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.

Book II. Analytic of Principles

General logic rests on an outline that lines up quite precisely with the way the higher powers of cognition are divided. They are: understanding, the power of judgment, and reason. In its Analytic, accordingly, that doctrine deals with concepts, judgments, and inferences, matching exactly the functions and the sequence of those mental powers that fall under the broad label of understanding taken as a whole.

Because the aforementioned purely formal logic leaves aside every content of cognition (be it pure or empirical) and concerns itself only with the form of thought (that is, of discursive cognition) as such: its analytic portion is able to encompass the canon for reason too, whose form possesses a reliable precept of its own — one discernible a priori, by nothing more than resolving the operations of reason into their moments, and without any regard for the particular character of the cognition there at work.

Transcendental logic, being tied to one determinate content — merely the pure cognitions a priori — cannot proceed in the same way when it comes to this division. For what emerges is this: that the transcendental use of reason has no objective validity whatever, and so has no place in the logic of truth, i.e., in the Analytic, but instead, being a logic of illusion, demands for itself a distinct section of the scholastic system of doctrine, going under the title of transcendental dialectic.

Understanding and the power of judgment thus find, within transcendental logic, the canon of their objectively valid — and therefore true — employment, and on that account they fall within its analytic part. But reason, whenever it endeavors to determine anything about objects a priori and to push cognition past the boundaries of possible experience, is dialectical through and through, and its specious assertions simply cannot be accommodated in a canon of the kind the Analytic is supposed to hold.

The Analytic of Principles, then, will amount to nothing beyond a canon for the power of judgment, instructing it in how to bring the concepts of understanding — which hold within them the condition for rules a priori — to bear upon appearances. On this ground, in taking the genuine principles of the understanding as my subject, I shall adopt the title of a doctrine of the power of judgment, a name that pins down this business more exactly.

Introduction. On the transcendental power of judgment in general

Where the understanding as such counts as the faculty of rules, the power of judgment is the capacity to subsume under rules, that is, to discern whether something stands under a given rule (casus datae legis) or not. General logic contains no precepts whatever for the power of judgment, nor could it contain any. For, since it abstracts from every content of cognition: there remains to it nothing but the business of setting forth analytically the bare form of cognition in concepts, judgments, and inferences, and of thereby bringing about formal rules for all use of the understanding. Now were general logic to try to show, in a general way, how one is to subsume things under these rules, that is, how to discern whether something belongs there or not, this could come about in no other way than, once again, through a rule. But this rule, just because it is a rule, once again calls for an instruction of the power of judgment; and thus it becomes evident that the understanding, to be sure, admits of instruction and equipment by rules, whereas the power of judgment is a special talent that can never be taught but only practiced. Hence it also constitutes the distinctive feature of so-called native wit, whose want no school can make good; for even though a school may hand a narrow understanding a full complement of rules, borrowed from others' insight, and, so to speak, implant them: still the power to make correct use of them must belong to the pupil himself, and no rule that one might lay down for him with this intent is, absent such a gift of nature, proof against misuse.²⁴ A physician, then, a judge, or one versed in statecraft may carry in his head many fine pathological, juridical, or political rules, and to such a degree that he could himself become a sound teacher of them, and yet he will readily transgress in applying them — either because he wants natural power of judgment (though not understanding) and, though he apprehends the universal in abstracto, cannot make out whether a case belongs under it in concreto, or else because he has not been drilled enough for this judgment through examples and real business. This, too, is the one great benefit that examples afford: that they hone the power of judgment. For as concerns the correctness and precision of the understanding's insight, examples usually do it rather some harm, since only seldom do they satisfy the condition of the rule adequately (as a casus in terminis), and besides they often blunt the effort of the understanding to grasp rules in their sufficiency universally and apart from the particular circumstances of experience, thereby habituating one at last to use them more as formulas than as principles. Thus examples are the go-cart of the power of judgment, which anyone who lacks its natural talent can never do without.

But however true it is that general logic can furnish the power of judgment with no precepts, the case stands entirely otherwise with transcendental logic — so much so that the latter seems to have as its very task the correcting and safeguarding, through determinate rules, of the power of judgment in its use of the pure understanding. For if the aim is to enlarge the understanding within the domain of pure a priori cognitions, and thus to serve as a doctrine, philosophy appears wholly unnecessary, or rather ill-placed, seeing that all previous attempts have won little or no territory by it; but as a critique, serving to forestall the power of judgment's missteps (lapsus judicii) in handling the few pure concepts of the understanding at our disposal, philosophy — though its use is then merely negative — is called up with the whole of its acuity and its skill in examination.

Transcendental philosophy, however, has a peculiar feature: over and above the rule (or better, the general condition for rules) supplied in the pure concept of the understanding, it can at once specify a priori the very case to which they are to be applied. The ground of the precedence it enjoys in this respect over all other instructive sciences (apart from mathematics) lies just here: that it is concerned with concepts meant to bear a priori upon their objects, whence their objective validity admits of no a posteriori demonstration; for that would leave the dignity of those concepts wholly untouched, and it must rather, at the same time, exhibit — in general but adequate marks — the conditions under which objects can be given in conformity with those concepts, without which they would lack all content and so be mere logical forms and not pure concepts of the understanding.

Now this transcendental doctrine of the power of judgment is to fall into two main parts: the first treats the sensible condition on which alone the pure concepts of the understanding can be brought into use, that is, the schematism of the pure understanding; the second, however, the synthetic judgments that issue a priori from the pure concepts of the understanding under those conditions and that ground all remaining a priori cognitions, that is, the principles of the pure understanding.

Chapter 1. On the schematism of the pure concepts of the understanding

Whenever an object is subsumed under a concept, the representation of the former has to be homogeneous with the latter, that is, the concept has to contain what gets represented in the object that is to be subsumed beneath it; for that is exactly the import of the phrase that an object stands contained under a concept. In this way the empirical concept of a plate has something of the same kind in common with the pure geometrical concept of a circle, inasmuch as the roundness that one thinks in the plate admits of being intuited in the circle.

Pure concepts of the understanding, however, when set against empirical intuitions (or sensible intuitions of any sort), are wholly heterogeneous, and can never be met with in any intuition at all. So how can intuitions be subsumed under such concepts, and the category thereby applied to appearances, when surely no one is going to claim that a category — causality, say — is itself something the senses can take in and that it lies within the appearance? It is precisely this query, at once so obvious and so consequential, that in truth necessitates a transcendental doctrine of the power of judgment — necessitates it, namely, so as to exhibit how pure concepts of the understanding could possibly find any application to appearances whatsoever. Across every other science, the concepts by which an object is thought universally differ so little, and are so little heterogeneous, from the ones that present it in concreto in the way it is given, that no special treatment of how the one applies to the other is called for.

Clearly, then, some third thing has to exist that is akin on one side to the category and on the other to the appearance, thereby rendering it possible to apply the one to the other. Such a go-between representation has to be pure — free of everything empirical — while being at once intellectual on the one side and sensible on the other. This is what the transcendental schema is.

What a concept of the understanding holds within it is the pure synthetic unity of the manifold as such. Time, being the formal condition under which the manifold of inner sense stands, and thus the condition for linking all representations together, harbors within pure intuition a manifold given a priori. A transcendental determination of time, then, is of a kind with the category (which makes up the unity of that very determination) to the extent that it is universal and grounded upon an a priori rule. Yet it is likewise akin to the appearance, seeing that time figures in each empirical representation of the manifold. It thus becomes feasible to apply the category to appearances through the transcendental determination of time, which — serving as the schema for the concepts of the understanding — brings about the subsuming of those appearances under those concepts.

In light of what the deduction of the categories has already brought out, one may hope that nobody will be left uncertain how to settle the question whether these pure concepts of the understanding admit only of empirical or also of transcendental use — that is, whether, as conditions of a possible experience, they bear a priori upon appearances and nothing more, or whether instead, as conditions for the possibility of things as such, they may be stretched to objects in themselves, quite apart from any restriction to our sensibility. For we saw on that occasion that concepts are altogether impossible, and can carry no meaning, save where some object is furnished either to the concepts themselves or at any rate to the constituents out of which they are built — so that they cannot reach things in themselves at all (irrespective of whether, and how, such things might be given us); we saw, moreover, that sensibility's being modified is the one and only manner in which objects come to be given us; and we saw, lastly, that pure concepts a priori must, over and beyond the understanding's function within the category, further hold formal conditions of sensibility (those of inner sense especially) a priori — conditions embracing the general requirement under which alone a category can be brought to bear upon any object at all. This formal and pure condition of sensibility — the one to which a concept of the understanding is confined in the using of it — we shall term the schema belonging to that concept, and the understanding's way of operating with such schemata we shall term the schematism of the pure understanding.

Taken on its own, a schema is at all times nothing more than a product of the imagination; but because the imagination's synthesis has as its aim no single intuition, but only unity in how sensibility is determined, the schema must all the same be kept distinct from the image. So, if I see five dots in a row: ....., what I have is an image of the number five. If, on the other hand, I merely think number as such — it might now come to five, or to a hundred — then my thinking amounts less to that image itself than to the representation of a procedure for depicting some quantity (a thousand, for instance) in an image conformably to a given concept; and that image, in this second case, I would scarcely be able to take in at a glance and hold up against the concept. It is this notion of a general way in which the imagination goes about supplying a concept with an image belonging to it that I designate the schema for the concept in question.

As a matter of fact, what underlies our pure sensible concepts is not images of objects but schemata. To the concept of a triangle as such, no image of one could ever be adequate. For any such image would fall short of the concept's universality — the universality whereby it covers every triangle, whether right-angled, oblique-angled, and so on — and would instead stay restricted to a single portion of that sphere. Nowhere but in thought can the triangle's schema have its existence, and what it stands for is a rule governing the imagination's synthesis as this bears on pure figures in space. Even less does an object of experience, or its image, ever measure up to the empirical concept; on the contrary, such a concept is at all times related without mediation to the imagination's schema, which serves as a rule for settling our intuition in keeping with some general concept. Take the concept of a dog: it stands for a rule whereby my imagination is able to delineate the figure of a four-footed creature in a general way, tied down neither to any one particular figure that experience lays before me nor to every image I might render in concreto. Such a schematism, at work in our understanding upon appearances and the bare form they have, is an art kept concealed within the depths of the human soul, and its genuine workings are ones we shall hardly ever wring from nature so as to spread them open, unconcealed, before our gaze. Only this much are we in a position to say: the image issues from the empirical capacity of the productive imagination, while the schema of sensible concepts (concepts of spatial figures) issues from pure imagination a priori and is, so to speak, its monogram — that by which, and according to which, images can arise in the first place, images that nonetheless have to be tied to the concept solely through the schema they mark out, and that on their own do not correspond to it completely. The schema of a pure concept of the understanding, on the other hand, is something admitting of no image whatsoever; it is nothing but the pure synthesis carried out by a rule of unity that the category gives voice to, following concepts as such — a transcendental product of the imagination that has to do with how inner sense at large is determined under the conditions of its form, namely time, across all representations, to the degree that these ought to hang together a priori within a single concept as the unity of apperception requires.

Rather than hold ourselves up with a dry and wearisome anatomy of everything that transcendental schemata of pure concepts of the understanding call for in general, we prefer to lay them out in the sequence of the categories and bound up with them.

Space is the pure image of all magnitudes (quantorum) as presented to outer sense, while time is the pure image of every object of the senses taken generally. As for the pure schema of magnitude (quantitatis), regarded as a concept of the understanding, this is number — a representation drawing into one the step-by-step adding of unit to (homogeneous) unit. Number, accordingly, comes to no more than the synthetic unity belonging to the manifold of some homogeneous intuition as such, a unity I achieve by producing time itself as I apprehend the intuition.

Within the pure concept of the understanding, reality is whatever answers to a sensation as such — whatever, in other words, whose very concept points to a being (in time); negation is whatever whose concept sets forth a non-being (in time). What sets the two against each other, then, lies in a distinction drawn within one selfsame time, according as that time is full or empty. Because time is nothing but the form of intuition — and thus the form of objects insofar as they are appearances — whatever answers to sensation in these appearances is the transcendental matter of all objects considered as things in themselves (thinghood, reality). Every sensation, moreover, carries a degree or magnitude, and by this it can occupy that same time — inner sense, that is — to a greater or lesser extent as regards one and the same representation of an object, right down to where it lapses into nothing (= 0 = negatio). There is thus a bond and interconnection — or better, a passage — leading from reality over to negation, and it lets each reality be pictured as a Quantum; the schema of a reality, understood as the quantity of something to the extent that it occupies time, just is this steady and even bringing-forth of that reality throughout time, as one moves downward through time from a sensation possessing some degree until it disappears, or climbs by degrees upward from negation toward the magnitude of that sensation.

Substance has for its schema the permanence of the real throughout time — that is, the real represented as a substrate underlying empirical time-determination generally, a substrate that stays put while all else shifts. (Time as such does not run out; what runs out within it is the existence of the alterable. So to time, which of itself neither alters nor passes away, there answers in the appearance whatever is unalterable in existence — namely substance — and it is on substance alone that the sequence and the coexistence of appearances admit of being fixed in temporal terms.)

As the schema of cause, and of the causality of any thing as such, we have the real which, once it is posited at pleasure, is always trailed by something further. It lies, accordingly, in a succession of the manifold, so far as that succession stands under a rule.

For community (mutual interaction), or for the reciprocal causality that substances exercise upon one another in respect of their accidents, the schema is the coexistence of the one substance's determinations alongside the other's, in keeping with a general rule.

Possibility has as its schema the concord between the synthesis of assorted representations and the conditions of time at large (for instance, that whatever is opposed cannot inhere in a thing at once but only one after the other), and hence the pinning of a thing's representation to one time or another.

For actuality the schema is existence at a determinate time.

For necessity it is an object's existing throughout all time.

From the whole of this it now emerges that the schema of every category holds within it, and renders picturable, its own portion of time — the schema of magnitude, the production (synthesis) of time itself as an object is successively apprehended; that of quality, the synthesis of sensation (perception) with the representation of time, or time's being filled; that of relation, how perceptions stand to one another across all time (that is, by a rule for determining time); and lastly the schema of modality together with its categories, time itself as the correlate through which it is settled whether, and how, an object belongs to time. Hence the schemata amount to nothing beyond time-determinations framed a priori by rules, and, in the sequence of the categories, these determinations pertain to the time-series, the time-content, the time-order, and at last the sum-total of time as regards every possible object.

It thereby comes to light that the understanding's schematism, effected by the transcendental synthesis of the imagination, issues in nothing else than the unifying of every manifold of intuition within inner sense, and so, by an indirect route, in the unity of apperception as a function answering to inner sense (a receptivity). The schemata of the pure concepts of the understanding are, then, the genuine and only conditions that can secure for those concepts a bearing on objects, and thus meaning; and so the categories prove, in the last analysis, to admit of nothing beyond a possible empirical use, since all they do is to place appearances under general rules of synthesis — doing so on the strength of a unity that is necessary a priori (because all consciousness must be joined together in one original apperception) — and thereby to fit those appearances for thoroughgoing connection inside a single experience.

Yet the whole of all possible experience is where every one of our cognitions resides, and transcendental truth — which runs ahead of all empirical truth and is what makes it possible — lies in the universal bearing that our cognitions have upon that whole.

All the same, it likewise leaps to the eye that the schemata of sensibility, even as they are what first make the categories real, at the very same time hem them in — that is, tie them down to conditions situated beyond the understanding (namely, within sensibility). Hence, strictly speaking, the schema is only the phenomenon, or the sensible concept of an object, so far as it squares with the category itself (numerus est quantitas phaenomenon, sensatio realitas phaenomenon, constans et perdurabile rerum substantia phaenomenon — aeternitas, necessitas phaenomenon etc.). Suppose now that we drop a condition that restricts: we thereby broaden, so it appears, the concept that had earlier been hemmed in; the categories, on that supposition, would in their pure meaning, shorn of every condition of sensibility, hold good of things in general as they are, rather than their schemata setting them forth merely as they appear, so that the former would carry a meaning that owes nothing to any schema and reaches a great deal further. And indeed, once every sensible condition has been set apart, there does still cling to the pure concepts of the understanding a meaning, though a merely logical one, consisting in the bare unity of representations — a unity to which, however, no object, and so no meaning capable of yielding a concept of the object, is furnished. Were one, for example, to drop the sensible determination of permanence, substance would then signify no more than a something thinkable as subject (without figuring as the predicate of anything else). Out of this representation I can now make nothing, for it gives me no indication at all of what determinations that thing possesses which is supposed to count as such a first subject. So the categories, apart from schemata, are merely functions of the understanding directed toward concepts, and set no object before us. It is from sensibility that this meaning accrues to them, sensibility which makes the understanding real by the very act of hemming it in.

Chapter 2. System of all principles of pure understanding

In the foregoing chapter we examined the transcendental power of judgment solely with regard to the universal conditions that alone entitle it to put the pure concepts of the understanding to use in synthetic judgments. Our business now is: to present in systematic connection the judgments that the understanding, under this critical caution, genuinely produces a priori — a task in which our table of the categories is bound to offer us natural and secure guidance. For it is precisely these categories whose relation to possible experience must make up all pure a priori cognition of the understanding, and whose relation to sensibility as such will, for that very reason, display all the transcendental principles governing the use of the understanding completely and within a single system.

Principles a priori bear this name not simply because they contain the grounds of other judgments within themselves, but also because they do not rest on any cognition that is higher and more general than they are. This feature, however, does not in every instance excuse them from a proof. For although this proof can no longer be carried out objectively, but instead underlies all cognition of its object, that fact by no means rules out the possibility — indeed the necessity — of furnishing a proof that proceeds from the subjective sources on which the possibility of cognizing an object at all rests, since otherwise the proposition would still lie under the gravest suspicion of being nothing but a surreptitiously smuggled-in assertion.

Second, we will confine ourselves solely to those principles that bear on the categories. The tenets of the transcendental aesthetic — on which space and time count as conditions under which all things are possible as appearances — together with the limitation placed on these principles, namely that they admit of no application to things in themselves, thus fall outside the field of inquiry we have staked out. In the same way, the mathematical principles form no part of this system, since they are drawn purely from intuition rather than from the pure concept of the understanding; still, their possibility, since they are after all synthetic judgments a priori, must necessarily find its place here — not, to be sure, in order to establish their correctness and apodictic certainty, something they have no need of whatever, but solely to make comprehensible and to deduce how such evident a priori cognitions are possible.

We will, however, also have to speak of the principle of analytic judgments, and this indeed by way of contrast with that of the synthetic ones, with which we are properly occupied, since it is precisely this juxtaposition that liberates the theory of the latter from every misunderstanding and lays it plainly before our eyes in its distinctive nature.

Section 1. On the highest principle of all analytic judgments

No matter what the content of our cognition may be, or how it may relate to the object, the universal—albeit only negative—condition governing all our judgments as such is that they must not contradict themselves; otherwise these judgments, taken in themselves (even without regard to the object), are nothing . But even granting that our judgment harbors no contradiction, it may nevertheless combine concepts in a manner the object itself does not warrant, or else in a manner for which no ground—neither a priori nor a posteriori—is given us that would entitle such a judgment; and thus a judgment may, for all its freedom from any internal contradiction, still be either false or groundless.

Now the proposition that no thing can have a predicate contradicting it is called the principle of contradiction, and it is a general, albeit merely negative, criterion of all truth; but precisely for that reason it belongs solely to logic, for it bears upon cognitions purely as cognitions in general, taking no account of their content, and asserts that contradiction utterly destroys and cancels them.

Yet one may also put it to a positive use—that is, not simply to drive out falsehood and error (insofar as the latter rests upon contradiction), but likewise to cognize truth.

For if the judgment is analytic, be it negative or affirmative, its truth must in every case be capable of being sufficiently cognized by means of the principle of contradiction. For of that which already lies and is thought as a concept in the cognition of the object, the counterpart is at all times rightly denied, whereas the concept itself must of necessity be affirmed of it , and this because its contrary would run counter to the object.

We must therefore allow the principle of contradiction to hold as the universal and entirely sufficient principle of all analytic cognition; beyond this, however, as a sufficient criterion of truth, its standing and utility do not reach. For the circumstance that no cognition can be at odds with it without destroying itself does indeed make this proposition a conditio sine qua non, though not the determining ground of the truth belonging to our cognition. Since, however, what actually occupies us is only the synthetic portion of our cognition, we shall of course be forever mindful never to transgress this inviolable principle, though from it we can look for no enlightenment whatever concerning the truth of cognition of that kind.

Yet there does exist a formula of this celebrated principle—which, though divested of all content and purely formal, nonetheless has mixed into it, through carelessness and quite needlessly, a synthesis. It reads: It is impossible that something at once be and not be. Apart from the fact that the apodictic certainty is here superfluously tacked on (by means of the word impossible)—a certainty that must in any case be evident of itself from the proposition—the proposition finds itself saddled with the condition of time and, so to speak, declares: a thing = A, being something = B, cannot be non B at one and the same time; but it may perfectly well be the two of them (both B and non B) one after another. To take an example: a man who is young cannot simultaneously be old, though one and the very same man may quite well be young at one time and, at another, not young—i.e., old. As a purely logical principle, however, the principle of contradiction must in no way confine its assertions to relations of time, and for this reason a formula of that sort runs wholly counter to what it intends. The misconception stems solely from the following: that one begins by detaching a predicate of a thing from the concept of that thing, and afterward connects the opposite of this predicate with that predicate—something that yields no contradiction with the subject, but rather only with the predicate that has been synthetically bound up with the latter, and this, indeed, only where the first and the second predicate are laid down at the same time. Should I say: a man who, being unlearned, is not learned, then the condition at once, must stand alongside it; for someone unlearned at one moment may perfectly well be learned at another. If, by contrast, I say: no unlearned man is learned, then the proposition proves analytic, for the mark (that of unlearnedness) now goes to make up the concept of the subject; and in that case the negative proposition follows directly from the principle of contradiction, without the condition at once, needing to be brought in. This, indeed, is likewise why, further up, I so recast its formula that the nature of an analytic proposition finds clear expression through it.

Section 2. On the highest principle of all synthetic judgments

Accounting for how synthetic judgments are possible is a task with which general logic has no business whatever, one that it is not even permitted to know by name. Within a transcendental logic, on the other hand, it counts as the weightiest undertaking of them all — indeed, as the only one — whenever the possibility of synthetic judgments a priori is what stands in question, along with the conditions and the extent of their validity. For once this has been carried through, transcendental logic can fully satisfy its aim, namely that of determining the scope and the boundaries of the pure understanding.

Within an analytic judgment I stay put within the given concept in order to make out something concerning it. If it is to be affirmative, I attach to this concept nothing but what was already thought within it; if it is to be negative, I do no more than shut out from it its own contrary. In synthetic judgments, however, I am to pass beyond the given concept so as to view something entirely distinct from what was thought within it as standing in a relation to that very concept, a relation that is on that account never one of identity, nor yet one of contradiction, and one wherein the judgment, taken in itself, betrays neither its truth nor its error.

Granting, then, that one is obliged to move outside a given concept so as to set it synthetically alongside another: some third thing is needed, wherein alone a synthesis of two concepts can come to be. Now what, though, is this third thing, taken as the medium of all synthetic judgments? It is nothing but a single whole encompassing every one of our representations, namely inner sense along with its form a priori, time. It is the power of imagination on which the synthesis of representations depends, whereas their synthetic unity (which judgment demands) depends on the unity of apperception. It is here, then, that we must look for the possibility of synthetic judgments, and — inasmuch as all three harbor the wellsprings of representations a priori — for the possibility of pure synthetic judgments too; indeed, for just these reasons they must be necessary, provided a cognition of objects is to be achieved that rests upon the synthesis of representations alone.

Should a cognition possess objective reality — that is, should it bear upon an object and hold meaning and sense therein — then the object has to be capable of being given in one way or another. Lacking this, the concepts are empty, and though one has indeed thought thereby, in fact through such thinking one has cognized nothing, having merely toyed with representations. To give an object — supposing this is not, yet again, meant only mediately, but rather to present it immediately within intuition — amounts to nothing else than referring its representation to experience (be it actual, or at least possible). Even space and time, however purified these concepts may be of everything empirical, and however certain it is that they are represented entirely a priori in the mind, would nonetheless be devoid of objective validity and of sense and meaning if their indispensable application to the objects of experience were not displayed; indeed, their representation is a mere schema that forever refers to the reproductive power of imagination, which calls forth the objects of experience, in whose absence they would carry no meaning; and the same holds of all concepts, one and all.

It is thus the possibility of experience that lends objective reality to the whole of our cognitions a priori. Experience, for its part, is grounded in the synthetic unity of appearances — that is, in a synthesis carried out under concepts of an object of appearances as such, without which experience would not so much as be cognition but a mere rhapsody of perceptions, ones that would knit themselves into no context answering to the rules of a thoroughgoingly connected (possible) consciousness, and thus into no transcendental and necessary unity of apperception. Experience, then, has lying at its ground principles of its form a priori, namely universal rules governing unity within the synthesis of appearances, the objective reality of which, in their role as necessary conditions, can at every point be pointed out in experience, and indeed in the very possibility of experience. Divorced from this relation, however, synthetic propositions a priori are altogether impossible, for they have at their disposal no third thing — that is, no object — upon which the synthetic unity belonging to their concepts might make good an objective reality.

Hence, however much we may cognize a priori in synthetic judgments concerning space taken generally, or concerning the figures that imagination in its productive capacity traces out within it — so that in truth we stand in need of no experience whatever for this — this cognition would all the same come to nothing, would be but a preoccupation with a sheer figment of the mind, were space not to be viewed as a condition of the appearances that constitute the material for outer experience; and so those pure synthetic judgments relate — in a mediate fashion, to be sure — to possible experience, or rather to its very possibility, and it is upon this alone that they rest the objective validity of their synthesis.

Seeing, then, that experience — qua empirical synthesis — constitutes, in respect of its possibility, the one and only kind of cognition that confers reality on every other synthesis, this latter synthesis, as a priori cognition, likewise possesses truth (concordance with the object) solely because it holds within it nothing beyond that which is requisite for a synthetic unity of experience in general.

The supreme principle of all synthetic judgments is thus the following: every object stands under those necessary conditions belonging to the synthetic unity of intuition's manifold within a possible experience.

In this manner synthetic judgments a priori become possible: we bring the formal conditions of intuition a priori, imagination's synthesis, and the necessary unity that this synthesis has within a transcendental apperception, into relation with an experiential cognition that is possible in general, and we then assert that the conditions for the possibility of experience at large are simultaneously the conditions for the possibility of the objects of experience, which is precisely why they hold objectively within an a priori synthetic judgment.

Section 3. Systematic representation of all synthetic principles of pure understanding

That there should be principles anywhere at all must be credited to the pure understanding alone, which not only constitutes the faculty of rules in respect of what takes place, but is itself the wellspring of the principles by which everything (whatever can come before us as an object) is necessarily bound by rules, for lacking such rules appearances could never attain any cognition of an object answering to them. Even the laws of nature themselves, once they are viewed as principles of the empirical employment of the understanding, bring with them at once an expression of necessity, and thus at least the surmise of a determination out of grounds that hold a priori and antecedently to all experience. But every law of nature without distinction is subordinate to higher principles of the understanding, being merely an application of the latter to particular cases of appearance. It is these higher principles alone, then, that furnish the concept containing the condition and, so to speak, the exponent of a rule as such, while experience furnishes the case that falls under that rule.

There can hardly be any genuine risk of mistaking merely empirical principles for principles of the pure understanding, or the other way round; for the necessity in accordance with concepts by which the latter are distinguished—and whose want in any empirical proposition, however broadly it may hold, is easily detected—can readily guard against such a confusion. There are, though, pure principles a priori that I would still hesitate to assign properly to the pure understanding, and this because they are derived not from pure concepts but from pure intuitions (though by the mediation of the understanding); the understanding, after all, is the faculty of concepts. Mathematics has principles of just this sort, and yet their application to experience, and thus their objective validity—indeed the very possibility of such a priori synthetic cognition (the deduction of it)—still reposes throughout upon the pure understanding.

For this reason I shall not reckon the principles of mathematics among my own, though I shall indeed reckon those on which the possibility and the objective validity a priori of mathematics rest, principles that are consequently to be viewed as the principles of these very principles and that pass from concepts over to intuition, rather than from intuition over to concepts.

When the pure concepts of the understanding are brought to bear on possible experience, their synthesis is used in a manner that is either mathematical or dynamical: for it is directed partly upon the mere intuition, partly upon the existence of an appearance as such. The a priori conditions of intuition, by contrast, are wholly necessary in regard to any possible experience, whereas those bearing on the existence of the objects of a possible empirical intuition are, taken in themselves, merely contingent. For this reason the principles governing the mathematical use will read as unconditionally necessary, that is, apodictic, while those of the dynamical use, though they too bear the mark of a necessity that is a priori, do so only on the presupposition of empirical thought within some experience, and hence only mediately and indirectly; they accordingly lack that immediate self-evidence (notwithstanding a certainty of their own that extends universally to experience) which belongs distinctively to the former. This, however, will be easier to assess once we reach the close of this system of principles.

The table of the categories affords us entirely natural guidance toward the table of the principles, for the latter are, when all is said, nothing but rules for the objective employment of the former. The principles of the pure understanding, taken altogether, are thus as follows:

These names I have selected advisedly, so as not to let the differences in respect of the self-evidence and the exercise of these principles pass unnoticed. It will soon emerge, however: that as far as concerns both the self-evidence and the a priori determination of appearances under the categories of magnitude and of quality (attending merely to the form of the latter), the principles proper to them are on this score conspicuously distinct from the two that remain, inasmuch as the former admit of an intuitive, but the latter of a merely discursive, certainty—each side, though, of a complete one. Accordingly I shall name the former the mathematical, the latter the dynamical principles.²⁵ It will be readily observed, however: that what I have before me here is as little the principles of mathematics on the one side as those of general (physical) dynamics on the other, but solely the principles of the pure understanding in their relation to inner sense (without any distinction among the representations given within it), whereby the former, one and all, come by their possibility. I name them, then, with an eye to their application rather than to what they contain, and now proceed to examine them in the very same order in which they stand presented in the table.

1. Axioms of Intuition

Their principle is: All intuitions are extensive magnitudes.

Proof.

In respect of their form, all appearances contain within them an intuition in space and in time, one that lies at the basis of them all alike a priori. They therefore admit of being apprehended—i.e., received into empirical consciousness —in no way other than by a synthesis of the manifold through which the representations of some determinate space, or of time, get produced, that is, by putting together what is homogeneous, together with the consciousness of the synthetic unity of this homogeneous manifold. Now, the consciousness of the homogeneous manifold in intuition generally—insofar as it is through this that the representation of an object first becomes possible—just is the concept of a magnitude (quanti). Thus even the perception of an object, as appearance, becomes possible only by means of that very synthetic unity of the manifold belonging to the given sensible intuition, by means of which the unity in the putting-together of the homogeneous manifold gets thought under the concept of a magnitude; that is, appearances are, without exception, magnitudes, and specifically extensive magnitudes, because, being intuitions in space or in time, they have to be represented by the very synthesis that also determines space and time as such.

I give the name extensive to a magnitude in which the representation of the parts renders possible the representation of the whole (and therefore necessarily comes before it). No line, however small, can I represent to myself except by drawing it in thought—that is, by generating its parts successively out of a point, and so first sketching out this intuition. And matters stand no differently with any time, even the very smallest. Within it I conceive nothing but the successive progression from one instant to the next, by which, out of the several parts of time and their accumulation, a determinate temporal magnitude is at last brought forth. Because in all appearances the bare intuition constitutes either space or else time, each appearance, taken as intuition, is an extensive magnitude, since it admits of being cognized in apprehension only by a successive synthesis (proceeding from part to part). Every appearance is on this account already intuited as an aggregate (a set of parts given in advance), which is precisely not so for every sort of magnitude, but holds only for those we represent and apprehend extensively as such.

It is on this successive synthesis of the productive imagination, at work in producing figures, that the mathematics of extension—that is, geometry—rests, together with its axioms; these state a priori the sensory-intuition conditions that alone allow the schema for a pure concept of an outer appearance to be established: for instance, between any two points a single straight line, and no more, can be drawn; two straight lines fence off no space. Such are the axioms that, strictly speaking, bear only upon magnitudes (quanta) as such.

As regards magnitude (quantitas), however—that is, the reply to the question of how great something is—there are, with respect to it, no axioms at all in the strict sense, even though several such propositions are synthetic and immediately certain (indemonstrabilia). For that equals joined to equals, or taken away from equals, give an equal, are analytic propositions, seeing that I am directly aware of the identity of the one production of a magnitude with the other; axioms, though, are meant to be synthetic propositions a priori. The self-evident propositions concerning numerical relations, on the other hand, are admittedly synthetic, yet not general in the way those of geometry are, and just for that reason they are not axioms either, though they may be termed numerical formulas. That 7 + 5 = 12 is not an analytic proposition. For the number 12 is something I think neither when I represent 7 to myself, nor when I represent 5, nor when I represent the two of them combined (whether I am to arrive at it through their addition is not what is in question here; for in an analytic proposition the sole thing asked is whether I genuinely think the predicate within the representation of the subject). Yet even granting that it is synthetic, it remains for all that only a single proposition. So far as what is looked to here is merely the synthesis of the homogeneous (of the units), this synthesis can proceed in but one single manner, however general the use of these numbers may afterward be. If I state: out of three lines, two of which taken together exceed the third, a triangle admits of being drawn: here I have merely the function of the productive imagination, which can draw the lines longer or shorter and can likewise have them meet at any angles one pleases. The number 7, on the other hand, is possible in one single way only, and so is the number 12, which arises through the synthesis of the former with 5. Such propositions must therefore be called not axioms (for otherwise there would be endlessly many of them) but numerical formulas.

This transcendental principle of the mathematics of appearances affords our cognition a priori a considerable enlargement. For it is this alone that renders pure mathematics, in the whole of its precision, applicable to objects of experience—something which, absent this principle, would not become so evident of itself, and has indeed given rise to more than one contradiction. Appearances are in no way things in themselves. Empirical intuition becomes possible solely by means of the pure intuition (that of space and of time); accordingly, what geometry asserts of the latter holds, without any gainsaying, of the former as well, and the evasions, as if objects of the senses were not required to conform to the rules of construction in space (e.g., to the unlimited divisibility of lines or angles), must be discarded. For in doing so one strips space—and along with it all of mathematics—of objective validity, and no longer knows for what reason, or how far, it is to be brought to bear upon appearances. It is the synthesis of spaces and of times—the form essential to all intuition—that at once renders feasible the apprehension of an appearance, and hence every outer experience, and in consequence all cognition of the objects belonging to it; and whatever mathematics proves of the former in its pure employment holds of necessity for the latter also. Every objection raised against this amounts to no more than the quibbling of a reason wrongly schooled, one that mistakenly supposes it can free the objects of sense from that formal condition to which our sensibility is subject and, notwithstanding that they are nothing but appearances, sets them forth as objects in themselves handed over to the understanding; in which event, to be sure, not a thing could be cognized of them a priori—hence not even synthetically by means of pure concepts of space—and the very science that fixes these, namely geometry, would itself be impossible.

2. Anticipations of Perception

The principle governing them is: In every appearance the real—that which forms an object of sensation—possesses an intensive magnitude, i.e., a degree.

Proof.

Perception is empirical consciousness—consciousness, that is, wherein sensation is likewise contained. As objects of perception, appearances are not pure intuitions—merely formal ones, such as space and time (which in themselves admit of no perception whatever). Over and above the intuition, then, they harbor within themselves the material for some object as such (whereby a thing existing in space or in time comes to be represented)—namely the real of sensation, which, as a purely subjective representation, permits us only the awareness that the subject stands affected, and which we relate to an object as such. Now from empirical consciousness up to pure consciousness a stepwise alteration is possible, wherein the real belonging to it disappears completely and there remains only a formal (a priori) consciousness of the manifold in space and in time: and hence, likewise, a synthesis whereby the magnitude of a sensation is generated, beginning from its origin—the pure intuition = 0—and running up to some magnitude or other of it. Given that sensation, taken by itself, is no objective representation whatever, and that within it one meets with the intuition neither of space nor of time, what accrues to it will be a magnitude that is not extensive yet is a magnitude all the same (arising, namely, by way of its apprehension, wherein empirical consciousness is able, over a certain span of time, to grow up from nought = 0 to its given measure)—an intensive magnitude, therefore; and answering to this, every object of perception, so far as it comprises sensation, has to be credited with an intensive magnitude, i.e., with a degree of influence upon sense.

Every cognition by means of which I am able a priori to cognize and settle what pertains to empirical cognition may be termed an anticipation; and this, beyond question, is the meaning Epicurus attached to his expression prolepsis. But because appearances contain an element that is at no time cognized a priori—one which for that reason marks off what genuinely distinguishes the empirical from a priori cognition, namely sensation (the matter, that is, of perception)—it follows that just this is what altogether resists anticipation. The pure determinations in space and in time, by contrast—those bearing on shape as much as on magnitude—we might well name anticipations of appearances, since what they present a priori is precisely that which is liable always to be furnished a posteriori within experience. Suppose, however, that after all there proved to be something admitting of a priori cognition in each sensation, taken as sensation as such (though no particular sensation be given): such a thing would earn the name of anticipation in an exceptional sense, for it appears odd to run ahead of experience in the very point that touches its matter—a matter derivable from experience alone. And such is genuinely the case here.

Apprehension carried out solely through sensation occupies but a single instant (assuming, that is, that I leave out of account the succession of numerous sensations). Being something in the appearance whose apprehension is no successive synthesis advancing from the parts toward the entire representation, it accordingly lacks extensive magnitude: were sensation wanting at that very instant, the instant would be presented as void, and so = 0. Now that which answers to sensation within empirical intuition is reality (realitas phaenomenon); that which answers to its lack, negation = 0. Yet every sensation admits of being reduced, so that it may grow less and by degrees fade away entirely. Consequently, between reality in the appearance and negation there stretches a continuous linkage of numerous possible intermediate sensations, the gap separating any two of them being forever less than the gap between the given sensation and zero—that is, complete negation. In other words: the real in the appearance invariably possesses a magnitude, one that is nevertheless not met with in apprehension, seeing that apprehension takes place through bare sensation within a single instant rather than by a successive synthesis of many sensations, and so does not advance from the parts up to the whole; it does, then, possess a magnitude, only not an extensive one.

A magnitude apprehended purely as a unity, and in which plurality is representable only by way of approach toward negation = 0, is what I now designate intensive magnitude. Every reality in the appearance, accordingly, carries intensive magnitude, i.e., a degree. Should one regard this reality as a cause (be it of sensation or of another reality in the appearance, e.g. of an alteration): then the degree of reality qua cause is termed a moment—the moment of gravity, say—and this because the degree marks out nothing but the magnitude whose apprehension is instantaneous rather than successive. This, however, I mention only incidentally at this point, for causality is not yet my concern just now.

Thus every sensation—and consequently every reality in the appearance too, be it ever so slight—possesses a degree, i.e., an intensive magnitude still open to further reduction, and between reality and negation there runs a continuous linkage of possible realities and of possible fainter perceptions. Any color whatever—red, for instance—has a degree that, be it ever so slight, is at no point the least, and matters stand likewise throughout with warmth, with the moment of gravity, and so on.

That characteristic of magnitudes whereby no part within them is the least one possible (no part being simple) is what one calls their continuity. Space and time count as quanta continua, for no portion of either can be given except by fencing it in between limits (points and instants)—thus only in such fashion that the portion is once again itself a space or a time. Space, then, is built up of nothing but spaces, and time of times. Points and instants are only limits—bare places at which space and time are bounded; but places invariably presuppose the very intuitions they are supposed to bound or determine, and from mere places, treated as building-blocks that might be furnished ahead of space or time, no space and no time can be put together. Magnitudes of such a kind admit of being termed flowing as well, since the synthesis (belonging to the productive imagination) that brings them forth is an advance through time, a continuity that one is wont to denote above all by the word "flowing" ("elapsing").

Every appearance whatsoever, then, is a continuous magnitude—extensive if regarded by its intuition, intensive if by mere perception (sensation and thus reality). Where the synthesis of an appearance's manifold suffers interruption, what results is an aggregate composed of several appearances (rather than, strictly, an appearance as a quantum)—something produced not by simply prolonging a productive synthesis of some given sort, but by reiterating a synthesis that keeps breaking off. When I speak of 13 thalers as a quantum of money, the designation is apt to the extent that I mean thereby the content of one mark of fine silver—which is, to be sure, a continuous magnitude wherein no part ranks as the least , each part being capable instead of making up a coin whose matter would forever suffice for yet smaller ones. If, on the other hand, by that name I mean 13 round thalers as just so many coins (let their silver content be whatever it will), then it is inaptly styled a quantum of thalers, and I must call it rather an aggregate—a number, that is, of coins. And since some unity must lie at the base of every number, the appearance qua unity is a quantum, and, being such, is at all times a continuum.

If, then, all appearances—viewed extensively no less than intensively— are continuous magnitudes, the thesis that every alteration as well (a thing's passage out of one state into another) is continuous would admit here of an easy proof carrying mathematical evidence, did the causality of an alteration as such not fall entirely beyond the confines of a transcendental philosophy and rest on empirical principles. For of the possibility that some cause should change the state of things—should determine them, that is, to the contrary of a certain given state—the understanding affords us a priori no intimation whatever, and this not merely because it fails to see into the possibility involved (an insight we go without in more than one a priori cognition), but because mutability bears solely on certain determinations of appearances that experience alone is able to teach, while their cause is lodged in what does not change. But seeing that what lies before us here, the only thing we can employ, is nothing other than the pure basic concepts of every possible experience—among which nothing empirical whatever may figure—we are unable, short of disrupting the system's unity, to run ahead of general natural science, resting as it does upon certain foundational experiences.

All the same, we are not without evidences of the considerable influence this principle of ours exerts in anticipating perceptions, and even in making good their want, to the point of bolting the door against every false inference that might be drawn from that want.

Granting that every reality in perception owns a degree, that between it and negation an unending series of steadily diminishing degrees falls, and that each sense nonetheless is bound to have some fixed degree of receptivity toward sensations: then there can be no perception—and thus no experience—capable of establishing a total want of all that is real in the appearance, whether immediately or mediately (through whatever circuitous chain of inference one may please), which is to say that experience can at no time yield a proof of empty space or of empty time. For the utter lack of the real in sensible intuition can, in the first place, not itself be perceived; and in the second, it can neither be concluded from any one appearance together with the disparity in the degree of its reality, nor ever be posited in order to account for that appearance. For suppose the whole intuition of some determinate space or time to be real through and through—no part of it, that is, being empty: even so there must, since each reality carries its degree, which (the extensive magnitude of the appearance staying fixed) is able to sink by infinite steps down to nothing (the void), be an infinity of distinct degrees to which the filling of space or of time may answer, and the intensive magnitude may turn out lesser or greater across differing appearances, notwithstanding an equal extensive magnitude of the intuition.

An illustration may be offered. Well-nigh all students of nature, on perceiving a wide disparity in the quantity of matter of diverse kinds occupying an equal volume (in part by way of the moment of gravity or weight, in part by way of the moment of resistance to other matters in motion), draw from this with one voice the conclusion: that this volume (the extensive magnitude of the appearance) has to be empty in every matter, albeit in unlike measure. Yet which among these investigators of nature, mathematical and mechanical for the most part, would ever have imagined that they were founding this conclusion of theirs on nothing but a metaphysical presupposition—the very kind they profess so earnestly to shun—inasmuch as they take the real in space (I would rather not here name it impenetrability or weight, those being empirical concepts) to be everywhere one and the same, differentiable merely in extensive magnitude, i.e., in amount. To this presupposition—one for which they could possess no warrant in experience, and which is on that account purely metaphysical—I oppose a transcendental proof, not designed, indeed, to explain the difference in how spaces are filled, yet fully removing the alleged necessity of that presupposition (the necessity, namely, of explaining the said difference in no way but by positing empty spaces), and possessing the merit of at least leaving the understanding at liberty to conceive this diversity in some other manner too, should the explanation of nature render any hypothesis necessary to that end. For here it becomes evident that, even though equal spaces may stand wholly filled by differing matters , such that within none of them is there a point where their presence would be missing, still each real of the same quality has its degree (of resistance, or of weighing) which, with no lessening of the extensive magnitude or amount, may grow infinitely smaller before it crosses over into the void and disappears. So a distension filling a space—warmth, say—and, on the same footing, any other reality (in the appearance), may, without in the slightest leaving the least portion of that space vacant, dwindle infinitely in its degrees, and for all that fill the space by these lesser degrees no worse than another appearance does by greater ones. It is in no way my aim here to maintain that things really do stand thus with regard to the difference of matters as measured by their specific gravity, but merely to establish, out of a principle of the pure understanding, that the very nature of our perceptions leaves room for such a mode of explanation—and that it is a mistake to assume the real of the appearance uniform in degree and varying only in aggregation and the extensive magnitude thereof, and even to advance this, on pretended grounds, by way of an a priori principle of the understanding.

Even so, for an investigator schooled in transcendental reflection and thereby made wary, this anticipation of perception never wholly loses a certain startling character, and it awakens some hesitation that the understanding should be capable of anticipating a synthetic proposition of the sort in question—one bearing on the degree of all that is real in the appearances, and thus on the possibility of the intrinsic difference within sensation itself, once its empirical quality is set aside; and there thus persists a question by no means undeserving of resolution: namely, how the understanding can here deliver synthetic pronouncements about appearances a priori, and can anticipate them even in what is properly and purely empirical, that is, in what pertains to sensation.

A sensation's quality is in every instance nothing but empirical and cannot be represented a priori in the least (colors, for example, or taste, and the like). The real, however, which answers to sensations at large, as set over against negation = 0, presents merely a thing the very concept of which harbors a being, and denotes nothing beyond the synthesis within an empirical consciousness taken generally. For within inner sense empirical consciousness admits of being heightened from 0 up to any higher degree whatever, so that one and the same extensive magnitude of intuition (an illuminated surface, say) may stir a sensation as strong as an aggregate of many other things (less illuminated) combined. One may accordingly abstract wholly from the extensive magnitude of the appearance and still picture to oneself, in the bare sensation within a single moment, a synthesis of even ascent from 0 as far as the given empirical consciousness. Every sensation as such, then, is admittedly furnished only a posteriori, and yet the fact that it has a degree—this feature of it—can be cognized a priori. It is a striking thing that, of magnitudes as such, we are able to cognize a priori but one sole quality, namely continuity, whereas of all quality (the real of appearances) we cognize a priori nothing beyond its intensive quantity—that is, that they possess a degree; all the rest is consigned to experience.

3. Analogies of Experience

The principle of these is: Experience is possible only through the representation of a necessary connection of perceptions.

Proof.

Experience amounts to an empirical cognition — that is, a cognition determining an object by means of perceptions. It is accordingly a synthesis of perceptions, a synthesis not itself lodged within perception but one that holds together, in a single consciousness, the synthetic unity belonging to their manifold, and this unity is precisely what makes up the essential feature of any cognition of the objects given to the senses, that is, of experience (and not merely of sensory intuition or sensation). Now within experience the perceptions admittedly meet one another merely by chance, and so no necessity governing their linkage either does or could shine forth from those perceptions themselves; for apprehension yields nothing beyond an assembling of the manifold of empirical intuition, and within it there is to be found no representation of the necessary conjoined existence of the appearances that it assembles in space and time. Since experience, however, is a cognition of objects by way of perceptions, so that what has to be represented in it is the relation obtaining in the existence of the manifold — represented not according to the order in which it gets assembled in time, but as it stands objectively in time — whereas time itself admits of no perception: the existence of objects in time can be determined only through their connection within time as such, and thus only by means of concepts that link them a priori. And since such concepts invariably bring necessity along with them, experience can arise only by means of a representation in which the perceptions are necessarily linked.

Time has three modi: persistence, succession, and simultaneity. There will accordingly be three rules for all the temporal relations of appearances — rules by which the existence of each appearance can be fixed in regard to the unity of all time — and these rules go ahead of every experience and are what render it possible in the first place.

The universal principle of all three analogies rests on the necessary unity of apperception, taken in relation to every possible empirical consciousness (perception) at any given time, and hence — since that unity lies a priori at the foundation — on the synthetic unity of all appearances in keeping with how they stand related within time. For original apperception has reference to inner sense (the totality of all representations), and specifically a priori to the form thereof, that is, to the way the manifold of empirical consciousness stands related in time. Within original apperception, then, the whole of this manifold is to be brought into unity as its temporal relations require; for this is just what that manifold's transcendental unity affirms a priori, a unity beneath which falls everything destined to count as part of my (that is, my one single) cognition and thus capable of becoming an object for me. Hence this synthetic unity governing the temporal relation of all perceptions, a unity that is settled a priori, amounts to the following law: every empirical determination of time is obliged to fall beneath rules governing the determination of time in general; and the analogies of experience that we now propose to treat can be nothing other than rules of just this sort.

What is distinctive about these principles is that their concern is not with appearances and the synthesis of their empirical intuition, but solely with the existence of appearances and with their relation to one another in respect of that existence. Now the manner in which something within the appearance comes to be apprehended may be fixed a priori in such a way that the rule for its synthesis simultaneously furnishes this intuition a priori in any given empirical instance that lies before us, that is, can generate it out of that instance. Yet the existence of appearances is not something cognizable a priori; and even supposing this route allowed us to reach an inference to some existence or other, we would still have no determinate cognition of it, that is, we could not anticipate whatever it is that would set its empirical intuition apart from others.

The two foregoing principles — which I termed mathematical, seeing that they entitle us to bring mathematics to bear on appearances — dealt with appearances as regards their bare possibility and showed how, in respect both of their intuition and of the real in their perception, such appearances might be produced under rules of a mathematical synthesis; and so, in the one case as much as in the other, numerical quantities, and along with them the appearance's determination as a magnitude, become available for use. So I shall be able, for instance, to build up the degree of the sensations of sunlight out of roughly 200,000 moon-illuminations, and to present it as fixed a priori, that is, to construct it. These earlier principles may therefore be called constitutive.

Matters must stand entirely differently with those principles whose task is to place the existence of appearances under rules a priori. For since existence of that kind does not admit of being constructed, such principles can address nothing beyond the relation of existence and can supply none but merely regulative ones. Here, then, axioms are out of the question, and so are anticipations; instead, once a perception has been given to us standing in some temporal relation toward others (indeterminate though these be), what cannot be pronounced a priori is this: which other perception, and one of what magnitude, but rather in what way, as to its existence, it must be necessarily bound up with that other within this modo of time. Within philosophy, analogies mean something quite other than what they stand for in mathematics. In the latter they amount to formulas expressing that two ratios of magnitude are equal, and they are on every occasion constitutive, so that once three terms of the proportion are supplied, the fourth is supplied thereby as well, that is, it can be constructed. In philosophy, by contrast, an analogy is the equality not of two quantitative but of two qualitative relations, and here, out of three given terms, all I can cognize and supply a priori is the relation to a fourth, never that fourth term itself, though I am indeed left with a rule for hunting it out in experience and a mark by which to locate it there. An analogy of experience, then, comes to no more than a rule whereby, out of perceptions, a unity of experience is meant to spring (not in the way perception itself does, as empirical intuition taken generally), and, as a principle bearing on the objects (the appearances), it counts not constitutively but only regulatively. Precisely the same, however, holds of the postulates of empirical thought as such — postulates that jointly bear on the synthesis of bare intuition (appearance's form), of perception (its matter), and of experience (how these perceptions stand related) — the point being that they are regulative principles only, and that, while they part company with the mathematical, constitutive ones not in the certainty which in both stands fixed a priori, they do so nonetheless in the character of their evidence, that is, in the intuitive quality it carries (and hence in that of the demonstration as well).

But the reminder issued in the case of every synthetic principle, and to be stressed here in particular, comes to this: that these analogies carry their whole meaning and validity not as principles for the transcendental use of the understanding but purely for its empirical use, so that they too admit of proof only in that capacity, and that appearances must accordingly be brought not under the categories outright, but only under their schemata. For were the objects to which these principles are supposed to apply things in themselves, then gaining any synthetic a priori cognition of them would be flatly impossible. As it stands, they are nothing but appearances, whose full cognition — the terminus toward which every a priori principle must in the last resort run out — is simply possible experience; and so those principles can aim at nothing except the conditions under which empirical cognition is unified in the synthesizing of appearances; this unity, in turn, gets thought solely in the schema belonging to the pure concept of understanding, and it is of such a unity, taken as a synthesis in general, that the category holds the function which no sensible condition restricts. By these principles, then, we come to be entitled to piece appearances together only on an analogy to the logical and universal unity that concepts possess; and for this reason, while in the principle as such we do avail ourselves of the category, in carrying it out (in the application to appearances) we put in the category's place its schema, which serves as the key to how the category is used, or rather we set the category itself off to the side, as a restricting condition, under the name of a formula of the former.