the content of the judgment (for apart from magnitude, quality, and relation nothing else remains that might constitute a judgment's content), but bears only on the worth of the copula with reference to thought in general. Problematic judgments are those in which one takes the affirming or denying to be merely possible (optional); assertoric ones, where it is regarded as actual (true); apodictic ones, in which one views it as necessary.¹¹ So the two judgments whose relation makes up the hypothetical judgment (antec. and consequ.), and equally those on whose reciprocal interplay the disjunctive judgment rests (the members of the division), are one and all merely problematic. In the example given above, the proposition "a perfect justice exists" is stated not assertorically but merely thought as an optional judgment that someone could possibly embrace; and the consequence alone is assertoric. Such judgments may therefore even be manifestly false and nonetheless, taken problematically, serve as conditions for the cognition of truth. So the judgment the world is there through a blind accident carries, within the disjunctive judgment, only a problematic import—namely that someone might, for an instant, take up this proposition—yet it still serves (much as marking out the wrong path among all those that might be taken) to locate the right one. The problematic proposition is thus the one giving voice merely to logical possibility (a possibility that is not objective), i.e., an unconstrained choice to let such a proposition count as valid, a purely arbitrary taking of it up into the understanding. The assertoric proposition tells of logical actuality or truth—as, for example, in a hypothetical syllogism the antecedent figures problematically in the major premise but assertorically in the minor—and signals that the proposition is already conjoined with the understanding in accordance with its laws. The apodictic proposition conceives the assertoric one as itself determined by these laws of the understanding, and hence as affirming a priori, and in this manner gives expression to logical necessity. Since here everything gets incorporated into the understanding step by step—so that one at first judges a thing problematically, then goes on to take it as assertorically true, and at last affirms it as inseparably tied to the understanding, i.e., as necessary and apodictic—these three functions of modality may correspondingly be named just so many moments of thought in general.

§10. 3. Section. On the pure concepts of the understanding, or categories.

General logic, as has been noted more than once, leaves out of account the entire content of cognition and looks to have representations furnished to it from some other quarter, no matter its source, so as first to turn these into concepts—a procedure that is analytic. Transcendental logic, by contrast, has lying before it a manifold of sensibility a priori, which the transcendental aesthetic presents to it in order to supply a material for the pure concepts of the understanding, without which they would be devoid of all content and hence entirely empty. Now space and time do contain a manifold of pure intuition a priori, but they belong all the same to those conditions of our mind's receptivity under which alone it is able to take in representations of objects, and which must accordingly, on every occasion, affect the concept of those objects as well. But the spontaneity of our thought demands that this manifold be run through, absorbed, and joined together in a particular manner before a cognition can be produced from it. This act I call synthesis.

By synthesis, however, taken in its most general sense, I understand the act of adding various representations to one another and of grasping their manifoldness in a single cognition. A synthesis of this sort is pure if what is given as manifold is not empirical but a priori (as holds for the manifold in space and in time). Before any analysis of our representations can take place, the representations themselves have to be given beforehand, and by no analytic route can concepts spring up as far as their content goes. But it is the synthesizing of a manifold (no matter whether that manifold be furnished empirically or a priori) that first gives rise to a cognition—one which to begin with may well be crude and muddled, and so calls for analysis; synthesis, all the same, is what truly assembles the elements into cognitions and draws them together into some determinate content; and it is thus the first matter we have to heed when we set out to judge about the earliest origin of our cognition.

Synthesis in general is, as we shall see in what follows, the mere effect of the imagination, a blind though indispensable function of the soul, without which we would have no cognition whatsoever, yet one of which we are seldom even once conscious. But the raising of this synthesis to concepts is a function that pertains to the understanding, and it is by this function that the understanding first supplies us with cognition in the strict sense.

Pure synthesis, represented in general terms, now yields the pure concept of the understanding. The synthesis I have in mind here, however, is the one grounded in an a priori basis of synthetic unity: our counting, for instance (more perceptibly so with larger numbers), is a synthesis according to concepts, for it is carried out on a shared basis of unity (say, the decimal system). Under this concept, then, the unity in the synthesis of the manifold becomes necessary.

Analytically, various representations are brought under a single concept (a business with which general logic deals). But transcendental logic teaches how to bring to concepts not the representations, but the pure synthesis of the representations. What must be given to us a priori in the first place, for the sake of cognizing any object whatever, is the manifold that pure intuition supplies; the synthesis of this manifold through the imagination comes second, though as yet it affords no cognition. The concepts that lend unity to this pure synthesis, having their whole being in the representing of that necessary synthetic unity, supply the third ingredient needed for the cognition of an object that comes before us, and they have their seat in the understanding.

The very function that confers unity upon the several representations within a judgment likewise confers unity upon the mere synthesis of several representations within an intuition, a unity which, stated in general terms, is termed the pure concept of the understanding. The same understanding, therefore, and indeed through the very same acts by which, in concepts, it brought about the logical form of a judgment by means of analytic unity, likewise imports—through the synthetic unity that the manifold possesses in intuition at large—a transcendental content into its representations, on account of which they are termed pure concepts of the understanding that bear a priori upon objects—something general logic cannot accomplish.

In just this way there spring up precisely as many pure concepts of the understanding, bearing a priori upon objects of intuition at large, as the previous table held logical functions across all possible judgments: for the understanding is fully drained by those functions, and its capacity thereby completely surveyed. Following Aristotle, we shall call these concepts categories, since our aim is at bottom identical with his, however far it may depart from his in its execution.

This, then, is the register of all the originally pure concepts of synthesis that the understanding contains within itself a priori, and on account of which alone it is a pure understanding, since through them alone it can understand something in the manifold of intuition, that is, think an object of it. This classification is brought forth systematically out of a single shared principle—that is, the power of judging (which comes to the same thing as the power of thinking)—and was not thrown together rhapsodically from a hit-or-miss hunt after pure concepts, whose full tally one could never vouch for, given that it is arrived at only by way of induction—leaving aside that this latter route never lets one grasp why it should be just these concepts, and no others, that inhabit the pure understanding. It was an undertaking worthy of an acute man, this attempt of Aristotle to seek out these basic concepts. But since he possessed no principle, he snatched them up as they came his way, and rounded up ten of them at first, which he named categories (predicaments). Afterward he believed he had turned up five more, which he appended under the name of post-predicaments. Yet his table still remained defective. Besides, there are also found among them several modi of pure sensibility (quando, ubi, situs, likewise prius, simul), as well as one empirical modus (motus), which do not belong at all in this ancestral roster of the understanding; or else derived concepts are counted in among the original ones (actio, passio), and some of the latter are missing altogether.

With a view to the latter, then, one thing more should be noted: that the categories, being the genuine root concepts of the pure understanding, likewise possess their own equally pure derived concepts, such as could in no wise be left aside in any full system of transcendental philosophy, though for a merely critical essay I may be satisfied with barely mentioning them.

Permit me to name these pure but derived concepts of the understanding the predicables of the pure understanding (in contrast to the predicaments). Once one has the original and primitive concepts, the derived and subordinate ones can readily be added and the genealogical tree of the pure understanding fully filled out. Because my concern here is not the system's completeness but only the principles that a system requires, I put off this filling-in for a different occasion. One can, however, fairly well attain this aim by taking up the ontological textbooks and subordinating, for example, to the category of causality the predicables of force, of action, of passivity; to that of community those of presence, of resistance; to the predicaments of modality those of coming to be, of passing away, of alteration, and so forth. The categories, combined with the modis of pure sensibility or also with one another, yield a great multitude of derived concepts a priori, which it would be a useful and not disagreeable, though here dispensable, labor to note and, where possible, to catalogue to the point of completeness.

I deliberately spare myself, in this treatise, the definitions of these categories, even though I might well be in possession of them. In the sequel I shall analyze these concepts only so far as suffices for the purposes of the doctrine of method on which I am at work. Within a system of pure reason such definitions could with justice be required of me: here, however, they would merely pull the inquiry's principal point from view, stirring up doubts and objections that one may perfectly well defer to another undertaking without robbing the essential aim of anything. Meanwhile, it emerges clearly from the little I have adduced on this matter that a complete dictionary, with all the requisite explanations, is not only possible but also easy to bring about. The pigeonholes stand ready; all that remains is to fill them in, and a systematic topic like the one before us seldom lets the proper place of any given concept be missed—the place peculiarly its own—while at the same time making it easy to spot whichever place still stands empty.

§11.

This table of the categories invites a number of nice reflections that could conceivably carry weighty consequences for the scientific shape of every rational cognition. For it is self-evident that this table proves extraordinarily useful—indispensable, even—in philosophy's theoretical part for laying out in full the plan for the whole of a science, so far as that science rests on a priori concepts, and for systematically dividing it up along determinate principles: this is plain from the very fact that the table in question holds every elementary concept of the understanding in full, and holds indeed the form of a system of them within the human understanding, thereby furnishing guidance as to all the moments of any projected speculative science, and even as to their order, of which I have moreover supplied a specimen elsewhere.¹² Here, then, are a few of these observations.

The first is: that this table—comprising, as it does, four classes of the understanding's concepts—admits of being separated at the outset into two sections, the earlier of which bears on objects of intuition (pure no less than empirical), whereas the latter bears on the existence of those objects (whether in their relation to one another or to the understanding).

The first class I would name that of the mathematical, the second that of the dynamical categories. As one can see, the first class is without correlates, such correlates being encountered solely within the second class. A distinction like this must, after all, rest on some ground lying in the understanding's own nature.

2nd Remark. That everywhere there is an equal number of categories in each class, namely three, which likewise invites reflection, since otherwise every division a priori through concepts must be a dichotomy. To this, moreover, is added that the third category arises throughout from the combination of the second with the first of its class.

Thus totality (Totalität) is simply plurality considered under the aspect of unity; limitation simply reality taken together with negation; community, the causality exercised reciprocally by one substance in determining another; and necessity, finally, simply that existence which possibility itself already yields. But let one by no means suppose that the third category is on that account a merely derived concept and not a root concept of the pure understanding. For uniting the first and the second in order to yield the third concept calls for a distinctive act on the understanding's part, one not the same as the act performed with the first and the second. Thus a number (a concept falling under the category of totality) is not invariably possible wherever the concepts of multitude and of unity occur (for example, in representing the infinite); nor, merely because I couple the concept of a cause with the concept of a substance, is the influence thereby straightaway intelligible—that is, how one substance may come to cause something in another. From this it is evident that a special act of the understanding is required for it, and likewise with the rest.

3rd Remark. For one category alone—that of community, standing under the third heading—the accord with the form of a disjunctive judgment answering to it in the table of the logical functions is not as plainly evident as it is with the rest.

To make sure of this agreement, one has to observe the following: that in every disjunctive judgment the sphere (that is, the totality of all that falls under it) is represented as a whole partitioned into parts (the concepts subordinate to it), and that, since no one of them can be contained beneath another, they are conceived as coordinated with one another rather than subordinated, so that they determine one another not unilaterally, as within a series, but reciprocally, as within an aggregate (such that positing one member of the division excludes all the rest, and vice versa).

Now a comparable linkage is thought within a whole of things, inasmuch as no one thing is subordinated, qua effect, to another as the ground of its existence, but each is instead coordinated with the rest, at once and reciprocally, as a cause bearing on the determination of the others (for instance, in a body whose parts mutually draw and likewise resist one another); and this is an altogether different mode of linkage from the one we find in the bare relation of a cause to its effect (of a ground to what follows from it), where the consequence does not reciprocally determine its ground in turn, and hence forms no whole together with it (as the world's creator forms none with the world). The very procedure the understanding follows when it represents to itself the sphere of a divided concept, it observes as well when it thinks a thing as divisible; and just as the members of the division in the former exclude one another and yet stand combined in one sphere, so it pictures to itself the parts of the latter as items whose existence (as substances) accrues to each apart from the others, and yet as bound together in one whole.

§12.

In the transcendental philosophy of the ancients, however, there is found yet another chief part that contains pure concepts of the understanding which, although they are not counted among the categories, are nonetheless supposed to hold, on a par with them, as concepts a priori of objects—in which case, however, they would augment the number of the categories, which cannot be. It is the proposition so celebrated among the schoolmen that gives voice to this: quodlibet ens est unum, verum, bonum. Now although the use of this principle with regard to its inferences (which yielded nothing but tautological propositions) turned out very meagre, so that in more recent times it has come to be set up in metaphysics almost merely for honor's sake, still a thought that has sustained itself for so long a time, however empty it may appear, always merits an investigation of its origin and justifies the surmise that its basis lies in some rule of the understanding—one that, as frequently occurs, has simply been misinterpreted. These allegedly transcendental predicates of things amount to nothing beyond logical requisites and criteria for every cognition of things as such, and they take as their foundation the categories of quantity—namely unity, plurality, and totality—save that these categories, which strictly would have to be understood materially, as pertaining to the possibility of the things themselves, were actually put to use only in a formal sense, as pertaining to the logical demand bearing on any cognition whatever, and thus these criteria of thinking were, without due caution, converted into properties of things in themselves. For in the cognition of any object there is a unity of the concept—one that may be termed qualitative unity so far as nothing more is thought under it than the oneness by which the manifold of the cognitions is drawn together, much as a single theme gives oneness to a play, an oration, or a fable. Secondly, truth with respect to the consequences. The more true consequences follow from a given concept, the more marks there are of its objective reality. One might designate this the qualitative plurality of those marks which pertain to a concept as their shared ground (and are not counted within it as a magnitude). Finally, thirdly, perfection, which consists in this, that conversely this plurality taken together leads back to the unity of the concept and accords completely with this concept and with no other, which one may call qualitative completeness (totality). Whence it becomes clear that these logical criteria of the possibility of cognition as such here convert the three categories of magnitude—wherein the unity in generating the quantum must throughout be assumed homogeneous—solely with an eye to the linkage of even heterogeneous pieces of cognition within one consciousness, by way of the quality of a cognition serving as principle. So it is that the criterion for a concept's possibility (not the possibility of its object) lies in the definition, wherein the concept's unity, the truth of all that can be drawn immediately from it, and lastly the completeness of what has been extracted from it together make up what the whole concept requires for its constitution; or, in like fashion, the criterion of a hypothesis consists in the intelligibility of the ground of explanation one assumes, that is, in its unity (with no ancillary hypothesis), in the truth (its concord with itself and with experience) of the consequences derivable from it, and lastly in the completeness with which that ground of explanation covers them, they pointing back to neither more nor less than was posited in the hypothesis, and rendering back through analysis, a posteriori, what had been conceived synthetically a priori, in agreement therewith. — And so the concepts of unity, truth, and perfection do not in the least round out the transcendental table of the categories, as if that table were somehow wanting, but merely, once the bearing of these concepts on objects has been wholly set to one side, bring our dealing with them under general logical rules for the accord of cognition with itself.

Chapter 2. On the Deduction of the Pure Concepts of Understanding

Section 1. §13 On the principles of a transcendental deduction in general.

When jurists speak of entitlements and of presumptions, they draw, within a legal dispute, a line between the question of right (quid iuris) and the question that turns on the matter of fact (quid facti); and because a proof is demanded for each, the first of these — the one charged with establishing the entitlement, or indeed the legal claim — is what they call the deduction. We make use of a host of empirical concepts without anyone's objection, and we consider ourselves entitled, even without a deduction, to assign to them a sense and a supposed meaning, because we have experience at hand at all times to prove their objective reality. There are, however, also usurped concepts, such as fortune, fate, which circulate with almost universal indulgence, yet are now and then challenged by the question: quid iuris, whereupon one is thrown into no small embarrassment regarding their deduction, since one can adduce no clear ground of right, from either experience or reason, by which the entitlement of their use would become evident.

But among the many concepts that go to compose the deeply intermixed web of human cognition, some are appointed for a pure employment a priori as well (in complete independence from all experience), and an entitlement of this kind stands in perpetual need of a deduction: since experiential proofs fall short of vindicating the lawfulness of such an employment, while one must still grasp how concepts of this sort can bear on objects that they draw from no experience whatever. Accordingly, the account of how concepts a priori manage to bear on objects is what I name their transcendental deduction, setting it apart from the empirical deduction, which shows the way in which a concept comes to be won through experience and through reflection upon experience, and which for that reason touches not the lawfulness but the fact out of which the possession has sprung.

At this point we already possess two sorts of concepts, wholly diverse in kind, that yet coincide in one respect: each of them bears on objects in a fully a priori manner — on the one side the concepts of space and time, taken as forms of sensibility, on the other the categories, taken as concepts of the understanding. Any wish to attempt an empirical deduction of these would prove wholly wasted effort, for the very mark that sets their nature apart consists in this, that they reach their objects without drawing anything from experience toward the representation of those objects. Should a deduction of them be required, then, it will have to be transcendental in every case.

With these concepts, as with all cognition, one may nevertheless search out in experience, if not the principle that makes them possible, then the occasioning grounds of how they come to be generated; here the sensory impressions supply the first prompting for unlocking the whole power of cognition in regard to them and for producing experience, a thing that holds within it two profoundly unlike ingredients — a matter for cognition, supplied by the senses, and a certain form by which that matter is ordered, springing from the inner wellspring of pure intuiting and thinking; and these, prompted by the occasion of the first, are set into operation for the first time and give rise to concepts. To follow up in this way the earliest strivings of our power of cognition, as it climbs from single perceptions upward to general concepts, is beyond doubt of great service, and it is to the renowned Locke that the credit belongs for first having thrown open this path. Yet by such means a deduction of the pure concepts a priori is never achieved; it does not lie on this road at all, for given their prospective employment — one meant to stand wholly free of experience — they are obliged to produce a birth certificate of a wholly different order than descent from experiences. This attempted physiological derivation — which in truth does not deserve the name of deduction at all, seeing that it bears on a quaestionem facti — I shall instead label the account of how a pure cognition comes to be possessed. It stands to reason, then, that for these alone a transcendental — and in no way an empirical — deduction is possible, and that where the pure concepts a priori are concerned the latter amounts to nothing but empty exertions, the sort of thing that can occupy only a person who has failed to grasp the wholly distinctive nature of these cognitions.

Now even granting that the one possible manner of deducing pure cognition a priori — namely by the transcendental route — is admitted, this still does not by itself make plain that such a deduction is so indispensably necessary. Earlier we pursued the concepts of space and of time back to their origins through a transcendental deduction, thereby setting out and fixing the objective validity they possess a priori. And yet geometry advances with confident stride by means of cognitions that are one and all a priori, never obliged to beg of philosophy any voucher attesting the pure and law-governed lineage of the basic concept it employs, that of space. But then, in this science the concept is put to work only upon the outer world of sense, for which space furnishes the pure form under which it is intuited; and just there, because it rests upon intuition a priori, every geometrical cognition carries immediate evidence, while the objects themselves come to be given in intuition, as to their form, through that very cognition a priori. With the pure concepts of the understanding, on the other hand, there sets in the inescapable requirement to seek a transcendental deduction for space no less than for the concepts themselves, since, inasmuch as what they say of objects is voiced not through predicates belonging to intuition and to sensibility but through pure thought a priori, they hold of objects at large apart from every condition of sensibility, and, having no footing in experience, can likewise point to no object in intuition a priori upon which to rest their synthesis ahead of all experience, so that they not only awaken misgivings as to how far their use is objectively valid and where its limits fall, but also lend an equivocal cast to that concept of space itself, being prone as they are to carry it past the bounds of sensible intuition — which is precisely why, above, a transcendental deduction of it too was called for. The reader, then, has to be brought to conviction concerning how indispensable such a transcendental deduction is, and this before ever he sets one foot within the domain of pure reason, for failing that he gropes his way in the dark and, once he has wandered this way and that, finds himself driven back to the very ignorance he started from. He must, however, discern clearly beforehand the difficulty that cannot be evaded, lest he grumble about darkness where the subject itself lies deeply enfolded, or lose heart too soon at the removal of the obstacles, for the alternative is stark: either to surrender outright every claim to insights of pure reason in its most cherished territory — the region lying past the frontiers of all possible experience — or else to carry this critical inquiry through to completeness.

In the earlier case, with space and time as our concepts, it cost us little trouble to render intelligible how these, being cognitions a priori, must for all that bear of necessity upon objects, and how they opened the way to a synthetic cognition of such objects owing nothing to experience. For seeing that an object can show itself to us — can be an object of empirical intuition — solely through such pure forms of sensibility, space and time count as pure intuitions which hold within them, a priori, the condition under which objects are possible as appearances, and the synthesis carried out within them is objectively valid.

The categories of the understanding, by contrast, set before us no conditions at all under which objects come to be given in intuition; consequently objects may well make their appearance to us without any necessity of their relating to functions of the understanding, and hence without the understanding's holding a priori the conditions of them. And so at this point a difficulty comes to light that had no counterpart in the domain of sensibility, the difficulty of grasping how subjective conditions of thought are to carry objective validity, that is, are to supply the terms on which any cognition of objects is possible at all: for even in the absence of functions of the understanding, appearances can still be furnished within intuition. Consider, say, the concept of a cause, by which is meant a synthesis of its own special sort, whereby to some A there is posited a wholly distinct B under a rule. There is no seeing a priori why appearances ought to harbor anything of that kind (experiences being unavailable as evidence here, inasmuch as the objective validity of this concept has to admit of proof a priori); and thus it remains open to a priori doubt whether such a concept may not be void through and through, encountering nowhere among the appearances an object to answer to it. That the objects of a sensible intuition have to accord with those formal conditions of sensibility that reside a priori in the mind is plain enough, for on any other footing they would fail to be objects for us at all; but that they must, beyond this, accord as well with the conditions the understanding stands in need of for thought's synthetic unity — that this follows is by no means so readily discerned. It is entirely conceivable, after all, that appearances be of such a make that the understanding should discover in them no agreement whatever with what its unity demands, everything lying in a confusion so complete that — to give an instance — the run of appearances offered up nothing capable of yielding a rule for synthesis, nothing answering to the concept of cause and of effect, in which case this concept would stand wholly hollow, void, and bereft of meaning. Appearances would go on presenting objects to our intuition all the same, since intuition has no need whatever of the functions of thought.

Should someone hope to wriggle free of the laboriousness of these inquiries by saying: experience holds out without cease instances of just such regularity among appearances, instances that afford ample occasion for lifting the concept of cause away from them and, in the same stroke, for making good the objective validity of a concept of that kind, then it escapes his notice that along this route the concept of cause can never take its rise, but must either find its ground wholly a priori in the understanding or else be given up entirely as a bare fancy of the brain. For what this concept demands, without exception, is that some A be so constituted that a further B ensue from it necessarily and in accordance with a rule of unqualified universality. Appearances do, to be sure, put before us cases out of which a rule may be framed telling us what commonly comes to pass, yet never one telling us that the result is necessary: and this is why there clings to the synthesis of cause with effect a certain dignity past all empirical rendering, the dignity, namely, whereby the effect is not simply appended to the cause but is set down through the cause and made to ensue out of it. That a rule should be strictly universal is, moreover, in no way a feature that empirical rules possess, for by way of induction such rules attain a universality that is merely comparative — an enlarged serviceability, that is to say. But then the whole employment of the pure concepts of the understanding would be transformed, were one minded to handle them as nothing more than empirical products.

§14. Transition to the transcendental deduction of the categories.

Just two cases, and no others, are possible in which a synthetic representation and the objects belonging to it can come together, stand necessarily related, and, so to speak, encounter one another: either when the object alone renders the representation possible, or when this latter alone renders the object possible. Should the first hold, then this relation is merely empirical, and such a representation can never be possible a priori. And that is precisely how matters stand with appearances, in respect of what within them pertains to sensation. Should the second case obtain, however — for a representation in its own right (its causality by way of the will being wholly beside the point here) does not produce its object as concerns that object's existence — the representation is still what determines a priori in respect of the object, provided that through it alone it becomes possible to cognize something as an object. Two conditions, though, and only under them, make the cognition of an object possible: first intuition, by which the object is given, though solely as appearance; second concept, by which one thinks an object answering to that intuition. Yet it is evident from what precedes that the first of these conditions — that under which objects can be intuited at all — does in truth underlie the objects, as to their form, a priori in the mind. With this formal condition of sensibility, then, all appearances necessarily accord, since only by means of it can they appear, that is, be empirically intuited and given. The question now presents itself whether concepts, too, do not run ahead a priori, serving as conditions under which alone a thing — even where it goes un-intuited — is nonetheless thought as an object as such; for then every bit of empirical cognition of objects must square with concepts of that kind, seeing that without presupposing them nothing whatever is possible as an object of experience. Now every experience holds within it, over and above the sensory intuition whereby something is given, a concept as well of an object presented in intuition or coming to appearance: accordingly, concepts of objects as such will underlie, as conditions a priori, all cognition drawn from experience: and so the objective validity of the categories, taken as concepts a priori, will turn on this — that through them alone experience (in respect of the form of thinking) is possible. For then they bear, necessarily and a priori, upon objects of experience, since it is only by their mediation that any object of experience can be thought at all.

Hence the transcendental deduction of all concepts a priori possesses a principle upon which the entire investigation has to be trained, this namely: that they must be acknowledged to be a priori conditions for the possibility of experience (whether of the intuition met with within it or of the thinking). Concepts that supply the objective ground for the possibility of experience are, on that very account, necessary. The elaboration of the experience wherein they are met with, however, constitutes not their deduction but their illustration, since therein they would after all be merely accidental . Lacking this original bearing upon possible experience, within which every object of cognition makes its appearance, one could form no conception whatever of how such concepts bear upon any object at all.

For lack of such reflection, and because he came upon pure concepts of the understanding amid experience, the renowned Locke derived these too from experience, and yet went to work so inconsistently that he ventured, by their means, upon attempts at cognitions reaching far past every frontier of experience. David Hume saw that, to be capable of the latter, it was requisite for these concepts to hold their origin a priori. But because he could in no way make it intelligible to himself how it should be possible that the understanding must think concepts — ones not, of themselves, conjoined within the understanding — as nevertheless necessarily conjoined in the object, and because it never struck him that the understanding might perhaps, by these very concepts, be itself the originator of the experience wherein its objects come to be encountered: pressed by need, he traced them back to experience (that is, to a subjective necessity sprung from repeated association in experience, one taken in the end, and falsely, for objective — namely, custom), though he thereafter proceeded quite consistently in pronouncing it impossible, with these concepts and the principles they set going, to press past the frontier of experience. That empirical derivation, however, which the two of them hit upon, will not square with the actuality of the scientific cognitions a priori that we do have — pure mathematics, that is, and general natural science — and is thus overturned by the fact itself.

The first of these two renowned men flung wide the gates to enthusiasm, for reason, once it has warrants on its side, will no longer be confined within bounds by indeterminate exhortations to moderation; the second delivered himself over wholly to skepticism, having believed he had once detected so universal a delusion of our cognitive faculty, a delusion that had been taken for reason. — We now find ourselves on the point of attempting to determine whether human reason might not be brought safely between these two reefs, be marked out with determinate limits, and nonetheless keep the entire field of its purposive activity thrown open before it.

Beforehand I mean only to preface an account of the categories. They are concepts of an object as such, whereby the intuition of that object, in regard to one of the logical functions for judging, comes to be regarded as determined. The function of the categorical judgment, for one, lay in the relation between a subject and its predicate — for instance, all bodies are divisible. Regarding the merely logical employment of the understanding, however, it stayed open which of the two concepts one would care to assign the function of subject, and to which that of predicate. For one may just as well say: some divisible thing is a body. Once, however, the concept of a body is subsumed under the category of substance, it is thereby settled that this body's empirical intuition must, in experience, be taken always as subject only and never as a bare predicate; and so throughout all the remaining categories.

Section 2. Transcendental deduction of the pure concepts of the understanding. §15–27

§15. On the possibility of combination as such.

A manifold of representations may be given within an intuition that is nothing but sensible — mere receptivity, that is — and this intuition's form may reside a priori in our representational capacity while amounting to nothing more than the way the subject undergoes affection. Yet the combination (conjunctio) of any manifold whatever can never enter us by way of the senses, and for that reason cannot lie already included within the pure form of sensible intuition; for combination is an act of the spontaneity belonging to the power of representation, and because this power, as against sensibility, has to be named understanding, every combination alike — whether or not it rises to our consciousness, whether what it joins is the manifold of intuition or instead a plurality of concepts, and, in the former case, whether the intuition be sensible or not — counts as an operation of the understanding, one to which we would attach the blanket term synthesis, thereby marking at once that nothing can be represented by us as conjoined in the object unless we have first conjoined it ourselves, and that combination stands out among all representations as the sole one incapable of being given through objects, since the subject alone can perform it, it being an act of that subject's own activity. It is easy to notice at this point that such an action must be original, single, and of equal force for every combination, and that decomposition — analysis — though seemingly its contrary, in fact always takes it for granted; for wherever the understanding has combined nothing beforehand, there too it has nothing to undo, since only through it could anything reach the power of representation as already combined.

The concept of combination, however, brings along with it — over and above the concepts of the manifold and of its synthesis — the further concept of that manifold's unity. To combine is to represent the synthetic unity of a manifold.¹³ This unity's representation, then, cannot spring from the act of combining; rather it is by attaching itself to the representation of the manifold that it first renders the very concept of combination possible. Such unity, going before every concept of combination a priori, is certainly not the category of unity treated in §10; for the categories one and all rest upon logical functions of judgment, and within these, combination — and with it the unity of the concepts given — is something already thought. So the category, for its part, already takes combination for granted. This unity (a qualitative one, §12) must accordingly be sought at a still higher level — in whatever it is that supplies the ground for uniting distinct concepts within judgments, and thereby for the understanding's very possibility, its logical employment included.

§16. Concerning the originally-synthetic unity of apperception.

It must be possible for the I think to accompany every one of my representations; for otherwise something would be represented within me that could not be thought whatsoever — which comes to saying that the representation would be either impossible or, at the least, nothing so far as I am concerned. A representation that can be given before any thinking whatever is termed intuition. Hence the entire manifold of intuition bears a necessary relation to the I think within the very subject in which that manifold is met with. This representation, though, is an act of spontaneity; in other words, it cannot be counted as part of sensibility. I name it pure apperception so as to set it apart from empirical apperception, or else original apperception, seeing that it is the self-consciousness which, in bringing forth the I think, a representation bound to be able to accompany every other and remaining identical throughout all consciousness, can itself be accompanied by no representation beyond it. Its unity, too, I label the transcendental unity of self-consciousness, doing so to signal that a priori cognition may be drawn from it. For the several representations handed over in some given intuition would not, taken together, be mine were they not, taken together, to belong to a single self-consciousness; which is to say that, precisely as my representations (even where I have no consciousness of them as such), they must yet, and of necessity, meet the condition under which alone they are able to stand alongside one another within a single universal self-consciousness — for otherwise they would not belong throughout to me. From this original combining, a great deal follows.

Namely: this thoroughgoing sameness of apperception, in the case of a manifold supplied through intuition, harbors a synthesis of representations and becomes possible solely by means of the consciousness of that synthesis. For empirical consciousness, which attends now this and now that representation, is by itself scattered and bears no relation to the subject's sameness. That relation, accordingly, is not yet established merely because I accompany each representation with consciousness; it arises rather because I annex one representation to another and grow conscious of their synthesis. And so it is only by being able to combine a manifold of given representations within one consciousness that I am in a position to represent to myself the identity of the consciousness in these representations; put otherwise, the analytic unity of apperception can obtain only on the assumption of some synthetic unity or other.¹⁴ Thus the thought that these representations, given in intuition , one and all pertain to me signifies just this — that I bring them together in a single self-consciousness, or can at least bring them together there; and although that thought is not yet itself the consciousness of the representations' synthesis, it does presuppose the latter's possibility; that is, it is only in so far as I am able to comprehend their manifold within one consciousness that I title them, collectively, my representations — for otherwise I should possess a self as motley and varied as the representations of which I am conscious. The synthetic unity of the manifold belonging to intuitions, given as it is a priori, therefore forms the ground of apperception's own identity, an identity that goes a priori before all my determinate thinking. Combination, though, has no seat in the objects, nor can it be borrowed from them — through perception, say — and thereby first taken up into the understanding; instead it is exclusively a doing of the understanding, which is itself nothing beyond the capacity to combine a priori and to bring the manifold of given representations under apperception's unity — a principle that ranks as the highest in the whole of human cognition.

This principle of the necessary unity of apperception is, to be sure, itself an identical proposition, and so analytic; yet it announces as necessary a synthesis of the manifold given within an intuition, apart from which that thoroughgoing sameness of self-consciousness would be unthinkable. For the I, as a simple representation, yields nothing manifold; only in intuition, which differs from it, can a manifold be given, and be thought by means of combination within a single consciousness. An understanding whose self-consciousness would at once furnish the whole manifold would intuit; ours, by contrast, is able only to think, and has to look to the senses for its intuition. I am conscious, then, of the selfsame I as regards the manifold of representations delivered to me in an intuition, for the reason that I designate them, every one, my representations constituting a single one. But that comes to saying that I am aware a priori of a necessary synthesis of them — the so-called original synthetic unity of apperception — beneath which every representation given to me falls, though they must also be brought beneath it by way of a synthesis.

§17. The principle of the synthetic unity of apperception is the highest principle for every use of the understanding.

As the transcendental aesthetic had it, the highest principle governing the possibility of all intuition, taken with respect to sensibility, ran thus: that every manifold of intuition falls under the formal conditions of space and time. The highest principle of that same possibility, taken now with respect to the understanding, runs: that every manifold of intuition falls under conditions of the originally synthetic unity of apperception.¹⁵ Beneath the first fall all the manifold representations of intuition in so far as they are given to us; beneath the second, in so far as they must admit of being combined within a single consciousness — for lacking this nothing could be thought or cognized through them at all, since the given representations would not share the apperceptive act, the I think, and so would fail to be gathered into one self-consciousness.

Understanding, broadly put, is the faculty of cognitions. A cognition consists in the determinate relating of given representations to an object. An object, for its part, is that within whose concept the manifold of some given intuition stands united. But every uniting of representations demands unity of consciousness within their synthesis. It follows that unity of consciousness is the sole thing establishing representations' relation to an object — and thus their objective validity, and thus their attaining to cognition — so that upon it, in turn, the understanding's own possibility depends.

The very first pure cognition of the understanding, then — the one supporting all its further use, and at the same time wholly free of every condition of sensible intuition — is precisely the principle of that original synthetic unity of apperception. The bare form of outer sensible intuition — space — is thus not yet any cognition whatever; all it furnishes is the manifold of intuition a priori, material for a possible cognition. To cognize anything at all in space — a line, for instance — I must draw it, and so produce synthetically a determinate combining of the given manifold, in such a way that the unity of this act coincides with the unity of consciousness (in the concept of a line), whereby an object — a determinate space — first comes to be cognized. Synthetic unity of consciousness is on this account an objective condition of all cognition — not simply one I require for myself if I am to cognize an object, but one to which every intuition is subject in order to become an object for me, since apart from it, by any other route, the manifold would not come together within a single consciousness.

This latest proposition is, as I said, analytic in its own right, notwithstanding that it turns synthetic unity into the condition of all thought; for it asserts no more than this: that all my representations in any given intuition must fall under the condition that alone allows me to ascribe them, as my representations, to the selfsame I, and hence — as synthetically combined in a single apperception — to sum them up in the general formula I think.

Still, this principle is not one for every conceivable understanding as such, but holds only for that understanding whose pure apperception, in the representation I am, delivers as yet nothing manifold whatever. An understanding whose self-consciousness would at the same stroke supply the manifold of intuition — an understanding by whose representing the objects of that representation would simultaneously come to exist — would have no need of any special act of synthesizing the manifold for the sake of consciousness's unity, an act which the human understanding, thinking merely and not intuiting, does stand in need of. For the human understanding, however, it remains inescapably the first principle — so much so that this understanding cannot frame even the slightest concept of some other possible understanding, be it one that itself intuited, or one grounded in a sensible intuition of a sort differing from that in space and time.

§18. What objective unity of self-consciousness amounts to.

The transcendental unity of apperception is the one through which the whole manifold given within an intuition gets united into a concept of the object. On that score it earns the name objective, and is to be kept apart from the subjective unity of consciousness — a determination of inner sense — whereby the said manifold of intuition is furnished empirically for a combination of that kind. Whether my empirical consciousness of the manifold takes it as coexistent or as sequential turns on circumstances, on empirical conditions ; and so the empirical unity of consciousness, resting on association of representations, bears itself upon an appearance and is thoroughly contingent. By contrast the pure form of intuition in time — taken merely as intuition in general, one that holds a given manifold — falls beneath the original unity of consciousness purely through the necessary reference of intuition's manifold to the single I think, and therefore through the understanding's pure synthesis, which grounds the empirical synthesis a priori. That unity, and it alone, holds objectively; the empirical unity of apperception, left aside here, and in any case derived from the former only under given conditions in concreto, carries subjective validity only. This man ties the representation of a given word to one thing, that man to another; and where the empirical is concerned, the unity of consciousness does not, as regards what is given, hold necessarily and for all.

§19. In every judgment the logical form lies in the objective unity of apperception among the concepts it contains.

Never have I found satisfaction in the account the logicians offer of judgment as such: a judgment, so they say, is the representation of a relation holding between two concepts. Setting aside any dispute with them over the flaw in this account — that it suits, at best, only categorical judgments and not the hypothetical and disjunctive ones (these last enclosing a relation not of concepts but of judgments themselves) — and passing over the several vexing consequences that this lapse has bred for logic ¹⁶, I note merely that just what this relation amounts to goes here undetermined.

Yet once I look more nearly into how the given cognitions stand related within each judgment, marking off this relation — as one owing to the understanding — from the relation that follows laws of the reproductive imagination (a relation with subjective validity only), I discover that a judgment is nothing else than a way of bringing given cognitions under the objective unity of apperception. Toward that very thing the small copula is in them is directed, marking off the objective unity of given representations from the subjective one. For that word signals their relation to the original apperception together with their necessary unity, even where the judgment is itself empirical and thus contingent — e.g., bodies are heavy. By this I certainly do not intend that within the empirical intuition these representations belong necessarily to one another; my point is that they belong together by virtue of the necessary unity of apperception in the synthesis of intuitions — that is, by principles governing the objective determination of all representations so far as cognition may issue from them, principles every one of which flows from the principle of the transcendental unity of apperception. It is by this alone that the relation turns into a judgment, i.e., into a relation that is objectively valid and adequately marked off from the relation of those same representations wherein validity would be merely subjective — by laws of association, say. On the latter I could say no more than this: when I bear a body, I sense a pressure of heaviness; yet not: it, the body, is heavy; for this last comes to saying that the two representations are joined in the object itself — irrespective of the subject's state — and are not merely found together in perception, however often that may recur.

§20. Every sensible intuition falls beneath the categories, these being the conditions under which alone its manifold can gather into a single consciousness.

Whatever manifold is given within a sensible intuition falls, of necessity, beneath the original synthetic unity of apperception, since through it alone is the unity of intuition made possible (§17). But the act of the understanding whereby the manifold of given representations — be they intuitions or be they concepts — is gathered beneath an apperception in general is just the logical function of judgment (§19). Hence the whole manifold, in so far as it is given within one empirical intuition, stands determined in regard to one among the logical functions of judging — the very one by which it gets carried up to a consciousness in general. But the categories are nothing else than these functions of judging themselves, taken in so far as a given intuition's manifold stands determined in regard to them (§10). And so the manifold in a given intuition likewise falls, of necessity, beneath categories.

§21. Remark.

A manifold held within an intuition that I call my own gets represented, by the understanding's synthesis, as belonging to the necessary unity of self-consciousness — and this comes about through the category.¹⁷ What the category thus shows is this: that empirical consciousness of a given intuitional manifold lies under a pure self-consciousness a priori, exactly as empirical intuition lies under a pure sensible intuition that, no less, occurs a priori. With the foregoing proposition, then, a deduction of the pure concepts of the understanding has been set under way; and in it, because the categories spring up in the understanding alone, independently of sensibility, I must for now leave out of account the way in which the manifold for an empirical intuition is supplied, fixing on nothing but the unity that the understanding, by the category's means, adds to the intuition. Later on (§26) it will be made clear, from the way empirical intuition comes to be given in sensibility, that this unity is no other than the one the category — following the earlier §20 — lays down for the manifold of a given intuition in general; and so, once its a priori validity for every object of our senses has been made out, the deduction's purpose is for the first time fully reached.

There was, all the same, one item from which I could not abstract in the proof above — namely, that the manifold for intuition has to be given ahead of the understanding's synthesis and apart from it; but in what way, that is left open here. For were I to conceive an understanding that intuited on its own (a divine one, perhaps, which did not represent objects already given but through whose representing the objects themselves would at once be given or produced), the categories would carry no meaning at all for a cognition of that sort. They serve only as rules for an understanding whose entire power lies in thinking — in the act, that is, of raising the synthesis of the manifold (delivered to it from elsewhere, in intuition) to the unity of apperception — an understanding which on its own therefore cognizes nothing whatever, but merely combines and sets in order the stuff of cognition, the intuition, that must be given to it by the object. As for the singular fact about our understanding — that it achieves apperception's unity a priori only through the categories , and only through just this sort and this number of them — no further ground can be assigned, no more than for why it is precisely these and no other functions of judging that we possess, or why space and time are the sole forms of any intuition possible to us.

§22. Toward the cognition of things the category serves no otherwise than by being applied to objects of experience.

To think an object, then, and to cognize one are not one and the same thing. For cognition calls for two components: first, the concept, whereby an object gets thought at all (the category); second, the intuition, whereby that object is given; for should no answering intuition be available to the concept, it would be, in point of form, a thought, yet one void of any object, and by its means no cognition of anything at all would be feasible, since, for all I could tell, there would exist nothing — nor could anything exist — to which my thought might be applied. But since every intuition available to us is sensible (see the aesthetic), the thinking of an object in general, carried out by a pure concept of the understanding, can turn into cognition for us only to the extent that the concept gets referred to objects of the senses. Sensible intuition is either pure — space and time — or else empirical intuition of whatever is represented, by sensation, as straightaway actual in space and time. By determining the former sort we can secure a priori cognitions of objects (in mathematics), though only in respect of their form, as appearances; whether there could be things bound to be intuited under this form stays, for all that, unresolved. It follows that mathematical concepts, taken on their own, are not cognitions — save in so far as one assumes there to be things presentable to us only in keeping with the form of that pure sensible intuition. Things in space and time, though, come to be given only in so far as they are perceptions — representations attended by sensation — and hence by way of empirical representation. And so the pure concepts of the understanding, even where they get applied to a priori intuitions (as they do in mathematics), yield cognition only to the degree that these intuitions — and with them, through their mediation, the understanding's concepts — admit of application to empirical intuitions. In consequence the categories, working through intuition, likewise afford us no cognition of things except by their possible application to empirical intuition — which is to say, they subserve the possibility of empirical cognition and nothing more. And this last is what we call experience. The categories, therefore, have no further use toward cognizing things than in so far as such things are taken for objects of a possible experience.

§23.

The proposition just stated matters enormously; for it stakes out the bounds within which the pure concepts of the understanding may be used as regards objects, precisely as the transcendental aesthetic staked out the bounds for using the pure form of our sensible intuition. Space and time, being conditions for the possibility of objects' being given to us, reach no further than objects of the senses, and thus than experience alone. Past those bounds they exhibit nothing whatever, since they reside in the senses only and possess no actuality apart from them. The pure concepts of the understanding stand clear of this restriction and reach out to objects of intuition in general — like ours or not, it makes no difference — so long only as the intuition is sensible rather than intellectual. Yet this reaching of the concepts out beyond our sensible intuition gains us nothing. For in that case they are hollow concepts of objects, concepts by which we cannot so much as decide whether those objects are even possible — bare forms of thought, lacking objective reality — because we have no intuition on hand for the synthetic unity of apperception (which is all those concepts hold) to be applied to, an intuition they might thereby fix as an object. Our sensible, empirical intuition is the only thing that can lend them sense and meaning.

Suppose, then, one posits as given an object of a non-sensible intuition; one may of course represent it by way of all those predicates already lodged in the assumption that nothing appertaining to sensible intuition belongs to it — thus, that it is neither extended nor in space, that its lasting is no time, that no alteration (that is, succession of determinations in time) turns up in it, and so on. Even so, this is no genuine cognition when I do nothing but state how the object's intuition is not, while unable to say what it does then contain; for in such a case I have by no means represented the possibility of an object answering to my pure concept of the understanding — having been able to supply no intuition to match it, and able only to say that ours has no hold on it. The chief point, however, is that to such a something not even one solitary category could find application; take the concept of a substance — of something able to exist as subject yet never as bare predicate — where I have no idea at all whether any thing could answer to this determination of thought, unless empirical intuition were to hand me the occasion for applying it. More on this later.

§24. On applying the categories to objects of the senses at large.

By the understanding on its own, the pure concepts of the understanding bear upon objects of intuition in general — left open whether the intuition be ours or another's, provided it is sensible — and just for that reason they are nothing but forms of thought, by which no determinate object is as yet cognized. In them, the synthesis or combining of the manifold referred to apperception's unity and nothing besides, and was on that account the ground of the possibility of a priori cognition so far as such cognition rests on the understanding — thus not transcendental only, but also purely and merely intellectual. But seeing that a definite form of sensible intuition underlies us a priori — one grounded in the receptivity of the representational capacity (sensibility) — the understanding, in its role as spontaneity, is able to determine inner sense, by way of the manifold of given representations, so as to accord with the synthetic unity of apperception, and thus to think a priori the synthetic unity of the apperception of the manifold of sensible intuition, as the condition to which all objects of our (human) intuition must of necessity conform; and thereby the categories, mere forms of thought that they are, come by objective reality — that is, application to objects givable to us in intuition, yet only as appearances, for it is of these alone that we are capable of a priori intuition.

This synthesis of the sensible-intuition manifold — possible and necessary a priori — may be termed figurative (synthesis speciosa), as against the one that would be thought in the bare category with regard to the manifold of an intuition in general and is termed the understanding's combination (synthesis intellectualis); both count as transcendental, not just because they run their course a priori, but because they lay the ground for the possibility of further a priori cognition.

The figurative synthesis, however, when it bears merely on the originally synthetic unity of apperception — that is, on this transcendental unity thought in the categories — must, as set apart from the merely intellectual combination, carry the name transcendental synthesis of the imagination. Imagination is the faculty of representing an object within intuition even without its being present. Now because all our intuiting is sensible, imagination — given the subjective condition under which it alone can supply the understanding's concepts with a matching intuition — falls to sensibility; yet in so far as its synthesis is for all that an act of spontaneity, which determines rather than, like sense, being merely determinable, and can accordingly determine sense a priori in respect of its form to suit the unity of apperception, imagination is to that degree a faculty for determining sensibility a priori, and its synthesis of intuitions, matching the categories, has to be the transcendental synthesis of the imagination — an effect wrought by the understanding upon sensibility, and its earliest application (at once the ground of every later one) to objects of the intuition we can have. Being figurative, it stands apart from the intellectual synthesis, which is accomplished with no imagination at all, by the understanding alone. In so far as imagination amounts to spontaneity, I now and then style it the productive imagination as well, thereby marking it off from the reproductive kind, whose synthesis answers to empirical laws only — those of association — and which for that reason adds nothing to accounting for the possibility of a priori cognition, belonging thus not to transcendental philosophy but to psychology.

This, now, is the spot at which to render intelligible the paradox that must have struck everyone in the exposition of inner sense's form (§6): namely, how inner sense sets even our own selves before consciousness merely as we appear, not as we are in ourselves, the reason being that we intuit ourselves only in the way we are inwardly affected — which looks contradictory, since we should then have to stand toward ourselves as something passive; and this is why, in the systems of psychology, inner sense is commonly and preferably passed off as identical with the faculty of apperception (which we, for our part, keep carefully distinct).

What determines inner sense is the understanding, along with its original faculty for combining intuition's manifold — that is, for bringing that manifold beneath an apperception (the very thing on which the understanding's possibility rests). Now since in us human beings the understanding is not itself a faculty of intuitions, and cannot draw them into itself even where they are given in sensibility, so as, in a manner of speaking, to combine the manifold of its own intuition, its synthesis — taken purely on its own — comes to nothing more than the unity of that act of which it is conscious as such apart from all sensibility, an act by which it is nonetheless equipped to determine sensibility inwardly with regard to the manifold that may be given to it in keeping with the form of its intuition. So, under the heading of a transcendental synthesis of the imagination, the understanding performs that act upon the passive subject whose faculty it is — and of this we say, with justice, that inner sense is thereby affected. So little are apperception and its synthetic unity the same as inner sense that apperception, being instead the wellspring of all combination, reaches out to the manifold of intuitions in general, and — under the title of the categories, ahead of all sensible intuition — to objects in general; whereas inner sense, for its part, holds the bare form of intuition, yet without any combining of the manifold within it, and so no determinate intuition as yet — such an intuition being possible only through consciousness of inner sense's determination by the transcendental act of imagination (the understanding's synthetic influence on inner sense) that I have named the figurative synthesis.

This, too, we constantly notice within ourselves. We are unable to think a line without drawing it in thought, unable to think a circle without describing it, wholly unable to represent space's three dimensions without erecting three lines at right angles to one another from a single point, and unable to represent even time except by heeding, as we go about the drawing of a straight line (which is to serve as time's outward figurative representation), simply the act of synthesizing the manifold whereby we determine inner sense step by step, and heeding thereby the succession of that determining within it. Motion, taken as an act of the subject (not as an object's determination)¹⁸, and therewith the synthesis of the spatial manifold — where, that is, we abstract from space and heed only the act by which we determine inner sense to fit its form — is what first of all generates the very concept of succession. The understanding, accordingly, does not somehow come upon a combination of the manifold of this kind already lying in inner sense; rather it brings that combination about, by affecting the sense. But as to how the I that does the thinking is to be told apart from the I that intuits itself (for I can frame at least the possibility of yet another manner of intuition) while remaining, as the same subject, one and the same with this latter; and hence how I am entitled to say: I, as intelligence and thinking subject, cognize my own self as a thought object, in so far as I am, beyond that, given to myself in intuition as well — only, like the rest of the phenomena, not as I stand before the understanding but as I appear to myself — this carries with it neither more nor less difficulty than the question how I can be an object to myself at all, and indeed an object of intuition and of inner perceptions. That it must, though, really be so admits of clear demonstration — once space is allowed to pass for a merely pure form of the appearances of the outer senses — from this: that time, which is after all no object of outer intuition whatever, cannot be made representable to us save under the image of a line, in so far as we draw one, without which mode of presentation we should be quite unable to recognize the oneness of its measure; and likewise from this: that for every inner perception we must invariably take the fixing of time's length, or of its points, from what alterable things outside us present, so that we are bound to arrange the determinations of inner sense as appearances in time in exactly the fashion in which we arrange those of the outer senses in space; whence, if we concede of the latter that objects are cognized by us only to the extent that we are affected from without, we must grant of inner sense as well that by it we intuit ourselves only as we are inwardly affected by ourselves — that is, so far as inner intuition goes, we cognize our own subject merely as appearance and not as it is in its own self.¹⁹

§25.

By contrast I am conscious of myself, within the transcendental synthesis of the manifold of representations in general — and so within the synthetic original unity of apperception — not according to how I appear to myself, and not as I am in my own self either, but only that I am. Such a representation is an act of thinking, not of intuiting. Since now the cognition of our own selves demands, over and above the act of thinking that lifts the manifold of any possible intuition to the unity of apperception, some determinate kind of intuition through which this manifold is given, my own existence is indeed not appearance (still less mere semblance), yet the determining of that existence²⁰ can proceed only conformably to the form of inner sense, following the particular way in which the manifold I combine is given in inner intuition; and I therefore have, in consequence, no cognition of myself as I am, but merely of how I appear to myself. Consciousness of one's self, then, falls well short of being a cognition of one's self, for all the categories that make up the thinking of an object in general by combining the manifold within an apperception. Just as, to cognize an object other than myself, I need — beyond the thinking of an object in general (in the category) — an intuition by which I give that universal concept its determination, so likewise, to cognize my own self, I need, beyond the consciousness, or beyond my thinking myself, an intuition of the manifold within me by which I determine this thought; and I exist as an intelligence that is simply aware of its power of combination while, in regard to the manifold it is to combine, standing subject to a restricting condition — one it terms inner sense — namely that it can make that combination intuitable only along temporal relations lying wholly beyond the understanding's proper concepts, and can therefore still cognize its own self only as it merely appears to itself in view of an intuition (which cannot be intellectual, nor given by the understanding itself), not as it would cognize itself were its intuition intellectual.

§26. Transcendental deduction of the pure concepts of the understanding in respect of their universally possible use within experience.

In the metaphysical deduction the a priori origin of the categories in general was established by their thorough agreement with the universal logical functions of thought, whereas in the transcendental one their possibility was set forth as that of a priori cognitions of objects of an intuition in general (§20, 21). What must now be made clear is the possibility of cognizing a priori, by means of categories, the objects that may at any time present themselves to our senses — not, indeed, in respect of the form of their intuition, but in respect of the laws of their combination — and thus of laying down the law, so to speak, for nature , and even of first making nature possible. For were they not thus suited to the task, it would remain obscure how everything that can present itself to our senses must lie under laws springing a priori from the understanding by itself.

To begin with, let me observe that by the synthesis of apprehension I mean the putting-together of the manifold in an empirical intuition, through which perception — empirical consciousness of that intuition, as appearance — comes to be possible.

In the representations of space and of time we possess, a priori, forms of outer as well as of inner sensible intuition; and the apprehension-synthesis of appearance's manifold must at every point conform to these, since it can itself proceed in no other than this form. Space and time, however, get represented a priori not just as forms of sensible intuition , but as intuitions in their own right (holding a manifold), and so together with the determination of that manifold's unity within them (see the transc. aesthetic).²¹ Thus a unity of the synthesis of the manifold — outside us or within — and with it a combination to which whatever is to be represented as determinate in space or time must answer, is itself already given a priori, as the condition for the synthesis of all apprehension, given together with (though not inside) these intuitions. This synthetic unity, though, can be no other than the unity of the combination of the manifold of some given intuition in general within an original consciousness, conformably to the categories — merely brought to bear upon our sensible intuition. It follows that every synthesis by which perception itself is made possible lies under the categories; and since experience is cognition arising from perceptions bound together, the categories are conditions of the possibility of experience, and so hold a priori of all objects of experience as well.

Suppose, for instance, I turn the empirical intuition of a house into a perception by apprehending its manifold: the necessary unity of space, and of outer sensible intuition at large, then serves me as ground, and I sketch out, as it were, the house's shape to match this synthetic unity of the manifold in space. Yet this very synthetic unity, once I abstract from the form of space, is lodged in the understanding and is the category for the synthesis of the homogeneous in an intuition in general — the category of magnitude, that is — to which the said synthesis of apprehension, i.e. the perception, must be through and through conformable.²²

When (to take another example) I perceive water freezing, I apprehend two states — fluidity and solidity — as standing, one to the other, in a temporal relation. But in the time I place beneath the appearance as its inner intuition, I of necessity represent to myself a synthetic unity of the manifold, in whose absence the relation just mentioned could not be given, determinate as to temporal order, within an intuition. Now this synthetic unity — the a priori condition under which I combine the manifold of any intuition in general, once I abstract from the abiding form of my inner intuition, time — is the category of cause; and through it, applied to my sensibility, I fix everything that occurs, in its relation, throughout time as such. And so the apprehension in an event of this sort — and therewith the event itself, as far as possible perception is concerned — comes under the concept of the relation of effects and causes; and just so in every other case.

Categories are concepts that lay down laws a priori for appearances, and hence for nature as the totality of all appearances (natura materialiter spectata); and the question now arises — given that they are not drawn from nature and do not model themselves upon it (else they would be merely empirical) — how it can be understood that nature must model itself upon them, i.e. how they can settle a priori the combination of nature's manifold without taking that combination from nature. The riddle is resolved as follows.

It is in no way more surprising that the laws of nature's appearances should have to agree with the understanding and its a priori form — its faculty, that is, of combining the manifold at large — than that the appearances themselves should have to agree with the form of sensible intuition a priori . For laws no more exist in the appearances — existing only in relation to the subject in which those appearances inhere, so far as it possesses understanding — than the appearances exist in themselves, existing only in relation to that same being, so far as it possesses senses. Things in themselves would necessarily carry their lawfulness even aside from any understanding that cognizes them. Appearances, however, are but representations of things that are on hand while remaining unknown as to what they might be in themselves. As bare representations, though, they lie under no law of connection save the one the connecting faculty itself prescribes. Now the thing that connects the manifold of sensible intuition is imagination, which draws upon the understanding as regards its intellectual synthesis's unity, and upon sensibility as regards the manifoldness belonging to apprehension. And since all possible perception hangs on the synthesis of apprehension, while that synthesis, this empirical one, hangs in turn on the transcendental synthesis, and hence on the categories, it must be that all possible perceptions — and with them everything that can ever make its way into empirical consciousness, i.e. all the appearances of nature — stand, as regards their combination, beneath the categories, on which nature (looked at merely as nature in general) depends for the original ground of its necessary lawfulness (as natura formaliter spectata). Beyond the laws on which a nature in general rests, taken as the lawfulness of appearances in space and time, the pure faculty of the understanding does not, however, stretch far enough to prescribe laws a priori to appearances by categories alone. Particular laws, since they bear on empirically determined appearances, cannot be derived in full from the categories, notwithstanding that they all, without exception, fall under them. Experience has to supervene if the latter are to become known in the first place; but concerning experience in general, and whatever can be cognized as an object of it, those a priori laws are the sole source of instruction.

§27. The upshot of this deduction of the concepts of the understanding.

No object can we think save through categories; no thought object can we cognize save through intuitions answering to those concepts. But every one of our intuitions is sensible, and such cognition, in so far as its object is given to it, counts as empirical. Cognition of the empirical sort, however, just is experience. And so we can have no a priori cognition whatever except of objects of a possible experience.²³

This cognition, though confined to objects of experience alone, is not on that account wholly borrowed from experience; on the contrary, where the pure intuitions and the pure concepts of the understanding are concerned, these are elements of cognition met with in us a priori. Now only two routes lie open along which a necessary accord between experience and the concepts of its objects can be conceived: either experience gives rise to these concepts, or these concepts render experience possible. The first does not hold as regards the categories (nor as regards pure sensible intuition); for these are a priori concepts, and so independent of experience — to allege an empirical origin for them would be a sort of generatio aequivoca. Only the second, then, is left standing (a kind of system of the epigenesis of pure reason): namely that the categories, on the understanding's part, carry within them the grounds of the possibility of all experience whatever. But just how they make experience possible, and which principles of that possibility they hand us as they are applied to appearances, will be taught more fully by the chapter to come, the one on the transc. use of the power of judgment.

Should anyone wish to put forward a third path between the only two named — proposing that the categories are neither first principles a priori thought out for ourselves as our cognition's grounds, nor culled from experience, but subjective predispositions to thought, planted in us together with our existence and so ordered by our author that their use squared exactly with the laws of nature along which experience proceeds (a kind of preformation system of pure reason) — then (quite apart from the fact that on such a hypothesis one sees no stopping-point to how far the assumption of predetermined predispositions for future judgments might be pushed) there is a consideration decisive against the proposed middle path: that in that event the categories would want the necessity that belongs essentially to their concept. The concept of cause, for one, which pronounces the necessity of a result given some presupposed condition, would come out false were it to rest on nothing but an arbitrary subjective necessity, planted in us, of joining certain empirical representations by such a rule of relation. I should then be unable to say that the effect is bound up with the cause in the object (that is, necessarily); I could say only that I am so constituted as to be incapable of thinking this representation except as thus connected — which is exactly what the skeptic wishes for most of all; for on that footing all our insight, resting on a merely supposed objective validity of our judgments, is nothing beyond sheer illusion, and there would be no shortage, either, of people declining to own such a subjective necessity (a thing that has to be felt) in their own case; at the very least one could contend with no one over what rests solely on the way his subject happens to be organized.

Concise account of this deduction.

It consists in exhibiting the pure concepts of the understanding (and, with them, all theoretical a priori cognition) as principles of the possibility of experience — this possibility being taken, in turn, as the determination of appearances in space and time as such — and, finally, in exhibiting this from the principle of the original synthetic unity of apperception, as the form of the understanding taken in relation to space and time, the original forms of sensibility.

It is only thus far that I count the partition into paragraphs needful, since our concern has been with the elementary concepts. Now that we mean to set forth their use, the presentation will be free to run on in unbroken continuity without it.