Preface to the Second Edition

Whether or not the working-up of those cognitions that fall to reason's own enterprise is proceeding along the sure road of a science is something the results themselves soon reveal. Should it stall the moment it reaches its object, after all its many arrangements and preparations, or should it be forced again and again to double back and try a fresh route in order to arrive there; and should it likewise prove impossible to get the several collaborators to agree on how the shared intention ought to be carried through: then one may rest assured that a study of this kind has not yet come anywhere near the sure road of a science, but is merely fumbling in the dark, and reason already earns credit by tracking that road down wherever it can, even at the cost of surrendering as vain a good deal that had been comprised in the goal originally set up without due reflection.

As for logic, that it has been travelling this sure road ever since the most ancient days is evident from its having had no occasion, since the time of Aristotle, to retreat by so much as a step—unless one chooses to reckon among its improvements the clearing-away of certain expendable subtleties, or a sharper delineation of what it teaches, refinements that pertain to the science's elegance rather than to its reliability. A further curious thing about it is that neither has it managed to advance a single step, so that, by every indication, it appears to stand closed off and finished. For when certain more recent writers imagined they could broaden it—by smuggling in now psychological chapters on the assorted powers of cognition (imagination, wit), now metaphysical ones on where cognition originates or on how certainty varies with the diversity of objects (idealism, skepticism, and the like), now anthropological ones on prejudice (its sources and its antidotes)—this only betrays how little they grasped what is distinctive in the nature of this science. To let the boundaries of the sciences bleed into one another is not to augment them but to deform them; and logic's own boundary is fixed with complete precision by this, that it is a science charged with nothing beyond setting out in full, and proving with rigor, the merely formal rules of all thought (be that thought a priori or empirical, whatever its source or its object, and whether the obstacles it meets in our mind are contingent or built in).

Logic's success on this score is owed entirely to its own narrowness, which authorizes it—indeed requires it—to leave out of account every object of cognition together with all their differences, so that within it the understanding is occupied with nothing beyond its own self and the form belonging to it. In the nature of the case things had to prove far more difficult for reason once it must grapple not with itself alone but with objects besides; and this is why logic, functioning as a propaedeutic, amounts as it were merely to the antechamber of the sciences, so that where genuine bodies of knowledge are concerned, though a logic is indeed presupposed for appraising them, one has to look for the acquiring of them in those disciplines that are, strictly and objectively, entitled to the name of science.

Now to the extent that reason is to be present in such disciplines, something within them has to be cognized a priori, and the cognition reason yields can bear on its object in either of two ways: it may serve merely to determine that object together with its concept (which must be supplied from some other quarter ), or else to render it actual as well. The one is reason's theoretical, the other its practical cognition. In both cases the pure portion—no matter how much or how little it may amount to—namely that portion in which reason settles its object wholly a priori, must be laid out first and by itself, with nothing drawn from other wells allowed to contaminate it; for it is poor housekeeping to pay out blindly whatever comes in, unable later, once the treasury falls short, to tell which part of the receipts is able to cover the outlay and which part one is obliged to trim it back from.

The two theoretical cognitions in which reason is to fix its objects a priori are mathematics and physics—the first with complete purity, the second purely at least in part, though there also as measured against sources of cognition lying outside reason itself.

Among that admirable people the Greeks, mathematics had already set out upon a science's sure road as far back as the recorded history of human reason will carry us. Yet one ought not suppose that hitting upon that royal highway—or rather cutting it open for itself—came to mathematics as effortlessly as it came to logic, where reason deals with itself and nothing more; I incline instead to think that mathematics too long remained stuck in mere fumbling (above all still among the Egyptians), and that its turnabout is to be credited to a revolution which the lucky inspiration of one man carried through in a single trial, whereafter the route that had to be followed could nevermore be lost, and a science's sure march was launched and staked out for all ages and across unbounded reaches. No record has reached us either of the man fortunate enough to accomplish it or of the history of this upheaval in mankind's mode of thought—an upheaval of far greater moment than the finding of the sea-route around that celebrated headland. All the same, the story Diogenes Laertius has passed down to us, in which he supplies a name for the supposed discoverer of even the most trifling elements of geometrical proof—elements that, by ordinary reckoning, hardly call for proving at all—shows that the recollection of the shift set in motion by the first faint trace of this new road's discovery must have struck the mathematicians as momentous in the extreme, and so was rendered imperishable. Upon the first man to prove something of the isosceles triangle (be his name Thales or anything else one pleases ) a light broke; for it dawned on him that his task was not to pore over what the drawn figure presented to his eye, nor over the bare concept of the figure, reading off its properties as though from these, but rather to bring those properties forth by way of what he himself, guided by concepts, had thought into the figure and laid out in it a priori (by construction), and that, to secure any a priori knowledge, he was entitled to credit the thing with nothing save the consequences that followed of necessity from what, in keeping with his concept, he had himself deposited in it.

Natural science was much slower in striking the broad thoroughfare of science; for it is a mere century and a half or so since the recommendation of the shrewd Bacon of Verulam partly prompted this breakthrough and partly—one being already on its scent—gave it fresh impetus, a breakthrough that likewise admits of explanation only through a swiftly executed overturning of the mode of thought. My concern in the present remarks is with natural science solely in the measure that it rests on empirical principles.

The day Galileo sent his spheres rolling down the incline under a weight he had himself assigned them, or Torricelli got the atmosphere to hold up a weight he had reckoned in advance as matching a column of water of known height, or, later still, Stahl turned metals into their calx and the calx back into metal by taking something from them and handing it back:¹ on that day a light broke upon every student of nature. It became clear to them that reason discerns only what it brings forth after a plan of its own devising, that it has to march ahead holding the principles of its judgments under fixed laws and force nature to reply to what it asks, instead of suffering itself to be towed along by nature as if kept on a leash; for otherwise observations gathered by chance, on no plan sketched beforehand, never hang together in that necessary law which reason is nonetheless after and stands in need of. Reason, then, must go to nature carrying in the one hand its principles, which alone can lend agreeing appearances the status of laws, and in the other the experiment it has contrived by their lead—going, to be sure, in order to learn from nature, yet not as a schoolboy content to have the master recite to him whatever the master likes, but as a duly appointed judge who obliges his witnesses to respond to the queries he sets before them. And thus even physics is beholden for the so beneficial overturning of its mode of thought to nothing but the notion of hunting in nature—conformably to whatever reason has itself laid into nature—for that which reason must be taught by nature and would, on its own, have no inkling of (rather than foisting such things upon her). It is by this means that natural science was at long last placed upon a science's sure march, having for so many hundreds of years done nothing but fumble blindly.

With metaphysics—an entirely self-enclosed speculative cognition of reason that lifts itself clear above all schooling by experience, and does so through concepts alone (not, as mathematics does, by putting concepts to work upon intuition), so that here reason is to be its own pupil—fortune has thus far been too grudging for it ever to have gained a science's sure march, notwithstanding that it is more venerable than all the rest and would outlast them even were they, one and all, engulfed in the maw of a barbarism that devours everything. For within metaphysics reason keeps stalling without end, even where it presumes to grasp a priori those very laws that the most everyday experience corroborates. Here one is compelled to turn back time without number, finding that the road fails to reach the destination one is bound for; and as to its adherents ever concurring in what they assert , metaphysics falls so far short of this that it is rather an arena seemingly cut out for the express purpose of drilling one's powers in sham skirmishes, one on which no champion has yet succeeded in securing even a foot of ground or in resting upon his triumph any durable holding. Beyond dispute, then, its way of proceeding has so far been nothing but a fumbling in the dark—and, worse yet, a fumbling amid bare concepts.

Why is it, now, that no sure road of science has yet let itself be found in this quarter? Is such a road, perhaps, out of the question? From what source, then, has nature visited upon our reason this tireless urge to chase after that road as one of its weightiest affairs? More than that: how slender are our grounds for reposing trust in our reason, when, in one of the most consequential objects of our craving to know, it does not merely desert us but keeps us dangling with false shows and in the end plays us false! Or, if the road has thus far only been overlooked, what indication may we exploit so as to hope that this renewed pursuit will leave us luckier than those who went before us?

It is my view that the cases of mathematics and of natural science, which owe their present standing to a revolution brought off in one stroke, are striking enough to warrant our pondering the crucial ingredient in that recasting of the mode of thought which served them so well, and, at least by way of trial, our copying it here so far as their kinship with metaphysics, as cognitions of reason, will allow. Up to now the standing assumption has been that all our cognition has to regulate itself by the objects; and yet, on that footing, every effort to settle anything about them a priori by means of concepts, and so to widen our cognition, ended in failure. So let the experiment be made, for once, of whether we might not get on better with metaphysics' tasks by supposing instead that the objects have to regulate themselves by our cognition—a supposition that already squares more readily with the sought-for possibility of an a priori cognition of those objects, one meant to lay down something about them in advance of their being given to us. The case stands here exactly as with the opening idea of Copernicus, who, once accounting for the heavenly motions refused to go well on the supposition that the whole stellar array wheels about the spectator, tried whether he might not fare better by setting the spectator in motion and letting the stars stay still. In metaphysics , likewise, one can attempt something of this sort where the intuition of objects is concerned. Were intuition obliged to regulate itself by how the objects are constituted, then I fail to grasp how anything about it could be known a priori; but if instead the object (taken as an object of sense) regulates itself by how our capacity for intuiting is constituted, then this possibility is one I can represent to myself quite readily. Since, however, I cannot come to rest at these intuitions if they are to turn into cognitions, but must instead refer them, as representations, to some object and pin that object down by their means, I may suppose either that the concepts by which I accomplish such pinning-down likewise regulate themselves by the object—whereupon I land back in the very perplexity of before, as to how I could know anything on this head a priori—or else that the objects, or (what comes to the same) the experience wherein alone they are cognized as objects that are given, regulate themselves by these concepts, and here I catch sight straightaway of a smoother resolution, since experience is itself a mode of cognizing that calls for understanding, whose rule I have to presuppose within me even prior to any object's being given, hence a priori, a rule voiced in a priori concepts, to which accordingly every object of experience must of necessity defer and with which it must fall into accord. As regards objects insofar as reason thinks them and thinks them of necessity, though they cannot (at any rate as reason conceives them) be given anywhere in experience, the endeavors to think them—for think them we assuredly must be able to do—will thereafter furnish a superb assay-stone for what we are taking on as the transformed method of the mode of thought, namely that of things we cognize a priori only that which we have ourselves placed into them.²

This attempt turns out as one would wish, and it holds forth to metaphysics, in its opening part—where it is busied, that is, with concepts a priori whose answering objects can be supplied in experience to suit those concepts—the sure march of a science. For once the mode of thought has been so altered, the very possibility of a cognition a priori is readily accounted for, and, more than this, the laws that underlie nature a priori—nature being the aggregate of the objects of experience—can be equipped with adequate proofs, both of which lay beyond reach under the procedure hitherto followed. But this deduction of our power of cognizing a priori throws up, within metaphysics' opening part, a disconcerting upshot—one that looks highly damaging to the whole aim of the discipline, the aim taken up in the second part—namely that by this power we are never able to press past the frontier of experience that is possible, though this is precisely the discipline's most vital business. Yet just here resides the experiment furnishing a countercheck on the truth yielded by that initial appraisal of our a priori rational cognition, namely that such cognition bears upon appearances only, letting the thing in itself, by contrast, lie there real enough on its own account but unknown to us. For what drives us of necessity to overstep the frontier of experience and of every appearance is the unconditioned, which reason, in things in themselves, insists upon—rightfully and inevitably—for whatever is conditioned, and by that insistence demands the sequence of conditions brought to completion. Suppose it now emerges that, once we posit our experiential cognition as regulating itself by the objects taken as things in themselves, the unconditioned simply cannot be thought free of contradiction; whereas, once we posit that our representation of the things as given to us does not regulate itself by them as things in themselves, but that these objects rather, being appearances, regulate themselves by our manner of representing, the contradiction drops away; and suppose it emerges, in consequence, that the unconditioned is not to be met with in things so far as we know them (so far as they are given us), but is indeed to be met with in them so far as we do not know them, as things in themselves: then it comes to light that what at the outset we merely posited by way of trial rests on firm ground.³ There remains open to us still, now that speculative reason has been refused any headway across this supersensible terrain, the trial of seeing whether within reason's practical cognition data may not turn up for pinning down that transcendent rational concept of the unconditioned, and thus—as metaphysics wishes—for getting out past the frontier of all possible experience by means of an a priori cognition of ours that is, however, feasible only with a practical intent. And in a procedure of this kind speculative reason has at all events cleared us a space for such an enlargement, however much it had to leave that space vacant, so that we are still at liberty —indeed are positively summoned by reason itself—to fill it, if we are able, out of reason's own practical data.⁴

The undertaking of this critique of pure speculative reason consists, then, precisely in that attempt to overhaul metaphysics' erstwhile procedure, working a thoroughgoing revolution in it after the pattern set by the geometers and the investigators of nature. It is a treatise concerning method, and not a system of the science as such; and yet it charts the entire contour of that science, alike with respect to the science's bounds and with respect to its whole inner framework. For this is what is proper to pure speculative reason, that it is able—and is obliged—to take the gauge of its own capacity according to the diverse ways in which it selects objects for thinking, and moreover to run through in full the sundry ways of posing tasks to itself, thereby laying down the whole preliminary sketch for a system of metaphysics; because, touching the former, in cognition a priori the objects can be granted nothing but what the thinking subject draws out of its own resources, and, touching the latter, reason forms—as regards the principles of cognition—a wholly self-standing unity complete in itself, in which each member, as within an organized body, is there for the sake of all the rest and all for the sake of the single one, and no principle may be adopted with assurance in one bearing without its having been examined at the same time in its all-round bearing upon the entire pure employment of reason. In recompense, though, metaphysics enjoys the singular good luck—such as can accrue to no other rational science having objects for its concern (for logic busies itself merely with the form of thinking as such)—that, having been set by this critique upon a science's sure march, it can take in to the full the entire province of the cognitions that fall to it and so round off its labor and bequeath it to later ages, for their use, as a capital fund never open to increase, since it deals only with principles and with the limits upon their employment, limits fixed by those principles themselves. As a foundational science it is therefore bound over to this completeness as well, and of it one has to be able to say: nil actum reputans, si quid superesset agendum.

But then, it will be asked, what manner of treasure is this that we mean to hand down to those who come after us in a metaphysics thus refined by critique and thereby brought into a settled condition? Skimming this work, one will fancy one perceives that its worth is, after all, purely negative—that of never hazarding, with speculative reason, past the frontier of experience—and that is indeed its first worth. This worth turns positive, however, the instant one perceives that the principles with which speculative reason strays past its own frontier do not in reality yield enlargement but, examined at closer range, yield the contraction of our rational employment as their unfailing result, seeing that they genuinely threaten to spread the bounds of sensibility—where these principles in truth belong—across everything, and so to crowd out altogether the pure (practical) employment of reason. For that reason a critique reining the former employment in is to that degree indeed negative; but inasmuch as it thereby, at one and the same time, removes a barrier that hems in the latter employment—or even threatens to undo it—it proves in fact of positive and quite weighty worth, the moment one grows convinced that pure reason has a practical use that is unconditionally necessary (the moral one), wherein reason unavoidably reaches out beyond sensibility's bounds, needing for this no help from the speculative side, yet obliged all the same to make itself safe against that side's counter-thrust, lest it fall out with itself. To refuse this service of critique its positive worth would come to much the same as pronouncing that a police force renders no positive benefit, on the ground that its chief occupation is, after all, merely to bar the door against the acts of violence which citizens have cause to dread at one another's hands, so that each may go about his business in peace and safety. That space and time are but forms of sensible intuition, and hence but conditions on the existence of things as appearances; that, further, we possess no concepts of the understanding, and thus no elements whatever, toward the cognition of things save so far as an intuition answering to those concepts can be furnished; and that we can therefore have cognition of no object as a thing in itself, but only so far as it is an object of sensible intuition, i.e., as appearance—this is what the analytical part of the critique establishes; whence there of course results the confinement of all the speculative cognition reason can possibly have to nothing beyond objects of experience. All the same—and this deserves careful note—there is throughout the reservation that, though we cannot cognize these selfsame objects as things in themselves too, we must at the very least be capable of thinking them.⁵ For otherwise there would ensue the preposterous proposition that there is appearance and yet nothing that appears in it. Let us now grant that the distinction our critique makes indispensable—between things as objects of experience and those very things as things in themselves—had never been drawn: then the principle of causality, and with it nature's mechanism in the determining of such things, would have to obtain, without any exception, of all things at large regarded as efficient causes. Of one and the very same being, then—the human soul, say—I could not maintain that its will is free while at once subject to natural necessity, i.e., unfree, without tumbling into a manifest contradiction, for in both claims I would have taken the soul in one identical sense, that is, as a thing taken quite generally (as a thing in itself), nor, absent a prior critique, could I have taken it any differently. But if the critique has committed no error in teaching that the object is to be taken under two senses, i.e., as appearance or as thing in itself; if the deduction of its concepts of the understanding holds good, so that the causal principle too reaches only to things taken in the first of these senses—so far, that is, as they count as objects of experience—while under the second sense those same things stand outside its reach: then one and the very same will is conceived, in the appearance (the actions open to view), as necessarily conforming to natural law and to that extent not free, and yet, from the other side, as pertaining to a thing in itself and hence exempt from that law, and so as free, with no contradiction cropping up in the process. Now granted that no speculative reason (still less any empirical observation) lets me cognize my soul as viewed from this latter side, and hence lets me cognize freedom either, as a property of a being to which I attribute effects within the world of sense—the reason being that I should then have to cognize such a being as determinate in its existence and yet not as determinate in time (impossible, since to my concept I can lay no intuition underneath)—still I am able to think freedom to myself: which is to say, the representing of it harbors, at the least, no self-contradiction, provided our critical severance of the two modes of representing (the sensible and the intellectual), together with the resulting curb upon the pure concepts of the understanding and thereby upon the principles issuing from them, holds. Grant now that morality of necessity takes freedom (in the most rigorous sense) for granted as a property belonging to our will, in that it adduces, as its own a priori data, practical and original principles lodged in our reason—principles that, without freedom presupposed, would be flatly impossible—whereas speculative reason had proved freedom to be wholly unthinkable: then of necessity that moral presupposition would have to yield before the one whose contrary carries a manifest contradiction, and consequently freedom, and morality along with it (its contrary carrying no contradiction unless freedom be already presupposed), would have to cede the field to nature's mechanism. As matters stand, however, since for morality's sake I ask no more than that freedom not run counter to itself, and so at least admit of being thought—without my needing to see any further into it—so that it lays no impediment at all in the way of the natural mechanism of the very same action (taken under another bearing): the teaching of morality keeps its ground and the teaching of nature keeps its own, which could not have come to pass had critique not first schooled us in our unavoidable ignorance touching things in themselves and pared down everything we can cognize theoretically to appearances and nothing more. This very same treatment of the positive worth carried by critical principles of pure reason can be exhibited with respect to the concept of God and to the simple nature possessed by our soul, though for brevity's sake I let it pass. I cannot, then, so much as take up God, freedom, and immortality for the purpose of my reason's necessary practical use, unless I at the same time strip speculative reason of its pretension to insights that overreach, seeing that, in order to arrive at these, it is bound to lean upon such principles as—reaching in reality no further than objects of a possible experience—when nonetheless brought to bear on what can be no object of experience, really do convert this every time into an appearance, thereby pronouncing every practical enlargement of pure reason impossible. I had, accordingly, to remove knowledge so as to open a place for belief; and the dogmatism of metaphysics—the prejudice, that is, that one may make one's way in it without a critique of pure reason—is the genuine wellspring of all that unbelief which contests morality and which is at every turn thoroughly dogmatic. – If, that being so, it need be no hard matter, with a systematic metaphysics drawn up to the measure of the critique of pure reason, to leave a legacy to those who follow, this is a present not to be lightly prized; be it that one looks merely to reason's cultivation by way of a science's sure march in general, set beside its baseless fumbling and its heedless roving where critique is wanting, or to the better spending of the time of an inquisitive youth—one who, under the customary dogmatism, gets encouragement so early and so lavishly to reason at ease about matters it grasps not at all, and into which it, no more than anyone else alive, will ever gain any insight, or even to sally forth inventing thoughts and opinions of a novel kind and thus to let slip the learning of well-founded sciences—but most of all when one enters into the reckoning the priceless gain of putting paid, for all time to come, to every objection against morality and religion in the Socratic fashion, that is, by the plainest demonstration of the opponents' ignorance. For some metaphysics or another has been present in the world at all times, and doubtless will go on being met with there, and, bound up with it, a dialectic of pure reason as well, this being native to it. Philosophy's first and weightiest concern is therefore this: to deprive that dialectic, once and for all, of every harmful influence, and to do so by plugging up the very source of the errors.

Amid this weighty shift in the domain of the sciences, and the forfeiture that speculative reason must sustain in the holdings it had until now fancied its own, everything touching the universal concern of mankind, and the benefit the world has thus far reaped from the doctrines of pure reason, abides nonetheless in just the favorable state it ever occupied; and the forfeiture strikes only the schools' monopoly, never in the least the concern of humankind. Let me put it to the most unbending dogmatist : the demonstration of our soul's persistence past death drawn from the simplicity of substance, the demonstration of the will's freedom against the mechanism of the universe drawn through those fine yet feeble distinctions between subjective and objective practical necessity, the demonstration of God's existence drawn from the concept of an all-most-real being (from the contingency of what is mutable and the need of a prime mover)—once these had gone forth from the schools, were they ever able to reach the general public and to sway its conviction by so much as a hair? Now if that has not come about—and, given the common human understanding's unfitness for speculation so fine-drawn, can never be looked for either—if, on the contrary, as to the first point, the bent of his nature that every person notices, of never being able to find contentment in the temporal (as falling short of the endowments of his whole vocation), must all on its own beget the hope of a life to come ; as to the second, the merely lucid laying-out of the duties, set over against all the pretensions of the inclinations, must all on its own beget awareness of freedom; and, as to the third at last, the magnificent order, loveliness, and provident care that peer forth from nature on every side must all on its own beget belief in a wise and mighty maker of the world—these convictions, disseminating themselves among the public so far as they repose on grounds of reason, having to bring the whole of this about entirely of themselves: then not only does this possession stay undisturbed, but it gains all the more in esteem from the schools' being now taught to arrogate to themselves no loftier or more far-reaching insight, on a point bearing upon mankind's universal concern, than the insight to which the great throng (in our eyes the most estimable) can attain with equal ease, and so to hold themselves solely to the cultivating of these grounds of proof, universally intelligible and, for moral purposes, sufficient. The shift thus bears merely on the overweening claims of the schools, which would fain have themselves passed off, in this matter (as, with justice, they may elsewhere in much else), for the sole connoisseurs and keepers of truths of which they impart to the public only the use, reserving the key to those truths for themselves alone (quod mecum nescit, solus vult scire videri). For all that, a more equitable claim on the speculative philosopher's part is likewise provided for. He stays forever the sole trustee of a science that profits the public unbeknownst to it, namely the critique of reason; for that critique can never grow popular—nor has it any call to be so, since, just as the finely spun arguments on behalf of useful truths refuse to enter the people's heads, so the equally subtle objections against them never so much as occur to them; whereas, because the school, like every person who raises himself to speculation, is drawn without fail into both, the school is thereby under obligation, through a searching inquiry into the entitlements of speculative reason, to head off once and for all the scandal that must sooner or later break upon the people themselves out of the quarrels into which metaphysicians (and, as such, in the end presumably clergy as well) inescapably get tangled where critique is absent, quarrels that thereafter go on to falsify their own doctrines. By this critique alone can the taproot itself be severed of materialism, of fatalism, of atheism, of freethinkers' unbelief, of fanaticism and of superstition—all of which may grow harmful far and wide—and, in the last place, of idealism too and skepticism, which imperil the schools more than the rest and can scarcely find their way over into the public . Should governments after all see fit to occupy themselves with the affairs of the learned, it would accord far better with their sage solicitude for the sciences and for mankind alike to lend their favor to the freedom of a critique of this sort—the one means by which reason's labors can be placed on a solid footing—than to prop up the laughable despotism of the schools, who set up a loud hue and cry over public peril whenever their gossamer webs are pulled apart, webs the public never took the slightest notice of and whose loss it can therefore never feel.

Critique does not set itself against reason's dogmatic proceeding within its pure cognition considered as a science (for such cognition must invariably be dogmatic, i.e., strictly demonstrative from secure a priori principles); it sets itself rather against dogmatism, i.e., against the presumption of getting on with a pure cognition out of concepts (the philosophical sort), by principles of the kind reason has long been putting to use, and getting on with it single-handed, without first inquiring into the manner and the right whereby it came by them. Dogmatism, accordingly, is pure reason's dogmatic proceeding unaccompanied by any prior critique of its own capacity. This opposition, then, is not meant to plead the cause of that garrulous superficiality which usurps the name of popularity, nor indeed of the skepticism that makes short shrift of the whole of metaphysics; on the contrary, critique is the requisite preparatory measure toward advancing a well-grounded metaphysics as a science, which must of necessity be executed dogmatically and, by the sternest demand, systematically—hence in a school-fit (not a popular) manner—for this demand laid upon it, given that it pledges to discharge its task entirely a priori and so to the full contentment of speculative reason, admits of no relaxing. In carrying out the plan critique prescribes—that is, in the metaphysics yet to come—we shall one day be obliged to take after the exacting method of the celebrated Wolff, greatest among all the dogmatic philosophers, who first supplied the model (and by that model became the begetter of that spirit of thoroughness, not yet snuffed out, in Germany) of how a science's sure march is to be won through the orderly settling of principles, the distinct fixing of concepts, the striving after rigor in the proofs, and the forestalling of rash leaps in one's inferences—a man for that very reason eminently fitted to raise a science, such as metaphysics is, into this condition, had it but occurred to him to make the ground ready beforehand through a critique of the instrument, namely of pure reason itself: a lack chargeable not so much to him as to the dogmatic cast of thought of his age, and over which the philosophers of his own day and of every earlier day have no grounds for reproaching one another. Those who cast aside his manner of instruction and, in one breath, the procedure of the critique of pure reason as well can be harboring no other design than to throw off the shackles of science entirely—to turn labor into pastime, certitude into mere opinion, and philosophy into philodoxy.

Turning now to this second edition, I have, as was only proper, been unwilling to forgo the opening it affords for setting right, so far as may be, the difficulties and the obscurity out of which sundry misreadings may have arisen—misreadings that sharp-witted men have run up against in appraising this book, perhaps not without blame on my side. In the propositions themselves and in their probative grounds, and no less in the form and in the completeness of the plan, I have found nothing to change; a fact to be ascribed partly to the long testing I had put them through before submitting the work to the public, partly to the very make-up of the subject—the nature, that is, of a pure speculative reason, which comprises a genuine framework wherein everything is an organ, wherein, namely, all is for the sake of the one and each single thing for the sake of all, so that even the merest frailty, whether a fault (an error) or a shortcoming, cannot but give itself away in the using. In this unalterability the system will, I trust, go on holding its own hereafter as well. It is no self-flattery but merely the plain evidence—produced by the experiment showing the result to come out the same whether one proceeds outward from the slightest elements up to the whole of pure reason or works back from the whole (for this too is given on its own through reason's ultimate aim in the practical sphere) to each several part—that warrants me in such confidence, since any effort to recast even the smallest part at once conjures up contradictions, not of the system merely, but of universal human reason. In the manner of exposition, by contrast, much still remains outstanding, and on this head I have, with the present edition, essayed improvements meant to redress in part the misunderstanding of the Aesthetic, chiefly the one lodged in the concept of time, in part the obscurity of the deduction of the concepts of the understanding, in part the alleged want of ample evidence in the proofs of the principles of the pure understanding, and in part, finally, the misconstruing of the paralogisms laid to the charge of rational psychology. Only so far as this—namely, no further than to the close of the first main division of the Transcendental Dialectic—do my revisions of the mode of exposition reach,⁶ because time ran short and, as regards the remainder, no misapprehension on the part of knowledgeable and unbiased examiners had come my way—examiners who, even though I may not name them with the praise that is their due, will discover for themselves, each in its place, the heed I have paid to their reminders. Bound up with this improvement, though, is a slight loss to the reader, one not to be averted save by swelling the book to an unwieldy bulk: namely that various matters which, while not indispensable to the completeness of the whole, many a reader would nonetheless be loath to go without—since they may be serviceable toward another end—have had to be dropped or rendered in curtailed form, so as to make way for my presentation, now, I hope, more readily grasped, which at bottom leaves the propositions and even their probative grounds entirely untouched, yet here and there parts company with the earlier one in its method of delivery so widely that mere insertions could not have brought it off. This slight loss, which anyone may in any event make good at pleasure by collating with the first edition, is more than offset, I hope, by the greater ease of comprehension. In various published pieces (on occasion where I have reviewed certain books, on occasion in treatises of their own) I have registered with thankful satisfaction that the spirit of thoroughness in Germany is not extinct, but has only for a little while been drowned out by the modish note of a genius-like license in thinking, and that the thorn-strewn tracks of critique—which lead to a science of pure reason that is school-fit yet, being such, alone lasting and therefore in the highest degree needful—have not kept spirited and lucid minds from making themselves master of it. To these deserving men, who so felicitously wed thoroughness of insight with a gift for luminous presentation (a gift I am hardly aware of possessing myself), I leave the completing of my working-out, which in the latter respect is here and there still wanting; for in the present case the danger is not of being refuted but rather of not being understood. As for myself, from this point on I can enter into no controversies, albeit I shall heed with care every hint, whether it come from friends or from adversaries, so as to turn it to account in the future working-out of the system agreeably to this propaedeutic. Since in the course of these labors I have already moved on rather deep into old age (this very month into my sixty-fourth year), I must, if I mean to carry through my plan of furnishing the metaphysics of nature no less than that of morals, by way of vindicating the soundness of the critique of speculative and of practical reason alike, husband my time and look to have the clearing-up both of the obscurities scarcely to be shunned at the start of this work, and the defending of the whole, come from those deserving men who have taken it up as their own. In this or that passage any philosophical exposition may be nipped at (it cannot come forward armor-plated as the mathematical can), while the framework of the system, regarded as a unity, runs thereby not a particle of danger—a system for the surveying of which, when it is new, few command the nimbleness of mind, and fewer still the appetite, all novelty coming to them at an ill time. Seeming contradictions, too, can be picked out—by pitting isolated passages, wrenched from their setting, one against another—in any writing that runs on chiefly as free discourse; such contradictions cast, in the eyes of one who leans on others' verdicts, an unfavorable light upon it, yet come apart with great ease for anyone who has taken possession of the idea as a whole. Meanwhile, where a theory has soundness within itself, the action and reaction that at first menaced it with grave danger come in time to serve only for grinding down its unevennesses and—should men of impartiality, of insight, and of true popularity take it in hand—for procuring it, before long, the elegance it still requires as well. Königsberg, in April 1787.

Introduction

I. On the difference between pure and empirical cognition.

That all our cognition starts with experience admits of no doubt at all; for by what else would the faculty of cognition be roused into activity, were it not by objects that affect our senses and partly produce representations by themselves, partly set the activity of our understanding in motion to compare these, to combine or to separate them, and so to process the raw stuff of sensory impressions into a cognition of objects that goes by the name of experience? In respect of time, therefore, no cognition within us comes before experience, and it is with experience that all cognition starts.

But even if all our cognition sets out with experience, it still does not for that reason all spring from experience. For it might well be that even our experiential cognition is something compounded out of what we receive through impressions and what our own faculty of cognition (merely occasioned by sensory impressions) supplies from within itself — an addition that we do not tell apart from that basic material until long practice has drawn our attention to it and rendered us adept at sorting it out.

This is, then, at the least a question requiring closer investigation, and one not to be dismissed at once on first appearance: whether any cognition of this kind exists that is independent of experience and even of all the impressions of the senses. Such cognitions are termed a priori and are distinguished from empirical ones, whose sources lie a posteriori, that is, in experience.

That expression, however, is still not definite enough to indicate appropriately the full sense of the question posed here. For of many a cognition drawn from sources in experience one is accustomed to say that we are capable of it, or share in it, a priori, since we derive it not directly from experience but from a general rule — a rule which, all the same, we have ourselves taken over from experience. Thus of a man who dug away the foundation of his house one says: he could know a priori that it would cave in, i.e., he had no need to wait for the experience of its actually caving in. Yet wholly a priori he could not know this either. For that bodies have weight, and accordingly fall once their support is removed, had first to be made known to him by experience.

In what follows, then, we shall mean by cognitions a priori not those that take place independently of this or that experience, but those that take place independently of absolutely all experience. Set over against them are empirical cognitions, or those possible only a posteriori, that is, through experience. Among the cognitions a priori, however, those are termed pure to which nothing empirical whatsoever is admixed. Thus, for example, the proposition: every alteration has its cause, is a proposition a priori, though not a pure one, since alteration is a concept that can be obtained only from experience.

II. We are in possession of certain cognitions a priori, and even the common understanding is never without them

Everything here turns on a mark that lets us tell a pure cognition apart from empirical ones with certainty. Experience, to be sure, teaches us that a thing has this or that character, yet never that it could be no other way. So, firstly, should we come upon a proposition whose very thinking carries its necessity along with it, we have an a priori judgment; and should it in addition rest on no premise except one that is itself valid as a necessary proposition, then it is a priori without qualification. Secondly: to the judgments it yields experience grants no genuine or strict, but merely presumed and comparative universality (through induction), so that the proper formulation must run: so far as we have thus far observed, this or that rule admits of no exception. Hence whenever a judgment is conceived with strict universality, that is, so that not a single exception is allowed to count as possible, it has not been drawn from experience but holds with unconditional a priori validity. Empirical universality, then, is nothing but an arbitrary raising of a validity that obtains in most instances to one that obtains across the board, as in the proposition all bodies are heavy; where, on the other hand, strict universality is integral to a judgment, it marks out a peculiar cognitive source for that judgment, namely a capacity for cognizing a priori. Necessity and strict universality, accordingly, are reliable indicators of an a priori cognition, and the two are moreover inseparably bound to one another. Yet because, in applying them, it is now and then easier to point out a judgment's empirical restrictedness than its contingency, and at other times clearer to exhibit the unrestricted universality we attach to a judgment than to exhibit its necessity, one does well to deploy each of these two criteria on its own, since either taken singly is infallible.

It is a simple matter to show that judgments of this kind—necessary, universal in the strictest sense, and therefore pure and a priori—do genuinely occur within human cognition. Should an illustration from the sciences be wanted, the whole body of mathematical propositions supplies it; should one be wanted from the most ordinary exercise of understanding, the proposition that any alteration must have a cause will answer; indeed in this latter case the concept of a cause itself so manifestly harbors the concept of a necessary linkage to an effect, and of a rule holding with strict universality, that it would collapse altogether if, in Hume's manner, one sought to trace it back to a repeated pairing of what occurs with what came before, and to a habit springing from this (a necessity, therefore, that is merely subjective) of tying representations together. One might equally, with no need of such examples to establish that pure a priori principles are actual in our cognition, exhibit their indispensability to the very possibility of experience, and so exhibit it a priori. For from where could experience itself draw its certainty, were all the rules by which it advances themselves empirical through and through, and thus contingent; on which account one could scarcely allow them to pass for first principles. For the present, however, it suffices that we have exhibited, as a fact and together with its distinguishing marks, the pure use of our cognitive faculty. Yet an a priori origin for some of them shows itself not merely in judgments but even in concepts. Strip from your empirical concept of a body, one feature after another, all that is empirical in it, its color, its hardness or softness, its weight, its impenetrability even, and what still remains is the space that this body (now vanished entirely) had occupied, and that you are unable to strip away. In the same way, once you strip from your empirical concept of any object at all, bodily or not, every property that experience has taught you: there is still one you cannot take from it, the property whereby you think it as substance or as inhering in a substance (even though this concept carries more determination than does the concept of an object as such). Compelled, then, by the necessity with which this concept presses itself upon you, you must admit that its seat lies a priori within your cognitive faculty.

III. Philosophy stands in need of a science which shall determine the possibility, the principles, and the extent of all a priori cognition

What carries far greater weight than everything preceding is this: that there are cognitions which even quit the field of every possible experience, and which, through concepts for which no answering object can be supplied anywhere in experience, seem to widen the reach of our judgments past every boundary of that field.

And it is exactly within these latter cognitions, the ones that pass beyond the sensible world—where experience offers neither a thread to follow nor any means of correction—that the researches of our reason lie; researches which, by their weight, we rate as far more distinguished, and whose final purpose we take to be far loftier, than whatever the understanding is able to learn in the field of appearances, and for whose sake we will hazard anything, even at the risk of going astray, rather than give up inquiries of such moment on any grounds of misgiving, or from slight regard and indifference. Pure reason's own inescapable tasks are these: God, freedom, and immortality. The science, however, whose whole apparatus and final purpose are aimed in truth at nothing but the resolution of these tasks bears the name metaphysics; and its method is dogmatic to begin with, that is, it takes the execution of so vast an enterprise confidently in hand without any preliminary test of whether reason is or is not equal to it.

Now it does look natural that, having once quit the soil of experience, one would hardly go straight to raising an edifice out of cognitions in one's keeping—cognitions whose source one cannot name—and on the strength of principles of unknown descent, before making sure by careful inquiry of the groundwork beneath it; and that one would, rather, have posed long ago the question of just how the understanding is to reach all these cognitions a priori, and what scope, validity, and value they may possess. And in fact nothing could be more natural, provided one takes the word natural to mean that which in fairness and reason ought to take place; yet if one takes it to mean what customarily does take place, then again nothing could be more natural or more intelligible than that such an inquiry should have gone so long neglected. For one portion of these cognitions, the mathematical, has from of old held secure possession, and so raises a hopeful expectation for the rest as well, however wholly different in kind these may be. Besides, once one has passed outside the compass of experience, one is safe from any refutation by experience. So strong is the temptation to enlarge one's cognitions that nothing short of a clear contradiction, met head-on, can arrest one's advance. Yet even this can be sidestepped, if one is merely cautious in framing one's inventions—which for all that stay inventions no less. Mathematics affords us a brilliant instance of how far, independently of experience, we may carry cognition a priori. True, it busies itself with objects and cognitions only to the extent that these can be displayed in intuition. But that fact is readily missed, since the intuition at issue can itself be furnished a priori, and thus is scarcely to be told apart from a mere pure concept. Taken with such a demonstration of reason's might, the urge to expand recognizes no limits. The light dove, cleaving the air in unimpeded flight and feeling its resistance, might conceive the representation that in empty space it would fare better still by far. Just so did Plato quit the sensible world, since it hems the understanding in with such narrow bounds, and struck out past it, borne on the pinions of the ideas, into the void of the pure understanding. He failed to see that with all his striving he was winning no ground, for he had nothing to press against by way of a footing, no resistance on which to stiffen himself and against which to bring his powers to bear, so as to move the understanding from its place. It is, though, a familiar destiny of human reason in its speculation to run its edifice up as quickly as it can, and only after the fact to look into whether the foundation was soundly laid. By then, though, every sort of extenuation is fetched up, either to console us over its soundness, or else to fend off such a tardy and perilous test altogether. But what shields us throughout the building from all misgiving and mistrust, and flatters us with an apparent rigor, is this. A great share of our reason's business—perhaps the greatest—consists in dissecting the concepts we already possess of objects. This yields us a wealth of cognitions which, though they are nothing beyond clarifications or expositions of what our concepts (confusedly, to be sure) already contained, are nonetheless rated, in point of form at least, as equal to fresh insights , even while, in point of matter or content, they do not enlarge the concepts we possess but only unfold them. Now because this procedure does deliver a real a priori cognition, one that makes safe and profitable headway, reason, all unawares, smuggles in under this semblance claims of a quite different order, whereby it fastens onto given concepts others entirely alien to them, and does so a priori, without anyone's grasping how it manages this, and without so much as allowing such a question to cross one's mind. For that reason I mean to deal, from the very start, with the difference between these two sorts of cognition.

IV. On the difference between analytic and synthetic judgments

Whenever a judgment thinks the relation of a subject to its predicate (and I will weigh only the affirmative kind, the negative being an easy extension afterward), that relation can hold in one of two ways. In the one, predicate B pertains to subject A as a component lodged (though hidden) inside the concept A itself; in the other, B falls altogether beyond the concept A, notwithstanding that it stands linked to it. The former judgment I term analytic, the latter synthetic. Analytic judgments (the affirmative sort), then, are the ones whose linkage of predicate to subject rests on identity; where instead that linkage is conceived apart from identity, the judgment shall count as synthetic. One might equally name the first kind explicative and the second ampliative judgments, since the predicate in the former contributes nothing fresh to the subject's concept, but only dissects it into the part-concepts already (if obscurely) lying within it: the latter, by contrast, fasten onto the subject's concept a predicate nowhere thought within it, one that no dissection of that concept could ever have brought to light. By way of example, should I say that all bodies are extended, the judgment is analytic. For to locate extension as tied to it, I have no need to reach past the concept I attach to the word body; I have only to unfold that concept—to grow aware, that is, of the manifold I forever think in it—and there the predicate presents itself; the judgment is accordingly analytic. Should I instead say that all bodies are heavy, the predicate proves to be something quite other than anything the mere concept of body as such holds for my thinking. Appending such a predicate thus produces a synthetic judgment.

Judgments of experience as such are, without exception, synthetic. It would, after all, be incongruous to rest an analytic judgment upon experience, for in framing such a judgment I may not stray outside my concept in the least, and so stand in need of no experiential evidence whatever. That a body possesses extension is a proposition that a priori stands established, and is no verdict of experience. For prior to any recourse to experience, every condition of my judgment already lies ready in the concept, from which the predicate need merely be lifted out under the principle of contradiction, whereby I at once also apprehend the judgment as necessary—something experience could not even begin to instruct me in. Now even though I nowhere embed the predicate of heaviness in the concept of body as such, that concept still points to an object of experience by way of one portion of it, and to that portion I am free to append yet other portions of the selfsame experience, portions counted as belonging with the first . In advance I can cognize the concept of body analytically by way of its marks—extension, impenetrability, figure, and the like—each of them thought within this concept. But now I enlarge my cognition: turning back toward the experience out of which I had drawn this concept of body, I discover heaviness likewise forever conjoined with the marks just named, and I therefore annex it, synthetically, to that concept as a predicate. Experience, then, is what underwrites the possibility of synthesizing the predicate of heaviness with the body-concept; for the two concepts, though neither is lodged inside the other, still cohere—only contingently, to be sure—as members of a single whole, that whole being experience, itself nothing but a synthetic joining of intuitions.

With synthetic judgments a priori, however, this resource fails us wholly and entirely. If I am required to pass beyond concept A so as to cognize a further concept B as bound to it: on what do I lean for support, and by what means is the synthesis effected, seeing that in this case I lack the convenience of scanning the domain of experience for it? Consider the statement: whatever comes to pass has its cause. Within the concept of a thing that comes to pass I certainly think an existence upon which a time has gone before, and so forth, and out of that, analytic judgments admit of being formed. Yet the concept of a cause resides wholly outside the former, pointing to something other than what comes to pass, and hence is nowhere included in this latter representation. How, then, do I come to say of whatever comes to pass in general something altogether different from it, and cognize the concept of cause—though it is not held within the former—as nevertheless attaching to it, and attaching necessarily at that? What, in this case, is the unknown = x upon which the understanding steadies itself when, over and above the concept of A, it supposes it has lit upon a predicate B alien to that concept, one it nonetheless reckons to be joined with it? Experience it cannot be; for the principle just adduced has attached this second representation to the first not only with a universality surpassing anything experience might supply, but also under the stamp of necessity, and thus altogether a priori and from mere concepts. Now the entire final purpose of our speculative a priori cognition reposes on principles of this synthetic, that is, ampliative sort; the analytic principles , for their part, are of course supremely important and indispensable, yet serve only to bring concepts to the clarity demanded for a sure and wide-ranging synthesis, understood as a truly new gain.

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

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

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

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

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

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

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

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

VI. The general problem of pure reason.

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

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

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

How is pure mathematics possible?

How is pure natural science possible?

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

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

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

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

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

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

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

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

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

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

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

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

I. Transcendental Doctrine of Elements.

The Transcendental Doctrine of Elements

First Part. Transcendental Aesthetic

Introduction §1

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

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

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

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

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

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

Section 1. On Space

§ 2. Metaphysical exposition of this concept.

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

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

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

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

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

§3. Transcendental exposition of the concept of space.

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

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

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

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

Conclusions from the above concepts.

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

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

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

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

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

Section 2. On Time

§ 4. Metaphysical Exposition of the Concept of Time.

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

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

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

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

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

§ 5. Transcendental Exposition of the Concept of Time.

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

§ 6. Inferences from these Concepts.

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

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

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

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

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

§ 7. Elucidation.

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

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

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

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

§ 8. General Remarks on the Transcendental Aesthetic

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

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

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

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

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

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

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

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

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

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

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

Conclusion of the Transcendental Aesthetic

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

Second Part. Transcendental Logic

Introduction. Idea of a Transcendental Logic

I. On Logic in General

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

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

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

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

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

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

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

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

II. On Transcendental Logic

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

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

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