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.

First Analogy. Principle of the permanence of substance

Substance persists through every change of the appearances, and the quantity of it present in nature is neither augmented nor reduced.

Proof.

All appearances are found in time, in which — serving as substrate (as the permanent form of inner intuition) — both coexistence and succession can be represented at all. Time itself, accordingly, wherein all change of appearances must be thought, abides and does not itself change, being that in which sequence, or coexistence, can be represented only as determinations belonging to it. Now time on its own cannot be perceived. It follows that the objects of perception — appearances, that is — must contain the substrate representing time as such, upon which, through the appearances' relation to it, every instance of change or coexistence becomes perceptible in apprehension. But that substrate of all that is real — of all, that is, that pertains to the existence of things — is substance, and everything belonging to existence can be thought within it merely as a determination. The permanent, then — that whereby alone every temporal relation among appearances admits of determination — is substance within the appearance, that is, its real component, which, as the substrate underlying all change, stays ever the same. And because it can undergo no change in its existence, its quantity in nature likewise admits of neither increase nor decrease.

The apprehension whereby we take up the manifold of an appearance is invariably successive, and hence in constant flux. By that alone, therefore, we can never settle whether this manifold, taken as an object of experience, exists together or follows in sequence, unless something underlies it that is at all times, i.e., something abiding and permanent, in relation to which all change and coexistence amount to nothing more than the several modes (modi of time) according to which the permanent exists. Temporal relations, therefore, are possible only within the permanent (since the sole relations obtaining in time are simultaneity and sequence), which is to say that the permanent furnishes the substratum on which the very empirical representation of time reposes, and in it alone can any determination of time occur. Permanence gives expression to time in general as the abiding correlate of every existence of appearances, of every change and of all concomitance. Change, after all, does not touch time itself but only the appearances lodged in time (much as coexistence is no modus of time proper, given that in time no parts stand together but all lie one after another). If someone wished to attribute to time itself a succession one after another, he would be forced to posit a further time within which such a succession could take place. It is through the permanent alone that existence, across the successive stretches of the time-series, takes on a magnitude one calls duration. For in bare sequence taken by itself, existence is forever ceasing and starting up and never possesses even the slightest magnitude. Absent this permanent, therefore, no temporal relation obtains at all. Time as such, however, admits of no perception; and so this permanent in the appearances is what underlies every determination of time — and thus, too, the condition making possible any synthetic unity among perceptions, i.e., experience — while within this permanent all existence and all change in time can be regarded solely as a modus of the existence of that which remains and persists. In every appearance, accordingly, the permanent is the object itself, i.e., the substance (phaenomenon), whereas all that changes, or is capable of changing, pertains merely to the manner in which this substance or these substances exist, and hence to their determinations.

At every period, I observe, this permanence has been taken for granted — not by the philosopher alone but by ordinary understanding as well — as a substratum for all change of appearances, and it will always continue to be accepted as beyond question; only that the philosopher puts the matter somewhat more precisely, saying: through all alterations in the world the substance endures, and the accidents alone change. Yet nowhere do I come upon so much as an attempt at proving this thoroughly synthetic proposition; indeed, it but seldom stands where it by rights belongs, at the forefront of the pure laws of nature that hold wholly a priori. The proposition that substance is permanent is, in truth, a tautology. For it is this permanence alone that grounds our applying the category of substance to appearance, and one would have needed to show that in all appearances something permanent is present, in relation to which the mutable counts as nothing more than a way in which its existence is determined. But since a proof of this kind can never be carried through dogmatically, i.e., out of mere concepts — for it concerns a synthetic proposition a priori — and since it was never noticed that propositions of that sort hold good only in reference to possible experience, and can therefore be established only by a deduction of the possibility of the latter: it is no wonder that, though laid at the basis of all experience (one feels the need of it in empirical cognition), it has nevertheless never been proved.

A philosopher was once asked: how much does smoke weigh? He replied: from the weight of the burnt wood subtract the weight of the ash left behind, and the weight of the smoke is what remains. He thereby assumed as beyond dispute that even in fire matter (substance) does not perish, but only its form suffers a modification. In the same way, the maxim that nothing arises from nothing was but a further consequence drawn from the principle of permanence — or rather from the perpetual existence of the true subject underlying the appearances. For should whatever in an appearance we choose to call substance serve as the genuine substratum for every determination of time, then existence alike in time past and in time to come must be fixable in it, and in it alone. Hence we call an appearance a substance for one reason only: because we presuppose its existence at all times — which the word permanence does not even express particularly well, seeing as it bears more on time to come. Even so, the inner necessity of persisting is inseparably bound together with the necessity of having always been, and so the term may well be retained. Gigni de nihilo nihil, in nihilum nil posse reverti were two propositions that the ancients linked indissolubly, and that, through a misunderstanding, are nowadays now and then pulled apart, because one fancies that they bear on things in themselves, and that the first might stand opposed to the world's dependence on a supreme cause (even in respect of its substance); a concern which is needless, since what is here in question is merely appearances in the field of experience, whose unity could never be possible were we to let new things (in respect of substance) come into being. For in that event the very thing that alone can represent time's unity would fall away — namely the self-identity of the substratum, as that wherein all change alone possesses thoroughgoing unity. This permanence, though, is nothing beyond the manner in which we represent to ourselves the existence of things (in the appearance).

The determinations of a substance, being nothing but particular ways in which it exists, are termed accidents. They are in every case real, inasmuch as they bear on the substance's existence (negations being merely determinations that voice the non-being of something in the substance). Now if one assigns to this real element in the substance a distinct existence of its own (e.g., to motion as an accident of matter), then one names this existence inherence, as against the existence of the substance, which one names subsistence. From this, however, a good many misreadings arise, and one speaks with greater precision and correctness by designating the accident solely through the way a substance's existence is positively determined. Still, given the conditions attaching to the logical use of our understanding, it is unavoidable that we set apart, so to speak, whatever can vary in a substance's existence while the substance itself persists, and consider it in relation to the properly permanent and radical; and it is on this account that this category, too, falls under the heading of the relations, more as their condition than as itself containing any relation.

It is on this permanence, then, that the correction of the concept of alteration likewise rests. Coming-to-be and passing-away are not alterations of that which comes to be or passes away. Alteration, rather, is one manner of existing that succeeds upon another manner of existing in one and the very same object. Whatever undergoes alteration, then, is itself enduring, and it is only its state that changes. Since this change, then, bears solely on the determinations that can cease or likewise begin: we may put it in a somewhat paradoxical-sounding way and say that only the permanent (the substance) is altered, whereas the mutable undergoes no alteration but a change, some determinations ceasing and others beginning.

Alteration, accordingly, is perceptible only in substances, and a sheer coming-to-be or passing-away that did not concern merely some determination of the permanent could never amount to a possible perception at all, for it is precisely this permanent that first renders representable the passage out of one state into another and out of non-being into being — a passage, then, that can be cognized empirically only as the shifting determinations of what abides. Suppose something began to be absolutely, then you would need a point in time at which it was not. But onto what would you fasten that point, if not onto something already present? For an empty time preceding it is no object of perception; whereas if you attach this coming-to-be to things that existed beforehand and last up to the thing that arises, then the latter was but a determination of the former as the permanent. And it stands the same with passing-away, for this presupposes the empirical representation of a time at which an appearance no longer is.

Substances (in the appearance) are the substrates of all determinations of time. Were some of them to come to be and others to pass away, the one and only condition of time's empirical unity would thereby be cancelled , and the appearances would then be referred to two distinct times in which existence ran its course side by side — which is absurd. For time is but one, and within it all the different times must be posited not together but one after another.

Permanence, then, proves to be a condition necessarily required if appearances are to be determinable at all as things or objects within a possible experience. But as for what the empirical criterion of this necessary permanence — and with it of the substantiality of appearances — might be, the sequel will afford us occasion to note what is needful.

Second Analogy. Principle of succession in time in accordance with the law of causality

All alterations take place conformably to the law linking cause and effect.

Proof.

(That all appearances following one upon another in time are, one and all, nothing but alterations, i.e. a successive being and non-being of the determinations of the substance that endures — so that the being of this substance, coming after its own non-being, or its non-being, coming after its existence, in short, that the substance itself neither comes into being nor passes away — all this the earlier principle has demonstrated. One might just as well have phrased it thus: All change (succession) among appearances is nothing but alteration; for a substance's coming-to-be or ceasing-to-be does not count as its alteration, given that the very concept of altering demands that one selfsame subject be posited as existing — and thus as enduring — under two contrary determinations. With this advance notice in place, here is the proof).

What I perceive is that appearances come one after another — that at some given time the things are in a state whose contrary held in the state before. So what I am really doing is binding together two perceptions within time. Yet such binding is no achievement of sense and intuition on their own; it arises here from a synthesizing power of imagination, which fixes inner sense as regards the relation in time. Now this power is free to link the two states just mentioned in two opposite orders, letting either precede the other in time; for time on its own admits of no perception, and one cannot read off from the object, by reference to time and as if empirically, which member comes first and which after. Hence all I am aware of is that my imaginative power sets down the one before and the other after, not that within the object itself the one state runs ahead of the other; put differently, bare perception leaves the objective relation among the appearances that follow each other undecided. For this relation to be known as something settled, the connection between the two states has to be conceived so that it fixes, as necessary, which of them is to be set first and which second, ruling out the reverse. Now a concept bringing with it a necessity of synthetic unity can be nothing other than a pure concept of the understanding, absent from perception itself; and in the present case it is the concept governing the relation of cause and effect, by which the first fixes the second, in time, as what results from it — not as a thing that could merely run ahead in fancy (or fail to be perceived altogether). It follows that experience itself — namely empirical cognition of appearances — is possible only where we place the succession of appearances, and with it every alteration, under the causal law; and so those appearances, taken as objects of experience, are themselves possible only under this same law.

Apprehending the manifold that an appearance offers is at every turn successive. One representation of a part comes after the next. Whether the parts likewise succeed each other in the object is a further matter for reflection, not already settled by the former. Granted, anything at all — indeed each representation, so far as we are conscious of having it — may be termed an object; yet just what that term signifies when applied to appearances — taken not as representations that are themselves objects, but only as designating an object — demands more searching inquiry. To the extent that they, simply as representations, are also objects for consciousness, they cannot be marked off from the apprehending of them — their intake into imagination's synthesis; and so the verdict must be that the mind always brings forth the manifold of appearances one item after another. Were appearances things in themselves, no one could ever infer, from the sequence in which the representations of their manifold arrive, the way that manifold is joined together in the object. After all, our dealings extend to our representations and nothing more; what things in themselves might be — leaving aside the representations by which they act upon us — falls wholly outside the range of what we can cognize. So, although appearances are not things in themselves and yet remain the sole material offered us for cognition, my charge is to say what kind of temporal combination attaches to the manifold in the appearances themselves, even while, in apprehension, its representation runs on successively. Take, for instance, a house that stands before me: my apprehending of the manifold it presents proceeds bit by bit. The question now is whether that house's manifold is, in its own right, likewise successive — something no one, of course, would concede. Yet the moment I lift my concepts of an object to their transcendental import, the house ceases to be any thing in itself and becomes merely an appearance — a representation, that is — with a transcendental object left unknown; so what am I really asking when I ask how the manifold could be joined within the appearance itself (which, after all, is nothing on its own)? In this setting, whatever lies within the successive apprehending counts as representation, while the appearance handed to me — though it is no more than the aggregate of those representations — counts as their object, one with which the concept I extract out of the apprehended representations ought to square. It quickly becomes plain that, because truth is cognition's agreement with its object, the only thing open to question here is the formal requirements of empirical truth, and that an appearance, set over against the apprehended representations, can be presented as the object marked off from them solely when it falls under a rule setting it apart from any other apprehension and making some one manner of combining the manifold obligatory. Whatever in the appearance holds the condition for this compulsory rule of apprehending — that is the object.

Let us now carry on with the problem before us. That something occurs — i.e. that some thing, or state, arises which was not there before — is nothing we can empirically take in unless it is led by an appearance lacking that state; for an actuality succeeding an empty stretch of time, a coming-to-be with no prior state of things, is as unapprehensible as empty time is on its own. So each apprehending of an event amounts to a perception that comes after some other. Yet, because matters stand this way throughout every synthesis of apprehending — as my earlier house-example brought out — this feature alone does not set one apprehension apart from the rest. I remark, however, this further point: if, within an appearance harboring some occurrence, I label the earlier perceptual state A and the later one B, then in apprehension B can come only after A, while the perception A can only run ahead of B and never trail it. Suppose I watch a ship carried down the current. My perceiving of its downstream position comes after my perceiving of its upstream position along the river's flow, and there is no way, in apprehending this appearance, for the ship to register first downstream and only afterwards upstream. Thus the order of the perceptual sequence within apprehension is here fixed, and the apprehending is tied down to it. By contrast, in the earlier case of the house my apprehending perceptions could start from the roof and close at the base, or equally start from the bottom and finish at the top, and just as well run through the manifold of empirical intuition rightward or leftward. Across that string of perceptions, then, no fixed order compelled me to any particular starting point in apprehending if I was to bind the manifold together empirically. With the perception of what occurs, however, such a rule is present without fail, and it renders the order of the successive perceptions (in apprehending this appearance) necessary.

Here, accordingly, I am obliged to read the subjective sequence of my apprehending off the objective sequence of the appearances; otherwise the former stays entirely loose and tells no one appearance apart from the next. Taken by itself the subjective sequence establishes nothing regarding how the manifold hangs together in the object, since it is wholly a matter of caprice. The objective sequence, by contrast, lies in that ordering of the appearance's manifold whereby apprehending the one member (the thing that occurs) trails apprehending the other (the antecedent) in accordance with a rule. This alone licenses me to assert of the appearance itself — not just of my act of apprehending — that a sequence resides in it, which comes to the same as saying I can conduct the apprehending in no other order than exactly this one.

By such a rule, then, whatever in general leads up to an event must contain the condition for a rule under which that event invariably and of necessity ensues; the reverse route, though, is closed to me — I cannot start from the event and pin down (by apprehending) what went before. For out of a later moment no appearance travels back to the earlier one, though it does bear on some preceding one or other; whereas from a given time the passage forward to the determinate subsequent time cannot be escaped. So, being after all a thing that comes after, it has of necessity to be referred to some other, antecedent thing that it succeeds under a rule — necessarily, that is — so that the event, qua conditioned, points reliably to a condition, and this condition in turn settles the event.

Imagine that nothing at all precedes an event on which it would have to follow by a rule; then every perceptual sequence would reside in apprehension alone — would be simply subjective — and would fix nothing objectively about which perception truly ought to rank as prior and which as posterior. On these terms we would be left with a mere play of representations answering to no object whatever; that is, our perceiving would fail to separate one appearance from another in point of temporal relation, since apprehending runs the same course everywhere and so nothing within the appearance pins it down in a way that would make a determinate sequence objectively necessary. Hence I shall decline to say that two states succeed each other in the appearance, and say only that one act of apprehending trails another — a thing wholly subjective, settling no object, and therefore incapable of passing for cognition of any object at all (not even within the appearance).

Whenever, then, we experience that something takes place, we invariably take for granted that some antecedent exists which it succeeds by a rule. Lacking that, I would never predicate 'following' of the object, for the bare succession within my apprehending, unless a rule fixes it in relation to our experience, entitles me to no succession in the object. It is thus always by appeal to a rule — one whereby the appearances in their succession, i.e. as they come to pass, are governed by the antecedent state — that I turn my subjective synthesis (of apprehending) into an objective one; and only on this single assumption does experience of an occurring thing become possible at all.

Admittedly this looks like a clash with everything that has ever been observed about how our use of the understanding proceeds — the view being that only by noticing and comparing the agreeing sequences whereby many events trail preceding appearances were we first guided to hit upon a rule under which certain events forever come after certain appearances, and thereby first moved to fashion for ourselves the concept of a cause. So construed, the concept would be empirical through and through, and the rule it furnishes — that whatever comes about has some cause — would prove no less contingent than experience is: its universality together with its necessity would in that case be a mere fiction, devoid of genuine universal force, resting as it would not upon anything a priori but merely upon induction. The situation, though, is the same as with the other pure representations a priori (space and time, say): we can draw them out of experience as clear concepts only because we had already laid them into experience and by their means first made experience come about. True enough, the logical clarity of this representation — a rule fixing the series of events, i.e. the concept of a cause — comes within reach only after we have employed it in experience; yet regarding it as the condition for the synthetic unity of appearances throughout time was all the same what grounded experience itself, and so ran ahead of experience a priori.

What it comes down to, therefore, is showing by an example that never, not even in experience, do we assign the succession (of an event, wherein something arises that formerly was not) to the object, and mark it off from the subjective succession belonging to our apprehending, save where a rule underlies things and forces us to keep to this arrangement of the perceptions in preference to any other — indeed that this very forcing is what makes the representation of a succession in the object possible in the first place.

Within us there are representations that we are able to become aware of. But however widely this awareness reaches, and however exact or meticulous it is, they never cease to be mere representations — inner determinations of our mind standing in some temporal relation or other. By what route, then, do we get to setting an object over against these representations, or crediting them, beyond their subjective reality as modifications, with some objective reality or other, I know not what? Objective meaning cannot lie in a relation to some further representation (namely of what one would like to call the object), else the question simply recurs: how does this second representation, for its part, step outside itself and gain objective meaning over and above the subjective meaning that belongs to it as a determination of the mind's condition? When we probe what fresh quality the relation to an object bestows on our representations, and what standing they acquire by it, we discover that it accomplishes only this: it makes the joining of the representations necessary after a certain fashion and places them under a rule; and, the other way around, only because a certain ordering is necessary in the temporal relation of our representations does objective meaning accrue to them.

Throughout the synthesis of appearances the manifold of representations comes ever one after another. By this, however, no object whatever gets represented, for a succession shared by every apprehension alike keeps nothing marked off from anything else. The instant, though, that I notice or assume within this succession a bearing on the antecedent state, from which the representation issues by a rule, something is thereby represented as an event, as what comes to pass — that is, I cognize an object that has to be lodged at one definite spot in time, a spot that the preceding state permits it to receive in no other way. So, in perceiving that something occurs, my representation carries first of all that something goes before it, since it is exactly by reference to this that the appearance gets its place in time — namely, that of coming to exist after an earlier time in which it did not. Its fixed temporal place within this relation, however, it can obtain only if something is assumed in the antecedent state upon which it invariably — that is, by a rule — comes after; whence it follows, first, that I may not turn the series around and set what occurs ahead of that which it succeeds, and, second, that once the preceding state is posited, this determinate event ensues unfailingly and of necessity. In this way there arises an ordering among our representations wherein the present (so far as it has come to be) directs us to some antecedent state as a correlate — as yet undetermined though it be — of this given event, a correlate that all the same bears determiningly on the event as its consequence and knits it necessarily to itself along the time-series.

Now if it belongs to the necessary law of our sensibility — hence to a formal condition shared by all perceptions — that earlier time determines later of necessity (seeing that I reach the later by no path but the earlier), then it is likewise an inescapable law of the empirical representation of the time-series that whatever existence falls in the later time is settled by the appearances of the time gone by, and that these, as events, occur only to the extent that the earlier appearances mark out for them their existence in time, i.e. lay it down by a rule. For in the appearances alone are we able empirically to know this continuity within the interconnection of times.

Understanding is requisite for all experience and its very possibility, and its first contribution here is not to render the representation of objects distinct but rather to make the representation of an object possible in the first place. It brings this about by carrying the order of time over to the appearances and their existence, allotting to each — as a member that follows — a temporal place fixed a priori relative to the appearances before it, a place without which it would fail to accord with time itself, which apportions to every one of its parts its place a priori. This assignment of place cannot, however, be drawn from any relation of the appearances to absolute time (that being no object of perception); on the contrary, the appearances have to determine one another's temporal places and make such placing necessary within the order of time — meaning that whatever follows or occurs must come, under a universal rule, after what the antecedent state held; and out of this grows a series of appearances which, through the understanding, produces and renders necessary, in the field of possible perceptions, that very order and unbroken connection already found a priori in the form of inner intuition (time), where every perception would have to take its place.

So that something occurs is a perception belonging to a possible experience — one made actual once I treat the appearance as fixed as regards its temporal place, and thus as an object retrievable at any time within the nexus of perceptions under a rule. And this rule — for pinning something down in the order of time — runs thus: within the antecedent there must be found the condition under which the event forever (i.e. necessarily) ensues. Hence the principle of sufficient reason is what grounds possible experience — that is, the objective cognition of appearances as they stand related in time's succession.

The proof-ground of this principle, however, hinges on nothing but the following points. Every empirical cognition involves imagination's synthesis of the manifold, forever successive; within it, that is, the representations come always one upon another. Yet in imagination this sequence carries no fixed order (nothing dictating what shall go first and what after), and the run of successive representations may be traversed backward no less than forward. Should this synthesis, though, be one of apprehension (of the manifold given in a particular appearance), then the order does stand fixed in the object — or, put more exactly, there resides in it an order of the successive synthesizing that determines an object, an order by which something has necessarily to precede and, that being posited, the other has necessarily to ensue. Accordingly, for my perception to hold the cognition of an event — of a thing that genuinely occurs — it has to be an empirical judgment wherein one conceives the succession as settled: as presupposing, that is, another appearance in time which it succeeds necessarily, or by a rule. Were it otherwise — were I to posit the antecedent and yet have the event not follow it of necessity — I should have to regard the thing as no more than a subjective sport of my fancies, and, should I still picture something objective in it, dub it a bare dream. So the relation among appearances (viewed as possible perceptions), whereby the later member (what occurs) has its existence fixed necessarily, and by a rule in time, through something earlier — in short, the relation of cause to effect — constitutes the condition for the objective validity our empirical judgments possess in regard to the run of perceptions, and hence for their empirical truth, and so for experience. The principle asserting a causal relation across the succession of appearances therefore holds good of every object of experience as well (given the conditions of succession), precisely because it is what grounds the very possibility of any such experience.

At this point, though, a further misgiving surfaces, and it needs clearing away. Our formulation confines the principle of causal linkage among appearances to their succession, yet in applying it one notices that it fits their coexistence too, cause and effect being capable of simultaneity. Consider the warmth in a room, which one does not encounter out in the open air. Casting about for its cause, I light upon a stove that has been fired up. This stove, as the cause, coexists with its effect, the room's warmth; so no time-order separates cause from effect here — they are contemporaneous — and still the law stands. Most of nature's operative causes run alongside their effects, and any time-order among the latter springs merely from the cause's inability to discharge its full effect in one moment. Even so, at the moment when the effect first emerges it always coincides with its cause's causality, for had that cause left off being a moment sooner, the effect would never have come about. One must be careful to see that what counts is time's order and not its elapsing : the relation holds even where no time has passed. The interval between the cause's causality and its immediate effect may shrink to the vanishing point (making them contemporaneous), and yet how the one stands to the other stays forever determinable in terms of time. Should I take as cause a ball resting on a stuffed cushion and denting a hollow into it, it is contemporaneous with its effect. All the same, I tell the two apart by the temporal relation in the dynamical linkage between them. Lay the ball onto the cushion, and the hollow succeeds its formerly even surface; but let the cushion already bear (from I know not where) a hollow, and no leaden ball comes after it.

Time-order, then, really is the one empirical mark of the effect as against the causality of the cause going before. A glass is what causes water to climb above its own level surface, even though the two appearances are contemporaneous. For no sooner do I scoop the water out of some larger vessel with the glass than something happens, namely the turning of the flat level it kept there into the concave one it takes on within the glass.

Such causality points onward to the concept of action, action to that of force, and by this route to the concept of substance. Because I have no wish to clog my critical project — aimed strictly at the springs of synthetic cognition a priori — with dissections that bear only on clarifying concepts (not enlarging them), I hand their thorough discussion over to some future system of pure reason, even though analysis of this kind already abounds in the familiar handbooks of the subject. What I cannot pass over, however, is the empirical mark of a substance, so far as substance appears to disclose itself not by the appearance's persistence but, more readily and better, through action.

Wherever action is present — and with it activity and force — substance too is present, and it is in substance alone that we must locate the seat of that teeming wellspring of appearances. Well and good as far as it goes; but when it comes to spelling out what one means by substance, and doing so without the faulty circle, the account is not so cheaply given. How, from the action, is one to conclude at once to the persistence of the agent — that being, after all, so essential and distinctive a sign of substance (phaenomenon)? Yet on the strength of what we said earlier the question resolves without any such trouble, however insoluble it would prove in the customary way (of working merely analytically upon one's concepts). Action, by its very meaning, denotes how the subject of causality stands to the effect. And because every effect lies in what comes to pass — thus in the changeable, which time marks off by succession — its final subject is the abiding, the substratum underlying all that shifts, i.e. substance. For by the causal principle actions constitute at all times the primary ground for every change among appearances, and so cannot reside in a subject that is itself changing, since that would call for yet further actions and a further subject to determine the change. On this basis action now establishes substantiality as a sufficient empirical mark, sparing me any prior search for the substance's persistence by way of compared perceptions — a search that could not, in any event, be carried through this way with the completeness that the scope and rigorous universality of the concept demand. For it follows securely that the primary subject of the causality behind all coming-to-be and passing-away cannot, within the field of appearances, itself come to be or pass away — an inference that terminates in empirical necessity and abidingness in existence, and thus in the concept of a substance as appearance.

Whenever an event occurs, the sheer coming-to-be — leaving aside what the thing is that comes to be — already forms, on its own, a topic for inquiry. The passage out of a state's non-being into that state — even supposing the state carried no quality within the appearance — stands by itself as something requiring examination. As was set out under heading A, this arising touches not the substance (which does not arise) but its state. It is thus alteration only, and not a springing-up out of nothing. Where such a springing-up is taken as the effect of an external cause, it is termed creation, which we cannot admit as an event among appearances, since its bare possibility would at once cancel the unity of experience; though if I view all things not as phenomena but as things in themselves and as objects of the mere understanding, they may — for all their being substances — be looked on as hanging, in their existence, upon an external cause; but that would then drag along wholly other senses of the words and would not suit appearances taken as possible objects of experience.

In what way anything whatever admits of alteration; how it can come about that a state at one temporal point gives way to its opposite at another — of all this we hold not the faintest concept a priori. What it takes is familiarity with real forces, obtainable only by experience — the moving forces, say, or, amounting to the same thing, certain successive appearances (motions) that betoken such forces. The form of any alteration, however — the condition on which alone it can go forward as the emergence of another state (no matter what its content, i.e. no matter which state is being altered) — and therefore the succession of the states themselves (the thing that happens) can all the same be weighed a priori under the causal law together with the conditions of time.²⁶

Let a substance move from a state a to another state b: the moment of the second differs from the moment of the first state and comes after it. In the same way the second state, as a reality (within the appearance), is set off from the first — in which that reality was absent — just as b is set off from zero; that is, even were b to diverge from a in magnitude alone, the alteration amounts to a coming-to-be of b - a, absent from the antecedent state, relative to which the latter equals 0.

The query, accordingly, is this: in what manner a thing crosses over from a state = a to another = b. Two moments are always parted by a time, and the two states holding in them always by a difference possessing magnitude (since the parts of appearances are, once more, magnitudes throughout). Hence each crossing from one state to the next takes place within a time lying between two moments, the earlier settling the state the thing quits, the later the state it reaches. The pair of them, therefore, bound the time of an alteration — and so the intermediate state between the two states — and in that capacity form part of the alteration as a whole. Every alteration, moreover, has a cause that displays its causality across the entire time through which the alteration runs. So this cause brings forth its alteration not in a flash (all at once, in one moment) but over a span of time, such that, as the time swells from the opening moment a to its close in b, the reality's magnitude (b - a) is generated too, passing through every lesser degree lying between the first and the last. Every alteration, then, can happen solely through an unbroken action of causality, which — so far as it stays uniform — one terms a moment. Out of such moments the alteration is not composed; rather they beget it as their effect.

Here, then, we have the law governing the continuity of all alteration, whose basis is this: that neither time nor the appearance within time is built out of smallest parts, and that even so, in altering, the thing's state moves through all those parts — as elements — to its second state. It holds that there is no difference of the real within the appearance, just as no difference among the magnitudes of times is the smallest; and so the fresh state of reality springs from the first — wherein that reality was lacking — across all its infinite degrees, whose mutual differences are, all told, tinier than the one between 0 and a.

Whatever service this proposition might render in the study of nature is nothing that concerns us at present. How a proposition of this sort, seemingly such an enlargement of our cognition of nature, can be possible fully a priori — that emphatically calls for our scrutiny, even where the plain evidence shows it to be genuine and correct, so that one might fancy oneself let off the question of how it came to be possible. For groundless claims to enlarge our cognition by pure reason are so various that one has to adopt it as a universal principle to stay utterly wary on this head, and, lacking papers that can supply a solid deduction, to credit and take up nothing of the kind, however lucid the dogmatic proof.

Any growth in empirical cognition, any forward step of perception, is merely a further determining of inner sense — a progress in time — no matter what the objects are, appearances or pure intuitions. This progress through time settles everything while itself receiving no further determination from anything ; its parts, that is, are given within time and by time's synthesis, never in advance of it. On that account, each passing-over in perception to a temporal successor is a determining of time through the bringing-forth of this perception; and because that time is at every point and throughout a magnitude, what we have is the bringing-forth of a perception as a magnitude, running through all degrees — none of them least — from zero up to its settled degree. Hereby the possibility now comes to light of knowing, as to their form , a law of alterations a priori. We do no more than forestall our own apprehending, whose formal condition, residing in us ahead of every appearance that is given, has surely to be knowable a priori.

And so, precisely as time holds the sensible condition a priori for the possibility of an unbroken passage of the existent to what comes next, so too, through the unity of apperception, the understanding supplies the a priori condition for the possibility that all the places of the appearances within this time be continuously determined — by way of the chain of causes and effects, whereby the former unfailingly drag the existence of the latter after them, and thereby lend the empirical cognition of time-relations validity for every time (universally), and hence objective validity.

Third Analogy. Principle of coexistence in accordance with the law of reciprocity or community

All substances, to the extent that they can be perceived as coexisting in space, stand in thoroughgoing reciprocity.

Proof.

Two things are simultaneous if, in empirical intuition, perceiving the one can, upon the perception of the other, follow reciprocally (which, within the temporal succession of appearances, is impossible, as the second principle already established). Accordingly I may cast my perception first upon the moon and afterwards upon the earth, or in reverse order first upon the earth and then upon the moon, and it is just because the perceptions of these objects admit of following one another in turn that I declare them to coexist. Coexistence, now, consists in the manifold's existing within one and the same time. Time itself, however, cannot be perceived, such that from things being posited in the same time one might gather that the perceptions of them can succeed one another in turn. Hence the imagination's synthesis in apprehension would exhibit each of these perceptions merely as one present in the subject while the other is absent, and conversely, yet not as showing that the objects coexist—that is, that if the one is there the other too is there within the same time, and that this is necessary if the perceptions are to be capable of succeeding one another in turn. A concept of the understanding concerning the mutual sequence of the determinations of these things, coexisting outside one another, is therefore demanded, so that one may assert the mutual sequence of perceptions to be grounded in the object, and so represent the coexistence as objective. But the relation of substances in which the one harbors determinations whose ground lies in the other is the relation of influence, and where each in turn harbors the ground of the other's determinations, it is the relation of community, or reciprocity. The coexistence of substances in space, then, admits of being cognized in experience only on the supposition of a reciprocity obtaining among them; and this reciprocity is accordingly likewise the condition under which the things themselves are possible as objects of experience.

Things coexist to the extent that they exist within one and the same time. But by what does one recognize this: that they lie in one and the same time? By the order in the synthesis by which this manifold is apprehended remaining indifferent, that is, by its being able to run from A through B, C, D to E, or in reverse from E to A as well. For were it successive in time (in the order commencing at A and terminating at E), it would be impossible to set the apprehension going from the perception of E and to travel back to A, since A belongs to elapsed time and can therefore no longer be an object of apprehension.

Now suppose that, within a manifold of substances as appearances, each were wholly isolated—that is, none acted upon another or received influences from it in turn: then I maintain that their coexistence would form no object of any possible perception, and that the existence of the one could, by no route of empirical synthesis, lead over to the existence of the other. For should you conceive them as sundered by a wholly empty space, the perception advancing from the one to the other in time would indeed fix the latter's existence through a succeeding perception, yet could not settle whether the appearance objectively succeeds the first or is instead together with it.

Beyond bare existence, then, there must be something more, by which A assigns to B its position in time and, reciprocally, B again to A, since only on this condition can substances so conceived be represented in experience as coexisting. Now that alone assigns to another its position in time which is the cause of it, or of its determinations. Every substance, accordingly (given that only in respect of its determinations can it be an effect), must contain within it the causality of certain determinations in the other and, at once, the effects of the other's causality—that is, they must stand in dynamical community (whether directly or through intermediaries), if coexistence is ever to be cognized in some possible experience. But everything is necessary in respect of the objects of experience without which experience of those very objects would be impossible. It is therefore necessary that all substances in the field of appearance, to the extent they coexist, stand in thoroughgoing community of reciprocity with one another.

In our language the word community is equivocal and may signify as much communio as commercium. Here we take it in the latter acceptation, as a dynamical community, apart from which even local community (communio spatii) could never be cognized empirically. Our experiences readily show that only continuous influences, present at every point of space, are able to guide our sense from one object across to another; that the light which plays between our eye and the heavenly bodies sets up a mediate community between us and those bodies, and so demonstrates their coexistence; that we can alter no place empirically (that is, perceive such alteration) unless matter on every side renders possible for us the perception of our own position, and that this position, solely through its reciprocal influence, can exhibit its coexistence and, reaching thereby to the remotest objects, their coexistence as well (though only mediately). Without community every perception (of appearance in space) stands cut off from the rest, and the chain of empirical representations—that is, experience—would, upon a new object, commence wholly afresh , without the previous chain being in the slightest connected with it or standing in any relation of time. I have no wish hereby to refute empty space at all: it may well subsist wherever perceptions simply fail to reach, so that no empirical cognition of coexistence occurs there; but in that case it is, for all our possible experience, no object whatever.

The following may serve by way of clarification. Within our mind all appearances, as belonging to one possible experience, must stand in a community (communio) of apperception; and to the extent the objects are to be represented as bound together in coexisting, they must reciprocally fix their position in one time and thereby make up a whole. Should this subjective community rest upon an objective ground, or be referred to appearances as substances, then the perception of the one must, as ground, render the perception of the other possible, and vice versa, in order that the succession forever present in perceptions qua apprehensions not be imputed to the objects, but that these instead admit of being represented as coexisting. This, however, is a reciprocal influence—that is, a real community (commercium) of substances—apart from which, accordingly, the empirical relation of coexistence could not occur in experience. By means of this commercium the appearances, in so far as they lie outside one another yet in interconnection, make up a composite (compositum reale), and composites of such a kind become possible in manifold ways. The three dynamical relations, out of which all the others spring, are thus that of inherence, that of consequence, and that of composition.

Such, then, are the three analogies of appearances. They are nothing more than principles for fixing the existence of appearances in time in keeping with all three of its modes: their relation to time itself, viewed as a magnitude (the magnitude of a thing's existence, namely its duration); their relation within time as a series (successively); and finally their relation within it as the sum of all existence (togetherness). This unity of time-determination is dynamical through and through; time, that is, is not looked upon as that wherein experience would directly assign to each existence its place—an impossibility, given that absolute time is nothing perceivable by which appearances could be held together—but rather the rule of the understanding, whereby alone the existence of appearances can gain synthetic unity in respect of temporal relations, assigns to each of them its place in time, and does so a priori and with validity for any and every time.

By nature (understood empirically) we mean the interconnection of appearances, as regards their existence, under necessary rules—that is, under laws. There are, then, certain laws—and indeed a priori ones—that first render a nature possible at all; the empirical laws can obtain and be discovered only through experience, and this in conformity with those original laws by which experience itself first grows possible. Our analogies, then, properly present the unity of nature in the interconnection of all appearances under certain exponents, which give voice to nothing but the relation of time (in so far as it embraces all existence within itself) to the unity of apperception—a unity realizable solely in synthesis conducted by rules. Together, therefore, they declare: all appearances lie within a single nature and must so lie, for without this a priori unity there could be no unity of experience, and hence no determination of the objects contained in it.

Yet concerning the mode of proof we have employed with these transcendental laws of nature, together with its distinctive character, a remark must be made that is at the same time of great weight as a precept for any other attempt to demonstrate propositions that are intellectual and at once synthetic a priori. Had we set out to prove these analogies dogmatically, that is, from concepts —namely, that whatever exists is met with solely in what is enduring; that every event presupposes something in the foregoing state upon which it follows by a rule; and finally that, in the manifold which is together, the states stand in mutual relation and are together by a rule (stand in community)—every exertion would have been utterly futile. For from a given object and its existence one simply cannot reach the existence of another, or its manner of existing, through bare concepts of the things in question, however one may choose to dissect them. What, then, was left to us? The possibility of experience, as a cognition wherein all objects must in the end be capable of being given to us, if their representation is to possess objective reality for us. Within this third element, whose essential form lies in the synthetic unity of apperception across all appearances, we came upon conditions a priori for the thoroughgoing and necessary determination in time of everything existing in appearance—conditions without which even empirical time-determination would be impossible—and upon rules of synthetic unity a priori by which we were able to anticipate experience. For lack of this method, and beguiled by the notion of proving dogmatically synthetic propositions that the understanding's empirical use commends as its principles, it has repeatedly come to pass that the principle of sufficient reason has had a proof attempted for it, always in vain. To the remaining two analogies no one gave a thought, however constantly they were drawn upon in silence,²⁷ because the guiding thread of the categories was absent—the thread which alone can uncover and make conspicuous every gap in the understanding, whether in concepts or in principles.

4. The postulates of empirical thought in general

1. Anything that accords with experience's formal conditions (with respect to intuition and to concepts alike) is possible.

2. Anything bound up with the material conditions of experience (with sensation) is actual.

3. Anything whose connection to the actual stands determined by experience's general conditions is (exists) necessary.

Elucidation.

A distinctive feature attaches to the categories of modality: as predicates appended to a concept, they add nothing whatever to it as a determination of the object, and merely voice its bearing on the faculty of cognition. Even where the concept of a thing is already fully complete, I may yet inquire, regarding that object, whether it is merely possible, or actual as well, or—should it be the latter—whether it is moreover necessary? No additional determinations get thought into the object itself by this means; what is asked is solely how the object (with all its determinations included) is situated toward the understanding and its empirical employment, toward the empirical power of judgment, and toward reason (as applied to experience).

It is for just this reason, too, that the principles of modality amount to nothing beyond clarifications of the concepts of possibility, actuality, and necessity as employed empirically, and with that, simultaneously, to restrictions confining every category to a merely empirical employment, disallowing and refusing the transcendental one. For should these concepts carry more than a bare logical import and do more than express analytically the form of thinking—should they instead pertain to things together with their possibility, actuality, or necessity—then their reach must extend to possible experience and to its synthetic unity, wherein alone objects of cognition come to be given.

The postulate concerning the possibility of things demands, accordingly, that the concept of them harmonize with the formal conditions of an experience as such. These conditions, however—that is, the objective form of experience taken generally—embrace every synthesis demanded for cognizing objects. Should a concept enclose a synthesis within it, that concept counts as empty and answers to no object whenever the synthesis in question lies outside experience—either drawn from experience, whereupon we speak of an empirical concept, or serving as the a priori condition upon which experience generally (its very form) rests, whereupon we have a pure concept belonging to experience even so, since its object admits of being met with nowhere but there. For whence should one fetch the sign of an object's possibility, where that object has been thought by way of an a priori synthetic concept, if not from the very synthesis constituting the form under which objects are cognized empirically ? Freedom from contradiction within such a concept is, to be sure, a logical condition that cannot be dispensed with; yet for the concept's objective reality—that is, for the possibility of the sort of object thought through it—this falls far short of sufficing. So it is that the concept of a figure bounded by two straight lines harbors no contradiction, since the concepts of two straight lines and of their intersection do not by themselves negate a figure; the impossibility here rests not with the concept as such but with constructing it in space—that is, with the conditions of space and its determining; and these conditions, in turn, possess objective reality of their own, which is to say they bear upon possible things, for they hold within themselves, a priori, the form of experience in general.

Let us now bring before our eyes just how widely useful and influential this postulate of possibility proves to be. Suppose I represent to myself an abiding thing, such that whatever undergoes change belongs only to its state: from a concept of that kind, taken by itself, I can never make out that a thing so conceived is possible. Or suppose I represent something meant to be so constituted that, once it is posited, invariably and without fail something further ensues from it—such a thing may well be conceivable free of contradiction; but whether any property of this sort (namely causality) is encountered in some possible thing is not thereby settled. Lastly, I may represent to myself several things (substances) constituted so that the state of one entails a consequent state in another, and this reciprocally; yet whether a relation of that kind can belong to any things is in no way to be gathered from these concepts, which hold nothing but an arbitrary synthesis. Their objective reality—that is to say, their transcendental truth—is recognized, then, on this ground alone: that these concepts articulate a priori the relations that perceptions bear within every experience; recognized, indeed, in a manner free of dependence on experience, and yet not free of all reference to the form of an experience as such and to that synthetic unity wherein alone objects lend themselves to empirical cognition.

But were someone to wish to fashion wholly novel concepts of substances, of forces, of reciprocal actions from the material that perception lays before us, without taking over from experience itself any instance of their combination, then he would lapse into nothing but fantasies of the brain, whose possibility is attended by no sign at all, seeing that with them experience is neither enlisted as instructress nor made the source from which the concepts are drawn. Fabricated concepts of this kind cannot come by the sign of their possibility after the manner of the categories—a priori, as conditions on which all experience hangs—but only a posteriori, as concepts furnished through experience itself, and their possibility is either known a posteriori and empirically or not known whatsoever. Take a substance that would be abidingly present in space and yet leave it unfilled (that intermediate entity between matter and thinking beings which certain people have wanted to bring in), or some peculiar basic power of our mind for intuiting the future beforehand (rather than merely inferring it), or, lastly, a capacity of the mind for sharing in a community of thoughts with other human beings (however far off they might be): these are concepts whose possibility rests on nothing at all, since it admits of no grounding in experience and its familiar laws, and apart from these it comes to no more than an arbitrary linkage of thoughts—one that, contradiction-free though it is, can lay no claim to objective reality, and thus none to the possibility of any such object as one means here to think. Where reality is concerned, it more or less rules itself out to think a reality in concreto without summoning experience to assist: for reality can bear on sensation alone, as experience's matter, and does not touch the form of the relation—that form with which, if anything, one might toy in inventions.

I set aside, however, everything whose possibility is only to be gleaned from actuality within experience, and I dwell here solely on the possibility of things by way of a priori concepts, of which I go on to assert that it can obtain never from such concepts standing alone, but on every occasion only as the formal and objective conditions of an experience as such.

There is, admittedly, a semblance that a triangle's possibility might be recognized from its concept taken on its own (independent of experience it surely is); for we can in truth confer on it an object entirely a priori—that is, construct it. Yet since this yields only the form of an object, the triangle would forever stay a mere product of imagining, its object's possibility still in doubt, inasmuch as something further is called for—namely, that such a figure be thought under nothing but those conditions upon which all objects of experience repose. That space is a formal a priori condition of outer experiences; that the selfsame figurative synthesis by which we construct a triangle in imagination is one and the same as that which we carry out in apprehending an appearance so as to frame an empirical concept of it—this, and this alone, is what ties to the concept the representation of such a thing's possibility. And in this way the possibility of continuous magnitudes—indeed of magnitudes at large, their concepts being one and all synthetic—first grows clear never out of the concepts on their own, but out of them functioning as formal conditions for determining objects in experience generally; and where, after all, would one so much as look for objects answering to the concepts, if not within experience, by which alone objects reach us? This despite the fact that, without actually dispatching experience itself in advance, we can—purely by reference to the formal conditions under which anything at all is determined within experience as an object, and hence altogether a priori, though still only by reference to those conditions and inside their limits—recognize and characterize the possibility of things.

The postulate for cognizing the actuality of things calls for perception, and so for sensation of which one is aware; not, indeed, in immediate touch with the object itself whose existence is to be cognized, but at least the object's connection with some actual perception, following the analogies of experience, which lay out every real linkage within an experience taken generally.

Within the mere concept of a thing not a single sign of its existence can be come upon. For however complete that concept may be—so that nothing in the least is wanting for thinking a thing along with all its inner determinations—existence has, for all that, no bearing on any of this, but bears solely on the question whether such a thing is given to us, so that its perception might, if it comes to that, run ahead of the concept . For the concept's running ahead of the perception betokens the thing's mere possibility, whereas the perception, which supplies the matter for the concept, is the one and only sign of actuality. One may, however, cognize a thing's existence even ahead of perceiving it—thus comparatively a priori—provided only that it hangs together with certain perceptions by the principles governing their empirical linkage (the analogies). For then the thing's existence does, after all, cohere with our perceptions within a possible experience, and, guided by the thread of those analogies, we are able to pass from our actual perception across to the thing along the series of possible perceptions. It is thus that we cognize the existence of a magnetic matter pervading every body from our perception of iron filings drawn toward it, notwithstanding that a direct perception of this stuff lies beyond us, given how our organs are constituted. For, generally speaking, following the laws of sensibility and the connectedness of our perceptions within an experience, we should light upon the direct empirical intuition of that matter as well, were our senses more refined—their coarseness being wholly irrelevant to the form of possible experience as such. Wherever, then, perception together with its train extends by empirical laws, there likewise extends our cognition of the existence of things. Should we not set out from experience, or fail to advance by the laws of the empirical interconnection of appearances, we vainly make a show of trying to guess at or track down the existence of any thing whatever. One forceful objection, though, against these rules for proving existence in a mediated way is pressed by idealism, and here is the fitting place to refute it.

Refutation of idealism.

Idealism—the material sort is what I have in mind—is that doctrine which pronounces the existence of objects in space beyond us to be either merely questionable and indemonstrable or else outright false and impossible; the former is the problematic idealism of Descartes, who holds but a single empirical claim (assertio)—to wit, I am—beyond doubt; the second is the dogmatic idealism of Berkeley, who pronounces space , along with all the things it clings to as their inseparable condition, to be something impossible in itself, and on that account pronounces the things in space, too, mere figments. Dogmatic idealism becomes inescapable once space is viewed as a property meant to belong to things in themselves; for then space, with everything it underlies as condition, turns into an absurdity. The basis of that idealism, however, we have already removed in the transcendental aesthetic. Problematic idealism, by contrast—advancing no thesis on the matter and merely professing our inability to demonstrate, through immediate experience, an existence apart from our own—is reasonable and befits a searching philosophical cast of mind: namely, to sanction no conclusive judgment until a sufficient proof has been secured. The proof thus called for has to establish that of outer things we possess experience and not bare imagination; and this can scarcely be accomplished otherwise than by showing that even our inner experience—undoubted by Descartes—the very experience in question, is possible only on the supposition of an outer experience.

Theorem.

The bare consciousness of my own existence—empirically determined though it is—establishes the existence of objects in space beyond me.

Proof.

Of my own existence I am conscious as determined within time. Every time-determination presupposes something abiding in perception. This abiding element, however, cannot be anything lodged in me, precisely because my own existence in time is what first stands to be determined by means of it. The perception of this abiding element is therefore possible solely through a thing external to me, and not through the bare representation of such a thing. It follows that my existence in time can be determined only by way of the existence of actual things that I perceive outside myself. Now consciousness in time is necessarily bound up with consciousness of the possibility of this time-determination; hence it is likewise necessarily bound up with the existence of things outside me as the condition of that time-determination—which is to say, consciousness of my own existence is at one and the same time an immediate consciousness of the existence of other things beyond me.

Remark 1. In the foregoing proof one notices that the very game idealism was playing is turned back upon it, and with the better right. Idealism took it that the sole immediate experience is the inner one, from which outer things are then only inferred—yet unreliably, as happens whenever one reasons from given effects to determinate causes, since the cause of the representations we may wrongly pin on outer things could just as well reside within ourselves. Here, however, it is demonstrated that outer experience is in fact the immediate one,²⁸ and that only through its mediation does there become possible—not the consciousness of our own existence, to be sure, but the determining of that existence in time, which is to say inner experience. Granted, the representation I am, giving voice to the consciousness capable of accompanying all thinking, is what immediately carries within it the existence of a subject, yet without any cognition of that subject as yet, and so no empirical cognition either, i.e., experience; for such cognition demands, over and above the thought of something existent, intuition besides—here inner intuition—with respect to which, namely time, the subject has to be determined, a task for which outer objects are indispensable throughout, so that inner experience itself turns out to be possible only mediately, and only by way of outer experience.

Remark 2. With this every empirical employment of our cognitive faculty in determining time now falls perfectly into line. Not merely can we perceive all time-determination solely through the alteration of outer relations (motion) as referred to what abides in space (say, the sun's motion relative to the objects on earth); beyond that, we possess nothing abiding at all to place beneath the concept of a substance by way of intuition, save matter alone, and even this abidingness is not skimmed from outer experience but presupposed a priori as the necessary condition of all time-determination, and thus likewise as a determination of inner sense—regarding our own existence—by the existence of outer things. My consciousness of my own self in the representation I is no intuition whatever, but a purely intellectual representation of the self-activity belonging to a thinking subject. This I, accordingly, carries not the slightest predicate of intuition that might, as something abiding, serve time-determination in inner sense for a correlate—the way impenetrability, for instance, attaches to matter as empirical intuition.

Remark 3. That the existence of outer objects is requisite for the possibility of a determinate consciousness of our own selves does not entail that every intuitive representation of outer things carries their existence along with it, for such a representation may perfectly well be the sheer work of imagination (in dreams no less than in madness); it is so, however, only through reproducing former outer perceptions, which, as has been shown, are themselves possible only through the actuality of outer objects. All that was to be proved at this point is that inner experience in general is possible only by means of outer experience in general. Whether some supposed experience or other might be nothing but imagination is a thing to be settled by that experience's particular determinations and by measuring it against the criteria of all actual experience.

Turning at last to the third postulate: it concerns the material necessity belonging to existence, not the merely formal and logical necessity found in the linkage of concepts. Now, since no existence of objects of the senses admits of being cognized wholly a priori—though it may be so comparatively a priori, relative to some other, already given existence—and since even then one can only ever reach the existence that has to be lodged somewhere within the experiential nexus of which the given perception forms a part: the necessity of an existence is never to be cognized out of concepts, but on every occasion only out of its linkage with whatever is being perceived, in keeping with the universal laws of experience. Now there exists nothing that could be cognized as necessary under the condition of other given appearances save the existence of effects issuing from given causes according to laws of causality. It is therefore not the existence of things (substances), but that of their state, whose necessity is all that we can cognize, and that from other states given in perception, following empirical laws of causality. Whence it follows that the touchstone of necessity resides entirely in the law of possible experience: that whatever comes to pass stands determined a priori through its cause within appearance. Hence it is only the necessity of effects within nature, whose causes are given us, that we cognize; and the token of necessity in existence stretches no farther than the field of possible experience, and even inside that field it does not apply to the existence of things as substances, since these can never be looked upon as empirical effects, nor as anything that comes to pass and arises. Necessity, then, has to do only with the relations among appearances by the dynamical law of causality, and with the possibility, resting thereon, of inferring a priori from some given existence (a cause) to another existence (its effect). Whatever comes to pass is hypothetically necessary; such is the principle that places the world's alteration under a law—a rule of necessary existence, absent which no nature could so much as occur. Hence the maxim that nothing comes about by blind hazard (in mundo non datur casus) is an a priori law of nature; and equally, that no necessity in nature is a blind one, but rather conditioned and thereby comprehensible necessity (non datur fatum). Both are laws through which the interplay of alterations is made subject to a nature of things (as appearances)—or, what amounts to the same, to the unity of the understanding, within which alone those alterations can belong to a single experience as the synthetic unity of appearances. These two principles fall among the dynamical ones. The first is, strictly, a corollary of the principle of causality (as it stands among the analogies of experience). The second falls among the principles of modality, which annex to the causal determination the further concept of necessity—a necessity that, however, stands beneath a rule of the understanding. The principle of continuity had barred, within the series of appearances (alterations), every abrupt leap (in mundo non datur saltus), and barred as well, within the whole assemblage of empirical intuitions in space, every gap or chasm between two appearances (non datur hiatus); for the proposition admits of being put thus: nothing can find its way into experience that would evidence a vacuum, or even let one pass as a part of the empirical synthesis. As for the void one might think outside the field of possible experience (outside the world), that does not come before the tribunal of the mere understanding, which passes verdict only on questions bearing on the use of given appearances toward empirical cognition; it is instead a matter for idealizing reason, which reaches out past the sphere of a possible experience and would pronounce on what encloses and delimits that experience itself, and so must be pondered within the transcendental dialectic. These four propositions, namely (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum), we could readily set forth, as with every principle of transcendental provenance, in an order matching the order of the categories, and prove to each its allotted place; but the reader already practiced will manage this unaided, or will easily hit upon the thread leading to it. They all converge, however, on this single aim: to let nothing into the empirical synthesis that might do damage or detriment to the understanding and to the continuous interconnection of all appearances—that is, to the unity of its concepts. For the understanding is the sole place in which the unity of experience, where all perceptions must find their station, comes to be possible.

Whether the field of the possible outruns the field embracing all that is actual, and whether the latter in turn outruns the sum of what is necessary—these are pretty questions, calling moreover for a synthetic resolution, and they too fall to nothing but the tribunal of reason; for they amount to asking, roughly, whether all things as appearances belong collectively to the single assemblage and context of one experience—of which each given perception is a part , one incapable therefore of being joined with any further appearances—or whether my perceptions may belong to more than a single possible experience (within its general interconnection). To experience at large the understanding furnishes a priori only the rule, conforming to the subjective and formal conditions of sensibility no less than of apperception, which alone render experience possible. Other forms of intuition (than space and time), and other forms of understanding as well (than the discursive form of thinking, or of cognition through concepts), we are utterly unable to devise or render intelligible to ourselves, possible though they might be; and even could we do so, they still would not belong to experience—the one cognition wherein objects are given us. Whether perceptions other than those belonging generally to our whole possible experience, and thus a wholly other field of matter, might yet occur is something the understanding cannot decide; its concern runs only to the synthesis of what is given. Otherwise, how paltry our customary inferences are—by which we conjure up a vast kingdom of the possible, whereof everything actual (every object of experience) is but a slight portion—stands glaringly plain. Everything actual is possible; from which, by the logical rules of conversion, there naturally issues the merely particular proposition that some possible things are actual, which then appears to signify as much as: many things are possible that are not actual. There is, granted, a semblance that one might even, outright, set the count of the possible above that of the actual, on the ground that something must still accrue to the former in order to constitute the latter. This accrual to the possible, however, is unknown to me. For whatever were to be superadded over and above it would be impossible. To my understanding there can accrue only something beyond the concord with the formal conditions of experience—namely, linkage with some perception or other; and whatever is linked to that by empirical laws is actual, even where it goes unperceived directly. But that, in thoroughgoing linkage with what perception gives me, a further series of appearances—and hence more than one all-encompassing experience—should be possible is not to be inferred from what is given, and, where nothing at all is given, still less so, since without matter nothing whatever lends itself to thought. Whatever is possible only under conditions that are themselves merely possible is not possible in every respect. It is in this latter sense, though, that the question gets taken up when one wants to know whether the possibility of things ranges further than experience is able to reach.

I have touched on these questions only so as to leave no gap in what, on the common view, is reckoned to fall among the concepts of the understanding. In fact, however, absolute possibility (the possibility that holds good in every respect) constitutes no mere concept of the understanding and can be of no empirical service whatever; it belongs to reason alone, which reaches out beyond every possible empirical employment of the understanding. For that reason we have had to rest content here with a purely critical remark, leaving the matter otherwise in obscurity pending some further, future handling.

As I mean now to bring to a close this fourth number, and with it the entire system of the principles of the pure understanding, I owe still an account of why I have styled the principles of modality postulates in particular. I decline to take the term here in the sense certain more recent philosophical writers have lent it—against the usage of the mathematicians, to whom it truly belongs—namely, that to postulate should amount to putting forward a proposition as immediately certain, without any warrant or proof; for were we to concede this in the case of synthetic propositions, however self-evident they might appear—conceding that, deduction aside, they may be pinned upon unqualified assent on the strength of their own mere pronouncement—then the whole critique of the understanding is forfeit, and since bold pretensions are never in short supply, ones from which even common belief (which is no credential, though) does not hold back, our understanding will lie exposed to every fancy, powerless to refuse its assent to pronouncements which, illegitimate though they be, nonetheless demand admission as genuine axioms in that very same tone of self-assurance. Whenever, then, a determination gets added a priori and synthetically to the concept of a thing, such a proposition must, without exception, have appended to it—if not a proof, then at the least a deduction of its assertion's legitimacy.

The principles of modality, however, are not objectively synthetic, since the predicates of possibility, actuality, and necessity in no degree enlarge the concept of which they are predicated, as though they set something more alongside the representation of the object. Yet being, all the same, forever synthetic, they are so only subjectively—that is, to the concept of a thing (of something real), about which they otherwise pronounce nothing, they annex the cognitive power in which that concept springs up and has its seat: so that, standing merely in the understanding in linkage with the formal conditions of experience, its object is termed possible; standing in connection with perception (sensation as the matter of the senses) and determined thereby, through the understanding's mediation, the object is actual; determined through the connection of perceptions in keeping with concepts, the object is termed necessary. What the principles of modality state of a concept, then, is nothing beyond the act of the cognitive faculty by which that concept is brought forth. Now in mathematics a postulate designates the practical proposition holding nothing but the synthesis by which we first supply ourselves an object and bring forth its concept—say, to describe a circle on a plane, from a given point, with a given line; and a proposition of that kind is for that very reason unprovable, since the procedure it prescribes is precisely the one by which we first bring forth the concept of such a figure. On just the same warrant, accordingly, we are entitled to postulate the principles of modality, for they contribute no increase to their concept of things as such,²⁹ but merely register the manner in which such a concept comes to be bound up with the cognitive power at all.

General remark on the system of principles

It is a very remarkable circumstance that the possibility of no thing whatever is open to our insight from the mere category; instead, an intuition must always lie ready at hand, one upon which the pure concept of understanding can have its objective reality set forth. Consider, say, the categories of relation. That 1) something might exist solely as subject and not as a mere determination belonging to other things—might, that is, be substance; or that 2) since something exists, something further must exist, so that anything at all might function as a cause; or 3) that, where a plurality of things is present, the presence of one of them should entail something for the others, and this mutually, so that on this footing a community of substances might obtain—none of this admits of being seen from mere concepts. The same goes for the other categories too—e.g., how one thing taken along with many might be one and the same, i.e., a magnitude, and so on. So long, then, as intuition is wanting, there is no telling whether an object is being thought at all by means of the categories, nor whether any object could ever answer to them anywhere; and this bears out that, on their own, they amount to no cognitions whatever but are mere forms of thought, serving to fashion cognitions from intuitions once these are given. For just this reason, too, no synthetic proposition can ever be built up out of categories alone. Take: in all existence there is substance, i.e., something able to exist only as a subject and never as a mere predicate; or again, each and every thing is a quantum, and so forth—cases in which nothing at all is available to carry us past a given concept so as to attach a further one to it. This is also why no one has ever managed to demonstrate a synthetic proposition from pure concepts of understanding taken by themselves—say, the proposition: whatever exists contingently has a cause. The furthest one has ever reached is the proof that, lacking this relation, the existence of what is contingent would be wholly beyond our comprehension—i.e., that through the understanding we could not cognize a priori the existence of any such thing; yet this yields no conclusion that the very same relation is at the same time what conditions the possibility of the matters themselves. Should one therefore turn back to look at the way we proved the principle of causality, one will become aware that our demonstration held good only of objects of a possible experience: whatever happens (every occurrence, that is) presupposes a cause—and this, moreover, in such a fashion that the proof went through only as a principle for the possibility of experience, hence for the cognition of an object presented in empirical intuition, and by no means from concepts alone. Granted, one cannot deny that this proposition—that everything contingent has to have a cause—shines forth clearly to anyone from concepts alone; but by then the concept of the contingent has already been framed so as to carry within it not the modal category (something whose non-being admits of being thought) but rather the category of relation (something capable of existing only as the upshot of another), and on that understanding it is, to be sure, an identical proposition: whatever can exist solely as a consequence carries its cause with it. Indeed, whenever we are called upon to give examples of contingent existence, it is always to alterations that we appeal, and not merely to the bare possibility of the thought of the opposite.³⁰ An alteration, though, is an occurrence, and as such is made possible only by a cause, so that its own non-being is, taken by itself, possible; contingency is accordingly recognized in the circumstance that a thing can exist only as a cause's effect, and so, once a thing is posited as contingent, to assert that it has a cause is an analytic proposition.

Still more remarkable, however, is the following: that to grasp how things are possible according to the categories, and so to display the objective reality of these latter, what we need is not intuitions merely but, throughout, even outer intuitions. Suppose we take the pure concepts of relation: we then find that 1) to furnish, as a correlate to the concept of substance, something persistent within intuition—and by that means to secure this concept's objective reality—we have need of an intuition in space (namely, of matter), since space alone stands persistently determined, whereas time, and with it everything belonging to inner sense, is in perpetual flux. 2) To exhibit alteration—the intuition that answers to the concept of causality—we have to take as our example motion, i.e., alteration in space; and it is indeed by this alone that alterations become intuitable to us whose possibility lies past the comprehension of any pure understanding. Alteration consists in the union, within the existence of one and the very same thing, of determinations contradictorily opposed to one another. By what means it is possible that a given state should be succeeded, in the same thing, by one opposed to it—of this no reason can render itself an account without an example, nor can it so much as be made intelligible short of intuition; and the intuition in question is that of a point's motion through space, whose existence at differing locations (a succession, that is, of opposed determinations) is what alone first sets alteration before us; for, to make even our own inner alterations thinkable afterward, we are obliged to picture time—the form of inner sense—by figure as a line, and inner alteration by the tracing out of that line (motion), so that the successive existing of ourselves across differing states is brought home to us through outer intuition; and the real ground of this lies in the fact that every alteration takes for granted something persistent in intuition if it is so much as to be perceived as an alteration at all, while within inner sense no persistent intuition is ever encountered. – Finally, so far as its possibility is concerned, the category of community simply cannot be grasped through bare reason, and thus there is no gaining insight into this concept's objective reality apart from intuition—outer intuition in space, that is. For how is the possibility to be thought that, given the existence of several substances, something (as effect) should follow reciprocally in the existence of the others from that of a single one—so that, since something is present in the first, on this ground something must be present in the rest as well, a thing not to be understood from the existence of these latter taken alone? For precisely this is what community demands, and yet, among things each of which isolates itself utterly through its own subsistence, it remains wholly unintelligible. Thus Leibniz, when he assigned the substances of the world a community such as the understanding alone thinks them to have, found a deity necessary as intermediary; for taken by their existence alone, that community struck him—rightly enough—as inconceivable. We, on the other hand, are quite able to make the possibility of such community (of substances taken as appearances) intelligible to ourselves, provided we represent them in space, that is, in outer intuition. For space already harbors within itself, a priori, formal outer relations that serve as conditions for the possibility of the real ones (in action and counteraction, hence in community). — By the same token it is readily shown that things can be possible as magnitudes—and the category of magnitude thereby have its objective reality made out—only within outer intuition, and that by the latter's mediation alone can this afterward be carried over to inner sense too. To keep from being prolix, however, I shall have to consign the examples of all this to the reader's own reflection.

This entire observation carries great weight—not solely for corroborating the refutation of idealism given above, but far more for marking out for us, once the topic becomes self-knowledge drawn from mere inner consciousness and from the determining of our nature with no assistance from outer empirical intuitions, just where the bounds of the possibility of any such cognition lie.

The concluding upshot of this whole section runs, then, as follows: the principles of the pure understanding, one and all, are nothing further than a priori principles for the possibility of experience, to which alone, likewise, every synthetic proposition a priori has its reference—indeed, the very possibility of such propositions rests wholly upon this reference.

Chapter 3. On the ground of the distinction of all objects in general into Phaenomena and Noumena

By now we have not merely journeyed across the territory of the pure understanding, giving each portion of it a careful inspection; we have also paced it out and fixed the position of every thing that lies within it. This territory, however, is an island that nature herself has locked within limits that cannot be altered. It is the territory of truth (a charming name), and around it lies a broad and tempestuous ocean, the very home of semblance, where more than one fog-bank, and more than one patch of ice on the verge of thawing, counterfeits fresh coastlines and, forever taunting with idle hopes the voyager who cruises about hunting for discoveries, draws him into escapades from which he is unable to desist and which he is nevertheless equally unable to see through to their close. Yet before we hazard ourselves upon this sea, in order to comb it across every latitude and to satisfy ourselves whether there is anything in those regions worth hoping for, it will pay us to throw one more look at the chart of the territory we are on the point of quitting, and to ask, in the first place, whether its contents might not after all suffice us, or whether sheer necessity forces us to rest content with them, should there prove to be no other soil anywhere for us to settle upon; and, in the second place, on what title it is that we hold this territory of ours and may count ourselves safe against every hostile pretension. These questions have, to be sure, been given a satisfactory answer already as the Analytic proceeded; even so, a brief recapitulation of how they were resolved may fortify our conviction, in that it gathers the several moments of the matter into one focus.

What we have found, in effect, is this: whatever the understanding produces out of its own resources, rather than taking it on loan from experience, is possessed by it all the same for one end only, namely to be applied within experience. The pure understanding's principles —be they a priori constitutive, as with the mathematical, or nothing more than regulative, as with the dynamical—amount to no more than, so to speak, the bare schema for a possible experience; for such experience owes its unity entirely to that synthetic unity which the understanding, spontaneously and from the first, imparts to the imagination's synthesis with respect to apperception, a unity toward which the appearances, serving as data for a cognition that is possible, must already stand a priori in a relation of accord. Now granted that these rules belonging to the understanding are not merely true a priori but are indeed the very wellspring of all truth—that is to say, of the concord between our cognition and its objects, inasmuch as they harbor within themselves the ground on which experience, taken as the entire compass of cognition wherein objects can come to be given to us, is possible—it still strikes us as insufficient merely to have set before us what is true; what one craves, rather, is to know it. Suppose, then, that this critical inquiry teaches us nothing beyond what, in the plainly empirical employment of the understanding, we would have carried out well enough on our own even without so fine-grained an investigation: in that case the gain to be had from it would seem not to repay the outlay and the elaborate apparatus. To this, admittedly, one might retort that nothing does more harm to the enlargement of our cognition than a certain officious curiosity which insists on knowing the benefit beforehand, every time, prior to embarking on any research and before it could so much as frame the faintest notion of that benefit, even were the latter set right before its eyes. Still, there is after all one benefit that can be brought home, and made a matter of concern, even to the most obstinate and least willing apprentice in such transcendental research, and it is this: that an understanding busied solely with its empirical exercise, one that never ponders the wellsprings of its own cognition, can indeed make excellent headway, yet is incapable of a single task—that of marking out for its own sake how far its exercise reaches, and of knowing what falls inside and what outside the whole of its province; for it is precisely to this end that the searching investigations we have conducted are demanded. Should it prove unable to tell whether given questions fall within its horizon or fall outside it, then it can never rest assured of its entitlements or its holdings, and has to brace itself for repeated, mortifying reprimands whenever it transgresses the frontiers of its domain—as inevitably it does—and strays off into fancy and deceptive show.

The thesis, then, that the understanding is competent to put none but an empirical use, and never a transcendental one, to any of its a priori principles—indeed to any of its concepts whatsoever—is one which, once it can be recognized with conviction, opens onto consequences of weight. What the transcendental employment of a concept within any given principle consists in is this: that the concept bears upon things in general and in themselves; whereas its empirical employment consists in its bearing merely upon appearances, that is, upon objects of an experience that is possible. That in fact only the latter is ever admissible becomes evident as follows. Every concept calls, to begin with, for the logical form of a concept (of thought) as such, and then, in addition, for the possibility of supplying it with an object upon which it might bear. Lacking this second requirement, it carries no sense and stands wholly void of content, however much it may yet retain the logical function of shaping a concept out of whatever data may be to hand. But an object gets furnished to a concept in no way save through intuition, and even where a pure intuition is available a priori in advance of the object, this pure intuition too can secure an object of its own—and hence objective validity—only by way of empirical intuition, of which it constitutes nothing more than the form. And so every concept—and with it every principle, no matter how far they may be possible a priori—still points back to empirical intuitions, that is, to data for a possible experience. Without that, they possess no objective validity whatever, and are a mere game—whether the imagination's or the understanding's—played, in each case, with their respective representations. Take just the concepts of mathematics for an example, and, to begin with, in their pure intuitions. Space is of three dimensions; between two points no more than a single straight line is possible; and so forth. Even though the whole of these principles, together with the representation of the object that this science takes as its business, arises entirely a priori within the mind, they would yet signify precisely nothing were we not in a position always to display what they mean in appearances (empirical objects). This is why one demands, of an abstracted concept, that it be made sensible—in other words, that the object answering to it be displayed in intuition—since, failing that, the concept would (as the saying goes) be left without sense, which is to say without significance. Mathematics meets this demand by constructing the figure, which is an appearance laid before the senses (though one produced a priori). Within that very science the concept of magnitude looks for its footing and its sense in number, and number in turn looks for these in the fingers, in the beads of the abacus, or in the strokes and dots that are put before the eyes. The concept, along with the synthetic principles or formulas drawn from such concepts, stays a priori in its origin throughout; but the deploying of them, and their bearing on supposed objects, can in the last resort be tracked down nowhere except in experience, whose possibility (so far as its form goes) those very principles hold a priori.

That the very same holds, moreover, of all the categories and of the principles spun out of them is likewise borne out by this: that not so much as one of them can be really defined by us—that is, have the possibility of its object rendered intelligible—without our stooping at once to conditions of sensibility, and thus to the form of appearances, beyond which, as their only objects, these categories must accordingly be confined; for once that condition is struck out, all significance, that is, all bearing on an object, vanishes, and no example can bring home to oneself just what sort of thing is really intended under concepts of this kind.

Nobody can spell out the concept of magnitude in general otherwise than roughly thus: that it is that determination of a thing whereby we are enabled to think how often a unit has been posited within it. This 'how often', however, rests upon successive repetition, and therewith upon time and upon the synthesis (of what is homogeneous) carried out in time. Reality, as set over against negation, admits of explanation solely on condition that one conceives a time (as the whole compass of all being) which is either occupied by something or else stands empty . Should I drop persistence (which is existence throughout all time), then for the concept of substance I am left with nothing but the logical representation of a subject, and this I fancy myself to realize by picturing to myself something capable of figuring purely as subject (never as the predicate of anything else) . But quite apart from the fact that I am acquainted with no conditions under which this logical privilege would attach to any thing at all, there is furthermore nothing to be got out of it and not the least conclusion to be drawn, since by its means no object is fixed for the use of this concept, so that one has no idea whether it means anything anywhere. As for the concept of cause, were I to set aside the time in which one thing succeeds another according to a rule, I should discover in the bare category nothing further than that it is a something from which the existence of a further something may be inferred; and by this means not only would cause and effect be left wholly indistinguishable from each other, but—since this licence to infer soon calls for conditions of which I know nothing—the concept would be furnished with no determination as to how it might fit any object. The alleged principle that everything contingent has a cause makes its entrance, to be sure, with a certain gravity, as though it bore its own dignity within itself. But if I put the question—what do you mean by contingent? and you reply, that whose non-being is possible—then I would gladly learn by what token you propose to make out this possibility of non-being, unless within the series of appearances you picture to yourselves a succession, and within that succession an existence supervening upon a non-existence (or the reverse), and hence a change; for the claim that the non-being of a thing does not conflict with itself is a limp appeal to a logical condition which, necessary though it be for the concept, falls far short of sufficing for real possibility; just as I am able to cancel in thought any substance whatever that exists, without falling into self-contradiction, and yet cannot on that basis draw any inference to its objective contingency in its existence—that is, to the possibility of its non-being taken in itself. Turning to the concept of community, it is readily gauged that, seeing as the pure categories both of substance and of causality allow of no explanation that would pin down the object, the mutual causality obtaining among substances in their relation to one another (commercium) is every bit as little susceptible of one. Possibility, existence, and necessity—no one has ever managed to explain these save through patent tautology, supposing one wished to derive their definition purely from the bare understanding. For the sleight of hand whereby the logical possibility of the concept (in that it does not clash with itself) is slipped in for the transcendental possibility of things (in that an object answers to the concept) can hoodwink and content none but the untried.³¹

From this it now issues past all contradiction: that the pure concepts of the understanding admit never of a transcendental, but always only of an empirical use; and that the principles of pure understanding may be brought to bear on objects of the senses solely under the universal conditions of a possible experience, but at no time on things in general (leaving out of account the mode in which we might happen to intuit them).

The transcendental Analytic thus yields this weighty upshot: that a priori the understanding can achieve nothing beyond anticipating the form of a possible experience as such, and that, given that whatever is no appearance can be no object of experience, it is never able to break past the barriers of sensibility, inside which alone objects come to be given to us. Its principles are no more than principles for expounding appearances, and the haughty title of an ontology—which lays claim to delivering, in a systematic doctrine, synthetic cognitions a priori about things in general (for instance the principle of causality)—must cede its place to the unassuming title of a mere analytic of the pure understanding.

Thought is the act by which a given intuition gets referred to an object. Where the kind of that intuition is in no wise given, the object remains merely transcendental, and the understanding's concept carries no use other than a transcendental one—namely, the unity of the thinking of a manifold as such. Through a pure category, then—one in which every condition of sensible intuition , as the sole kind open to us, is left out of account—no object gets determined at all; what gets expressed is merely the thinking of an object in general, under differing modes. Now the employment of a concept demands, in addition, a function of the power of judgment, by means of which an object comes to be subsumed beneath it—hence at the least that formal condition under which something is capable of being given in intuition. Where this condition of the power of judgment (the schema) is wanting, every subsumption collapses; for nothing is on offer that could be ranged under the concept. The purely transcendental employment of the categories is therefore, in truth, no employment whatever, and it possesses no object that is determinate, nor even one determinable as to its form. From this it results that the pure category likewise falls short of any synthetic principle a priori, that the principles of pure understanding hold only of an empirical, never of a transcendental employment, and that once one is out beyond the field of possible experience there can nowhere be synthetic principles a priori at all.

At the root of things here, however, lies an illusion not easily escaped. In point of origin the categories do not rest on sensibility, as do the forms of intuition, space and time, and they seem for that reason to license an application reaching out over all objects of the senses. Yet they for their own part are, once again, nothing but forms of thought, holding no more than the logical capacity to gather up a priori, into a single consciousness, whatever is given in intuition as manifold; and there, if the one intuition available to us be taken from them, they can carry even less import than those pure sensible forms, which do at any rate furnish an object—whereas a manner of combining the manifold that is proper to our understanding imports nothing whatever, so long as the intuition wherein alone that manifold can be given fails to be added to it. — And yet it already resides within our concept, once we name certain objects, qua appearances, entities of sense (Phaenomena) and thereby mark off the way we intuit them from their character as it is in itself, that we either set that self-same thing, taken by this latter character—though we do not intuit it under that character—or else set other possible things, no objects at all of our senses, over against the former, as objects thought through the understanding alone, and dub these entities of the understanding (Noumena). The question that then poses itself is whether our pure concepts of the understanding might not carry meaning as regards these latter, and count as a mode of cognizing them?

Right from the start, though, an ambiguity surfaces here, one apt to breed grave misunderstanding: namely that the understanding, whenever it labels an object mere appearance in one relation, at the same time frames for itself, outside that relation, a representation of an object in itself —and so imagines that it may frame concepts of such an object too, and, since the understanding hands over nothing save the categories, that the object in the latter meaning must at any rate be thinkable by way of these pure concepts of the understanding—and is thereby seduced into treating the wholly indeterminate concept of an entity of the understanding, as a something-in-general lying outside our sensibility, as though it were a determinate concept of an entity that we might, through the understanding, cognize in some fashion.

Taking a noumenon to mean a thing insofar as it is not an object of our sensible intuition, in that we leave our manner of intuiting it out of account, we have a noumenon in the negative acceptation. If, on the other hand, we take it to mean an object of a non-sensible intuition, we are thereby assuming a peculiar kind of intuition, the intellectual namely, which is not ours, however, and into whose possibility we can gain no insight either—and this would be the noumenon in its positive import.

The teaching about sensibility is at one and the same time the teaching about noumena in the negative acceptation—about things, that is, that the understanding is bound to think apart from this bearing on our manner of intuiting, and so not as mere appearances but as things in themselves, though of them it grasps, in this very act of setting them apart, that it can put no use of its categories to work in considering them after this fashion; for these categories, having meaning only with reference to the unity of intuitions within space and time, are able to fix that unity itself, and this precisely on account of the sheer ideality of space and of time, solely through universal concepts of connection a priori. Wherever this unity of time is nowhere to be met with—and thus in the case of the noumenon—there the whole use of the categories, indeed their whole meaning, lapses utterly; for even the possibility of the things meant to answer to the categories eludes all insight, on which score I may simply fall back on what I put forward, right at its outset, in the general remark appended to the foregoing chapter. But the possibility of a thing is never to be established out of the mere non-contradictoriness of a concept of it; it can be established only by underpinning that concept with an intuition answering to it. Were we, then, to seek to apply the categories to objects not regarded as appearances, we should have to put down as our basis an intuition of some kind other than the sensible, and in that event the object would be a noumenon in the positive import. Since such an intuition—intellectual intuition, that is—falls flatly beyond our cognitive faculty, the categories' use can in no way stretch past the boundary that the objects of experience mark out; and although entities of the understanding do of course answer to the entities of sense, and although there may well be entities of the understanding to which our sensible faculty of intuiting bears no relation whatever, still our concepts of the understanding, being mere forms of thought meant for our sensible intuition, do not reach out to these in the slightest; whatever, then, gets called noumenon by us must, as such, be understood in the negative import alone.

Should I strip from an empirical cognition the whole of thought (namely, thought through categories), then no cognition at all of any object is left over; for through bare intuition nothing gets thought whatsoever, and the circumstance that this affection of sensibility resides in me establishes no bearing of a representation of that kind upon any object at all. If, by contrast, I dispense with all intuition, there yet abides the form of thought—the manner, that is, of settling an object for the manifold of a possible intuition. To that extent, therefore, the categories range wider than sensible intuition does, for they think objects in general without as yet looking to the special way (belonging to sensibility) in which such objects might get given. They do not, however, thereby stake out a larger sphere of objects; for that objects of this sort can be given is something one is in no position to grant unless one first posits as possible a kind of intuition other than the sensible—an assumption to which we are by no means entitled.

A concept I term problematic when it holds no contradiction, when it also hangs together with other cognitions as a bounding of given concepts, and yet its objective reality is in no manner open to being cognized. The concept of a noumenon—that is, of a thing meant to be thought not in the least as an object of the senses, but rather as a thing in itself (by means of a pure understanding alone)—carries no contradiction whatever; for one is surely not entitled to maintain of sensibility that it is the sole possible manner of intuition. This concept is, further, indispensable if sensible intuition is not to be spread out over things in themselves as well, and so if the objective validity of sensible cognition is to be kept within bounds (for the remainder, upon which such intuition has no purchase, are given the name noumena for that very reason, so as to signal thereby that cognitions of that sort cannot push their territory out over all that the understanding thinks). In the last analysis, though, the possibility of such Noumenorum resists all insight, and the expanse beyond the sphere of appearances is, for us, void—which is to say, we are furnished with an understanding that reaches problematically further than the appearances do, but with no intuition, nor even so much as the concept of a possible intuition, whereby objects might be given to us outside the field of sensibility, and whereby, out past that field, the understanding might be exercised assertorically. The concept of a noumenon , accordingly, is no more than a boundary concept, serving to curb the presumption of sensibility, and hence is of a merely negative use. For all that, it is not fabricated at will, but hangs together with the curbing of sensibility, though without being competent to posit anything positive outside the compass of the latter.

For this reason the sorting of objects into Phaenomena and Noumena, and of the world into, on the one hand, a world of sense and, on the other, a world of understanding, cannot in any positive meaning be conceded, even granting that concepts do indeed permit a sorting into the sensible and the intellectual ones; for to the latter no object can be assigned, and hence they cannot be passed off as objectively valid either. Once one takes leave of the senses, how is one to render intelligible that our categories (which would be the sole concepts left over for noumena) still signify anything at all, seeing that, for them to bear on any object whatever, something beyond the bare unity of thought—namely, over and above it, a possible intuition—must be supplied for those categories to be applied to? Taken merely in its problematic character, the concept of a noumenon stays, notwithstanding all this, not only permissible but, as a concept that fences sensibility about with limits, downright inescapable. But in that case there is no special intelligible object here for our understanding; rather, an understanding to which such an object would pertain is itself a problem—the problem, that is, of cognizing its object not by way of discourse, through categories , but by way of intuition, in a non-sensible intuiting—an understanding of whose very possibility we can form for ourselves not the faintest representation. In this way our understanding comes by an enlargement that is negative—which is to say, far from being hemmed in by sensibility, it rather hems sensibility in, precisely by giving the name noumena to things in themselves (not viewed as appearances). But at the same stroke it draws limits about itself, to cognize them through no categories, and thus to think them under nothing but the name of an unknown something.

In the writings of the moderns, meanwhile, I come upon a wholly different use of the terms mundus sensibilis and intelligibilis,³² one that parts ways entirely with the ancients' meaning, and that, while it presents no difficulty of course, likewise yields nothing but empty haggling over words. On this usage it has pleased some to give the sum total of appearances, so far as it is intuited, the name world of sense, but, so far as the interconnection of that total is thought according to universal laws of understanding, the name world of understanding. Theoretical astronomy, which sets forth the bare observation of the star-strewn sky, would exhibit the first of these, whereas contemplative astronomy (expounded, say, along the lines of the Copernican world-system, or indeed of Newton's laws of gravitation) would exhibit the second—an intelligible world, namely. But a wrenching of words of this kind is a merely sophistical shift, meant to sidestep an awkward question by tuning its sense down to suit one's own comfort. Where appearances are concerned, understanding and reason are certainly of service; but the question is whether they retain any service once the object is no appearance (a noumenon), and it is in this sense that one takes the object when it is thought in its own right as bare intelligible—which is to say, as consigned to the understanding alone and in no way to the senses. So the question comes to this: whether, over and above that empirical employment of the understanding (even in the Newtonian representation of the world's fabric), a transcendental one is still possible, one bearing on the noumenon as an object—a question we have settled in the negative.

If, accordingly, we say that the senses set objects before us as they appear, but the understanding as they are, the second phrase is to be understood not in a transcendental but in a plainly empirical meaning—namely, as those objects, being objects of experience, have to be represented within the thoroughgoing interconnection of appearances, and not in terms of what they may be apart from any relation to possible experience, and hence to the senses at large, that is, as objects of the pure understanding. For this will forever stay hidden from us—so much so that it stays hidden even whether a transcendental (out-of-the-ordinary) cognition of that sort is so much as possible, at any rate as one falling under our customary categories. Understanding and sensibility, in our case, can determine objects only in conjunction. Sever them, and we are left with intuitions devoid of concepts, or concepts devoid of intuitions, but in either case with representations that we are unable to refer to any determinate object.

Should someone, in spite of all these expositions, still scruple to forswear the merely transcendental employment of the categories, let him put them to the test in some synthetic assertion or other. For an analytic assertion carries the understanding no further along, and since it busies itself with nothing except what is thought already within the concept, it leaves it unsettled whether that concept, in its own right, bears on objects or signifies merely the unity of thought as such (a unity that abstracts wholly from the way in which an object may get given); to know what lies within its concept suffices the understanding; toward what the concept may itself be directed is, to it, a matter of indifference. Let him accordingly have a go with some synthetic and ostensibly transcendental principle, such as: whatever there is exists either as substance or as a determination inhering in one; all that is contingent exists as the effect of some other thing, that is, of its cause, and so on. Now I put the question: whence does he mean to fetch these synthetic propositions, given that the concepts are meant to hold good not with reference to possible experience but of things in themselves (noumena)? Where, in this case, is the third thing that a synthetic proposition invariably demands, so as to knit together within it concepts that share no logical (analytic) affinity at all? He will never make his proposition good—indeed, what is more, he will prove unable so much as to justify the very possibility of such a pure assertion—without taking the empirical use of understanding into account, and thereby forswearing outright the pure, sense-free judgment. And so the concept of pure, merely intelligible objects turns out to be utterly bereft of any principles for its application, since there is no devising a way in which such objects ought to be given; and the problematic thought, which for all that keeps a spot open for them, does duty only after the fashion of a vacant space, hedging in the empirical principles, yet without holding within itself, or bringing to light, any further object of cognition beyond the sphere of those principles.

Appendix.

On the amphiboly of concepts of reflection, brought about by mistaking the understanding's empirical employment for its transcendental one.

Reflection (reflexio) does not deal with objects themselves in order to draw concepts straightaway from them; it is instead that condition of the mind in which we initially set about tracing the subjective conditions that would let us reach concepts at all. It consists in an awareness of how given representations stand toward our several sources of cognition, and this awareness is the only thing by which their mutual relation can be fixed aright. Before we handle our representation any further, the initial question runs thus: within which faculty of cognition do they have their common place? Is it before the understanding, or before the senses, that they get linked together or set side by side? Any number of judgments are adopted from habit or fastened together by inclination; yet since no reflection comes before them—or at any rate follows critically after—they count as judgments that took their rise in the understanding. Not every judgment calls for an investigation—that is, a heeding of the grounds of truth—since, when a judgment is certain without mediation (for instance, that only one straight line can lie between two points), there is no closer indication of its truth to be pointed out than what it already states of itself. Every judgment, though—indeed every comparison—does call for a reflection, namely a discrimination of which cognitive power the given concepts fall under. That operation whereby I set the comparison of representations as such alongside the very cognitive power within which the comparing takes place, and by which I make out whether the representations are being weighed against each other as items of the pure understanding or of sensible intuition—this I name transcendental reflection. Now the relation under which the concepts are able to stand toward each other within a mental state is one of identity and difference, of agreement and conflict, of the inner and the outer, and lastly of the determinable together with its determination (matter and form). Whether this relation is settled rightly turns on the cognitive power within which the concepts subjectively go together—that is, on whether it be sensibility or the understanding. For a difference in the latter yields a large difference in the manner in which the former are to be conceived.

Ahead of any objective judgment we set the concepts against one another so as to arrive at identity (of a plurality of representations gathered under a single concept), which serves universal judgments, or at their difference, which yields particular ones, or at agreement, out of which affirmative judgments may spring, and at conflict, out of which negative ones may come, and so on. On this ground, it would seem, the concepts cited above deserve the name concepts of comparison (conceptus comparationis). But once the point at stake is no longer the logical form but the content of the concepts—that is, whether the things on their own account are alike or unlike, concordant or at odds, and so forth—those things may stand in a double relation to our cognitive power, to sensibility on the one hand and to the understanding on the other; and because everything hinges on the site, where they have their home, and on the fashion in which they are to belong together: it is transcendental reflection—the bearing of given representations upon one or the other manner of cognition—that alone can settle how they stand to each other; and whether the things are alike or unlike, in accord or in conflict, and the like, is not to be made out immediately from the concepts as such by bare comparison (comparatio), but first through telling apart the manner of cognition under which they fall, with the help of a transcendental reflection (reflexio). One might grant, to be sure, that logical reflection amounts to nothing more than a comparison, since in its course the cognitive power under which the given representations fall is left wholly out of view, so that, as regards where they are lodged in the mind, they may be handled as of one kind; transcendental reflection, by contrast (which reaches to the objects themselves), holds within it the basis on which any objective comparing of representations against each other becomes possible at all, and for that reason stands far apart from logical reflection, seeing that the cognitive power the two fall under is not one and the same. Such transcendental reflection is an obligation that no one may throw off who means to pass any a priori judgment upon things. We shall now put it to work, and it will shed on the task of fixing the understanding's genuine office a light that is far from slight.

1. Identity and difference. Suppose an object comes before us on several occasions, yet each time carrying the very same inner determinations (qualitas et quantitas): then, taken as an object of the pure understanding, it stays throughout one and the same, not a multitude but a single thing (numerica identitas); if, on the other hand, it is appearance, the comparison of concepts no longer matters, for however thoroughly alike everything about them may be, the diversity of the sites this appearance occupies at one and the same time already suffices to ground the numerical difference of the object (of the senses) itself. So with a pair of water-drops one may set aside every inner difference (of quality and of quantity) entirely, and their being intuited at once in separate places already warrants counting them as numerically distinct. Leibniz treated the appearances as things in themselves, and so as intelligibilia, that is, objects of the pure understanding (though, because their representations were confused, he tagged them with the name of phenomena); on that footing his principle of indiscernibles (principium identitatis indiscernibilium) truly could not be gainsaid—but inasmuch as they are objects of sensibility, and the understanding's use upon them is not pure but only empirical, multiplicity and numerical difference are supplied already by space in its own right, as that which conditions outer appearances. For a given portion of space, no matter how fully it resembles and matches another, lies all the same beyond it and by that very fact ranks as a portion different from the first, one adjoined to it so as to yield a larger space; and the same must accordingly apply to whatever occupies at one time the sundry positions of space, be it otherwise ever so alike and equal.

2. Agreement and conflict. Where reality is pictured through the pure understanding alone (realitas noumenon), no conflict admits of being thought among realities—no relation, that is, in which, brought together within one subject, they cancel each other's consequences, giving 3 − 3 = 0. What is real in appearance (realitas phaenomenon), on the other hand, can quite well stand in conflict among themselves, and, joined in one and the same subject, one part may destroy, in whole or in part, the consequence of the other—as with two motive forces along one straight line, in that they pull or press a point toward opposite sides, or again as with a gratification that offsets a pain.

3. The inner and the outer. Within an object of the pure understanding, that alone counts as inner which bears no relation at all (so far as existence goes) to anything set apart from it. The inner determinations of a substantia phaenomenon in space, by contrast, are relations and nothing besides, and the substance itself is, from top to bottom, a sum made up of relations alone. Substance in space is known to us solely by way of forces at work within it—forces that either urge other things toward a spot (attraction) or bar them from forcing their way in (repulsion and impenetrability); of further properties composing the concept of the substance that shows itself in space, the substance we name matter, we have no acquaintance. Regarded as an object of the pure understanding, on the contrary, each substance is bound to possess inner determinations and forces directed upon inner reality. Yet what inner accidents am I able to conceive apart from the ones my inner sense holds out to me—that is, apart from whatever is itself a thinking or bears an analogy to thinking? This is why Leibniz turned every substance—since he pictured them to himself as Noumena—and indeed the very components of matter, once he had stripped away from them in thought all that could stand for an outer relation, and with it composition too, into simple subjects furnished with powers of representation, in short monads.

4. Matter and form. Here are two concepts placed beneath every other act of reflection as its ground—so tightly are they woven into each employment of the understanding. The first stands for what is determinable at large, the second for the determining of it (each taken in a transcendental sense, once one leaves aside all difference in what gets given and in the way it comes to be determined). Logicians of an earlier day gave the name matter to the universal, but reserved form for the specific difference. Within any judgment the concepts supplied may be styled its logical matter, while the way they are related (through the copula) may be styled the judgment's form. In any essence, the pieces that constitute it (essentialia) make up the matter, and the mode of their linkage within a thing makes up the essential form. So too, as concerns things at large, boundless reality was looked upon as the matter belonging to all possibility, while the curbing of that reality (negation) was looked upon as the form whereby, on transcendental concepts, one thing gets marked off from another. The understanding, after all, insists to begin with that something be furnished (in the concept at the very least) if it is to be capable of determining that something in one manner or another. So within the concept of the pure understanding matter comes before form, and on that account Leibniz posited things (monads) first, and inwardly a representational power lodged in them, meaning afterward to build upon this their outer relation and the commerce of their states (the states, that is, of their representations). On this view space and time became possible—space merely by dint of the relation among substances, time by dint of tying their determinations together, one to another, as grounds and as consequences. And thus, in fact, it would have to stand, could the pure understanding be brought to bear on objects without mediation, and were space and time determinations belonging to things in themselves. But if these are nothing more than sensible intuitions, within which we fix every object solely as appearance, then intuition's form (being a subjective make-up of sensibility) runs ahead of all matter (the sensations), so that space and time go before every appearance and before all the datis of experience, and are what first render experience possible in the first place. The philosopher of the intellect could not abide that form should stand ahead of the things themselves and settle what they can be—a wholly justified reproach, granted his premise that we intuit things just as they are (albeit under a confused representation). Since sensible intuition, however, is an altogether peculiar subjective condition underlying every perception a priori, and since its form is original, that form stands given on its own account; and rather than matter (or the appearing things themselves) lying at the base—as one would be forced to conclude by mere concepts—the possibility of that matter instead takes a formal intuition (time and space) as something already given.

Remark on the amphiboly of concepts of reflection

Grant me leave to name the position we allot to a concept—whether within sensibility or within the pure understanding—its transcendental location. On such an approach, the appraisal of this position—one that falls to each concept in keeping with how its use varies—along with the directions, laid down by rules, for assigning that location to all concepts, would amount to the transcendental topic: a teaching that would keep us soundly safe from the pure understanding's surreptitious overreaches and the illusions bred by them, since at every turn it would sort out which cognitive power the concepts genuinely answer to. Any concept whatever, any rubric beneath which a host of cognitions gather, may be termed a logical location. Upon this rests the logical topic of Aristotle, which schoolmasters and orators could enlist in order to hunt, beneath certain rubrics of thought, for what best fitted a matter at hand, and thereupon to argue with a show of thoroughness or to prate copiously.

The transcendental topic, on the other hand, holds nothing beyond the four rubrics of all comparing and distinguishing already named, which part ways with the categories in this: through them it is not the object—taken by what makes up its concept (magnitude, reality)—but merely the comparison of representations, a comparison prior to the concept of things, that gets set out in the whole of its variety. Such comparison, though, demands before anything else a reflection—a settling, that is, of the location where the representations of the things under comparison belong, whether the pure understanding thinks them or sensibility tenders them in appearance.

One may compare concepts on the logical plane without any concern for where their objects have their seat—whether, as noumena, before the understanding, or, as phenomena, before sensibility. Yet should we mean to carry these concepts over to the objects, transcendental reflection becomes indispensable at the outset, telling us for which cognitive power the objects are meant to serve—the pure understanding or sensibility. Lacking this reflection, my handling of the concepts grows quite unsure, and there spring up would-be synthetic principles that critical reason is unable to endorse, principles resting on nothing but a transcendental amphiboly—a mix-up, that is, of the understanding's pure object with appearance.

In the absence of any such transcendental topic, and so taken in by the amphiboly of concepts of reflection, the renowned Leibniz raised up an intellectual system of the world—or rather fancied that he discerned the inner make-up of things—by weighing every object against the understanding alone and against the detached formal concepts of his thought. Our table of the concepts of reflection hands us the unlooked-for gain of setting out plainly what sets his doctrine apart in each of its parts, and along with it the steering ground of this odd cast of mind, a ground that lay in nothing more than a misunderstanding. He set all things side by side by way of concepts only, and came upon, as one would expect, no differences save the ones by which the understanding tells its pure concepts apart. The conditions of sensible intuition, which bring differences of their own along with them, he declined to count as original; for sensibility struck him as merely a muddled sort of representation, not a source of representations in its own right; appearance was to his mind the representation of the thing in itself, set apart from cognition through the understanding only in respect of logical form, since the former, in its habitual want of analysis, pulls a certain blend of side-representations into the concept of the thing, a blend the understanding is able to strain off. To put it briefly: Leibniz intellectualized the appearances, much as Locke, on his system of noogony (if these coinages may be allowed me), had, one and all, sensualized the concepts of the understanding—that is, palmed them off as nothing beyond empirical or detached concepts of reflection. Rather than looking to the understanding and to sensibility as two thoroughly distinct wells of representations that, only in combination, could yet judge of things with objective validity, each of these great men clung to just one of the pair—the one he took to bear directly on things in themselves—while leaving the other to do nothing except muddle or arrange what the first supplied.

Leibniz, then, set the objects of the senses—things as such—against one another within the understanding alone. First, so far as it is to pronounce them alike or unlike. Because he kept in view only their concepts, and not the place they hold in intuition, where alone objects can be furnished, and because he passed over entirely the transcendental location of these concepts (whether the object should fall among appearances or among things in themselves), it could hardly turn out but that he stretched his principle of indiscernibles—valid only of concepts of things at large—across to the objects of the senses (mundus phaenomenon) into the bargain, and took himself to have thereby won for natural cognition no slight enlargement. Granted, should I know some drop of water, as a thing in itself, by the whole of its inner determinations, I can allow none of them to pass for different from another once the full concept of the one matches the other. If, however, it is appearance within space, its place lies not just in the understanding (beneath concepts) but in sensible outer intuition (in space); and there the physical positions stay wholly indifferent toward the inner determinations of things, so that a position = b can take in a thing fully like and equal to another at the position = a exactly as readily as though it differed from that other ever so much within. The diversity of positions, all on its own and with no added conditions, renders the multiplicity and separation of objects as appearances not merely possible but necessary as well. Hence that seeming law is no law of nature at all. It is nothing but an analytic rule for setting things side by side through concepts alone.

Second, the tenet that realities (being sheer affirmations) never come into logical conflict with one another is a perfectly true proposition touching the relation of concepts, yet says nothing at all about nature, and nothing whatever about any thing in itself (of which no concept is ours). For real conflict occurs wherever A − B = 0, that is, wherever one reality, paired with another in a single subject, cancels the effect of that other—as every obstacle and counter-effect in nature keeps unceasingly displaying to us, and as, resting on forces, must all the same bear the name realitates phaenomena. General mechanics is even able to lay down the empirical condition of this conflict in an a priori rule, by attending to the opposition of directions—a condition of which the transcendental concept of reality has not the least inkling. Though Herr von Leibniz did not quite herald this proposition with the fanfare of a fresh principle, he nonetheless turned it to fresh claims, and his successors wrote it in so many words into their Leibnizian-Wolffian structure of doctrine. By this principle, to take one case, all evils amount to nothing beyond consequences of the bounds set to created things—negations, in short—since these are the sole thing at odds with reality (in the bare concept of a thing at large it truly does hold so, though not in things regarded as appearances). In the same spirit his followers judge it not merely possible but even natural to gather all reality into one being without any troublesome conflict, for they recognize no conflict apart from that of contradiction (whereby the concept of a thing cancels itself), and none of mutual curtailment, wherein one real ground cancels the effect of another—and the conditions for picturing such a case to ourselves we light upon in sensibility alone.

Third, the Leibnizian monadology rests on no ground save this: that our philosopher framed the difference of inner and outer purely by reference to the understanding. Substances at large are bound to hold something inner, which stands accordingly clear of every outer relation, and so clear of composition too. Thus the simple forms the groundwork of what is inner in things in themselves. Yet the inner side of their state can rest neither on place, nor figure, nor contact, nor motion (all of them determinations that are outer relations), and so we are able to credit substances with no inner state other than the very one by which we inwardly determine our own sense—to wit, the state of representations. And so the monads came finished, cast as the raw stuff of the whole universe, though their active force lies in representations only, whereby they are strictly at work nowhere but inside themselves.

It was for precisely this reason, too, that his principle of the possible community of substances among themselves had to take the shape of a preestablished harmony and could be no physical influence. For as everything busies itself only within, that is, with its own representations, the representational state of the one substance could hold no effective bond of any sort with that of another; instead, some third cause, flowing alike into them all, had to bring their states into mutual accord—not, indeed, by occasional aid fitted specially to each single case (Systema assistentiae), but through the oneness of the idea of a cause holding good for all, wherein every one of them must draw its existence and permanence, and with these its reciprocal correspondence under universal laws.

Fourth, his famed doctrine of time and space, wherein he intellectualized these forms of sensibility, sprang from none but this same deception of transcendental reflection. Should I want to represent to myself outer relations of things by the bare understanding, it can come about only through a concept of their mutual action, and should I have to join one state of a given thing to another state, it can come about only within the sequence of grounds and consequences. In this manner, then, Leibniz conceived space as a particular ordering within the community of substances, and time as the dynamical run of their states. The trait proper to both, though, and independent of things—the trait they appear to own of themselves—he charged to the confusedness of these concepts, a confusedness that led what is a bare form of dynamical relations to be mistaken for an intuition subsisting by itself, standing on its own and going before the things themselves. So space and time turned into the intelligible form of the linkage of things (substances and their states) taken in themselves. The things, meanwhile, were intelligible substances (substantiae noumena). Even so he meant to press these concepts into service for appearances, since he conceded to sensibility no manner of intuition of its own, but hunted for every representation of objects, the empirical included, inside the understanding, and left the senses no office beyond the paltry one of blurring and marring the representations of the former.

But suppose we could pronounce something synthetically about things in themselves by way of the pure understanding (a thing that is in any case impossible)—even then it could in no wise be carried over to appearances, seeing that these do not present things in themselves. So in this second case I shall, within transcendental reflection, be obliged at all times to weigh my concepts only beneath the conditions of sensibility, whence space and time come out as determinations not of things in themselves but of appearances: what things may be in themselves I neither know nor have any need to know, since a thing can never reach me save in appearance.

I go to work likewise with the concepts of reflection that remain. Matter is a substantia phaenomenon. Whatever pertains to it within I look for across all the parts of space it fills and in all the effects it works, effects that of course can never be anything but appearances of outer sense. Thus I am left with nothing inner in the strict sense, but only with what is inner by comparison, which in its turn is itself built out of outer relations. But the strictly inner of matter, judged by the pure understanding, is likewise a mere whim; for matter is in no place an object for the pure understanding; the transcendental object, on the other hand, that might underlie this appearance we name matter is a bare something whose nature we should fail to grasp even were somebody in a position to tell it to us. For nothing lies open to our understanding but what brings along with it, within intuition, a counterpart to our words. If the laments—We have no insight whatever into the inner of things—are meant to say no more than: by the pure understanding we do not make out what the things appearing to us may be in themselves, then they are altogether unjust and unreasonable; for they ask that one be able to cognize things, and so to intuit them, with no senses at all, and hence that we possess a faculty of cognition parting from the human not in degree merely but even in the very intuition and sort, so that we should be, not human beings, but beings of whom we cannot so much as declare whether they are once possible, far less how they might be constituted. Into nature's interior push observation and the dissection of appearances, and there is no telling how far this may reach as time goes on. Those transcendental questions, though, which pass beyond nature, we should for all that never manage to answer, even were the whole of nature bared to us, for it is not so much as granted us to watch our own mind by any intuition other than the one belonging to our inner sense. In that inner sense, after all, the secret of our sensibility's origin lies hidden. How it bears on an object, and what the transcendental ground of that unity might be, lie past doubt buried too far down for us—who are acquainted even with ourselves through inner sense alone, and thus as appearance—to put so ill-fitted a tool of inquiry to any use except turning up, again and again, mere appearances, whose nonsensible cause we would nonetheless dearly like to track down.

What lends this critique of the inferences drawn from the sheer acts of reflection its great usefulness is this: it shows up in plain terms the emptiness of every inference about objects that are matched against one another within the understanding alone, while at once bearing out the point we have chiefly pressed home—that appearances, though not taken up as things in themselves among the objects of the pure understanding, are for all that the sole ones in which our cognition can carry objective reality, precisely where intuition answers to the concepts.

In reflecting on the merely logical plane, we match our concepts against each other within the understanding by itself: whether the two hold the very same content, whether they clash or not, whether something sits inside the concept or comes to it from without, and which of them is the one given while the other is to rank only as a mode of thinking the given one. Yet let me bring these concepts to bear on an object as such (in the transcendental sense), leaving it open whether the object belongs to sensible or to intellectual intuition, and straightaway restrictions come to light (bidding us not to step outside this concept) that upset every empirical use of the concepts, and by that very fact establish that the representation of an object as a thing as such is not simply inadequate but, absent any sensible determination of it and set loose from every empirical condition, contradictory in its own right—so that one has either to leave every object aside (in logic) or, in adopting an object, to think it beneath the conditions of sensible intuition; whence the intelligible would call for a quite peculiar intuition, which we lack, and, wanting that, would be, for us, nothing, while, on the other side, the appearances likewise cannot be objects in themselves. For if I do no more than think things as such, then admittedly the difference of outer relations cannot make for a difference in the things themselves but rather takes such a difference for granted; and where the concept of the one is inwardly in no way marked off from that of the other, I am only setting one and the same thing into differing relations. Furthermore, by joining one bare affirmation (reality) to a second, the positive is of course increased and nothing taken from it or cancelled; and so what is real in things as such cannot come into conflict with one another, and so on.

The concepts of reflection, as has been made plain, wield—by dint of a certain misreading—so strong a sway over how the understanding is used that they proved able to lure even one of the keenest-sighted among all philosophers into an alleged system of intellectual cognition, a system that sets out to fix its objects with no help coming from the senses. For just that reason, unfolding the deceptive source of these concepts' amphiboly—the source that gives rise to false principles—proves of great service in pinning down and safeguarding, dependably, the bounds of the understanding.

True enough, one has to say that whatever belongs to a concept universally, or runs counter to it, belongs likewise, or runs counter, to all the particular items falling under that concept (dictum de Omni et Nullo); but it would be preposterous to recast this logical principle so as to read: what a universal concept fails to hold is held, too, by none of the particular concepts ranged beneath it; for these rank as particular concepts for the very reason that they carry more within them than gets thought in the universal. Now the whole intellectual system of Leibniz is in fact reared upon this second principle; with it, then, that system collapses, and with it too all the double-meaning it breeds in the understanding's use.

The principle of indiscernibles truly rested on the assumption that, where a given distinction is not found in the concept of a thing as such, it is not to be found in the things themselves either; and hence that all things are through and through identical (numero eadem) that do not already differ from one another in their concept (in point of quality or quantity). But since, in the bare concept of any thing whatever, one has left aside sundry necessary conditions of an intuition, by an odd rush to judgment that which is left aside gets treated as something met with nowhere at all, and the thing is granted nothing beyond what its concept holds.

The concept of a cubic foot of space, think it where and as often as I please, stays in itself wholly the same. Two cubic feet, all the same, are set apart in space by their places alone (numero diversa); and these places are conditions of the intuition wherein the object of this concept is furnished, conditions that fall not to the concept but rather to sensibility taken whole. Just so, there is no conflict at all inside the concept of a thing when nothing negative has been coupled with something affirmative, and concepts that are merely affirmative can, once joined, bring about no cancellation of any kind. In sensible intuition, though, where reality (say, motion) is furnished, there turn up conditions (opposing directions) that had been left aside in the concept of motion as such, and these make a conflict possible—one that is admittedly not logical—namely, out of the sheerly positive, a zero = 0; nor could one say that all reality is on that account in accord with one another, merely because no conflict crops up among the concepts of it.³³ Judged by bare concepts, the inner serves as the substratum for all relational, or outer, determinations. Should I therefore lay aside every condition of intuition and keep solely to the concept of a thing as such, I may leave aside all outer relation, and yet there has to be left over a concept of what marks no relation whatever but only inner determinations. Here it looks as though the upshot were this: that in each thing (substance) there dwells something strictly inner, going before all outer determinations by first making them possible; that this substratum is accordingly a thing harboring no further outer relations within, and hence simple (bodies being, when all is said, forever nothing but relations, at least of parts lying outside one another); and, since we are acquainted with no strictly inner determinations save those by way of our inner sense, that this substratum is not simple only but, on the analogy of our inner sense, determined as well through representations—which is to say, that all things would in truth be monads, or simple beings dowered with representations. The whole of this would even hold good, did there not enter, over and above the concept of a thing as such, something further among the conditions on which alone objects of outer intuition can reach us—conditions the pure concept leaves out of account. For at this point it comes to light that an abiding appearance in space (impenetrable extension) may hold relations and nothing besides, nothing strictly inner whatever, and still may serve as the first substratum of all outer perception. Through bare concepts, that is, concepts of things in themselves, I can of course think nothing outer without something inner, exactly because relational concepts take for granted things given without qualification and are impossible apart from them. But since intuition holds within it something that has no place at all in the bare concept of a thing as such, and since this yields the substratum—which bare concepts would never cognize—namely a space that, with all it embraces, is built of nothing but formal, or else real, relations, I cannot say that, because no thing can be represented through bare concepts without something strictly inner, there is likewise, in the things themselves ranged under these concepts and in their intuition, no outer that fails to rest on something strictly inner. For once we have set aside every condition of intuition, nothing, to be sure, is left us within the bare concept beyond the inner at large and its relation to itself, whereby alone the outer becomes possible. This necessity, though, resting on abstraction and on nothing else, has no hold over things once they are furnished in intuition bearing determinations that voice mere relations and rest on nothing inner—and this for the reason that they are not things in themselves but appearances and no more. All that we know even of matter is relations and relations only (what we style its inner determinations is inner only by comparison); yet among these are some self-standing and abiding, and by their means a determinate object comes to be furnished us. My having nothing further to think, once these relations are set aside, cancels the concept neither of a thing qua appearance nor of an object in abstracto; what it does cancel is every possibility of an object of the kind determinable by bare concepts, that is, of a noumenon. Granted, it gives one pause to be told that a thing should be made up, wholly and utterly, of relations; but a thing of that sort is likewise appearance only, and cannot be thought through pure categories in the least; it consists, itself, in the bare relation borne by something as such toward the senses. In like fashion, setting out from bare concepts, one can scarcely think the relations of things in abstracto in any way but that the one is cause of determinations lodged in the other; for that just is the understanding's concept of relations as we hold it. Yet as we are in that case leaving aside all intuition, a whole mode by which the manifold could assign one another their place—the form of sensibility, namely (space)—falls away, though it goes before every empirical causality.

Take merely intelligible objects to be those things thought by pure categories with no schema of sensibility of any sort, and things of that description turn out impossible. For what conditions the objective use of every one of our understanding's concepts is simply the manner of our sensible intuition, whereby objects come to us; strip that manner away, and those concepts bear no relation to any object at all. Indeed, were one to posit some kind of intuition apart from this sensible one of ours, our functions for thinking would even so carry no weight at all in regard to it. Should we mean by them nothing but objects of a nonsensible intuition—objects our categories admittedly do not govern, and of which, therefore, no cognition can ever be ours (neither intuition nor concept)—then Noumena in this purely negative sense must certainly be let in: for they then declare no more than that our style of intuition does not reach out to all things but only to the objects of our senses, that its objective validity is bounded in consequence, and that room accordingly stays open for some other style of intuition, and so for things as its objects too. In that event, however, the concept of a Noumenon is problematic—the representation, that is, of a thing about which we are able to say neither that it can be nor that it cannot be, since no manner of intuition is known to us but our sensible one, and no manner of concepts but the categories, while neither of the two fits a supersensible object. We are not, then, entitled on that ground to widen positively the domain of the objects of our thought past the conditions of our sensibility, and to grant, alongside the appearances, objects of pure thought as well—noumena, that is—for the latter own no positive meaning that could be stated. For of the categories one has to own that by themselves they still fall short of cognizing things in themselves, and that, lacking the data of sensibility, they would be no more than subjective forms of the understanding's unity, an object nowhere among them. Thinking, true, is of itself no product of the senses and to that degree suffers no limit from them, yet it does not thereby become at once of a use its own and pure with no accession of sensibility, for then it wants an object. Neither may the noumenon be styled such an object; for that word points to exactly the problematic concept of an object meant for an intuition and an understanding altogether unlike ours, and hence itself a problem. So the concept of the noumenon is not the concept of an object but a task, one tied past escape to the boundedness of our sensibility: whether there might not be objects set entirely loose from that intuition of ours—a question open to none but an indeterminate answer, to wit, that because sensible intuition does not reach all things alike, room stays over for further and other objects, which therefore cannot be denied outright, yet, for want of a determinate concept (no category being equal to the task), cannot be affirmed as objects for our understanding either.

The understanding, then, draws a bound about sensibility without thereby widening its own province, and, in cautioning sensibility to lay no claim upon things in themselves but only upon appearances, it frames for itself an object in itself—though merely as a transcendental object, cause of appearance (and so no appearance itself), one thinkable neither as magnitude, nor as reality, nor as substance, and the like (these concepts demanding always sensible forms wherein to determine an object); an object, accordingly, of which it stays wholly unknown whether it is to be found in us or outside us as well, whether it would be cancelled along with sensibility or would linger on once we took sensibility off. Should we choose to name this object a Noumenon on the ground that our representation of it is not sensible, we are at liberty to. But as not one of our understanding's concepts can be brought to bear on it, this representation stays for all that empty in our hands and does no work beyond marking off the limits of our sensible cognition and leaving vacant a space we are able to fill neither by possible experience nor by the pure understanding.

The critique of this pure understanding, then, gives no leave to fashion for oneself a fresh domain of objects over and above those that may present themselves to it as appearances, nor to wander off into intelligible worlds, not so much as into the concept of them. The blunder that most plausibly tempts one this way—pardonable, though never to be vindicated—consists in this: the understanding's use is, against its calling, rendered transcendental, and the objects, that is, possible intuitions, are bent to fit the concepts, in place of the concepts being bent to fit possible intuitions (whereon their objective validity rests, and on nothing else). The cause of that, in its turn, is that apperception, and thinking along with it, runs ahead of every possible determinate arrangement of the representations. So we think something as such and, on one side, determine it sensibly, while yet setting the universal object pictured in abstracto apart from this manner of intuiting it; and there stays behind for us a manner of determining it by thinking alone, which is, granted, a bare logical form void of content, but which strikes us none the less as a manner in which the object is in itself (Noumenon), with no glance at the intuition penned within our senses.

Before quitting the transcendental analytic, we ought to append one thing further, which, trifling though it be in itself, may yet look to be called for if the system is to be complete. The topmost concept from which a transcendental philosophy is wont to set out is, as a rule, the split into the possible and the impossible. But because each division takes for granted a concept being divided, one higher still has to be named, and this is the concept of an object as such (taken problematically, and left unsettled whether it be something or nothing). Since the categories are the sole concepts bearing on objects as such, the sorting of an object—whether it be something or nothing—will run along the order and lead of the categories. 1) Over against the concepts of all, of many, and of one stands the concept that cancels everything, that is, none; and thus the object of a concept to which no specifiable intuition answers is nothing—a concept, that is, lacking an object, as the noumena are, which may not be reckoned among the possibilities, though neither on that account need they be given out as impossible (ens rationis), or as certain new fundamental forces are that one entertains in thought, free of contradiction, to be sure, but likewise free of any instance drawn from experience, and so not to be reckoned among the possibilities. 2) Reality is something, negation is nothing—a concept, namely, of an object's absence, as with the shadow, with the cold (nihil privativum). 3) The bare form of intuition, apart from substance, is of itself no object but only the formal condition of one (as appearance)—as pure space and pure time are, which, though they are something as forms for intuiting, are not themselves the objects intuited (ens imaginarium). 4) The object of a self-contradicting concept is nothing, since the concept itself is nothing—the impossible, as, for instance, the two-sided rectilinear figure (nihil negativum).

Accordingly, the table for this division of the concept of nothing (the matching division of something falling out on its own) would have to be set up thus:

Nothing, as

One notices that the thought-thing (no. 1) parts from the non-thing (no. 4) in this: the first is not to be reckoned among the possibilities, being a mere invention (albeit not a self-contradicting one), whereas the second stands against possibility, in that its concept even cancels itself. The two of them, though, are concepts standing empty. By contrast, empty data for concepts are furnished by the nihil privativum (no. 2) and the ens imaginarium (no. 3). Had light never been given to the senses, no darkness could be pictured either; and had no extended beings been perceived, no space could be pictured. Both negation and the bare form of intuition, lacking anything real, are no objects at all.

Second Division. Transcendental Dialectic

Introduction

I. On transcendental illusion

We designated dialectic in general, earlier on, as a logic of illusion. This does not mean that it is a doctrine of probability; for probability is truth all the same, only truth known through grounds that fall short, so that although such cognition is defective it is not therefore misleading, and hence there is no call to sever it from logic's analytic part. Even less should one conflate appearance with illusion. For it is not the object, as it is intuited, but the judgment passed on it, as it is thought, that harbors truth or illusion. So it is quite right to say that the senses never err — though the reason is not that their judgments are always correct, but that they pass no judgment whatsoever. For this reason truth and error alike — and with them illusion, which lures us into error — are found nowhere but in judgment, i.e., solely in how the object stands related to our understanding. Where a cognition accords throughout with the laws of the understanding, error has no place. And a sensory representation, containing as it does no judgment at all, is equally free of error. Yet no natural force can, on its own, depart from the laws that govern it. It follows that error would arise neither in the understanding taken in isolation (with no other cause acting on it) nor in the senses taken on their own; not in the understanding, because whenever it proceeds strictly by its own laws the resulting effect (the judgment) is bound to conform to those laws. And conformity to the laws of the understanding is precisely what constitutes the formal side of every truth. Within the senses no judgment occurs, be it true or false. Since, then, we possess no source of cognition beyond these two, the conclusion is this: error comes to pass only through the unremarked bearing of sensibility upon the understanding, in consequence of which the subjective grounds of a judgment merge with the objective ones and pull the latter away from what they ought to determine ³⁴; much as a body in motion would, left to itself, forever hold to a straight line in one and the same direction, yet, should a second force press upon it at once along another direction, veers off into curved motion. So as to tell apart the understanding's own characteristic operation from the force that mixes itself in, we shall have to treat the mistaken judgment as a diagonal lying between two forces that pull the judgment along two divergent directions and thereby, so to speak, span an angle between them, and then to break this compound effect down into the separate contributions of understanding and sensibility; and with pure judgments a priori this has to be accomplished by way of transcendental reflection, through which (as was noted already) every representation gets allotted its proper place in the cognitive faculty suited to it, so that the bearing of the one faculty upon the other is likewise kept distinct.

It is no part of our task here to deal with empirical illusion (the optical sort, say), which crops up when otherwise sound rules of the understanding are put to empirical use and which leads the power of judgment astray under the sway of imagination; our concern, rather, is with transcendental illusion alone, an illusion that works upon principles never even framed for use in experience — had they been so framed, we should at least possess some test of their soundness — but that instead, in defiance of every caution critique may issue, sweeps us clean past the empirical employment of the categories and dangles before us the delusive prospect of enlarging the pure understanding. Those principles that confine their application wholly within the limits of possible experience we shall term immanent, while those meant to soar past these limits we shall term transcendent principles. By the latter, though, I have in mind not the transcendental employment or misemployment of the categories — that being a simple failing of a power of judgment insufficiently reined in by critique, one that keeps too little watch over the boundary of the ground where alone the pure understanding may carry on its game — but genuine principles that press us to level every one of those boundary markers and to seize for ourselves a wholly fresh ground acknowledging no line of demarcation anywhere. So transcendental and transcendent are by no means interchangeable. The principles of the pure understanding presented earlier are meant to have an empirical employment only, never a transcendental one — that is, an employment stretching past the limit of experience. A principle, by contrast, that clears these barriers away — indeed one that bids us cross them outright — counts as transcendent. Should our critique manage to expose the illusion belonging to these presumptuous principles, then those principles of merely empirical use, set over against the latter, will be entitled to the name immanent principles of the pure understanding.

Logical illusion — the illusion at work in fallacious inferences — amounts to nothing more than an imitation of reason's form, and it springs merely from inattention to the logical rule. The moment that rule is brought to bear keenly on the case before us, the illusion dissolves without remainder. Transcendental illusion, on the other hand, persists undiminished even once it has been laid bare and its emptiness plainly grasped through transcendental critique (consider, for instance, the illusion lodged in the claim that the world had to begin at some point in time). The reason for this lies in the following: within our reason — taken subjectively, as one of the human powers of cognition — there reside fundamental rules and maxims for its employment that wear the full appearance of objective principles, and by which it happens that a subjective necessity — the necessity of joining our concepts in a certain way for the benefit of the understanding — comes to be mistaken for an objective necessity governing the determination of things in themselves. An illusion, then, that admits of no avoidance whatever — no more than we can keep the sea from looking higher to us at its center than along the shore, since we behold the one by rays of light set higher than those disclosing the other, or, more strikingly still, no more than the astronomer himself can stop the rising moon from looking larger to him, notwithstanding that this illusion does not take him in.

Accordingly, the transcendental dialectic will rest content with laying bare the illusion of transcendent judgments and, at once, with guarding against its deceiving us; that this illusion should moreover (as the logical sort does) altogether vanish and stop being an illusion at all — this it can never bring about. For what confronts us here is a natural and inescapable illusion, one that is grounded in subjective principles of its own yet foists them upon us as though they were objective; whereas logical dialectic, in dissolving fallacious inferences, contends merely with a slip in applying principles, or with a contrived semblance got up in imitation of them. Pure reason, then, harbors a dialectic that is natural and inescapable — not one into which some bungler tangles himself for want of knowledge, nor one that a sophist has cunningly devised to bewilder reasonable folk, but one bound up with human reason past all thwarting, an illusion that, even after we have uncovered its deceptive play, will never leave off deceiving reason afresh and thrusting it again and again into fleeting aberrations that stand in need of removal every time.

II. On pure reason as the seat of transcendental illusion

A. On reason in general

Every one of our cognitions begins with the senses, moves on from there to the understanding, and terminates in reason, above which we find nothing higher within us for working up the raw material of intuition and gathering it under the supreme unity of thinking. Now that I am expected to give an account of this highest cognitive power, I find myself in something of a quandary. There is, as with the understanding, a use of it that is purely formal—that is, logical—in which reason leaves aside every content belonging to cognition, but there is likewise a real use, inasmuch as reason itself is the source of certain concepts and principles that it derives from neither the senses nor the understanding. The former capacity has of course long since been accounted for by the logicians as the power of inferring mediately (as distinct from immediate inferences, consequentiis immediatis); the latter, however, which itself brings forth concepts, is thereby still not comprehended. Since what emerges at this point is a partition of reason into a logical and a transcendental capacity, we must look for some higher concept of this cognitive source—one broad enough to embrace both of the aforementioned—while the analogy with the concepts of the understanding gives us grounds to expect that this logical concept will simultaneously unlock the transcendental one, and that the table listing the functions of the former will at the same time deliver the ancestral line of reason's own concepts.

Earlier, in the opening part of our transcendental logic, we defined the understanding by way of the faculty of rules; here we set reason apart from it by proposing to call it the faculty of principles.

The word 'principle' carries a double sense, and in ordinary usage it designates nothing more than a cognition capable of being put to use as a principle, notwithstanding that, taken on its own and by its own origin, it is not a principle at all. Every universal proposition whatsoever—even one lifted from experience (by way of induction)—is fit to function as the major premise of a rational inference; but this does not thereby make it a principle in its own right. The axioms of mathematics (for example, that between two points there can lie but one straight line) are indeed universal cognitions a priori, and hence they are, with good reason, termed principles in a relative sense—relative to whatever instances fall under them. Even so, that does not license me to say that I cognize this feature of straight lines universally and in itself out of principles; rather, I cognize it solely in pure intuition.

Accordingly, the label 'cognition from principles' I would reserve for the case in which, by means of concepts, I cognize the particular as contained in the universal. On this understanding, every rational inference amounts to a way of deriving one cognition out of a principle. For the major premise invariably supplies a concept of such a sort that whatever is brought under its condition comes to be cognized through it in conformity with a principle. And since any universal cognition is capable of standing as the major premise within a rational inference, and since the understanding puts forward universal propositions of this sort a priori, they too, in view of the use to which they might be put, may bear the name of principles.

Yet once we examine these principles of the pure understanding as they are in themselves, in respect of their origin, they turn out to be anything but cognitions drawn from concepts. For they would not so much as be possible a priori were we not to draw upon pure intuition (in mathematics) or upon the conditions of a possible experience taken quite generally. The proposition that everything that comes to pass has its cause is in no way derivable from the concept of that which comes to pass in general; on the contrary, it is the principle that first shows us how a determinate empirical concept of what comes to pass may be arrived at.

Synthetic cognitions out of concepts, therefore, lie altogether beyond what the understanding can provide, and it is these, strictly speaking, to which I give the name of principles outright: while every universal proposition whatever may pass merely for a comparative principle.

There is a long-standing wish—one that, who can tell how far off, may possibly at some point come true: that in place of the boundless multiplicity of civil statutes people might for once go in search of their principles; for it is here alone that the secret of what is called simplifying legislation can reside. But even in this case the laws are nothing more than curbs placed on our freedom, confining it to conditions under which it remains throughout in harmony with itself; they therefore pertain to something that is wholly a product of our own doing, and of which, through those very concepts, we can ourselves be the cause. But the question how objects in themselves, how the nature of things, could be subject to principles and admit of determination by nothing but concepts, is a demand that is, if not downright impossible, then at any rate thoroughly preposterous. However this matter may finally turn out (for the inquiry into it still lies ahead of us), this much at least becomes clear from what has been said: that cognition from principles (regarded in itself) is something wholly distinct from mere cognition of the understanding, which, though it may indeed stand ahead of other cognitions under the guise of a principle, does not of itself (so far as it is synthetic) rest upon thinking alone, nor does it hold within itself any universal proceeding by concepts.

Granting that the understanding is a faculty for bringing appearances to unity by means of rules, reason is then the faculty for bringing the rules of the understanding themselves to unity under principles. Hence it is never directed, in the first instance, upon experience or upon any object at all, but rather upon the understanding, so as to confer a priori, through concepts, a unity on the latter's manifold cognitions—a unity that one may name the unity of reason, and which is of a wholly different sort than anything the understanding is able to accomplish.

Such is the general concept of the faculty of reason, to the extent that it admitted of being rendered intelligible in the total absence of examples (which are not to be furnished until later on).

B. On the logical use of reason

A distinction is made between that which is immediately cognized and that which is only inferred. That a figure bounded by three straight lines contains three angles is immediately cognized; but that these angles together amount to two right angles is only inferred. Since we have perpetual need of inference, and thereby become at last quite habituated to it, we finally cease to notice this distinction and often regard something as immediately perceived—as with the so-called deception of the senses—when in truth we have only inferred it. With every inference there is a proposition lying at its basis, and another, namely the conclusion drawn from the former, and lastly the inferential sequence (consequence) whereby the truth of the latter is unfailingly linked to the truth of the former. If the inferred judgment is already contained in the first one in such a manner that it may be drawn from it without any third representation intervening, then the inference is termed immediate (consequentia immediata); I should prefer to call it an inference of the understanding. But if, over and above the cognition placed at the ground, a further judgment is needed to produce the conclusion, then the inference is termed an inference of reason. In the proposition all human beings are mortal there already lie the propositions: some human beings are mortal, some mortal beings are human beings, nothing immortal is a human being, and these are accordingly immediate consequences of the first one. The proposition that all scholars are mortal, on the other hand, is not contained in the underlying judgment (for the concept of the scholar does not figure in it at all), and it can be derived from it only by way of an interposed judgment.

In every inference of reason I first, by means of the understanding, think a rule (major). Second, I subsume a cognition beneath the rule's condition (minor) with the help of the power of judgment. Finally, I determine my cognition through the rule's predicate (conclusio), and thus a priori through reason. The relation, then, which the major premise, as the rule, represents between a cognition and its condition, makes up the various kinds of inferences of reason. They are on that account precisely threefold, just as all judgments in general are, insofar as they differ in the way in which they express the cognition's relation within the understanding, that is: categorical or hypothetical or disjunctive inferences of reason.

When, as for the most part happens, the conclusion has been set down as a judgment so as to see whether it does not follow from judgments already given—by which, that is, a wholly different object is thought—then I look in the understanding for the assertion of this concluding proposition, whether it may not be found there, under certain conditions, in accordance with a general rule. Should I then discover such a condition, and should the object of the concluding proposition admit of subsumption under the given condition, then this proposition stands inferred from the rule that holds also for other objects of cognition. From this it is evident that reason, in its inferring, strives to reduce the vast manifold of the understanding's cognition to the fewest possible principles (general conditions), and by this means to produce their highest unity.

C. On the pure use of reason

Can reason be isolated, and is it then still a source in its own right of concepts and judgments that arise solely out of it, and by means of which it relates itself to objects, or is it merely a subordinate faculty for giving to given cognitions a certain form, which is called logical, and through which the cognitions of the understanding are only ranked beneath one another and lower rules beneath other, higher ones (whose condition encompasses the condition of the former within its sphere), so far as this can be brought about by comparing them? That is the question that shall occupy us here, for the present only in a preliminary way. In fact, a multiplicity of rules together with a unity among principles is something reason demands, in order to place the understanding in thoroughgoing coherence with itself, just as the understanding, for its part, subsumes what is manifold in intuition beneath concepts and by that means binds it together. But a principle of this kind prescribes no law to the objects and carries within it no ground that would make it possible to cognize such objects and determine them as such at all; it is rather merely a subjective law of husbandry with the stock of our understanding, one that, through a comparison of its concepts, aims to reduce the universal use of them to the least possible number, without our being thereby warranted in demanding of the objects themselves any such concordance as might further the ease and expansion of our understanding, or in according that maxim objective validity into the bargain. In a word, the question runs thus: does reason in itself, that is, pure reason a priori, harbor synthetic principles and rules, and in what do these principles consist?

Its formal and logical procedure in inferences of reason already furnishes us with adequate guidance as to the ground on which its transcendental principle is to be founded within synthetic cognition by means of pure reason.

First, the inference of reason is not directed upon intuitions, so as to place them beneath rules (as the understanding is with its categories), but upon concepts and judgments. Hence, although pure reason likewise bears upon objects, it entertains no immediate relation to them and their intuition, but only to the understanding and its judgments, which turn first of all toward the senses and the intuition belonging to them, so as to fix the object of these. The unity of reason, then, is not the unity of some possible experience; rather, it stands essentially apart from the latter, which is the unity of the understanding. That whatever happens should have a cause is in no way a principle that reason cognizes and prescribes. It is what renders the unity of experience possible, and it takes nothing on loan from reason, which, apart from this relation to possible experience, could never have decreed any such synthetic unity out of mere concepts.

Second, in its logical employment reason searches for the universal condition of its judgment (the conclusion), and the inference of reason is itself nothing but a judgment effected through the subsumption of its condition beneath a universal rule (the major premise). Since this rule, in its turn, is subjected to the very same experiment of reason, so that the condition of the condition has to be sought out (through a prosyllogism) for as long as this remains feasible, one can see well enough that reason's own peculiar principle taken quite generally (in its logical employment) runs as follows: to locate, for the conditioned cognition of the understanding, the unconditioned by which the unity of that cognition is brought to completion.

This logical maxim, however, can turn into a principle of pure reason in no other way than by our supposing the following: that once the conditioned is given, the entire series of conditions ranked one beneath another—a series that is therefore itself unconditioned—is given along with it (that is to say, comprised within the object and its combination).

Yet a principle of pure reason of this sort is manifestly synthetic; for although the conditioned relates analytically to some condition or other, it does not relate to the unconditioned. From it, moreover, various synthetic propositions are bound to arise of which the pure understanding remains wholly ignorant, seeing that its concern extends only to objects belonging to a possible experience, whose cognition and synthesis stands under conditions at every point. The unconditioned, on the other hand, should it genuinely occur, admits of separate examination in accordance with all those determinations by which it is marked off from every conditioned thing, and must on that account yield material for a good many synthetic propositions a priori.

The principles that spring from this highest principle of pure reason will, however, be transcendent in respect of all appearances, that is, no empirical use answering to it can ever be made of it. It will accordingly stand wholly apart from every principle of the understanding (whose use is entirely immanent, since they take nothing but the possibility of experience for their theme). Now whether that principle—namely that the chain of conditions (whether in the synthesis of appearances or else in the thinking of things as such) reaches all the way to the unconditioned—possesses objective correctness or not; what conclusions issue from it for the empirical employment of the understanding, or whether, on the contrary, there is nowhere any objectively valid proposition of reason of this kind at all, but only a merely logical precept bidding us, as we ascend toward ever higher conditions, to draw nearer to their completeness and so to carry into our cognition the highest unity of reason attainable by us; whether, I repeat, this requirement of reason has, owing to a misconstrual, been mistaken for a transcendental principle of pure reason—one that overhastily postulates such an unbounded completeness on the part of the chain of conditions in the objects themselves; and further, what misreadings and illusions may in that case creep into those inferences of reason whose major premise has been taken over from pure reason (and which is perhaps a begging of the question rather than a postulate), and which climb from experience upward to the conditions it rests on: all of that will form our task in the transcendental dialectic , which we now propose to unfold from its sources, sources lying deeply concealed within human reason. We shall divide it into two chapters, the first of which shall deal with the transcendent concepts belonging to pure reason, the second with its transcendent and dialectical inferences of reason.