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.

First Book. On the Concepts of Pure Reason

Whatever the situation may be with respect to the possibility of concepts drawn from pure reason: they are nonetheless not merely reflected but inferred concepts. Concepts of the understanding are likewise thought a priori, prior to experience and for the sake of it; yet they hold nothing further than the unity that reflection brings to the appearances, insofar as these must of necessity pertain to a possible empirical consciousness. It is through them alone that cognition and the determination of an object become possible. They are thus the first to furnish the material for inference, and they are preceded by no a priori concepts of objects out of which they might be inferred. Their objective reality, by contrast, rests solely upon this: that, since they make up the intellectual form of all experience, their application must at all times be capable of being exhibited within experience.

The designation of a concept of reason, however, already indicates provisionally: that it will not allow itself to be confined within experience, because it concerns a cognition of which every empirical one is only a part (perhaps the whole of possible experience or of its empirical synthesis), a cognition to which no actual experience ever fully attains, yet to which such experience nonetheless at all times belongs. Concepts of reason serve the purpose of comprehending, just as concepts of the understanding serve that of understanding (perceptions). Should they contain the unconditioned, then what they concern is something under which all experience falls, but which is itself never an object of experience: something toward which reason leads in its inferences from experience, and by which it estimates and gauges the degree of its empirical use, though it never forms a member of the empirical synthesis. Should such concepts, this notwithstanding, possess objective validity, they may be called conceptus ratiocinati (correctly inferred concepts); if not, they are at least surreptitiously smuggled in through a semblance of inference and may be called conceptus ratiocinantes (rationalizing concepts). Since, however, this can first be settled in the chapter on the dialectical inferences of pure reason, we cannot yet take it into account, but shall for the present—in the same way that we gave the pure concepts of the understanding the name of categories—bestow a new name upon the pure concepts of reason and term them transcendental ideas, while now elucidating and justifying this designation.

Section 1. On ideas in general

For all the abundance our languages possess, a thinking mind is often left embarrassed for the very expression that would fit its concept exactly, and lacking which it can render itself, neither to others nor even to itself , properly intelligible. To coin new words is to lay claim to legislating in language—a pretension that rarely succeeds; and before one resorts to so desperate an expedient, the prudent course is to cast about in some dead and learned tongue to discover whether this concept, along with a fitting expression for it, may not already be present there; and even should the old usage of that word have been rendered somewhat wavering through the incaution of those who first framed it, it is still preferable to pin down the meaning that was distinctively its own (granting that it may remain uncertain whether precisely this same sense was intended back then) than to ruin one's enterprise outright by making oneself unintelligible.

For this very reason, should there happen to exist just one solitary word for a given concept—a word that in its already established usage fits that concept exactly, and whose separation from other cognate concepts carries great weight—the sensible thing is not to handle it wastefully, nor to deploy it merely for variety's sake as a synonym for others, but instead to guard carefully its own proper signification; for otherwise it readily comes about that, once the expression ceases to hold our attention in any special way and sinks from view amid the throng of others of widely differing meaning, the very thought is lost as well that it, and it alone, might have preserved.

Plato made use of the term idea in a manner that plainly reveals he meant by it something which is not merely never drawn from the senses, but which even rises far above those concepts of the understanding that engaged Aristotle, seeing that in experience one never lights upon anything congruent with it. For Plato the ideas are archetypes of the things themselves, not merely keys to possible experiences in the way the categories are. On his view they streamed forth from the highest reason, from which they passed to human reason, which, however, no longer stands today in its pristine condition, but must with effort summon back the old ideas, now heavily darkened, by means of a recollection (which is what philosophy is). I do not wish here to embark on any literary inquiry with a view to establishing the sense the sublime philosopher bound up with his expression. I note only that it is nothing whatever out of the ordinary—in everyday talk no less than in written works—to understand an author better than he understood himself, through a comparison of the thoughts he voices about his subject, since he failed to fix his concept adequately and thus at times spoke, or indeed thought, in opposition to his own purpose.

Plato observed quite well that our faculty of cognition feels a need far loftier than merely, in keeping with synthetic unity , to spell appearances out so as to make them legible as experience, and that our reason, of its own nature, lifts itself toward cognitions that reach so far that no object experience is able to supply could ever prove congruent with them—cognitions that for all that possess a reality of their own and are in no way mere fabrications of the brain.

It was above all across the whole domain of the practical that Plato located his ideas,³⁵ that is, in whatever rests upon freedom—freedom that on its side falls under cognitions constituting a distinctive product of reason. Anyone bent on drawing the concepts of virtue out of experience, anyone minded to take what can at most furnish an example for imperfect illustration and set it up as the model for the wellspring of cognition (as, in truth, no small number have done), would turn virtue into an equivocal monstrosity, shifting with time and circumstance and serviceable for no rule whatever. In contrast, everyone becomes inwardly aware that, when someone is set before him as a model of virtue, he yet retains the genuine original solely within his own head, against which he measures this alleged model and by reference to which alone he rates it. This, however, is the idea of virtue, in relation to which all conceivable objects of experience do duty indeed as examples (evidence that what the concept of reason demands is, to some degree, achievable), yet not as archetypes. The fact that no human being will ever conduct himself in a manner fully commensurate with what the pure idea of virtue holds within it does nothing at all to prove there is something chimerical in this thought. For all the same, every judgment upon moral worth or worthlessness is possible only through the mediation of this idea; consequently it lies of necessity at the basis of every advance toward moral perfection, however far the obstacles lodged in human nature—whose magnitude admits of no determination—may keep us at a distance from it.

Plato's Republic has passed into a byword, taken as a glaring specimen of a perfection merely dreamed up, one able to lodge nowhere but in the brain of the idle thinker, and Brucker finds it laughable that the philosopher should have asserted a prince would never rule well without partaking of the ideas. Yet it would be the wiser course to follow up this thought more closely and (at those points where that admirable man abandons us to our own devices) to set it in the light through fresh endeavors, rather than to push it aside as worthless on the utterly paltry and pernicious pretext that the thing cannot be done. A constitution affording the greatest human freedom under laws so framed that the freedom of each can coexist with that of everyone else (not the greatest happiness, for that will ensue of its own accord anyway) is at the very least a necessary idea that must be laid at the foundation not only of the initial sketch of a political constitution but of every one of its laws, and in drawing which one must at the start leave out of account the present impediments, which perhaps arise not so much unavoidably from human nature as, rather, from having neglected the authentic ideas in the framing of law. For nothing more injurious, and nothing more unworthy of a philosopher, can be turned up than the mob-like appeal to a supposedly recalcitrant experience, which after all would have no existence whatever had those provisions been instituted in good time according to the ideas, and had crude concepts not—for the very reason that they were scooped up out of experience—thwarted, in their place, every good design. The more closely legislation and administration were fashioned in agreement with this idea, the scarcer punishments would surely grow, and it is then wholly rational (as Plato contends) to hold that under a flawless arrangement of them not a single such penalty would be called for. Now granted that this last may never be realized, the idea is nonetheless perfectly sound that erects this maximum as an archetype, so that by its measure the lawful constitution of humankind may be brought forever closer to the greatest attainable perfection. For what the supreme degree may be at which humankind must halt, and thus how wide the chasm that inevitably persists between the idea and its realization may turn out to be, is a thing that no one is able, or entitled, to fix—precisely because it is a matter of freedom, which can overstep whatever limit one might name.

But it is not only in the field where human reason exhibits a true causality—where ideas turn into operative causes (of deeds and of their objects), namely in the moral sphere—but with regard to nature itself as well that Plato justly discerns clear proofs of its origin from ideas. A growing plant, an animal, the orderly arrangement of the cosmic edifice (and so, presumably, the entire order of nature) make it plain that nothing but ideas could render them possible; that no single creature, taken under the particular conditions of its existence, does match the idea of the most perfect of its kind (any more than the human being matches the idea of humanity, which he even carries within his own soul as the archetype of his deeds); that those ideas are all the same, within the highest understanding, individual, immutable, through and through determinate, and the primordial causes of things, and that only the totality of their interconnection throughout the universe is fully adequate, wholly and solely, to that idea. If one strips away what is overdone in the phrasing, then the philosopher's flight of spirit—mounting up from the corporeal contemplation of the physical side of the world-order to its architectonic conjunction according to purposes, that is, according to ideas—represents an effort worthy of respect and of emulation; but as concerns whatever bears on the principles of morality, of legislation, and of religion, where the ideas are what first render experience itself (of the good) possible, though they can never be given full expression within it, there is a merit entirely its own, one that goes unacknowledged solely because it is appraised by those very empirical rules whose validity as principles was to have been cancelled by precisely those ideas. For where nature is in question, experience places the rule in our hands and is the wellspring of truth; where the moral laws are in question, however, experience is (alas!) the mother of mere semblance, and nothing is more culpable than to borrow the laws governing what I ought to do from, or to seek to hem them in by, that which is done.

In lieu of all these reflections, whose proper carrying-through is what in fact makes up the peculiar dignity of philosophy, we now occupy ourselves with a less resplendent, though not therefore meritless , labor—namely, that of rendering level and structurally sound the ground beneath those majestic moral edifices—ground riddled with all manner of molehills thrown up by a reason that tunnels fruitlessly, though in high hopes of treasure, and that leaves the edifice above unsafe. It is therefore the transcendental employment of pure reason, its principles and its ideas, that we are now obliged to become precisely acquainted with, if we are to gauge and appraise, as we should, the influence of pure reason and its worth. Yet before I lay this preliminary introduction aside, I entreat those who hold philosophy dear (which says more than one ordinarily encounters), should they find themselves persuaded by the present remarks and by what is to follow, to take the term idea into their keeping in accordance with its original meaning, lest it drift henceforth in among the remaining expressions by which every sort of representation is habitually labelled in heedless disorder, and lest the science suffer a loss thereby. We are, after all, in no want of designations aptly matched to each kind of representation, without our needing to trespass upon the domain of another. Here is a graduated ladder of them. The genus is representation as such (repraesentatio). Beneath it falls representation accompanied by consciousness (perceptio). A perception bearing solely on the subject, as a modification of its state, is sensation (sensatio); an objective perception is cognition (cognitio). This last is either intuition or concept (intuitus vel conceptus). The one bears directly upon its object and is singular; the other only mediately, by way of a mark that may be shared among several things. A concept, again, is either empirical or a pure concept, and a pure concept, to the extent that it takes its rise within the understanding alone (and not within any pure image belonging to sensibility), bears the name Notio. A concept assembled out of notions, one that outstrips the possibility of experience, is the idea, or concept of reason. To anyone who has once grown at home with this distinction, it is bound to prove insufferable to hear the representation of the color red termed an idea. It cannot even properly be styled a notion (a concept belonging to the understanding).

Section 2. On transcendental ideas

In the transcendental analytic we were shown, by way of illustration, how the merely logical form belonging to our cognition is able to harbor the source of pure a priori concepts—concepts that present objects in advance of any experience, or that rather flag the synthetic unity through which alone an empirical cognition of objects becomes possible at all. Once the form of judgments had been transformed into a concept of the synthesis of intuitions, it yielded up the categories, which govern every employment of the understanding within experience. By the same token, we have reason to anticipate that the form of the inferences of reason—applied to that synthetic unity of intuitions in conformity with the categories—will likewise harbor the source of distinctive a priori concepts; these we are entitled to name pure concepts of reason, or transcendental ideas, and it is they that will fix, in accordance with principles, the employment of the understanding across experience regarded in its entirety.

What reason accomplishes in drawing its inferences lay in rendering cognition universal by way of concepts, and a syllogism, taken on its own, is a judgment determined a priori across the full extent of its condition. Take the proposition, Cajus is mortal: this I might just as well draw straight from experience by means of the understanding alone. Yet what I am after is a concept holding within it the condition on which the predicate of this judgment (its assertion, generally speaking) rests (that is, in the present instance, the concept of the human being); and having subsumed under that condition, taken across its entire extent (all human beings are mortal), I then determine, on that basis, the cognition of my object (Cajus is mortal).

And so it is that, in the conclusion of a syllogism, we confine a predicate to some particular object, having earlier entertained it in the major premise across its whole extent and under a certain condition. Such a completed magnitude of extent, referred to a condition of this kind, we term universality (Universalitas). Its counterpart, over on the side of the synthesis of intuitions, is allness (Universitas), that is, the totality of conditions. Consequently, the transcendental concept of reason turns out to be none but the concept of the totality of conditions belonging to some given conditioned thing. Since it is the unconditioned that alone renders any totality of conditions possible, while conversely a totality of conditions is at every point already unconditioned in itself: it follows that a pure concept of reason as such admits of explication by means of the concept of the unconditioned, provided this concept carries within it a ground for synthesizing the conditioned.

However many sorts of relation there are that the understanding pictures to itself through the categories, that same number of pure concepts of reason will there prove to be as well; and so we shall have to look, first, for an unconditioned belonging to the categorical synthesis within a subject, secondly, to the hypothetical synthesis of the members making up a series, and thirdly, to the disjunctive synthesis of the parts within a system.

For there exist correspondingly many species of syllogism, each of them pressing on through prosyllogisms toward the unconditioned: one toward a subject that is itself no longer a predicate at all, a second toward a presupposition presupposing nothing beyond itself, and a third toward an aggregate of the members of a division such that nothing further is called for to bring the division of a concept to completion. This is why the pure concepts of reason bearing on totality in the synthesis of conditions are indispensable—if only as problems set for us, whereby the understanding's unity is to be prolonged, so far as may be, right up to the unconditioned—and why they take root in the very nature of human reason; granted, these transcendental concepts may for the rest want any use befitting them in concreto, so that their sole utility consists in steering the understanding in a direction wherein its own employment, stretched to the very limit, is at once brought into thoroughgoing accord with itself.

But in speaking here of a totality of conditions, and of the unconditioned, under a heading shared by every concept of reason, we run up once more against a term that we can ill spare and yet, on account of an ambiguity that long abuse has fastened onto it, cannot deploy with confidence. The word absolute ranks among the handful of terms that in their primordial sense came to fit a concept so precisely that no other word of the very same language afterward suits it exactly—and whose loss, or what comes to the same thing, whose unsteady use, must on that account drag along with it the forfeiting of the concept itself, a concept, moreover, that, since it exercises reason to no small degree, can hardly be given up without serious damage to every transcendental appraisal. Nowadays the word absolute frequently serves simply to signal that something obtains of a thing taken in itself and therefore internally. On that reading, absolutely possible would designate whatever is possible in its own right (interne)—which is, in point of fact, the least that can be affirmed of any object. Now and then, by contrast, it is put to work to signal that something holds good under every relation (without restriction)—absolute sovereignty, say—and on this reading absolutely possible would pick out whatever is possible in every intention, in every relation, and this, in turn, is the utmost I am in a position to assert regarding the possibility of any thing. Granted, these two senses do on occasion converge. Whatever is internally impossible, to take one case, will likewise be impossible under every relation and therefore impossible in the absolute sense. For the most part, though, they stand infinitely far apart, and there is no route by which I might infer that a thing's being possible in itself makes it, for that reason, possible under every relation and so possible absolutely. Regarding absolute necessity, indeed, I shall establish further on that it by no means depends in all cases upon inner necessity, and must accordingly not be treated as saying the same thing as the latter. Where a thing's opposite is internally impossible, that opposite is of course impossible under every intention as well, so that the thing is itself necessary absolutely; but the converse inference is barred to me—that whatever is necessary absolutely has an opposite that is internally impossible, that is, that the absolute necessity of things amounts to an inner necessity; for such inner necessity is, in certain instances, an utterly hollow phrase to which we can attach not the slightest concept, whereas the necessity of a thing under every relation (with respect to all that is possible) brings along with it determinations of a quite distinctive kind. And since a philosopher can never look with indifference upon the loss of a concept of broad application within speculative philosophy, my hope is that he will likewise not regard with indifference the fixing and the careful safekeeping of the term to which that concept clings.

It is in this enlarged sense, accordingly, that I shall avail myself of the word absolute, setting it over against what holds only comparatively or under some special consideration; for the latter stands restricted to conditions, whereas the former is valid with no restriction whatever.

The transcendental concept of reason, then, is invariably directed at nothing but the absolute totality in the synthesis of conditions, and it comes to rest nowhere save at the unconditioned in the strict sense—unconditioned, that is, under every relation. For pure reason hands everything over to the understanding, which in the first place bears upon the objects of intuition, or rather upon their synthesis within the imagination. To itself alone reason keeps back the absolute totality in the employment of the concepts of the understanding, striving to carry the synthetic unity that gets thought in the category all the way out to the strictly unconditioned. The former, accordingly, may be styled the unity of reason among appearances, much as the latter, the one that the category articulates, may be styled the unity of the understanding. And so reason bears upon the employment of the understanding and upon nothing else—yet not insofar as this employment holds the ground of a possible experience (an absolute totality of conditions being no concept of any use within experience, seeing that no experience is ever unconditioned), but rather so as to lay down for it a bearing toward a certain unity that lies beyond any concept the understanding possesses, a unity that comes down to drawing together all the acts of the understanding, in regard to each and every object, into one absolute whole. For this reason the objective employment of the pure concepts of reason remains at all times transcendent, while that of the pure concepts of the understanding, being what it is by nature, must at all times stay immanent, confined as it is to possible experience alone.

What I mean by an idea is a necessary concept of reason for which the senses can furnish no congruent object. The pure concepts of reason we have just been weighing are, therefore, transcendental ideas. They count as concepts of pure reason; for they view all cognition drawn from experience as determined by way of an absolute totality of conditions. Far from being fabricated at will, they are laid upon us as a charge by the very nature of reason, and for that reason bear of necessity upon the whole employment of the understanding. They are, in the last place, transcendent, overshooting the bounds of all experience, within which, then, no object can ever turn up that would be adequate to the transcendental idea. To call something an idea is to claim, as measured by the object (as of an object of the pure understanding), a great deal, yet, as measured by the subject (in regard, that is, to its actuality under an empirical condition), on precisely that ground very little, since a maximum, of which it is the concept, can never be delivered congruently in concreto. And since it is this latter that, in the merely speculative employment of reason, really constitutes the entire aim—and since drawing near to a concept never in fact attained in the exercise counts for just as much as missing that concept altogether—one says of a concept of this sort: it is nothing but an idea. One might put it thus: the absolute whole of all appearances is nothing but an idea, for since we are never able to sketch its like in an image, it stays a problem admitting of no solution at all. By contrast, since in the practical employment of the understanding everything turns solely upon the carrying of rules into practice, the idea of practical reason can at all times be genuinely delivered, if only in part, in concreto—indeed, it is the condition, not to be dispensed with, of every practical employment of reason. The exercise of it is at every point bounded and deficient, yet the bounds themselves elude determination, so that it always stands under the sway of the concept of a completeness that is absolute. The practical idea, on this showing, is at every point supremely fruitful and, where actual actions are concerned, necessary past all avoidance. Within it pure reason possesses even a causality for actually bringing forth what its concept holds; and so of wisdom one may not, in a manner of speaking, say slightingly that it is nothing but an idea—rather, on the very ground that it is the idea of the necessary unity of all possible ends, it has to serve as the rule for everything practical, as an original condition, or at the least a limiting one.

However true it may be that of the transcendental concepts of reason we are bound to say they are nothing but ideas, we are in no way therefore to look upon them as idle and void. For even granting that no object gets determined through them, they can still, deep down and without being noticed, serve the understanding as a canon for the extended and concordant employment of itself—whereby it comes to cognize, true enough, no object over and above what its concepts would already let it cognize, and yet finds itself, within that very cognition, guided further and better . To say nothing of how they may perhaps open up a passage leading from the concepts of nature over to the practical ones, and in just this way secure for the moral ideas themselves a footing, together with a linkage to reason's speculative cognitions. Clarification on all of this we must look for as the inquiry proceeds.

As our purpose requires, however, we here lay the practical ideas to one side and so take reason up only in its speculative bearing, and, narrower still within that, only in its transcendental employment. The very road we struck out on earlier, in deducing the categories, we must now strike out on again: namely, to weigh up the logical form of rational cognition and to find out whether reason might not, by that route, itself become a wellspring of concepts under which objects, taken in themselves, come to be regarded as determined synthetically a priori in respect of one function of reason or another.

Reason, viewed as the capacity answering to a certain logical form of cognition, is the capacity for drawing inferences—that is, for judging in a mediated fashion (by subsuming the condition of some possible judgment beneath the condition of a judgment already given). This given judgment supplies the universal rule (the premise stated first, major). Placing the condition of some further possible judgment beneath the condition of the rule yields the premise stated below (minor). The actual judgment, which pronounces the rule's assertion in the subsumed case, is the closing proposition (conclusio). For the rule asserts something in a universal way under a certain condition. Now, in a case that comes up, the rule's condition is met. And so whatever held universally under that condition is taken to hold in the case that comes up as well (the case carrying this condition along with it). It is readily seen that reason reaches a cognition by way of acts of the understanding which together make up a series of conditions. Suppose I reach the proposition all bodies are alterable solely by setting out from the more distant cognition (one in which the concept of body has yet to appear, though it does hold the condition of that concept): everything composite is alterable; then move on from this to a nearer cognition, standing under the condition of the first: bodies are composite; and from this, only then, on to a third, which at last ties the distant cognition (alterable) to the one now before me: bodies, consequently, are alterable: in that case I have made my way, through a series of conditions (premises), to a cognition (conclusion). Now any series whatever whose exponent (that of the categorical or hypothetical judgment) is given admits of being carried on; and thus the selfsame act of reason issues in the ratiocinatio polysyllogistica, which is a chain of inferences extendable into indeterminate reaches either on the side of the conditions (per prosyllogismos) or on that of the conditioned (per episyllogismos).

One soon comes to notice, however, that the chain, or series, of prosyllogisms—that is, of cognitions inferred over on the side of the grounds or the conditions for a given cognition, or, to phrase it otherwise, the ascending series of syllogisms—must after all stand in another relation to the faculty of reason than does the descending series, i.e. reason's advance over on the side of the conditioned by way of episyllogisms. For seeing that, in the first case, the cognition (conclusio) is given merely as conditioned, one can arrive at it by means of reason in no other way than on the assumption, at the very least, that all the members of the series on the side of the conditions are given (a totality in the series of premises)—only on that assumption being the judgment at hand possible a priori; whereas on the side of the conditioned, or of the consequences, what gets thought is a series merely coming to be, not one already presupposed in full or given, and hence no more than a progression held in potential. For this reason, once a cognition is looked upon as conditioned, reason finds itself constrained to look upon the series of conditions along the ascending line as brought to completion and as given in respect of its totality. But if this very cognition is at the same time looked upon as the condition of other cognitions, which among themselves compose a series of consequences along the descending line, then it may be all one to reason how far this advance reaches out a parte posteriori, and whether a totality of the series is so much as possible anywhere; for reason has no need of such a series in reaching the conclusion set before it, that conclusion being already, through its grounds, sufficiently determined and secured a parte priori. It may well be that, on the side of the conditions, the series of premises does possess a first as its supreme condition, or that it does not and so runs on a parte priori without any limit; even so, it has to comprise a totality of the condition, granting that we could never manage to lay hold of it; and the whole series has to be true without condition if that conditioned thing which is viewed as a consequence springing from it is to pass for true. This is a demand made by reason, which proclaims its cognition to be determined a priori and to be necessary: whether in its own right, in which case no grounds are wanted, or, should it be derived, then as one link within a chain of grounds that is itself true in an unconditioned manner.

Section 3. System of transcendental ideas

What occupies us here is not a logical dialectic, one that abstracts from all content of cognition and merely lays bare the false semblance in the form of the inferences of reason, but a transcendental one, which is meant to contain, wholly a priori, the origin of certain cognitions springing from pure reason together with inferred concepts whose object can never be given empirically at all, and which for that reason lie entirely outside the capacity of the pure understanding. We have inferred, from the relation that the transcendental employment of our cognition must naturally bear to its logical employment—in judgments no less than in inferences—that dialectical inferences can be of only three kinds, answering to the three ways of inferring by which reason is able to reach cognitions from principles, and that in every case their task consists in climbing up from that conditioned synthesis, to which the understanding stays perpetually tied, toward an unconditioned one that it can never attain.

Now, the universal element in every relation that our representations are capable of having is this: 1) their relation to the subject, 2) their relation to objects, and here either as appearances or as objects of thinking in general. If this subdivision is combined with the one given above, then every relation of the representations—of which we are able to frame either a concept or an idea—turns out to be threefold: 1. its relation to the subject, 2. to the object's manifold in appearance, 3. to all things whatsoever.

Now, pure concepts as such all have to do with the synthetic unity of representations, whereas concepts of pure reason (transcendental ideas) are directed at the unconditioned synthetic unity embracing all conditions whatsoever. It follows that every transcendental idea can be assigned to one of three classes: the first takes in the thinking subject's absolute (unconditioned) unity; the second, the absolute unity belonging to the series of the conditions of appearance; the third, the absolute unity proper to the condition of all objects of thinking in general.

The thinking subject forms the object of psychology; the sum of all appearances (the world), that of cosmology; and that thing which holds the highest condition for the possibility of all that admits of being thought (the being of all beings), that of theology. In this way pure reason hands over the idea of a transcendental doctrine of the soul (psychologia rationalis), of a transcendental science of the world (cosmologia rationalis), and lastly of a transcendental cognition of God (theologia transscendentalis). Even the mere sketch of the one or the other of these sciences in no way stems from the understanding, even were it bound up with reason's highest logical use, i.e., with every conceivable inference, so as to move from one object of the understanding (an appearance) to all the rest, right down to the remotest members of the empirical synthesis; rather, it is merely a pure and genuine product or problem of pure reason.

Which modi of the pure concepts of reason stand under these three headings of all transcendental ideas will be set forth in full in the chapter that follows. They proceed along the guiding thread of the categories. For pure reason never relates directly to objects, but rather to the understanding's concepts of them. In the same way, only the complete working-out can show how reason, simply by the synthetic use of that very function which serves it in the categorical syllogism, is bound to come upon the concept of the thinking subject's absolute unity; how, in the hypothetical case, its logical procedure yields the idea of what is unconditioned outright in a series of given conditions; and how, lastly, the bare form of the disjunctive syllogism cannot but drag along with it the supreme rational concept of a being of all beings—a notion that strikes one, at first sight, as utterly paradoxical.

Of these transcendental ideas no objective deduction is, strictly speaking, possible, of the kind we were able to supply for the categories. For in truth they stand in no relation to any object that might be given as congruent with them, and this precisely because they are nothing but ideas. A subjective derivation of them from the nature of our reason, however, we could indeed undertake; and that has in fact been carried out in the present chapter.

One readily sees that pure reason aims at nothing other than the absolute totality of the synthesis on the side of the conditions (whether of inherence, of dependence, or of concurrence), and that it has no business with the absolute completeness on the side of the conditioned. For reason requires the former alone, so as to lay down in advance the entire series of conditions and thus supply them to the understanding a priori. Yet the moment a completely (and unconditionally) given condition is present, no concept of reason is any longer called for as regards the continuation of the series; for on its own the understanding accomplishes every step downward from the condition to the conditioned. Accordingly, the transcendental ideas are of service solely for the ascent through the series of conditions up to the unconditioned, that is, to the principles. As regards the descent to the conditioned, by contrast, our reason does make a far-reaching logical use of the laws of the understanding, yet no transcendental use whatever; and should we frame an idea of the absolute totality of such a synthesis (the progressus)—say, of the entire sequence of all future changes in the world—this is a thought-thing (ens rationis), one thought up merely at will and not necessarily presupposed by reason. For while the totality of a thing's conditions is presupposed for the possibility of the conditioned, the totality of its consequences is not. Such a concept, therefore, is no transcendental idea—and it is transcendental ideas alone that occupy us here.

Finally, one also comes to notice that a certain coherence and unity shines out among the transcendental ideas themselves, and that by means of them pure reason arranges the whole of its cognitions into a system. To advance from cognition of oneself (the soul) to cognition of the world, and by its means to the primordial being, is a progression so natural that it looks like the logical passage of reason from premises to conclusion ³⁶. Now whether a kinship of the same sort as that between the logical and the transcendental procedure really does lie secretly at the ground here is likewise one of those questions whose answer one may expect only as these investigations are pursued further. For the moment we have already gained our end, in that we have managed to lift the transcendental concepts of reason—which are otherwise wont to mingle, in the theorizing of the philosophers, among other concepts, without these philosophers even properly telling them apart from concepts of the understanding—out of this equivocal position, to specify their origin and, at one stroke, their determinate number, past which none can ever be added, and to exhibit them within a systematic coherence, whereby a special field is marked off and bounded for pure reason.

Second Book. On the Dialectical Inferences of Pure Reason

One may say that a merely transcendental idea has for its object something for which one possesses no concept, even though this idea is produced quite necessarily within reason in accordance with its original laws. For, in truth, an object that is supposed to correspond to reason's requirement likewise admits of no concept of the understanding — that is, of a concept that can be displayed and rendered intuitable within a possible experience. One would, however, express the matter better, and with less risk of being misunderstood, were one to say: that of the object which corresponds to an idea we can have no acquaintance, although we can indeed have a problematic concept of it.

Now the transcendental (subjective) reality of the pure concepts of reason rests at least upon the fact that a necessary inference of reason brings us to such ideas. There will accordingly be inferences of reason that contain no empirical premises and by means of which, from something we know, we draw a conclusion to something else of which we have no concept, yet to which, through an inevitable illusion, we grant objective reality. With respect to their outcome, such inferences are therefore to be termed ratiocinating rather than inferences of reason: although, on account of what occasions them, they may indeed carry the latter title, since they are neither invented nor arisen by chance but issue from the very nature of reason itself. They are sophistications that belong not to human beings but to pure reason itself, from which not even the wisest of all human beings can free himself, and though after much labor he may perhaps guard against the error, the illusion that unceasingly pinches and mocks him he can never entirely shake off.

Of these dialectical inferences of reason, then, there are only three sorts, precisely as many kinds as there are ideas onto which their concluding propositions issue. In the inference of reason of the first class I conclude, from the transcendental concept of the subject, which contains nothing manifold, to the absolute unity of this subject itself, of which in this way I have utterly no concept. This dialectical inference I shall call the transcendental paralogism. The second class of ratiocinating inferences is laid out upon the transcendental concept of the series of conditions, in its absolute totality, for a given appearance as such; and from this — that on the one side I invariably possess a self-contradictory concept of the series' unconditioned synthetic unity — I conclude to the correctness of the opposing unity, of which I nonetheless likewise have no concept. The state of reason in these dialectical inferences I shall call the antinomy of pure reason. Finally, in accordance with the third kind of ratiocinating inference, I conclude, from the totality of the conditions for thinking objects as such, so far as they may be given to me, to the absolute synthetic unity of all conditions of the possibility of things as such — that is, from things that I do not know through their mere transcendental concept, to a being of all beings, which I know even less through a transcendental concept, and of whose unconditioned necessity I am unable to form any concept. This dialectical inference of reason I shall call the ideal of pure reason.

Chapter 1. On the Paralogisms of Pure Reason

A logical paralogism has its falsity in the mere form of a rational syllogism, let its content be whatever it may. A transcendental paralogism, by contrast, rests on a transcendental ground that makes one draw a formally invalid conclusion. A fallacy of this sort, accordingly, is rooted in the very nature of human reason and brings with it an illusion that, while unavoidable, is not beyond resolution.

We arrive now at a concept that our earlier general roster of transcendental concepts did not list, though it nonetheless has to be reckoned among them—and this without in any way modifying that table or pronouncing it incomplete. It is the concept—or, should one rather have it so, the judgment—I think. Yet it is easy to see that this is the vehicle carrying all concepts whatever, the transcendental ones included, so that it is invariably co-thought along with them and is thus itself no less transcendental, though it merits no title of its own, since its whole office is to exhibit every act of thinking as something belonging to consciousness. Nevertheless, however free of the empirical (the imprint of the senses) it may be, it does help us mark off two sorts of object grounded in the very nature of our representational power. I, taken as thinking, count as an object of inner sense, and the name for this is soul. Whatever, on the other hand, stands as an object of the outer senses bears the name body. The phrase 'I, as a thinking being', therefore, already picks out the subject matter of that psychology which one may term the rational doctrine of the soul, on the assumption that I ask to know nothing of the soul beyond what may be concluded—apart from all experience (which fixes me more determinately and in concreto)—from the concept I so far as this turns up throughout all thinking.

Now the rational doctrine of the soul really is a venture of just this sort; for were even the slightest empirical element of my thinking—some specific perception of my own inner condition—admitted among this science's sources of cognition, it would thereby cease to be rational and turn into an empirical doctrine of the soul. So we already have before us a would-be science resting on the one proposition I think, and its soundness or unsoundness is something we may here examine quite appropriately, as befits the character of a transcendental philosophy. It should give no one pause that in this proposition, which voices the perception of oneself, I do in fact possess an inner experience, so that the rational doctrine of the soul built upon it can never be pure but rests partly on an empirical principle. For this inner perception amounts to nothing beyond the bare apperception I think—the very thing that first makes possible all the transcendental concepts, wherein one says: I think substance, cause, and so on. For inner experience as such together with its possibility—or, equally, perception as such together with its bearing on other perception, where no particular difference or determination among perceptions is empirically supplied—may not pass as empirical cognition; it has instead to be treated as cognition of the empirical taken generally, and it falls under the inquiry into how any experience whatever is possible, an inquiry that is of course transcendental. The tiniest object of perception (say, mere pleasure or displeasure) annexed to the general representation of self-consciousness would straightaway convert rational psychology into an empirical psychology.

I think, then, is the one and only text of rational psychology, and out of it the whole of that science's wisdom is meant to be unfolded. It is readily apparent that this thought, once it is made to bear on an object (my own self), admits of nothing but transcendental predicates of that object: for the faintest empirical predicate would ruin the science's rational purity and its freedom from all experience.

Here, though, our sole task will be to keep to the guiding thread of the categories; only, because in this instance a thing—namely I, as a thinking being—is what is first given, we shall leave the earlier ordering of the categories among themselves (as their table lays it out) untouched, yet start at this point from the category of substance, by which a thing in itself is represented, and then work our way back down their sequence. Hence the topic of the rational doctrine of the soul, the source from which all its remaining content has to be drawn, runs as follows:³⁷

Out of these elements every concept belonging to the pure doctrine of the soul springs solely by way of combination, without so much as acknowledging any further principle. Considered simply as an object of inner sense, this substance furnishes the concept of immateriality; as a simple substance, that of incorruptibility; through its identity, as an intellectual substance, it furnishes personality; and the three together furnish spirituality; its relation to objects in space furnishes commercium with bodies; the thinking substance is thereby represented as the principle of life within matter, that is, as soul (anima) and as the basis of animality, and this last, once curbed by spirituality, gives immortality.

It is upon this that there rest four paralogisms of a transcendental doctrine of the soul, a doctrine mistakenly regarded as a science of pure reason treating of what our thinking being is by nature. Yet at their basis we are able to place nothing beyond the plain representation I—wholly devoid of content in its own right, and such that one cannot even call it a concept, but only a bare consciousness attending every concept. By means of this I, or He, or It (the thing) that carries out the thinking, all that gets represented is a transcendental subject of the thoughts, = X; it is known only through those thoughts, which serve as its predicates, and taken by itself we can form of it not the slightest concept, so that we keep circling it perpetually, obliged as we are to draw on its representation before we can pass any judgment about it at all—an awkwardness inseparable from the case, since consciousness in itself is less a representation singling out some particular object than a form belonging to representation generally, so far as representation deserves the name of cognition; and it is of the latter alone that I can say I thereby think anything whatever.

Still, it must appear odd right from the start that the condition on which I think at all—which is accordingly no more than a feature of my own subject—should hold good at the same time for whatever thinks, and that on the basis of a seemingly empirical proposition we should venture to rest an apodictic and universal judgment, to wit: that everything which thinks is so constituted as the deliverance of self-consciousness pronounces it to be in my own case. The reason for this, however, is that to things we are bound of necessity to attribute a priori every property making up the conditions apart from which we cannot think them at all. Now no outer experience, but self-consciousness alone, can give me even the barest representation of a thinking being. Objects of that kind, therefore, come to no more than the carrying-over of this consciousness of mine onto other things, which are pictured as thinking beings by that transfer alone. The proposition 'I think' is, however, entertained here in merely problematic fashion—not as it might carry a perception of some existence (the Cartesian cogito, ergo sum), but purely in point of its possibility, so as to discover what properties might issue, from a proposition thus utterly simple, for the subject of it (whether or not any such subject actually exists).

Were anything more than the cogito to underlie our pure rational cognition of thinking beings as such; were we to enlist as well the observations on how our thoughts interplay and the natural laws of the thinking self derivable from them: what would emerge is an empirical psychology, a sort of physiology of inner sense, able perhaps to account for that sense's appearances, but never fit to bring to light properties lying wholly beyond possible experience (such as that of the simple), nor to teach anything apodictically about the nature of thinking beings in general; it would thus fall short of being a rational psychology.

Since the proposition I think (entertained problematically) carries within it the form of every judgment of the understanding whatever and rides along with all the categories as their vehicle: it becomes plain that whatever is inferred from it can involve only a transcendental employment of the understanding, one that refuses any admixture of experience, and about whose upshot—given what we established earlier—we can already form no favorable notion beforehand. Let us, then, track it with a critical eye across all the predicaments of the pure doctrine of the soul, yet, to be brief, allow the scrutiny of them to run on as a single unbroken sequence.

To begin with, one general observation may sharpen our vigilance toward this style of inference. I cognize no object simply in virtue of thinking; a given intuition must first be determined by me relative to that unity of consciousness in which all thinking has its being—only then can I cognize any object at all. Accordingly, my being aware of myself as thinking does not amount to my cognizing myself; that happens only when I am aware of the intuition of myself as determined in respect of the function of thought. For this reason all the modi of self-awareness in thinking are as yet no concepts of the understanding regarding objects (categories); they are mere logical functions, handing thought no object whatever to be cognized, and consequently handing me my own self no more than the rest as an object. What counts as the object is not the awareness of the determining self but solely that of the determinable self—that is, of my inner intuition (to the degree that its manifold admits of being conjoined according to the general condition governing the unity of apperception in thought).

1) Throughout every judgment I am, invariably, the determining subject of the relation that makes the judgment up. But that I who think must always, in thinking, hold as subject, as something not to be viewed as merely clinging to thought after the manner of a predicate, is a proposition apodictic and indeed identical; it does not, however, imply that I, qua object, am a being that subsists on its own or a substance. This latter claim reaches very far and hence calls for data nowhere to be found in thinking—perhaps (so far as I regard the thinking merely as such) more than I shall ever come across anywhere within it.

2) That the I of apperception is, in consequence, in each act of thinking a singular incapable of being resolved into a multitude of subjects, and hence marks out a logically simple subject—this already resides in the concept of thinking and is thus an analytic proposition; but it does not carry the meaning that the thinking I is a simple substance, which would make it a synthetic proposition. The concept of substance is invariably tied to intuitions, and these, in my case, can be nothing but sensible, lying therefore altogether beyond the field of the understanding and its thinking—though thinking is precisely what is at issue here when it is claimed that the I is simple in thought. It would, moreover, be astonishing if what ordinarily demands so much apparatus—in order to make out, within what intuition sets before us, which element in it is substance, and, harder still, whether that substance can also be simple (as with the parts of matter)—were here handed to me outright, as though by revelation, in the barest representation there is.

3) The proposition asserting my own identity amid all the manifold of which I am conscious is one that likewise lies within the very concepts, and so is analytic; but this identity of the subject, of which I can grow conscious across all its representations, has no bearing on the intuition of that subject whereby it is given as object, and it cannot therefore stand for the identity of the person—by which is meant the awareness that one's own substance, as a thinking being, stays identical through every alteration of its states—an identity whose proof the mere analysis of 'I think' could never furnish, calling instead for sundry synthetic judgments that rest upon the intuition given.

4) 'I set my own existence, as that of a thinking being, apart from other things beyond me (my body among them)'—this too is analytic; for by other things I mean just those I conceive as set apart from myself. But whether this awareness of myself could so much as occur in the absence of things beyond me by which representations reach me—whether, that is, I might exist as a merely thinking being (without being a human)—of this the proposition tells me nothing at all.

So it turns out that dissecting the awareness of myself in thinking as such yields not the least gain as regards cognizing myself qua object. The logical elucidation of thought in general gets mistaken for a metaphysical determination of the object.

One great stumbling block—indeed the single one—confronting our whole critique would appear were it feasible to establish a priori that every thinking being is in itself a simple substance, and, as such (a corollary of the very same proof-ground), bears personality inseparably about it and is aware of an existence divorced from all matter. For in that event we should after all have set foot past the sensible world, entering the domain of noumena, whereupon let none dispute our title to range further within it, to till it, and—according as each man's fortunate star smiles on him—to stake out holdings there. For the proposition 'Any thinking being as such is a simple substance' is synthetic a priori, because, first, it oversteps the concept placed at its base and appends the mode of existence to thinking as such, and, second, it fastens onto that concept a predicate (simplicity) incapable of being given in any experience. Synthetic propositions a priori, then, would prove workable and permissible not merely, as we maintained, with respect to objects of possible experience and specifically as principles for the very possibility of such experience, but might reach out to things generally and in themselves as well—an inference that would spell the close of this entire critique and enjoin us to leave matters as they stood. Yet the peril here proves less grave once one draws nearer to the matter.

Governing the procedure of rational psychology there is a paralogism, exhibited in the following rational syllogism.

Whatever admits of being thought only as subject likewise exists only as subject and is on that account substance.

Now a thinking being, viewed purely as such, admits of being thought only as subject.

Hence it too exists only as such—that is, as substance.

In the major premise the being spoken of is one thinkable at large, in every regard, and so also as it might be furnished in intuition. In the minor premise, by contrast, the being figures only so far as it regards itself as subject in bare relation to thinking and the unity of consciousness, and not concurrently in relation to the intuition by which it would be handed to thought as object. Thus it is per sophisma figurae dictionis—by a deceptive inference, that is—that the conclusion gets drawn.³⁸

That this diagnosis of the celebrated argument as a paralogism hits the mark exactly comes out clearly if one cares to look back here at the general remark on the systematic exhibition of the principles, and at the section dealing with the noumena, where it was shown: that the concept of a thing capable of existing on its own as subject but not as mere predicate still brings with it no objective reality whatever—that one cannot tell, in other words, whether any object could ever answer to it, since the possibility of such a manner of existing is not grasped, so that the concept delivers no cognition at all. If, then, it is under the title of a substance to point to an object that can be given—if it is to become a cognition—then some abiding intuition, being the condition one cannot dispense with for a concept's objective reality (namely the very means by which the object is given), has to be set beneath it. But in inner intuition we possess nothing abiding at all, since the I is merely my consciousness that I think; and so, if we halt at thinking alone, we are short of the condition required for bringing the concept of substance—of a subject that persists on its own, that is—to bear on oneself as a thinking being; whereupon the simplicity of substance tied to that concept collapses together with the concept's objective reality, converting into a bare logical and qualitative oneness of self-consciousness in thought as such, the subject being composite or not, no matter which.

Refutation of Mendelssohn's Proof of the Soul's Abidingness.

This penetrating philosopher was quick to detect, in the customary argument meant to show that the soul (granting it to be a simple being) cannot pass out of existence through partition, a shortfall in meeting the aim of guaranteeing it the requisite endurance, seeing that one might yet suppose its existence to lapse by fading away. In his Phädon he set out to keep this perishing—which would be genuine annihilation—away from the soul, presuming to demonstrate: that a simple being can in no way cease to exist, for, being incapable of diminution and hence of forfeiting bit by bit some portion of its existence and so of gradually passing into nothingness (having no parts, and thus no plurality, within it), it would leave no interval of time whatever between an instant in which it is and a further instant in which it is no more—which is impossible. — But he failed to reflect that, even were we to concede the soul this simple nature—that it holds, namely, no manifold lying side by side, and so no extensive magnitude—one can no more refuse it than any existing thing an intensive magnitude, a degree of reality, that is, in respect of all its powers, indeed of everything at all that constitutes existence, a degree that may fall away through endlessly many ever-slighter degrees, so that the supposed substance (the thing whose abidingness is not already settled on other grounds) could be turned to nothing, not indeed by partition, yet by a stepwise slackening (remissio) of its forces (through languescence, then, if I may help myself to the term). For consciousness itself possesses at all times a degree open to still further reduction³⁹, and hence so does the power of being conscious of oneself, and so do all the other powers. — The abidingness of the soul, viewed as a bare object of inner sense, thus stays undemonstrated and even indemonstrable, though its abidingness throughout life—since the thinking being (as a human) is at once an object of the outer senses to itself—is evident on its own; but with this the rational psychologist is in no way content, bent as he is on proving, out of mere concepts, the soul's absolute abidingness reaching even past life⁴⁰.

Suppose now we take the propositions above—as, taken they must be, holding for every thinking being within rational psychology considered as a system—in synthetic interconnection, and set out from the category of relation with the proposition that all thinking beings are, as such, substances, running back down their series until the circle comes round: we light in the end on the existence of these beings, an existence of which, within this system and in independence of external things, they are not only conscious but which they can, moreover (as regards the abidingness that necessarily belongs to the character of substance), settle out of their own resources. From this, however, it emerges that idealism—the problematic kind, at any rate—cannot be escaped within that very rationalist system, and that, if the existence of outer things is in no way needed for settling one's own existence in time, those outer things are assumed to no purpose whatever, past all power of ever proving them.

If instead we pursue the analytic route—where the 'I think', as a proposition already enclosing an existence within itself, is taken as given, so that modality forms the base—and take it apart to learn its content, namely whether and how this I settles its existence in space or time by that alone, then the propositions of the rational doctrine of the soul would set out not from the concept of a thinking being at large but from an actuality, and from the way in which this actuality is conceived—once all that is empirical about it has been detached—there would be inferred what belongs to a thinking being in general, as the table below displays.

Since the second proposition leaves it open whether I can exist and be conceived solely as subject and not likewise as another's predicate, the concept of a subject is being employed here in a merely logical way, and it stays undecided whether substance is to be meant by it or not. In the third proposition, by contrast, the absolute unity of apperception—the simple I within that representation to which every combining or separating that constitutes thought is referred—acquires weight in its own right, even while I have thus far fixed nothing touching the subject's makeup or subsistence. Apperception is a real something, and its simplicity is already contained in its very possibility. In space, meanwhile, nothing real is simple; for points (space's sole simple items) are nothing but boundaries, not themselves anything apt to constitute space as a part of it. What follows from this is the impossibility of accounting for my makeup, as a merely thinking subject, on the grounds of materialism. But since my existence is treated as given in the first proposition—which does not run 'every thinking being exists' (a claim that would assert absolute necessity and hence say far too much of them), but only 'I exist thinking'—the proposition is empirical and holds the determinability of my existence solely as concerns my representations in time. Since here again I stand in need, first of all, of something abiding, of which nothing whatever is given me in inner intuition so long as I merely think myself: the mode in which I exist—as substance or as accident—simply cannot be settled by this bare self-consciousness. And so, if materialism will not serve to explain my existence, spiritualism proves every bit as inadequate to it; the upshot being that by no means at all, whatever it might be, can we know a thing about our soul's makeup where the possibility of its detached existence is concerned.

And how, in any case, should it be possible—by way of the unity of consciousness, which we ourselves are acquainted with only because we cannot do without it for the possibility of experience—to pass beyond experience (our existence in life) and even to broaden our cognition to the nature of thinking beings generally through the proposition 'I think', empirical yet left undetermined as regards every kind of intuition?

There exists, then, no rational psychology as a doctrine capable of yielding us any supplement to our self-knowledge, but only one as a discipline—setting for speculative reason in this field boundaries not to be crossed, on one side that we may not cast ourselves into the embrace of a soulless materialism, on the other that we may not stray off, adrift, into a spiritualism baseless for us amid life; it prompts us rather to look on this refusal of our reason to answer satisfyingly the inquisitive questions that overreach the present life as a signal from reason itself, bidding us redirect our self-knowledge from barren, exorbitant speculation to a fruitful practical use—a use which, even while forever aimed only at objects of experience, nonetheless fetches its principles from higher and shapes our conduct as though our vocation stretched infinitely past experience, and thus past this present life.

From all of this it becomes visible that rational psychology owes its origin to nothing but a misunderstanding. The unity of consciousness underlying the categories is here mistaken for an intuition of the subject as object, and to it the category of substance is then applied. Yet it is no more than the unity within thinking, by which on its own no object is given, so that the category of substance—presupposing, as it forever does, a given intuition—finds no application to it, leaving this subject wholly uncognized. By thinking the categories, therefore, the subject of the categories cannot arrive at a concept of itself as an object falling under them; for to think them it has to place beneath them its own pure self-consciousness—the very thing that was to have been explained. By the same token, that subject wherein the representation of time takes its original rise is unable, by that means, to fix its own existence in time; and where the fixing of existence in time is barred, so too is that other fixing—of the subject itself (as a thinking being in general) by means of categories.⁴¹

And so a cognition ventured past the confines of possible experience, one belonging nevertheless to humanity's supreme interest, evaporates—so far as it is to be credited to speculative philosophy—into thwarted hope; wherein all the same the severity of the critique, by demonstrating at once that it is impossible to fix anything dogmatically about an object of experience past experience's boundary, renders reason, amid this interest of its own, a service far from trifling: it makes reason equally secure against every conceivable claim to the contrary; and this can come about in no other way than by one's either proving one's proposition apodictically or, failing that, hunting down the roots of the failure, which, should they lie within the necessary confines of our reason, must then bind every antagonist under that identical law of forgoing all pretension to dogmatic assertion.

Even so, none of this costs us in the slightest the warrant—indeed the necessity—of positing a life to come, on the principles of that practical use of reason which is joined to the speculative; for on ordinary human reason the merely speculative proof could in any case never have exerted the least influence. It is poised on so fine a needle-point that even the Schools can hold it there only so long as they keep it forever spinning round that point like a top, so that in their own view it affords no lasting groundwork on which anything might be raised. The proofs of use to the world all keep here their full, unlessened worth, and gain rather in lucidity and artless conviction once those dogmatic presumptions are cleared away, for they lodge reason within its proper province—the order of ends, which is withal an order of nature too—a province that then, as a practical faculty in itself unfettered by the conditions of the latter, is warranted to enlarge the former, and with it our own existence, past the limits of experience and of life. Reasoning by the analogy with the nature of the living beings in this world—in whom reason has necessarily to adopt as a principle that not one organ, faculty, or drive is to be met with that is dispensable, or out of proportion to its use, and thus purposeless, but that each is exactly fitted to its vocation in life—the human being, who alone can after all harbor within himself the final end of it all, would have to be the sole creature left out of the rule. For his natural endowments—not merely with respect to the talents and drives for putting them to work, but chiefly the moral law within him—run out so far past every use and gain he could wring from them in this life that this law schools him to value above everything else the mere consciousness of an upright disposition, even where every advantage fails, even down to the ghostly show of fame after death, and he feels an inward calling to render himself, through his bearing in this world and by forgoing many advantages, fit for citizenship in a better one that he holds in idea. This forceful proof-ground, never to be overthrown, attended by an ever-swelling cognition of the purposiveness in all that lies before our eyes, by a vista onto the boundlessness of creation, and hence too by the awareness of a certain limitlessness in the possible growth of our knowledge together with a drive matched to it, remains standing yet, even should we have to renounce discerning the necessary endurance of our existence from the merely theoretical cognition of ourselves.

Conclusion of the Resolution of the Psychological Paralogism.

What produces the dialectical semblance in rational psychology is the mix-up of an idea belonging to reason (that of a pure intelligence) with the utterly indeterminate concept, in every respect, of a thinking being as such. I think my own self on behalf of a possible experience, while abstracting still from all actual experience, and I draw from this the conclusion that I could grow conscious of my existence even outside experience and its empirical conditions. Thus I mistake the feasible abstracting from my empirically determined existence for a supposed awareness of an existence my thinking self might have in separation, and I take myself to cognize the substantial in me as the transcendental subject, when all I hold in thought is the unity of consciousness that underlies every act of determining, this being the mere form of cognition.

The problem of explaining the soul's community with the body does not, strictly, fall to the psychology under discussion here, since its purpose is to prove the soul's personality even apart from that community (after death), making it, in the strict sense, transcendent, notwithstanding that it busies itself with an object of experience—but only so far as that object stops being one of experience. That said, our doctrine allows an adequate reply to be given to this question as well. The difficulty prompting the problem consists, as everyone knows, in the assumed unlikeness between the object of inner sense (the soul) and the objects of the outer senses, since to the former only time attaches, to the latter space as well, as the formal condition of their intuition. But bear in mind that the two kinds of object are marked off from one another in this respect not inwardly, but only so far as the one shows itself outwardly to the other, so that whatever grounds the appearance of matter as a thing in itself might well be not so unlike after all—and with that the difficulty melts away, leaving none but this: how a community of substances is at all possible, a question whose solution lies quite beyond the field of psychology and, as the reader will easily gather from what the Analytic said of basic forces and faculties, past all doubt beyond the field of every human cognition too.

General remark concerning the transition from rational psychology to cosmology.

That I think, or: that I exist in thinking, is an empirical proposition. But at the basis of any such proposition lies empirical intuition, and consequently also the object thought of as appearance, so that it seems as though, on our theory, the soul were wholly and entirely, even in its thinking, transformed into appearance, and in this way our consciousness itself, as a mere semblance, would in fact have to come to nothing.

Thinking, considered on its own, is nothing but the logical function, and thus pure spontaneity in the connecting of the manifold belonging to a merely possible intuition; and it presents the subject of consciousness in no way as appearance, for this one reason: that it pays no regard at all to how the intuition is given, whether sensibly or intellectually. By this I represent myself, to myself, neither as I actually am nor as I appear to my own view, but I think of myself simply as any object as such, abstracting from the kind of intuition through which it is given. If I here represent myself as the subject of thoughts, or likewise as the ground of thinking, these ways of representing do not stand for the categories of substance or of cause, since the latter are precisely those functions of thought (of judgment) as already applied to our sensible intuition—an application that would, to be sure, be called for if I meant to cognize myself. But for now I wish to be aware of myself merely as something that thinks; the way in which my own self is given in intuition I leave aside, and in that respect it might well be, for me who does the thinking though not so far as I think, nothing more than appearance; when I am aware of myself in the act of mere thought I am the being itself, yet thereby nothing about it is yet given to me for thought.

The proposition, though: I think, taken to mean as much as: I exist thinking, is no mere logical function, but instead determines the subject (which at once is then also object) in regard to existence, and it can have no place apart from inner sense, whose intuition invariably yields the object not as a thing in itself but only as appearance. In it there is accordingly no longer merely the spontaneity of thought, but a receptivity of intuition as well, that is, my thinking of myself as brought to bear on the empirical intuition of that very same subject . In this latter intuition, then, the thinking self would be obliged to look for the conditions under which it employs its logical functions as categories of substance, of cause, and so on, so as to mark itself out as an object in its own right not merely by means of the I, but also to determine the mode of its existence, that is, to cognize itself as noumenon—which, however, cannot be done, since the inner empirical intuition is sensible and hands over nothing beyond data of appearance, data that contribute nothing to the object of pure consciousness for a knowledge of its separate existence, and can be of use solely for the aims of experience.

But grant that there should turn up further on—not within experience, but within certain laws of the pure use of reason (laws that are more than merely logical rules) which stand fixed a priori and bear on our existence—an occasion to presuppose ourselves, wholly a priori and as regards our own existence, to be legislative and to be ourselves the determiners of that existence: then a spontaneity would thereby come to light through which our actuality could be determined without any call for the conditions of empirical intuition; and at this point we would come to realize that within the consciousness of our existence there lies enclosed a priori a certain something, one able to help determine our existence—everywhere determinable, otherwise, only through the senses—as regards a particular inner power, and in relation to an intelligible (albeit merely thought) world.

But this would nonetheless not in the least advance any of the attempts made in rational psychology. For through that admirable faculty which the consciousness of the moral law first reveals to me I would indeed have a principle for the determination of my existence, one that is purely intellectual, but by means of which predicates? By none other than those that have to be supplied to me within sensible intuition; and so I would end up back once more at the spot where I stood in rational psychology, namely at the requirement for sensible intuitions in order to lend meaning to my concepts of the understanding—substance, cause, and the like—by which alone I am able to have cognition of myself; those intuitions, however, can never carry me out past the field of experience. Yet in regard to practical use—which after all is always aimed at objects of experience—I would still be permitted to apply these concepts to freedom and to the subject thereof, following the meaning analogous to their theoretical use, inasmuch as by them I take to be meant nothing but the logical functions of subject and of predicate, of ground and of consequence, conformably to which the actions or effects come to be determined, in keeping with those laws, in such a way that they admit of being explained—jointly with the laws of nature—always in conformity with the categories of substance and of cause, even should they arise from an altogether different principle. This was meant to be said only in order to forestall the misunderstanding to which the doctrine of our self-intuition as appearance is easily exposed. In what follows there will be occasion to make use of it.

Chapter 2. The Antinomy of Pure Reason

We showed, in the introduction to the present portion of our work, that all transcendental illusion of pure reason has its basis in dialectical inferences, for which logic furnishes the schema by way of the three formal kinds of inference of reason in general, roughly as the categories, for their part, encounter their logical schema within the four functions belonging to every judgment. The first kind of these ratiocinating inferences was directed at the unconditioned unity of the subjective conditions of all representations whatever (the subject, that is, or the soul), corresponding to the categorical inferences of reason, whose major premise, in its capacity as principle, asserts the relation that a predicate bears to a subject. The second kind of dialectical argument will therefore, following the analogy with hypothetical inferences of reason, make the unconditioned unity of the objective conditions in appearance into its content, just as the third kind, which is to come up in the next chapter, takes for its theme the unconditioned unity of the objective conditions of the possibility of objects in general.

What is noteworthy, however, is that the transcendental paralogism brought about only a one-sided illusion with respect to the idea concerning the subject of our thinking, while for asserting the opposite not the least illusion, drawn from concepts of reason, will present itself. The advantage falls entirely to the side of pneumatism, even though pneumatism cannot deny its inherited flaw of evaporating, for all the illusion in its favor, into sheer mist under critique's trial by fire.

Things fall out quite otherwise once we bring reason to bear on the objective synthesis of appearances, where, though it supposes it can assert its principle of unconditioned unity with a great show of plausibility, it soon entangles itself in contradictions of such a kind that it finds itself constrained, in its cosmological intent, to withdraw from its demand.

For at this point human reason displays a new phenomenon, namely: a thoroughly natural antithetic, one over which no one need brood or contrive to set snares, but into which reason lapses of itself, and indeed unavoidably, whereby it is preserved, on the one hand, from the slumber of an imagined conviction such as a merely one-sided illusion produces, yet is at the same time led into the temptation either of surrendering to a skeptical despair, or of assuming a dogmatic defiance and stubbornly fixing its mind on certain assertions while refusing to grant the grounds of the opposite a hearing and their due. Both spell the death of a sound philosophy, though the former could perhaps still be termed the euthanasia of pure reason.

Before we allow the scenes of the schism and of the disruptions to be witnessed that this conflict of laws (antinomy) of pure reason gives rise to, we mean to set down certain considerations capable of elucidating and vindicating the method that we employ in dealing with our object. To all transcendental ideas, insofar as they have to do with the absolute totality within the synthesis of appearances, I give the name world-concepts, partly because of just this unconditioned totality (upon which the concept of the world-whole itself reposes, though that concept is in turn only an idea), and partly because they bear merely on the synthesis of appearances, and hence on the empirical synthesis, whereas the absolute totality in the synthesis of the conditions of all possible things whatever will give rise to an ideal of pure reason, one wholly distinct from the world-concept, albeit standing in relation to it. Accordingly, just as the paralogisms of pure reason supplied the foundation for a dialectical psychology, so likewise the antinomy of pure reason is to hold up before us the transcendental principles of a putative pure (rational) cosmology, not so as to find them valid and adopt them as our own, but rather—as the very designation of a conflict of reason already makes plain—so as to present them, being an idea that admits of no reconciliation with appearances, in their dazzling yet deceptive illusion.

Section 1. System of cosmological ideas

Now, if we are to enumerate these ideas according to a principle and with systematic precision, we must first observe that pure and transcendental concepts can spring from the understanding alone, that reason of itself brings forth no concept whatever, but does no more than free a concept of the understanding from the inescapable restrictions of a possible experience, seeking thereby to enlarge it beyond the limits of the empirical, though still in conjunction with the empirical. This comes about as follows: on the side of the conditions (those beneath which the understanding brings every appearance under synthetic unity), reason lays claim, for some given conditioned, to absolute totality, and in this way a category is raised into a transcendental idea, the aim being to endow the empirical synthesis with absolute completeness by prolonging it up to the unconditioned (which is met with never in experience but solely in the idea). Reason's demand here proceeds from this principle: once the conditioned is posited, the entire sum of its conditions is likewise given, and therewith the utterly unconditioned as well, through which the conditioned was alone possible. Thus the transcendental ideas will, first, amount to nothing more than categories enlarged up to the unconditioned, and they will let themselves be set out in a table ordered by the titles of the categories. Secondly, however, not every category will serve this purpose, but only those whose synthesis makes up a series—and indeed a series of conditions subordinated one to another (not coordinated) running toward a conditioned. Reason exacts absolute totality only to the degree that it bears upon the ascending series of conditions belonging to a given conditioned, and thus not where what is at issue is the descending line of consequences, or the aggregate of coordinated conditions leading to those consequences. For with respect to the given conditioned the conditions are already presupposed and must be taken as given together with it; whereas, seeing that consequences do not render their conditions possible but on the contrary presuppose them, one may, as one advances toward the consequences (or descends from a given condition to what it conditions), stay unconcerned whether the series terminates or not, so that the question of its totality is in general no presupposition of reason whatever.

In just this way one necessarily represents a stretch of time, wholly run out up to the present moment, as itself given as well (albeit not determinable by us). But as regards time still to come, since it forms no condition for reaching the present, it is—for the purpose of comprehending the present—entirely indifferent what we care to make of future time, whether we would have it stop somewhere or run on without end. Take the series m, n, o, where n is given as conditioned in relation to m and yet at the same time as the condition of o; let the series ascend from the conditioned n up to m (l, k, i etc.) and equally descend from the condition n down to the conditioned o (p, q, r etc.): then I must presuppose the first series if I am to regard n as given, and, according to reason (the totality of conditions), n is possible only through that series, whereas its possibility in no way depends upon the following series o, p, q, r, which for that reason could be regarded not as given but merely as dabilis.

The synthesis of a series on the side of the conditions—starting from the condition nearest the given appearance and proceeding to ever more remote conditions—I shall term the regressive synthesis; the one that goes forward on the side of the conditioned, from the nearest consequence out to the more remote ones, I shall term the progressive synthesis. The former of these runs off into the antecedentia, the latter into the consequentia. The cosmological ideas, accordingly, concern themselves with the regressive synthesis in its totality, running off into the antecedentia and not into the consequentia. Should the latter be the case, we have an arbitrary and by no means necessary problem of pure reason, for to comprehend fully what is given in the appearance we require its grounds, but not its consequences.

Now, to set up the table of ideas in correspondence with the table of categories, we begin with the two primordial Quanta of all our intuition, namely time and space. Time is in and of itself a series (indeed the formal condition of every series), and so within it, relative to a given present, the antecedentia as conditions (the past) must be told apart a priori from the consequentibus (the future). It follows that the transcendental idea of an absolute totality in the series of conditions for a given conditioned reaches only over all bygone time. In keeping with the idea of reason, the entire course of elapsed time is of necessity thought as given, being the condition of the given moment. Space, on the other hand, contains in itself no distinction between progressus and regressus, for it makes up an aggregate and no series, its parts being all together at once. The present point in time I could, relative to time past, view only as conditioned and never as a condition of that past, since this moment arises in the first place solely through elapsed time (or rather through the elapsing of the time that went before). But because the parts of space stand not in subordination but in coordination to one another, no one part is the condition of another's possibility, and space does not, as time does in itself, make up a series. Still, the synthesis of space's manifold parts, whereby we apprehend it, does proceed successively; it therefore takes place in time and harbors a series. And since in this series of aggregated spaces (the feet in a rod, say), reckoning from a given one, each further space added in thought is invariably the condition of the boundary of the one before, the measuring of a space too must count as a synthesis of a series of conditions running to a given conditioned; save only that the side of the conditions is not, in itself, distinguished from the side on which the conditioned lies, so that in space regressus and progressus appear to coincide. But since one part of space is not given by means of another, only bounded by it, we must to that extent regard every bounded space as itself conditioned as well, presupposing a further space as the condition of its boundary, and so onward without end. In respect of bounding, then, advance in space is likewise a regressus, and the transcendental idea of the absolute totality of synthesis in the series of conditions applies to space as well; I may therefore ask after the whole of appearance in space no less than after the whole of it in time gone by. Whether an answer to any of this is possible at all will be something to settle later on.

Secondly, the reality in space—that is, matter—is a conditioned; its inner conditions are its parts, and the parts of those parts its more distant conditions, so that here a regressive synthesis obtains, the absolute totality of which reason demands—a totality attainable in no other way than through a completed division, by which the reality of matter disappears either into nothing or else into something that is matter no longer, namely the simple. Here too, then, we have a series of conditions and an advance toward the unconditioned.

Thirdly, as for the categories of the real relation among appearances, the category of substance together with its accidents does not lend itself to a transcendental idea; that is to say, reason has no ground to travel back regressively toward conditions in its case. For accidents, so far as they inhere in one and the same substance, stand coordinate with one another and form no series. And in relation to the substance they are not, strictly speaking, subordinate to it; they are rather the very mode in which the substance itself exists. The one thing here that might still look like an idea of transcendental reason would be the concept of the substantiale. Yet since this means nothing beyond the concept of an object as such that subsists—so far as one thinks in it the mere transcendental subject stripped of all predicates—while what is under discussion here is only the unconditioned within the series of appearances, it is evident that the substantiale can form no link in that series. The very same holds of substances in mutual community, which are mere aggregates and possess no exponent of a series, inasmuch as they are not subordinated one to another as conditions of their possibility—as could well be said of spaces, whose limit was never fixed in itself but always by another space. There remains, then, only the category of causality, which sets before us a series of causes for a given effect, one in which we can climb from that effect, as conditioned, up to those causes, as its conditions, and so give answer to the question of reason.

Fourthly, the concepts of the possible, the actual, and the necessary give rise to no series, except only to the extent that the contingent in existence must at all times be viewed as conditioned and, by the rule of the understanding, points back to a condition, under which it becomes necessary to point on to a still higher one, until reason lights upon the unconditioned necessity solely within the totality of this series.

Thus there are, all told, no more than four cosmological ideas, answering to the four titles of the categories, once one picks out those categories that necessarily bring a series with them in the synthesis of the manifold.

The first point to be noted is this: that the idea of absolute totality has to do with nothing beyond the exposition of appearances, and thus not with the pure concept of the understanding of a whole of things as such. Appearances, then, are here taken as given, and reason calls for the conditions of their possibility to be supplied in absolute completeness, so far as those conditions make up a series—hence for a synthesis that is complete without qualification (complete, that is, in every respect), by means of which the appearance admits of being expounded under laws of the understanding.

Secondly, what reason genuinely seeks in this synthesis of conditions—carried on step by step through the series, and regressively at that—is really nothing but the unconditioned: the completeness, so to speak, of the row of premises that, taken together, presuppose no further premise. This unconditioned is, at every turn, already contained within the absolute totality of the series whenever one pictures that series to oneself in imagination. Yet a synthesis thus brought to unqualified completion is, once again, no more than an idea; for one cannot tell, at least beforehand, whether anything of the kind is even possible in the case of appearances. If one pictures everything by means of pure concepts of the understanding alone, apart from the conditions of sensible intuition, then one may say straight out that, given a conditioned, the whole series of conditions subordinate to one another is given along with it; for the former is had only through the latter . With appearances, however, we meet a peculiar restriction on the way in which their conditions come to be given—namely, through a successive synthesis running across the manifold of intuition, one that is supposed to reach completeness in the regress. Whether such completeness is in fact possible on the side of sensibility remains a problem. The idea of that completeness, all the same, resides in reason quite apart from whether or not empirical concepts adequate to it can be attached. So, since the unconditioned is necessarily embraced within the regressive synthesis of appearance's manifold when taken in absolute totality (a synthesis guided by the categories, which present that manifold as a series of conditions running to a given conditioned)—and here one may leave undetermined whether and how such totality is to be achieved—reason adopts the course of setting out from the idea of totality, although its genuine final aim is the unconditioned, whether of the whole series or of a part of it.

This unconditioned now admits of being thought in either of two ways: either as residing simply in the entire series, in which case every member without exception would be conditioned and only the series as a totality would be unconditioned outright—and then the regress is termed infinite; or else the absolutely unconditioned is only some one part of the series, to which the remaining members are subordinate, while it itself falls under no further condition.⁴² In the former case the series, a parte priori, is boundless (without beginning), i.e. infinite, and nonetheless given in full, though the regress within it is never completed and can be styled infinite only potentialiter. In the latter case the series possesses a first member—one called, with respect to time elapsed, the beginning of the world; with respect to space, the boundary of the world; with respect to the parts of a whole given within its limits, the simple; with respect to causes, absolute self-activity (freedom); and with respect to the existence of alterable things, absolute necessity of nature.

We have two terms at our disposal—world and nature—which now and then run into each other. The first denotes the mathematical whole of all appearances together with the totality of their synthesis alike in the great and in the small, that is, in the progress of that synthesis both by composition and by division. This very same world, however, we call nature⁴³ once it is regarded as a dynamic whole—when we look not to the aggregation of things in space or time (a way of constituting it as a magnitude) but to the unity in the existence of appearances. At this point the condition of whatever happens we name the cause; the unconditioned causality of that cause within the appearance we name freedom; and the conditioned causality, by contrast, is what, in the narrower sense, we name a cause in nature. The conditioned in existence generally we call contingent, the unconditioned we call necessary. The unconditioned necessity that belongs to appearances may be termed a necessity of nature.

The ideas now occupying us I termed cosmological a moment ago, partly because "world" signifies the sum of all appearances and our ideas likewise aim only at the unconditioned among appearances, and partly too because the word "world", taken transcendentally, denotes the absolute totality of the sum of existing things, and it is on the completeness of the synthesis alone (though strictly only in the regress toward the conditions) that we fix our attention. Bearing in mind, moreover, that these ideas are one and all transcendent, and that, although they do not overstep their object—appearances—as to kind, having to do merely with the world of sense (not with noumena), they nonetheless push the synthesis to a degree exceeding every possible experience, I think one may quite aptly call them, collectively, world-concepts. In view of the difference between the mathematically and the dynamically unconditioned toward which the regress is directed, I would, even so, reserve the term world-concepts (of the world in the great and the small) for the first two in a narrower sense, calling the remaining pair transcendent concepts of nature instead. For the present this distinction carries no special weight, but as we go on it may take on greater importance.