Introduction

If I view the entire stock of cognition belonging to pure and speculative reason as a building, of which we do at least carry the idea within ourselves, then I can say this: in the transcendental Doctrine of Elements we took stock of the building materials and settled for what sort of edifice, and of what height and solidity, they would be sufficient. It turned out, admittedly, that although we had had a tower in view, one designed to reach up to heaven, the stock of materials was only enough for a dwelling-house — one just roomy and high enough for our affairs on the plane of experience to take them in; but that this bold venture was destined to fail for want of material, and this without even reckoning the confusion of tongues that could not but divide the workmen over the plan and disperse them throughout the world, each to build separately, following his own draft. Now what matters to us is not so much the materials as, rather, the plan itself, and though we have been cautioned against risking any arbitrary, blind draft that might well surpass our entire means, yet, being unable properly to abstain from raising a secure place of residence, we must frame our estimate for a building in keeping with the stock supplied to us and, at once, matched to what we require.

By the transcendental Doctrine of Method, then, I mean the determination of the formal conditions of a complete system of pure reason. For this purpose we shall be occupied with a discipline, a canon, an architectonic, and lastly a history of pure reason, and shall achieve, from a transcendental standpoint, what has been pursued in the schools under the title of a practical logic concerning the employment of the understanding as such, though poorly achieved, because, since general logic is not confined to any special sort of cognition of the understanding (not, for instance, to pure cognition), nor to any particular objects, it can, without drawing on knowledge borrowed from other sciences, do nothing more than put forward headings for possible methods together with technical terms of the kind used, in matters of systematic arrangement, across all manner of sciences — terms that make the names known to the apprentice beforehand, whose sense and use he is destined only afterwards to learn.

Chapter 1. The Discipline of Pure Reason

Negative judgments — those that are negative not merely in their logical form but also in their content — enjoy little particular esteem in the eyes of human curiosity; indeed they are often regarded as envious enemies of our drive for cognition, which strives unceasingly toward expansion, and it takes almost an apology to secure for them so much as toleration, and still more to secure for them favor and high regard.

To be sure, one can express logically any proposition one wishes in negative form, yet as concerns the content of our cognition as such — whether a judgment enlarges or limits it — the negating ones have the peculiar office of doing nothing but warding off error. Hence negative propositions designed to fend off a false cognition in a case where no error is ever possible are, though perfectly true, still empty — that is, not at all suited to their aim, and for precisely that reason frequently absurd; as with that rhetorician's dictum in the schools, that Alexander would have been unable to conquer any territory had he possessed no army.

Wherever, though, the bounds of the cognition available to us are exceedingly narrow, the temptation to judge strong, the semblance on offer highly deceptive, and the damage done by error substantial, there the negative side of instruction — which serves solely to secure us against errors — has still greater weight than many a positive lesson by which our cognition might be enlarged. We give the name discipline to the constraint by which the abiding inclination to stray from certain rules is held in check and at last stamped out. It is distinct from culture, which is meant merely to impart a skill without thereby removing another one already present. To the cultivation of a talent that already has of itself an impulse toward expression, discipline will therefore make a negative⁶⁸ contribution, whereas culture and doctrine make a positive one.

That temperament, and likewise that talents which readily allow themselves a free and unrestricted movement (such as imagination and wit), stand in need of a discipline in more than one respect, everyone will readily grant. That reason, however, whose proper task it is to prescribe its discipline to all other endeavors, should itself still require one, may indeed seem strange; and in fact it has thus far escaped such a humiliation precisely because, given the solemnity and the thorough decorum with which it comes forward, no one could easily fall into suspecting it of a frivolous play with figments in place of concepts and words in place of things.

Reason requires no critique in its empirical use, because there its principles are subjected, on the touchstone of experience, to continual testing ; and likewise none in mathematics, where its concepts must at once be exhibited in concreto in pure intuition, so that everything groundless and arbitrary at once becomes manifest. But wherever reason is held on no visible course by intuition, whether empirical or pure — that is, in its transcendental employment operating on concepts alone — its need for a discipline becomes so acute, one that would curb its bent toward extending itself past the cramped confines of possible experience and restrain it from excess and error, that the whole philosophy of pure reason is occupied with nothing beyond this negative usefulness. Isolated aberrations admit of correction by censure , and the sources from which they spring by critique. Where, however, one meets — as happens in pure reason — with a whole system of illusions and deceptive semblances that are tightly bound up with one another and drawn together under shared principles, there a wholly peculiar and indeed negative legislation appears to be called for, one that, under the title of a discipline, would raise up, from the very nature of reason and of the objects of its pure use, something like a system of circumspection and self-scrutiny, before which no fallacious, sophistical semblance could survive but would at once give itself away, whatever grounds it might muster to gloss itself over.

It should, however, be well noted that within this second principal part of the transcendental critique I aim the discipline of pure reason not at the content but solely at the method of cognition drawn from pure reason. The former was already accomplished in the Doctrine of Elements. Yet the exercise of reason bears so much resemblance to itself, no matter which object it is brought to bear upon, and is nonetheless, insofar as it is meant to be transcendental, at the same time so essentially set apart from everything else, that without the admonitory negative teaching of a discipline established expressly for it there is no averting the errors that must inevitably issue from an unfitting compliance with methods which do suit reason elsewhere, only not here.

Section 1. The discipline of pure reason in its dogmatic use

Mathematics affords the most dazzling instance of a pure reason that, with no help from experience, successfully broadens its own scope. Instances of this sort prove infectious, especially for a faculty that, by its nature, cannot help expecting the same good fortune elsewhere that it once met with in a single case. And so pure reason, when put to transcendental use, cherishes the hope of expanding itself with equal success and rigor as it did in mathematics—chiefly by carrying over the very method that yielded such palpable benefit in the one domain. A great deal therefore hangs, for us, on knowing this: whether the method of attaining apodictic certainty that the latter science calls mathematical is one and the same as that by which such certainty is pursued in philosophy, where it would have to bear the name dogmatic.

Philosophical cognition amounts to rational cognition from concepts, whereas the mathematical sort issues from the construction of concepts. To construct a concept, however, means this: to display a priori the intuition that answers to it. Constructing a concept thus calls for a non-empirical intuition, one that—being an intuition—is a single object, and which yet, precisely as the construction of a concept (of a general representation), has to convey in the representation a validity holding for every possible intuition ranged under that same concept. So it is that I construct a triangle when I display the object answering to this concept, whether through sheer imagination in pure intuition or, thereafter, on paper in empirical intuition too, on both occasions wholly a priori, having borrowed the model for it from no experience whatever. The single figure I have drawn is empirical, and serves all the same to convey the concept unimpaired in its generality, for in this empirical intuition one looks solely to the act of constructing the concept—an act to which numerous determinations, such as those of size, of the sides and of the angles, are wholly indifferent—so that one leaves out of account these variations, which do nothing to alter the concept of the triangle.

Philosophical cognition, then, regards the particular only within the universal, while mathematical cognition regards the universal within the particular, indeed within the single instance, and does so nonetheless a priori and by the agency of reason, so that, exactly as this single instance stands determined under certain general conditions of construction, the object of the concept—answered to by this instance merely as its schema—must likewise be conceived as determined in general.

The essential contrast between these two species of rational cognition lies, then, in this form, and by no means in any difference of their matter or their objects. Those who fancied that philosophy could be set apart from mathematics by declaring that the one takes for its object merely quality, the other merely quantity, have mistaken an effect for a cause. It is the form of mathematical cognition that causes it to reach only as far as quanta. For construction is possible for the concept of magnitudes alone—that is, a priori laying-out in intuition—whereas qualities allow of presentation in no intuition save an empirical one. A rational cognition of qualities is on that account possible through concepts only. Thus an intuition answering to the concept of reality can be drawn by no one from any source other than experience, and can never be come by a priori, from oneself, ahead of the empirical consciousness of it. The conical figure one will be able to render intuitive with no empirical help, simply by following the concept, but the color of this cone must first be furnished in some experience or other. As for the concept of a cause as such, I have no means of presenting it in intuition except by an example that experience puts into my hand, and so forth. Philosophy, besides, treats of magnitudes no less than mathematics does—of totality, say, of infinity, and so on. Mathematics likewise busies itself with the distinction between lines and surfaces as spaces of differing quality, and with the continuity of extension as one such quality of it. Yet though in cases like these the two share a common object, the way of handling it by reason turns out wholly different under philosophical as against mathematical treatment. The one confines itself to general concepts; the other can get nowhere with the mere concept and rushes forthwith to intuition, where it inspects the concept in concreto—not empirically, though, but only in an intuition it has displayed a priori, that is, constructed, and in which whatever issues from the general conditions of construction must hold likewise, and generally, of the object of the constructed concept.

Hand a philosopher the concept of a triangle and leave him to work out, after his own fashion, how the sum of its angles might come to stand toward a right angle. All he now possesses is the concept of a figure shut in by three straight lines, and along with it the concept of an equal number of angles. He may brood over this concept as long as he pleases, he will draw nothing new from it. He can take apart the concept of the straight line, or of an angle, or of the number three, and make it distinct, without ever reaching further properties that simply do not reside in these concepts. Let the geometer, by contrast, take the question up. He starts straightaway by constructing a triangle. Knowing that two right angles come, taken together, to exactly the sum of all the adjacent angles that may be drawn from a single point on a straight line, he prolongs one side of his triangle and gets two adjacent angles equal together to two right ones. He then divides the outer of these angles by running a line parallel to the triangle's opposite side, and observes that an outer adjacent angle here comes about which equals an inner one, and so forth. By such means, along a chain of inferences forever steered by intuition, he reaches a fully luminous and at once general resolution of the question.

Mathematics, though, constructs not magnitudes alone (quanta), as geometry does, but bare magnitude as well (quantitatem), as in algebra, where it leaves wholly aside the makeup of the object meant to be thought under such a concept of magnitude. It then settles on a particular notation for all constructions of magnitudes as such (numbers)—for addition, subtraction, and so on, and the extraction of roots; and once it has, in addition, marked out the general concept of magnitudes according to their several relations, it sets forth in intuition, under certain general rules, every operation by which magnitude is produced and modified; where one magnitude is to be divided by another, it brings their two characters together according to the notation for division, and so forth, and thereby attains, through a symbolic construction—just as geometry does through an ostensive or geometric one (of the objects themselves)—the very point beyond the reach of discursive cognition working with mere concepts.

What can be the cause of so divergent a predicament in which two artificers of reason find themselves, the one taking his route by concepts, the other by intuitions that he displays a priori in keeping with concepts? Given the transcendental groundwork laid out above, the cause is plain. The matter here does not turn on analytic propositions, producible by mere dissection of concepts (on this score the philosopher would surely outdo his competitor), but on synthetic ones—and, at that, such as are to be cognized a priori. For I am not to attend to what I really think in my concept of the triangle (that is nothing but the bare definition); I am, rather, to press past it toward properties that lie outside this concept and yet pertain to it. Now, this cannot happen otherwise than by my fixing my object according to the conditions either of empirical or of pure intuition. The first would supply only an empirical proposition (got by measuring its angles), one carrying neither generality nor, still less, necessity—and there is no talk of anything of that kind. The second procedure, however, is the mathematical, and in this case the geometric, construction, whereby, in a pure intuition as much as in an empirical one, I annex the manifold belonging to the schema of a triangle as such, and hence to its concept—by which means general synthetic propositions must indeed be constructed.

I would therefore be philosophizing about the triangle to no purpose—reflecting, that is, discursively upon it—without getting the least bit past that bare definition from which, in fairness, I should have to set out. There does exist a transcendental synthesis out of concepts alone, which once again is the philosopher's alone to accomplish, yet which bears never on more than a thing in general, and on the conditions under which a perception of it might belong to possible experience. But in mathematical tasks that is not in question, nor is existence at all; what is in question is the properties of the objects in themselves, and this only so far as those properties are bound up with the concept of them.

In the instance cited we have aimed merely at making plain how vast a difference lies between the discursive employment of reason by concepts and the intuitive employment through the construction of concepts. The question naturally follows what the cause may be that renders such a twofold employment of reason necessary, and on what conditions one is able to tell whether the first alone, or the second as well, has a place.

In the end, every cognition of ours bears on possible intuitions; for it is by these alone that an object gets given. Now an a priori concept (a non-empirical concept) either already carries a pure intuition within itself, and is then open to construction; or it carries nothing beyond the synthesis of possible intuitions not given a priori, and then one may indeed judge by its means synthetically and a priori, though only discursively, by concepts, and never intuitively, through construction of the concept.

Now, of all intuition, the sole thing given a priori is the naked form of appearances—space and time; and a concept of these, taken as quanta, admits of a priori display in intuition, that is, of construction, whether alongside their quality (their shape) or else as their mere quantity (the bare synthesis of the homogeneous manifold) by way of number. The matter of appearances, though—that through which things come to be given us in space and time—is representable in perception only, and hence a posteriori. The one concept that presents a priori this empirical content of appearances is the concept of the thing as such; and synthetic cognition of it a priori is competent to supply no more than the bare rule for synthesizing whatever perception may hand over a posteriori—never the a priori intuition of the real object, since that intuition has of necessity to be empirical.

Synthetic propositions directed upon things as such, whose intuition cannot be furnished a priori at all, are transcendental. Transcendental propositions, accordingly, admit of being furnished never by construction of concepts, but only by concepts a priori. They hold no more than the rule under which a certain synthetic unity of what cannot be a priori presented in intuition (of the perceptions) is to be pursued empirically. But not a single one of their concepts can they display a priori in any case whatever; this they accomplish only a posteriori, by way of the experience that first grows possible in keeping with those synthetic principles.

If one is to pass a synthetic judgment about a concept, one has to step out of that concept and, indeed, toward the intuition in which it stands given. For should one keep to what the concept holds, the judgment would be merely analytic, an unpacking of the thought in line with what actually lies inside it. But from the concept I am free to move to the pure or empirical intuition that answers to it, so as to weigh it there in concreto and, whether a priori or a posteriori, to learn what belongs to its object. The first is the rational and mathematical cognition by construction of the concept; the second is the merely empirical (mechanical) cognition, one incapable of ever delivering necessary and apodictic propositions. So I might well dissect my empirical concept of gold and thereby win nothing beyond the power to count off all that I really think at this word—by which my cognition undergoes, to be sure, a logical betterment, but takes on no increase or addition. What I do instead is take the matter that turns up under this name and run perceptions upon it, and these will hand me a variety of synthetic, yet empirical, propositions. The mathematical concept of a triangle I would construct—give it, that is, a priori in intuition—and along this road arrive at a synthetic, yet rational, cognition. But once the transcendental concept of a reality, a substance, a force, and the like is handed me, it marks out neither an empirical nor a pure intuition, but solely the synthesis of empirical intuitions (which for that reason cannot be furnished a priori); and so, since the synthesis is unable to pass a priori out to the intuition answering to it, there can spring from that concept no determining synthetic proposition, but only a principle for the synthesis⁶⁹ of possible empirical intuitions. A transcendental proposition is thus a synthetic rational cognition by mere concepts, and therefore discursive, since through it all synthetic unity of empirical cognition first grows possible, while by it no intuition whatever gets given a priori.

There is, then, a twofold employment of reason which—for all the generality of cognition and its a priori generation that the two hold in common—runs nonetheless very differently in its course, and this for the reason that within appearance, as that whereby every object comes to be given us, two ingredients are present: the form of intuition (space and time), open to being cognized and settled entirely a priori, and the matter (the physical), or the content, standing for a something encountered in space and time, one that consequently harbors an existence and answers to sensation. Touching the latter—which admits of determinate givenness by no route but the empirical—there is nothing we can hold a priori save indeterminate concepts for the synthesis of possible sensations, so far as these come under the unity of apperception (within a possible experience). Touching the former, we are able to settle our concepts in intuition a priori by fashioning for ourselves, in space and time, the very objects, through a uniform synthesis, in that we take them for nothing but quanta. The first is termed the employment of reason by concepts, wherein all we can do is bring appearances, as to their real content, under concepts—concepts thereupon determinable in no way but the empirical, that is, a posteriori (though in keeping with those concepts as rules of an empirical synthesis); the second is the employment of reason through construction of concepts, wherein these concepts, bearing already on an a priori intuition, can just for that reason be given as settled a priori, and without any empirical data, in pure intuition. To ponder everything that is there (a thing in space or in time)—whether, and how far, it is a quantum or not; that an existence in it, or else a lack, has to be represented; how far this something (the filler of space or time) is a primary substratum or a mere determination; whether its existence bears a relation to something else as cause or as effect; and, finally, whether, in point of existence, it stands isolated or in mutual dependence with others; to ponder the possibility of this existence, its actuality and its necessity, or the reverse of these: the whole of this pertains to rational cognition from concepts, and it is this we call philosophical. But to settle an intuition a priori in space (shape), to partition time (duration), or just to cognize what is common to the synthesis of one selfsame thing throughout time and space, together with the magnitude of an intuition in general that springs therefrom (number)—that is a business of reason by construction of concepts, and bears the name mathematical.

The signal good fortune that reason meets with by means of mathematics quite naturally breeds the surmise that, if not reason itself, at any rate its method will succeed outside the province of magnitudes as well, inasmuch as it reduces all its concepts to intuitions it can furnish a priori, thereby making itself, so to speak, lord over nature: pure philosophy, on the other hand, fumbles about within nature with discursive a priori concepts, unable to render the reality of them a priori intuitive and thus to warrant it. Nor, indeed, do the masters of this art seem to want for such confidence in themselves, nor the public to want for high hopes of their skill, were they ever to set their hand to the business. For, having hardly ever philosophized about their mathematics (a hard task, that!), the specific difference of the one employment of reason from the other never so much as crosses their mind. Current rules, empirically applied and borrowed from common reason, then serve them in the stead of axioms. Whence the concepts of space and time, with which they deal (as the sole original quanta), may arise concerns them not at all; and just so it strikes them as idle to inquire into the source of pure concepts of the understanding, and thereby into the compass of their validity, and preferable simply to put them to use. In all of this they act entirely rightly, provided only that they do not step beyond their allotted bound, namely that of nature. But so doing, they slip unawares off the field of sensibility onto the treacherous soil of pure and even transcendental concepts, where the ground (instabilis tellus, innabilis unda) suffers them neither to stand nor to swim, and lets only hurried steps be taken, of which time retains not the faintest trace—whereas their march in mathematics lays down a highroad that even the remotest posterity may tread in confidence.

Since we have laid it on ourselves as a duty to fix the bounds of pure reason in its transcendental use exactly and with certainty, while this species of striving carries the peculiarity that, for all the most forceful and lucid warnings, it still lets itself be kept in play by hope before it wholly renounces the design of pressing out beyond the bounds of experience into the enchanting tracts of the intellectual: it becomes necessary to strip away, as it were, this last anchor of a fanciful hope, and to show that adherence to the mathematical method can, in this species of cognition, procure not the slightest gain—unless the gain be that of laying open the bare spots of that method the more distinctly: that geometry and philosophy are two wholly separate things, however much, in natural science, they reach a hand to one another, so that the procedure of the one can never be aped by the other.

The soundness of mathematics rests upon definitions, axioms, and demonstrations. I shall be content to show this: that not one of these components can, in the sense the mathematician gives them, be furnished by philosophy, nor aped by it; that the geometer, working by his method within philosophy, brings off nothing but houses of cards, while the philosopher, working by his within the domain of mathematics, can raise nothing but idle prattle—although just this, the knowing of one's bounds, is what philosophy consists in—and that even the mathematician, unless his talent be already hemmed in by nature and penned within his specialty, can neither spurn philosophy's warnings nor override them.

1. On definitions. To define ought, as the very word conveys, to signify strictly no more than to lay out originally, within its bounds, the comprehensive concept of a thing.⁷⁰ Set against such a requirement, an empirical concept cannot be defined in the least, but only explicated. For, since in it we hold but a handful of marks belonging to some class of sense-objects, one can never be sure whether, under the word that stands for the same object, one thinks now more, now fewer of its marks . So the one may think, in the concept of gold, over and above weight, color, and ductility, the further property of not rusting, while the other perhaps knows nothing of it. One relies on certain marks only so long as they suffice for telling things apart; fresh observations, though, strike some out and put others in, so that the concept never rests between secure bounds. And what, besides, would be the use of defining such a concept, seeing that when, say, water and its properties come up for discussion, one will not dwell on what one thinks at the word water, but will move on to trials, and the word, with the scant marks clinging to it, is meant to make up merely a designation and not a concept of the thing—so that the supposed definition is nothing other than a settling of the word. Secondly, no a priori given concept, either, can strictly speaking be defined—substance, say, cause, right, equity, and the rest. For I can never rest assured that the distinct representation of a concept given (as yet confusedly) has been comprehensively developed, unless I know it to be adequate to the object. But since the concept of it, as it comes given, may hold many an obscure representation that we skip over in the dissecting, though we draw on them always in application: the comprehensiveness of my concept's dissection stays forever in doubt, and can be rendered only presumably, never apodictically, certain by way of manifold matching examples. In place of the term definition I would sooner press into service that of exposition, which stays cautious yet, and by which the critic may let the thing pass to a certain degree and still keep his misgivings as to its comprehensiveness. Since, then, concepts given neither empirically nor a priori lend themselves to definition, there are left over none but concepts thought up at will, on which one may try this trick. A concept of my own I can, in such a case, always define; for I must, after all, know what I meant to think, having myself devised it on purpose, with its coming to me neither by the nature of the understanding nor by experience—yet I cannot claim to have thereby defined a genuine object. For if the concept rests on empirical conditions—a ship's clock, say—then this arbitrary concept does not yet yield the object and its possibility; from it I do not so much as know whether it has any object at all, and my account may better be styled a declaration (of my project) than the definition of an object. Hence there would be left over no concepts fit for defining but those holding an arbitrary synthesis constructible a priori—so that mathematics, and it alone, has definitions. For the object it thinks, it also sets forth a priori in intuition, and this object can surely contain no more and no less than the concept, since through the account the concept of the object was given originally—that is, without the account's being drawn from anything else. The German tongue has, for the terms exposition, explication, declaration, and definition, nothing beyond the single word Erklärung; and so we must already give a little ground on the stringency of the requirement—having, that is, refused philosophical accounts the honorific of definition—and will hold this whole remark to the point that philosophical definitions come about only as expositions of given concepts, mathematical ones as constructions of concepts originally made, the former merely analytically, by dissection (whose completeness is not apodictically sure), the latter synthetically, and thus make the concept itself, whereas the former only explain it. From this there follows:

a) that one must not, in philosophy, ape mathematics by putting the definitions out in front, except perhaps by way of a mere trial. For, being dissections of given concepts, these concepts go before—confusedly still, but they go before—and the incomplete exposition precedes the complete, so that from a few marks drawn out of a dissection not yet finished we can settle a good deal in advance, before we have come to the complete exposition, that is, to the definition; in short, in philosophy the definition, as apportioned distinctness, ought to close the work sooner than open it.⁷¹ In mathematics, on the contrary, we have no concept whatever ahead of the definition, through which the concept is first given; it must, then, and it can too, always take its start from there.

b) Mathematical definitions can never go wrong. For, because the concept is first given through the definition, it holds exactly, and only, what the definition means to have thought by its means. But although nothing false, as to content, can arise in it, still, now and then—though rarely—a slip in the form (the dress) may occur, namely in point of precision. Thus the ordinary account of the circle, that it is a curved line all of whose points stand at equal distance from a single one (the center), carries the fault that the qualifier curved has crept in without need. For there has to be a particular theorem, drawn from the definition and readily proved: that any line all of whose points stand at equal distance from a single one is curved (no stretch of it straight). Analytic definitions, by contrast, can go wrong in manifold ways—either by importing marks that in truth did not lie in the concept, or by falling short of the comprehensiveness that makes up the essence of a definition, since one cannot be quite so sure of the completeness of one's dissection. For this reason mathematics' way of defining is not to be aped in philosophy.

2. On axioms. These are synthetic principles a priori, in so far as they are immediately certain. Now one concept does not admit of being joined to another synthetically and yet immediately, since, for us to get past a concept, a third, mediating cognition is wanted. And since philosophy is nothing but rational cognition by concepts, no principle will be met with in it that might earn the name of an axiom. Mathematics, on the other hand, has room for axioms, since, by constructing its concepts in the intuition of the object, it is able to tie that object's predicates to it a priori and immediately, as, for instance, that three points always lie in a single plane. A synthetic principle from bare concepts, by contrast, can never be immediately certain—take the proposition: whatever happens has its cause; for I have to cast about for a third thing, namely the condition of time-determination within an experience, and could not recognize such a principle straight off, immediately from the concepts alone. Discursive principles, then, are something altogether other than intuitive ones, that is, axioms. The former call, every time, for a deduction besides, which the latter can do wholly without; and since these last are self-evident on the very ground that philosophical principles, for all their certainty, can never lay claim to, it wants a very great deal for any synthetic proposition of pure and transcendental reason to be as manifest (as the defiant phrase runs) as the proposition that twice two make four. True, in the Analytic, at the table of the principles of the pure understanding, I did also bring in certain axioms of intuition; but the principle cited there was itself no axiom, and served merely to state the Principium of the possibility of axioms in general—and is itself only a principle from concepts. For the very possibility of mathematics has to be shown within transcendental philosophy. Philosophy, therefore, has no axioms, and may never lay down its a priori principles thus flatly, but has to make do with vindicating its warrant for them by thorough deduction.

3. On demonstrations. Only an apodictic proof, so far as it is intuitive, can be styled a demonstration. Experience does teach us what is there, but not that it could be in no way otherwise. On that account empirical grounds of proof can supply no apodictic proof. Out of a priori concepts, however (in discursive cognition), intuitive certainty—that is, self-evidence—can never spring, however apodictically certain the judgment may otherwise stand. It is mathematics alone, then, that holds demonstrations, since it draws its cognition not from concepts but from the construction of them—that is, from the intuition furnishable a priori to match the concepts. Even the way of algebra, with its equations, out of which it turns up the truth by reduction along with the proof, is admittedly no geometric but still a characteristic construction, in which one lays out at the signs the concepts—above all that of the ratio of magnitudes—in intuition, and, with never a glance at the heuristic side, secures every inference against error by setting each one before the eye. Philosophical cognition, on the contrary, must forgo this advantage, having always to view the general in abstracto (through concepts), whereas mathematics can weigh the general in concreto (in the single intuition) and yet by a pure a priori representation, whereby each false step shows itself. The former, accordingly, I would rather name acroamatic (discursive) proofs, since they can be conducted through nothing but words (the object in thought), as opposed to demonstrations, which, as the term itself already signals, go forward in the intuition of the object.

From all of this it now follows that it in no way suits the nature of philosophy, above all in the field of pure reason, to swagger with a dogmatic bearing and to trick itself out in the titles and sashes of mathematics, into whose order it does not, after all, belong—though it has every ground to hope for a sisterly bond with it. Those are hollow presumptions that can never come off, and must indeed thwart their own aim, which is to expose the illusions of a reason that misjudges its bounds and, by a sufficient clearing-up of our concepts, to bring the self-conceit of speculation back down to a modest but sound self-knowledge. Reason, then, in its transcendental ventures, will not be able to gaze ahead so assured, as though the road it has covered ran quite straight to the goal, nor to reckon so boldly on the premises it has laid at bottom that there were no need to look back time and again and mind whether, as the inferences run on, there might not turn up errors overlooked in the principles—errors making it needful either to fix them more closely or to recast them altogether.

I sort all apodictic propositions (be they now provable or immediately certain) into dogmata and mathemata. A directly synthetic proposition from concepts is a dogma; a like proposition through construction of concepts, on the other hand, is a mathema. Analytic judgments, strictly, teach us nothing further about the object than what the concept we hold of it already carries within it, since they do not widen the cognition past the concept of the subject but merely light it up. They cannot, therefore, aptly be styled dogmas (a word one might perhaps render by tenets). But of the two sorts of synthetic proposition a priori just considered, ordinary usage lets only those belonging to philosophical cognition carry this name, and one would scarcely call the propositions of arithmetic or of geometry dogmata. This usage thus bears out the account we gave, that only judgments from concepts, and not those from construction of concepts, may be styled dogmatic.

Now the whole of pure reason, in its merely speculative use, holds not one directly synthetic judgment from concepts. For by way of ideas it is, as we have shown, capable of no synthetic judgments at all that would carry objective validity; by way of concepts of the understanding, on the other hand, it does raise secure principles, yet in no way directly from concepts—always only indirectly, by referring these concepts to something wholly contingent, namely possible experience; for then, once this (something as an object of possible experiences) is presupposed, they are apodictically certain right enough, though in themselves (directly) a priori they cannot so much as be cognized. Thus no one can soundly see into the proposition: whatever happens has its cause, out of these given concepts alone. Hence it is no dogma, even though from another vantage—namely the sole field of its possible use, that is, experience—it admits of being proved perfectly well and apodictically. It is styled a principle and not a theorem, even though it must be proved, and this because it has the singular property of itself first making possible its own ground of proof, namely experience, and of having always to be presupposed in the latter.

If, then, in the speculative use of pure reason there are, as to content, no dogmata whatever, every dogmatic method—be it borrowed from the mathematician or meant to grow into a manner of its own—is unfitting in itself. For it does no more than veil the faults and blunders and beguile philosophy, whose true aim is to let all reason's steps be seen in their brightest light. The method may, for all that, still be systematic. For our reason (subjectively) is itself a system, though in its pure use, by way of bare concepts, only a system of inquiry after principles of unity, for which experience alone is in a position to yield the stuff. Of the peculiar method of a transcendental philosophy, though, nothing can be said in this place, since we are engaged only in a critique of how our resources stand—whether we are to build at all, and how high we may run up our building from the stuff we have (the pure a priori concepts).

Section 2. The discipline of pure reason in respect of its polemical use

Reason must submit itself to criticism in all of its undertakings and cannot curtail the freedom of criticism through any prohibition without harming itself and drawing upon itself a suspicion detrimental to it. Now there is nothing so important with respect to utility, nothing so sacred, that it might exempt itself from this testing and surveying examination, which respects no person. Upon this freedom rests the very existence of reason, which wields no dictatorial authority, but whose verdict is on every occasion nothing more than the concurrence of free citizens , every one of whom must be free to utter his misgivings—indeed his veto—without any reserve.

But even though reason can never refuse itself to criticism, it does not at all times have cause to dread it. But pure reason, in its dogmatic (as against mathematical) employment, is not so assured of scrupulously observing its highest laws that it could avoid presenting itself with diffidence—nay, with the wholesale surrender of every pretended dogmatic authority—before the scrutinizing gaze of a loftier, judicial reason.

Matters stand quite otherwise when its business is not with the judge's censure but with the pretensions of a fellow citizen, against which it has merely to defend itself. For since these wish to be every bit as dogmatic, albeit in denying, as the former in affirming: there arises a justification κατ' ἄνθρωπον that safeguards against every encroachment and yields a titled holding, one that need fear no alien presumptions, notwithstanding that it admits of no adequate proof κατ' ἀλήθειαν on its own account.

What I mean by reason's polemical employment is the vindication of its propositions in the face of the dogmatic denials brought against them. What is at stake here is not whether its claims might, for all that, turn out false, but solely that nobody could at any time uphold the contrary with apodictic certainty (or even with any stronger show of plausibility). For we do not then hold our possession merely on sufferance , if we have before us a title to it, though not a sufficient one, and it stands wholly assured that at no time could anyone establish the unlawfulness of this holding.

There is something disheartening, something that weighs one down, in the very fact that an antithetic of pure reason should exist to begin with, and that reason—which is, after all, the highest tribunal over every dispute—should come to blows with its own self. True, we had before us above just such a seeming antithetic of it; but it emerged that this rested upon a confusion—for, following the ordinary prejudice, one had taken appearances to be things in themselves and had then required an absolute completeness of their synthesis in this manner or that (though it was, on either manner, equally impossible), a completeness that can in no wise be looked for from appearances. So at that time there existed no genuine contradiction of reason with its own self in these propositions: that a series of appearances given in themselves possesses an absolutely first commencement, and, conversely: that such a series is, plainly and in itself, devoid of any commencement whatever; for the two claims are perfectly compatible, since appearances, regarded in respect of their existence (as appearances), amount in themselves to nothing whatsoever—that is, to something self-contradictory—so that positing them must, in the nature of the case, drag contradictory inferences in its train.

But no such confusion can be pleaded, and thereby the conflict of reason settled, if, for instance, one were to assert on the theist's part: there is a highest being, and on the atheist's, to the contrary: there is no highest being; or in psychology: whatever thinks is of an absolute and abiding unity and so is marked off from all perishable material unity, against which another might set: the soul is not an immaterial unity and cannot be spared from perishing. For in this case the object under question is clear of everything alien that would conflict with its nature, and the understanding is here concerned with things in themselves alone, and not with appearances. Here, then, a true conflict would indeed be met with, if only pure reason on the negating side had something to say that came close to the ground of an assertion; for as regards the critique of the proofs of the one who dogmatically affirms, one may well grant it to him without on that account giving up these propositions, which at least have the interest of reason on their side, something the opponent cannot appeal to at all.

I do not, to be sure, share the opinion that outstanding and thoughtful men (Sulzer, for one) have so frequently voiced whenever they sensed the frailty of the proofs offered up to now: that one may hope some day yet to hit upon self-evident demonstrations for the pair of cardinal tenets of our pure reason—that a God exists, that a life to come awaits. On the contrary, I am certain that it never will. For where is reason to find the ground for synthetic claims of that sort, claims bearing on no objects of experience nor on their intrinsic possibility? Yet it is likewise certain, with apodictic force, that no man shall ever step forth capable of maintaining the opposite with even the faintest semblance, still less dogmatically. For seeing that he could make it out through pure reason alone, he would have to set about proving: that a highest being, that the subject thinking within us as pure intelligence, is impossible. But from what quarter is he to draw the cognitions that would license him to judge so synthetically about things lying past all possible experience? We may accordingly rest wholly unperturbed that anyone will one day prove the contrary to us, and on that score have no call to devise proofs framed by the rules of the schools, being free rather to embrace those propositions that sit quite comfortably alongside our reason's speculative concern in its empirical employment and that furnish, besides, the one and only avenue for reconciling it with the practical concern. For the opponent (who here must not be regarded merely as a critic) we have our non liquet in readiness, which must infallibly disconcert him, while we do not refuse the retortion of it upon ourselves, since we constantly hold in reserve the subjective maxim of reason, which the opponent necessarily lacks, and under whose protection we can look upon all his blows in the air with calm and indifference.

So construed, there is properly no antithetic of pure reason whatever. For its one and only battlefield would have to be looked for within pure theology and pure psychology; yet that terrain sustains no fighter clad in full armor and bearing weapons one would have cause to dread. He can come forward only with mockery or braggadocio, which can be laughed at as child's play. This is a comforting remark that gives reason fresh courage; for on what else would it rely, if it, which alone is called to remove all errors, were itself in disarray, without being able to hope for peace and quiet possession?

Everything that nature itself ordains is good for some purpose. Even poisons serve to overpower other poisons that are generated in our own humors, and hence may not be missing from a complete collection of remedies (Officin). The objections against the persuasions and self-conceit of our merely speculative reason are themselves set as tasks by the nature of this reason, and must therefore have their good determination and purpose, which one must not cast to the winds. Why has providence placed some objects, even though they are bound up with our highest interest, so high above us that we are permitted almost only to encounter them in an indistinct and self-doubted perception, whereby prying glances are more provoked than satisfied? Whether it be useful to venture bold determinations with respect to such prospects is at least doubtful, perhaps even harmful. But always and without any doubt it is useful to set the inquiring as well as the examining reason into complete freedom, so that it may attend to its own interest unhindered, an interest that is promoted just as much by its setting bounds to its insights as by its extending them, and that always suffers when foreign hands interfere in order to steer it, against its natural course, toward forced purposes.

Let your opponent, then, only show reason, and combat him solely with the weapons of reason. For the rest, be untroubled about the good cause (the practical interest), for it is never brought into the game in a purely speculative contest. The quarrel then brings to light no more than a certain antinomy of reason which, resting as it does on reason's own nature, must of necessity be heard out and scrutinized. It cultivates that reason by weighing its object from two sides, and rectifies its judgment by hemming it in. What comes into contention here is not the matter, but the tone. For enough is left you still to speak that language, vindicated in the face of the keenest reason, of a steadfast belief, though you have been forced to relinquish the language of knowledge.

Were one to put the question to the cool-headed David Hume, fashioned as he genuinely was for a balanced judgment: what induced you to sap, by means of painstakingly excogitated scruples, the persuasion so consoling and serviceable to man—that its rational insight reaches as far as the assertion and the determinate concept of a highest being?, he would reply: nothing beyond the design of carrying reason further in its self-knowledge, coupled with a certain resentment at the constraint one would fain lay upon reason, in that one makes much of it while at the same time barring it from a frank avowal of the weaknesses that come to light for it in the examination of itself. Turn instead to Priestley—a man given over wholly to the principles that govern the empirical exercise of reason and disinclined toward any transcendent speculation—and ask what motive forces prompted him to pull down the freedom and immortality of our soul (with him the hope of a life hereafter amounts only to the anticipation of a miraculous re-awakening), two such load-bearing columns of all religion, he who is himself a devout and ardent teacher of religion: he could return no other answer than this—the interest of reason, which suffers loss when one seeks to withdraw certain objects from the laws of material nature, the sole laws that we are able to know and determine with precision. It would look unjust to cry down the latter—who contrives to square his paradoxical thesis with the ends of religion—and to wound a well-meaning man because he can no longer orient himself the moment he has strayed beyond the field of natural science. But this indulgence must fall no less to the equally well-disposed Hume, faultless as regards his moral character, who is unable to forsake his abstracted speculation, persuaded on good grounds that its object resides entirely beyond the confines of natural science, within the realm of pure ideas.

What, then, ought to be done in this situation, above all in view of the peril that appears to menace the public welfare as a result of it? There is nothing more natural, nothing more equitable, than the course you are obliged to adopt in the matter. Just let these people go about it; if they show talent, if they show deep and novel inquiry, in a word, if they only show reason, then reason wins every time. If you resort to other means than those of an unconstrained reason, if you cry high treason and call together the common public, which understands nothing of such subtle elaborations, as it were to help put out a fire, you make yourselves ridiculous. For it is by no means a question of what here works to the advantage or disadvantage of the common good, but only of how far reason may advance in its speculating that abstracts from every interest, and whether anything at all is to be reckoned upon here, or whether it must sooner be surrendered outright to the practical. Instead, therefore, of striking in with the sword, look on rather at this dispute calmly from the secure seat of criticism, a dispute that must turn out laborious for the combatants, entertaining for you, and—given a certainly bloodless outcome—profitable for your insights. For there is something thoroughly preposterous in demanding illumination of reason while dictating to it in advance the side on which its verdict must inevitably fall. Besides, reason is already of its own accord so thoroughly curbed and kept in check by reason that you have not the slightest need to muster armed patrols in order to mount civic resistance against whichever party's alarming preponderance strikes you as perilous. Within this dialectic no triumph arises over which you would have any reason to feel disquiet.

Reason, moreover, is greatly in need of such a dispute, and it would be desirable that it had been conducted earlier and with unrestricted public permission. For all the sooner would a mature critique have come about, upon whose appearance all these quarrels must fall away of themselves, since the disputants would learn to see through the delusion and prejudices that had set them at odds.

There is a certain impurity in human nature that in the end, like everything that comes from nature, must after all contain a predisposition to good ends, namely an inclination to conceal one's true dispositions and to put on display certain assumed ones that one holds to be good and creditable. It is quite certain that human beings, through this propensity both to conceal themselves and to assume an appearance advantageous to them, have not merely civilized themselves, but gradually, to a certain degree, moralized themselves, because no one could penetrate the veneer of decency, respectability, and propriety, and thereby discovered, in the ostensibly authentic instances of the good he beheld about him, a schooling toward his own betterment. But this predisposition to represent oneself as better than one is, and to express dispositions one does not have, serves only, as it were, provisionally to bring man out of crudeness and at least to let him first assume the manner of the good that he knows; for afterward, once the genuine principles have been developed and have passed into one's way of thinking, that falsehood must gradually be vigorously combated, because otherwise it corrupts the heart and does not let good dispositions come up under the choking weed of fair appearance.

It grieves me to detect this identical impurity, dissembling, and hypocrisy even within the pronouncements of the speculative cast of mind, in which, after all, men meet with far fewer impediments, and no gain at all, in disclosing the avowal of their thoughts, as fairness would have them do, in an open and unconcealed way. For what can be more detrimental to insights than to communicate to one another even mere thoughts in falsified form, to conceal doubts that we feel against our own assertions, or to give an air of evidence to proofs that do not satisfy even ourselves? As long, however, as it is merely private vanity that instigates these secret intrigues (which is commonly the case in speculative judgments that have no special interest and are not easily capable of apodictic certainty), the vanity of others resists it with public sanction, and things come at last to where the purest disposition and sincerity would have brought them, though far earlier. But where the common public supposes that subtle reasoners are bent on nothing short of unsettling the very base of public welfare, there it appears not merely in keeping with prudence but even sanctioned, indeed positively praiseworthy, to prop up the good cause by means of specious grounds rather than to concede to its putative adversaries so much as the advantage of pitching our tone down to the moderation of a merely practical conviction and forcing us to own the want of speculative and apodictic certainty. Meanwhile I should think that with the intention of upholding a good cause nothing in the world could well be worse combined than underhandedness, dissimulation, and deceit. That, in weighing up the reasons belonging to a bare speculation, all should go on honestly is assuredly the least one is entitled to ask. Yet could one but reckon with assurance on even this little, then the strife of speculative reason touching those weighty questions concerning God, the immortality of the soul, and freedom would long ago have been decided, or would reach its close before long. So it is that uprightness of disposition frequently runs contrary to how good the cause itself may be, and such a cause has, it may be, more candid and honest adversaries than champions.

I therefore presuppose readers who have no wish to see a just cause upheld by unjust means. With respect to them it is now settled that, on our principles of criticism, provided one attends not to what actually occurs but to what ought in fairness to occur, there can properly be no polemic of pure reason at all. For how are two persons to carry on a quarrel over a thing whose reality neither can exhibit in any actual, or even so much as possible, experience, over whose idea each broods in solitude so as to extract from it something more than mere idea—to wit, the very actuality of the object? By what means do they intend to extricate themselves from the dispute, given that neither is able to render his own case straightforwardly intelligible and certain, and each is confined to assailing and rebutting what the other maintains? For such is the destiny that befalls every assertion of pure reason: reaching past the conditions of any possible experience—outside which no attestation of truth is anywhere to be encountered—while yet being obliged to employ those laws of the understanding earmarked solely for empirical application, laws without which not a single stride in synthetic thought is feasible, these assertions perpetually offer their adversary a weak flank, and each turns the other's exposed side to his own account.

One may look upon the critique of pure reason as the genuine tribunal for all disputes belonging to it; for the critique is not itself caught up in those latter disputes, which bear directly upon objects, but is set in place to fix and pass judgment on the rights of reason as such, in keeping with the founding principles of its first establishment.

Deprived of it, reason stands, so to say, in a natural condition, and has no means of pressing or safeguarding its claims and pretensions save through war. Criticism, on the contrary, which takes all its rulings from the founding statutes of its own establishment, whose authority none can call in question, secures for us the tranquillity of a lawful state, wherein our disputes are to be pursued in no other manner than by litigation. That which puts an end to the feuds in the former condition is a victory boasted of by both parties, upon which there commonly ensues but an unstable peace, imposed by the magistrate who interposes himself between them, whereas in the latter it is the sentence which, striking here at the very wellspring of the disputes, is bound to afford a peace that lasts forever. The interminable quarrels of a purely dogmatic reason likewise drive one at last to seek repose in some critique of this very reason and in a body of legislation founded upon it; exactly as Hobbes contends: that the natural condition is one of wrong and violence, which we are bound of necessity to quit so as to place ourselves under a lawful constraint that alone confines our freedom in such fashion that it may stand together with the freedom of every other and, by that very means, with the common good.

To this freedom there also belongs that of publicly exhibiting for judgment one's thoughts and one's doubts, which one cannot resolve oneself, without being decried on that account as a restless and dangerous citizen. This is already contained in the primordial entitlement of human reason, which acknowledges no arbiter save the common reason of mankind at large, wherein each person holds a vote; and since every betterment our condition admits of must issue from this source, an entitlement of the kind is sacred and must not be pared down. Then, too, it is most imprudent to raise the cry of danger over certain bold claims or brazen assaults directed at those who already enjoy the concurrence of the largest and worthiest portion of the community; for to do so is to lend them a weight they ought by no means to possess. Should word reach me that some extraordinary intellect claims to have argued out of existence the freedom of the human will, the prospect of a life to come, and God's existence, I grow keen to open the book, since I count on his gifts to carry my own insights further. Yet this much I hold beforehand with complete assurance, that he will have achieved none of it; not that I fancy myself already holding unassailable proofs of these weighty propositions, but because transcendental critique, having laid bare to me the whole inventory belonging to our pure reason, has thoroughly persuaded me that, precisely as reason proves wholly unequal to affirmative claims in this domain, so it will command as little—indeed still less—wherewith to advance any negative claim about these questions. For whence is the self-styled freethinker to procure his cognition that, say, no highest being exists? Such a claim falls beyond the province of any possible experience, and hence past the frontier of everything human insight can reach as well. As for the dogmatic champion of the good cause who takes the field against this foe, I would decline to read him altogether, aware ahead of time that he assails his rival's spurious grounds merely to clear a passage for his own—and besides, a commonplace illusion yields nowhere near the stuff for fresh remarks that a strange and cleverly devised one supplies. The religious antagonist, on the other hand, dogmatic after his own fashion, would afford my critique the very occupation it could wish for, and an occasion to correct its principles yet further, with nothing whatever to be dreaded on his behalf.

But the young, who are consigned to academic instruction, ought at the very least to be cautioned against writings of this sort and held back from an early familiarity with such perilous propositions, before their faculty of judgment has ripened—or rather, before the doctrine one means to plant in them has struck firm root—so that it may stoutly withstand every inducement to the reverse, from whatever quarter it may issue?

If matters had to remain with the dogmatic procedure in affairs of pure reason, and the dispatching of opponents had to be genuinely polemical, i.e., so constituted that one entered into combat and armed oneself with proofs for opposed assertions, then to be sure nothing would be more advisable for the moment, while at the same time nothing would prove emptier or more barren in the long run, than to set youth's reason under wardship for a season and to keep it, at least that long, safe from seduction. But if subsequently either curiosity or the fashionable tone of the age plays such writings into their hands: will that youthful persuasion then still hold up? One who carries nothing but dogmatic arms to fend off his opponent's assaults, and has no idea how to unfold the concealed dialectic residing every bit as much in his own bosom as in his rival's, watches specious grounds that boast the charm of novelty rise up against specious grounds that possess it no longer, and that rather awaken the suspicion of a youthful credulity turned to abuse. He fancies there is no surer way to prove himself grown past the nursery's tutelage than to override those kindly meant warnings; and, inured to dogmatism, he swallows in deep draughts the poison that dogmatically ruins his principles.

Precisely the reverse of what is counseled here ought to take place in academic teaching, though naturally only where a searching grounding in the critique of pure reason has first been laid down. For if one is to set its principles to work as early as may be and to exhibit their adequacy against the most formidable dialectical semblance, it is altogether requisite to aim the assaults so dreadful to the dogmatist at his own reason—feeble as yet, but illuminated by critique—and to let him try his hand at testing the adversary's baseless claims one by one against those principles. It can be no difficulty at all for him to dissolve them into sheer vapor, and thus he feels early on his own power, against such harmful illusions, which in the end must lose all semblance for him, to secure himself completely. Now although the very same blows that strike down the enemy's edifice must be just as ruinous to his own speculative construction, should he perhaps think to erect one: yet he is entirely untroubled about this, since he has no need at all to dwell in it, but still has before him a prospect into the practical field, where he can with good ground look for firmer soil upon which to raise his reasonable and wholesome system.

And so, in the end, no genuine polemic exists within the field of pure reason. The two sides alike are shadow-fencers grappling with their own shadows, for they venture past nature, where nothing lies ready for their dogmatic clutch that could be grasped and held fast. They may fight to their heart's content; the shades they cleave asunder knit themselves whole again in a moment, after the manner of Valhalla's heroes, ready to divert themselves afresh in bloodless bouts.

But there is also no admissible skeptical use of pure reason, which one might call the principle of neutrality in all its disputes. To set reason at odds with its own self, to furnish it with arms on either side, and thereupon to watch its fiercest clash with unruffled derision, makes a poor showing when viewed dogmatically, and carries about it the look of a gloating and malignant temper. If, however, one considers the invincible delusion and the boasting of the sophists, who will let themselves be moderated by no criticism, then there really is no other counsel than to set against the braggadocio on the one side another that rests on the very same rights, so that reason may at least be given pause by the resistance of an enemy, in order to cast some doubt on its pretensions and to give criticism a hearing. But to let matters rest entirely with these doubts and to make it one's aim to recommend the conviction and confession of one's ignorance not merely as a remedy against dogmatic self-conceit, but at the same time as the way to bring the conflict of reason with itself to an end, is an entirely futile design and can by no means be suited to procuring for reason a state of repose, but is at most only a means of awakening it from its sweet dogmatic dream in order to draw its condition into more careful examination. Since, however, this skeptical manner of extricating oneself from a vexatious affair of reason seems to be, as it were, the short road to attaining a lasting philosophical repose, or at any rate the highway that those gladly take who imagine they lend themselves a philosophical air through a scornful disdain for all investigations of this order, I judge it needful to set out this manner of thought in the light peculiar to it.

On the impossibility of a skeptical satisfaction of pure reason in conflict with itself

The awareness of my own ignorance—unless that ignorance is at the same time recognized as necessary—is not something that should terminate my investigations, but is rather the genuine cause for arousing them. Ignorance of any sort pertains either to things or to the determination and limits of my cognition. Now if this ignorance happens to be contingent, then it must drive me on—in the first case, to pursue the things (objects) dogmatically; in the second, to pursue the limits of my possible cognition critically. That my ignorance, however, is unconditionally necessary, and hence releases me from any further inquiry, is not something that can be established empirically, out of observation, but only critically, by fathoming the earliest wellsprings of our cognition. The boundary-determination of our reason, accordingly, can be accomplished only on grounds that hold a priori; but its restriction—which amounts to a cognition, albeit an indeterminate one, of an ignorance that can never be entirely removed—admits also of being cognized a posteriori, by way of whatever, amid all our knowing, still remains left for us to know. That cognition of one's own ignorance which is possible solely by means of a critique of reason itself thus counts as science, whereas the latter is merely perception, and of it there is no saying how far the conclusion drawn from it may reach. Were I to picture the earth's surface to myself as a plate (in keeping with the sensible appearance), I would have no way of knowing how far it reaches. Yet experience does teach me the following: that no matter where I arrive, I invariably behold a space around me into which I might proceed still further; consequently I come to know the bounds of my geography as it actually stands on each occasion, but not the limits of every possible mapping of the earth. But once I have in fact progressed far enough to know that the earth is a globe and its surface the surface of a globe, then even from a small portion of it—say, the extent of a single degree—I am able to determine the diameter, and by means of it the complete delimitation of the earth, that is, its outer surface, and to cognize this according to principles that are a priori; and though I remain ignorant regarding the objects that this surface may hold, I am not ignorant regarding the compass it embraces, its magnitude and its bounds.

The totality of all possible objects for our cognition strikes us as a level surface furnished with its apparent horizon—that is, with what encompasses the whole extent of it—and this we have named the rational concept of unconditioned totality. To reach this totality empirically is out of the question, and every attempt to fix it a priori by a certain principle has proven futile. In the meantime, every question that our pure reason raises is nonetheless directed at whatever might lie beyond this horizon, or at most along its bounding line.

David Hume, that celebrated thinker, was one such geographer of human reason, and he supposed that he had adequately dealt with all those questions at a stroke by banishing them beyond reason's horizon—a horizon that he was nevertheless incapable of determining. He lingered above all over the principle of causality, and observed of it—quite correctly—that its truth (indeed, not even so much as the objective validity that belongs to the concept of an operative cause in general) rests upon no insight whatsoever, that is, upon no a priori cognition; and that, accordingly, what makes up its whole standing is not in the slightest the necessity of this law, but a merely general usefulness of it in the course of experience, together with a subjective necessity springing from that usefulness, which he terms habit. From the inability of our reason, then, to put this principle to any use that would carry beyond all experience, he drew the conclusion that all of reason's pretensions to reach past the empirical are null and void.

A procedure of this sort—one that submits the Facta of reason to scrutiny and, as circumstances warrant, to rebuke—may be termed the censure of reason. There is no doubting that such censure leads unfailingly to doubt directed against every transcendent employment of the principles. This, however, is merely the second step, one that by no means yet brings the labor to completion. The first step in the affairs of pure reason, the one distinctive of its childhood, is dogmatic. The second step just named is skeptical, and it bespeaks the wariness of a power of judgment grown shrewd through experience. But a third step is now required as well—one that falls to none but a matured and virile power of judgment, resting upon maxims that are firm and vindicated in their universality: namely, to submit to appraisal not reason's Facta but reason itself in the whole of its capacity and its aptitude for pure cognitions a priori; and this is not the censure but the critique of reason, through which not merely bounds but the determinate limits of reason are established—not merely ignorance in this or that part, but with respect to all possible questions of a certain sort, and that too not merely by conjecture but by proof from principles. Skepticism, then, is a place of rest for human reason, where it may take stock of its dogmatic wanderings and sketch out the terrain in which it stands, so as thereafter to choose its route with greater assurance—but it is no place of habitation for settled residence; for such a residence can be met with only in a complete certainty, whether of the objects themselves as cognized, or of the limits within which our every cognition of objects lies enclosed.

Our reason is by no means some plane spread out to an indeterminable breadth, whose bounds we discern only in a rough, general way; rather, it has to be likened to a sphere, the radius of which can be ascertained from the curvature of the arc across its surface (the nature of synthetic propositions a priori), and from which, moreover, its content and its delimitation can be stated with assurance. Beyond this sphere (the field of experience) nothing is an object for it; indeed, even questions concerning supposed objects of that kind touch only on subjective principles governing a thoroughgoing determination of the relations that may arise among the concepts of the understanding within this sphere.

We do in fact possess synthetic cognition a priori, as the principles of the understanding, which run ahead of experience, make plain. Now should someone find himself utterly unable to render the possibility of these cognitions comprehensible, he may well at the outset doubt whether they really do dwell in us a priori; but he is not yet in a position to declare them impossible by the mere powers of the understanding, nor to write off as null every step that reason takes along their guiding thread. He can say only this: could we but discern the origin and the genuineness of these cognitions, we should then be able to settle the compass and the limits of our reason; yet before that has come to pass, every assertion of the latter is ventured blindly. And in just this manner a pervasive doubt regarding all dogmatic philosophy—which pursues its way without any critique of reason itself—would be perfectly well grounded; yet this affords no reason to deny reason such an advance altogether, supposing that advance were made ready and made secure by a sounder laying of foundations. For, to begin with, every concept—indeed, every question that pure reason sets before us—lies not in experience at all, but once more within reason itself, and must therefore be capable of resolution and of being grasped with respect to its validity or its correctness. Neither are we entitled to turn these problems away under cover of our own incapacity—as though their resolution truly lay in the nature of things—and to refuse them any further inquiry, given that reason has, within its own womb alone, brought forth these very ideas, and is on that account answerable for their validity or their dialectical semblance.

All skeptical polemic is in truth aimed only at the dogmatist—who, without lodging any mistrust in his original objective principles, that is, without critique, proceeds gravely on his way—and its sole purpose is to throw him off his reckoning and bring him around to self-knowledge. Taken by itself, it settles nothing whatever concerning what we know and, conversely, what we cannot know. All the miscarried dogmatic ventures of reason are Facta, and to subject these to censure is always of use. This, however, can settle nothing about the expectations of reason—about its hoping for, and staking claims to, a happier outcome of its future exertions; and so bare censure can never bring to a close the quarrel over the rightful entitlements of human reason.

Since Hume is perhaps the most brilliant among all the skeptics, and beyond contradiction the foremost as regards the influence that the skeptical procedure is capable of exerting upon the awakening of a searching examination of reason, it is well worth the trouble to lay out—so far as befits my aim—the course of his reasonings and the wanderings of a man so discerning and so worthy of esteem, wanderings that had, after all, set out upon the track of truth.

Hume may perhaps have had it in his thoughts—though he never brought it to full development—that in a certain class of judgments we reach out beyond our concept of the object. Judgments of that kind I have called synthetic. As for how I might, by means of experience, pass beyond the concept I have hitherto possessed, there is nothing here to give one pause. Experience is itself a synthesis of this sort among perceptions, one that enlarges the concept I possess through a given perception by means of further perceptions that come to be added to it. But we take ourselves to be capable, a priori as well, of passing beyond our concept and enlarging our cognition . This we undertake either by means of the pure understanding, with regard to what can at the least be an object of experience, or else even by means of pure reason, with regard to such properties of things—or indeed the existence of such objects—as can never make their appearance in experience. Our skeptic failed to draw this distinction between the two kinds of judgment, as he really ought to have, and flatly took this enlargement of concepts out of their own resources—the self-parturition, so to speak, of our understanding (reason included), unfertilized by any experience—to be impossible, and thus took all the ostensible principles of it that are a priori to be figments, and concluded that they amount to nothing more than a habit arising out of experience and its laws, hence to merely empirical rules, contingent in themselves, to which we impute a spurious necessity and universality. In support of this odd proposition, however, he leaned upon the universally acknowledged principle governing the relation of cause to effect. For, since no faculty of the understanding can carry us from the concept of one thing to the existence of another that would thereby be given as universal and necessary, he supposed himself able to conclude from this that, apart from experience, we possess nothing that could enlarge our concept and warrant us in any such judgment that expands itself a priori. That sunlight, in illuminating the wax, should at once melt it while it hardens clay—this no understanding could guess from the concepts we previously held of these things, far less infer by way of a law, and only experience is able to instruct us in such a law. In the transcendental logic, by contrast, we saw that, although we can indeed never pass immediately beyond the content of the concept given to us, we are nevertheless able—wholly a priori, yet in reference to a third thing, namely possible experience, and so a priori after all—to cognize the law of its connection with other things. Thus, when wax that was formerly solid melts, I can cognize a priori that something must have gone before (the sun's warmth, say) upon which, by a constant law, this melting ensued—even though, without experience, I could cognize neither the cause from the effect nor the effect from the cause in any determinate fashion a priori and without experience's instruction. He thus wrongly inferred, from the contingency of our determining according to the law, the contingency of the law itself; and the stepping-out from the concept of a thing toward possible experience—which takes place a priori and constitutes that concept's objective reality—he mistook for the synthesis of objects belonging to actual experience, a synthesis that is of course invariably empirical; by this means, however, he converted a principle of affinity, which is seated in the understanding and pronounces a necessary connection, into a rule of association, such as is encountered solely within the reproductive imagination and can exhibit only contingent connections, never objective ones.

The skeptical wanderings of this otherwise supremely acute man, however, arose above all from a shortcoming he nonetheless had in common with all dogmatists—namely, that he did not systematically take in, at one view, all the modes of the understanding's synthesis a priori. For in that case—to say nothing of the rest here—he would have discovered, for instance, the principle of persistence to be one of the same kind, anticipating experience every bit as much as the principle of causality does. By that route he could likewise have marked out determinate limits for the understanding as it expands itself a priori, and for pure reason. But since he merely restricts our understanding without bounding it—bringing about a general mistrust, yet no determinate acquaintance with the ignorance that is for us unavoidable; since he hauls certain principles of the understanding before the censor without ever setting this understanding, in the whole of its capacity, upon the assaying-scales of critique; and since, having denied it what it genuinely cannot achieve, he presses on and contests its every capacity for self-expansion a priori, notwithstanding that he never brought this whole capacity to appraisal—there befalls him just what invariably fells skepticism: namely, that he is himself thrown into doubt, inasmuch as his objections rest merely upon Factis, which are contingent, and not upon principles capable of effecting a necessary renunciation of the entitlement to dogmatic assertions.

Because he likewise draws no distinction between the well-grounded claims of the understanding and reason's dialectical presumptions—against which, after all, his attacks are principally aimed—reason, whose wholly characteristic impetus is here not disturbed in the slightest but merely impeded, feels that the room for its own expansion has not been sealed off, and can never be turned aside altogether from its endeavors, however much it gets pinched here and there. For against attacks one girds oneself for a counterdefense, and plants one's head all the more rigidly upon the matter, so as to force one's demands through. A thorough reckoning, however, of the whole of its capacity, and the conviction that thereby arises of the certainty of a modest holding amid the vanity of loftier claims, removes all strife and prompts one to settle, peaceably, for a restricted but indisputable possession.

Against the uncritical dogmatist—who has taken no measure of the sphere of his understanding, and has thus never determined the limits of his possible cognition by principles, and who accordingly does not know beforehand how much lies within his power, but proposes to discover it through mere trial—these skeptical assaults are not merely dangerous but downright ruinous to him. For should he be caught out on so much as a single assertion that he cannot vindicate, whose semblance, moreover, he is unable to develop from principles, then the suspicion spreads to all of them, however persuasive they may in other respects always seem.

And so the skeptic is the disciplinarian who schools the dogmatic reasoner toward a sound critique both of the understanding and of reason itself. Once he has reached that point, he need dread no further assault; for he then marks off his own possession from whatever lies wholly beyond it, upon which he raises no claim and over which, accordingly, he cannot become entangled in disputes. The skeptical procedure, therefore, while in itself unsatisfying for the questions of reason, is nonetheless a form of preparatory practice, apt to rouse reason's wariness and to point it toward thorough means by which it can be secured in its rightful possessions.

Section 3. The discipline of pure reason in respect of hypotheses

Since, through the critique of our reason, we finally come to know at least this much—that in its pure and speculative use we are in fact capable of knowing nothing at all: ought it not, for that very reason, to throw open a wider field to hypotheses, seeing that we are at any rate allowed to invent and to opine, if not indeed to assert?

Where imagination is not to rave but is instead to invent beneath the strict oversight of reason, there must always be something settled in advance as wholly certain, neither fabricated nor a bare opinion, and that something is the possibility of the object itself. It is then quite legitimate, as regards the object's actuality, to fall back upon opinion—which, however, if it is not to hang in the air, must be linked, as a ground of explanation, to what is genuinely given and therefore certain, and only then earns the name of a hypothesis.

Now since we are unable to form even the faintest concept a priori of the possibility of dynamical connection, and since the category of the pure understanding is of no use for inventing such a thing, but only for understanding it wherever it turns up within experience: we cannot, in conformity with these categories, originally excogitate so much as a single object endowed with some novel character not specifiable on empirical grounds, and lay it down as the basis of a permissible hypothesis; for that would amount to slipping empty chimeras of the brain under reason in place of concepts of real things. Thus one is not at liberty to think up any new original forces whatever—e.g. an understanding equipped to intuit its object without the senses, or a force of expansion dispensing with all contact, or a novel species of substances, e.g. one that would be present in space without impenetrability, and consequently no community of substances distinct from every kind that experience affords us, no mode of presence other than in space, no persistence other than in time alone. In a word: our reason is capable only of employing the conditions under which experience is possible as conditions under which things themselves are possible, and in no way of fashioning conditions of its own, as it were, in complete independence of these, since concepts of that kind, free of contradiction though they be, would all the same remain devoid of any object.

The concepts of reason, as already stated, are nothing more than ideas and possess, to be sure, no object in any experience—yet they do not on that account denote objects that are invented and at the same time assumed to be possible. They are entertained in a merely problematic manner, so that upon them (treated as heuristic fictions) regulative principles may be founded for the systematic use of the understanding across the field of experience. Should one abandon this, they become mere entities of thought, whose possibility admits of no proof and which cannot, therefore, be laid down as the basis for explaining actual appearances by way of a hypothesis. To think the soul as something simple is entirely allowable, the aim being to posit, in keeping with this idea, a complete and necessary unity of all the mind's powers—even where it cannot be discerned in concreto—as the principle by which we appraise its inner appearances. But assuming the soul to be a simple substance (a transcendent concept) would yield a proposition that is not merely indemonstrable (as a number of physical hypotheses are) but reckless as well, arbitrary and blind, since the simple can turn up in no experience at all, and, if substance is here taken to mean the abiding object of sensible intuition, the very possibility of a simple appearance eludes all comprehension. Beings that are purely intelligible, or purely intelligible properties belonging to the things of the sensible world, cannot, with any legitimately grounded warrant of reason, be adopted as opinion—though, seeing that we possess no concepts of their possibility or impossibility, they can equally not be dogmatically disavowed by appeal to some presumed superior insight.

In explaining given appearances one is entitled to cite no things and no grounds of explanation beyond those already tied to the given ones in accordance with laws of appearance that are already familiar. A transcendental hypothesis, one that would press a bare idea of reason into service for explaining the things of nature, would on that account amount to no explanation whatever, since what one fails to understand adequately from familiar empirical principles would then be accounted for by something one understands not at all. Besides, the principle of such a hypothesis would in truth serve merely to appease reason, contributing nothing to the advancement of the understanding's employment in respect of its objects. Order and purposiveness within nature must, once again, receive their explanation from grounds drawn from nature herself and in conformity with natural laws, and in this domain even the most extravagant hypotheses, so long as they remain physical, prove more bearable than a hyperphysical one—that is, an appeal to a divine author posited to serve this end. For that would be a principle of indolent reason (ignava ratio)—to bypass in one stroke every cause whose objective reality, at least as to its possibility, we might yet come to learn through ongoing experience, merely to settle down in a bare idea that suits reason's convenience so well. But as concerns the absolute totality of the ground of explanation within the series thereof, this can raise no obstacle with respect to the objects of the world, since, these being nothing but appearances, nothing consummated in the synthesis of the series of conditions may ever be expected of them.

Transcendental hypotheses belonging to the speculative use of reason, together with a license to resort, at a pinch, to hyperphysical grounds of explanation in order to compensate for the absence of physical ones, cannot be conceded at all—partly because reason is not thereby carried any further but on the contrary severs the whole onward course of its use, and partly because such a license would in the end have to rob it of every fruit that the cultivation of its own proper soil, namely experience, might yield. For should the explanation of nature grow difficult for us at this point or that, a transcendent ground of explanation stands perpetually ready to hand, one that spares us that labor of inquiry, and our search terminates not in insight but in the utter unintelligibility of a principle already so contrived beforehand that it could not but contain the concept of the absolutely first.

The second thing demanded, if a hypothesis is to deserve acceptance, is that it suffice for determining a priori the consequences that are given. Whenever, to that end, one finds oneself driven to conjure up auxiliary hypotheses, they carry with them the suspicion of sheer fiction, since each of them severally calls for precisely the same warrant that the underlying thought itself stood in need of, and can therefore supply no trustworthy witness. Granting the presupposition of a cause unlimited in its perfection, there is admittedly no shortage of grounds for explaining every purposiveness, order, and magnitude to be met with in the world; that cause, nonetheless, in view of the deviations and evils that present themselves—at least by our concepts—stands in need of yet further hypotheses if it is to be salvaged against these as objections. Should the simple self-subsistence of the human soul, laid down as the ground of its appearances, come under attack from the difficulties raised by phenomena akin to the alterations of matter (its growth and diminution), then fresh hypotheses have to be summoned to its aid—hypotheses not, indeed, without a semblance of truth, yet destitute of all credentials save the one lent them by the opinion adopted as the chief ground , an opinion on whose behalf they are all the same meant to plead.

If the rational assertions cited here by way of illustration (the incorporeal unity of the soul and the existence of a supreme being) are meant to hold not as hypotheses but as dogmas demonstrated a priori, then they are simply not under discussion. In such an event, however, one had better make sure that the proof carries the apodictic certainty of a demonstration. For wishing to make the actuality of such ideas merely probable is a preposterous design, on a par with proposing to establish a theorem of geometry by nothing more than probability. Reason cut off from all experience is able to cognize everything solely a priori and as necessary, or else not at all; its judgment, accordingly, is never an opinion, but consists either in withholding every judgment or in apodictic certainty. Opinions, and judgments of probability regarding what pertains to things, can arise only as grounds explaining what is actually given, or as consequences—following empirical laws—of that which lies at the basis as actual, and thus only within the series of the objects of experience. Beyond this field, to opine is as much as to toy with thoughts—unless it were that one merely held the opinion that, along some insecure route of judgment, one might perhaps come upon the truth.

Yet even though, in questions merely speculative belonging to pure reason, hypotheses find no place as a foundation on which to erect propositions, they remain wholly permissible for the mere purpose of defending such propositions should the need arise—that is , not in a dogmatic but rather in a polemical use. By defense, though, I understand not the piling up of further grounds of proof for one's assertion, but simply the thwarting of the adversary's specious insights, which are meant to do damage to the proposition we have put forward. Now every synthetic proposition arising from pure reason carries with it this distinctive feature: that whoever affirms the reality of certain ideas can never command enough knowledge to render his proposition certain, while the adversary on the opposing side is equally unable to muster the knowledge required to affirm its contrary. Such parity in the fortune allotted to human reason confers no advantage on either party where speculative cognition is concerned, and precisely here lies the true arena of quarrels that admit of no settlement. It will, however, be shown in what follows that, as regards the practical employment, reason does possess a right to assume something which, within the province of bare speculation, it could by no means be authorized to presuppose absent adequate grounds of proof, since presuppositions of that sort all diminish the completeness of speculation—a completeness about which the practical interest troubles itself not in the slightest. There, accordingly, it holds a possession whose legitimacy it is not required to prove, and for which, in fact, it could furnish no proof either. The opponent, then, is the one obliged to furnish proof. Yet since this adversary, aiming to establish the non-being of the disputed object, knows just as little of it as the first party who affirms its actuality: an advantage here declares itself on the side of whoever advances something as a presupposition necessary on practical grounds (melior est conditio possidentis). For he is free, in a kind of self-defense, to press into service on behalf of his good cause the very means his adversary directs against it, namely hypotheses, serving not in the least to reinforce the proof of his position, but only to make plain that the adversary grasps far too little of what the quarrel is about to preen himself on any superiority of speculative insight where we are concerned.

Within the domain of pure reason, then, hypotheses are licensed solely as instruments of warfare—not to establish a right by their means, but merely to defend one. The adversary, however, is one we must in this case invariably look for inside ourselves. For speculative reason, in its transcendental use, is dialectical in itself. Those objections we might have cause to dread reside within us. We are obliged to hunt them out, as one hunts down old claims that yet never fall under any statute of limitations, so as to build a lasting peace upon their destruction . Any outward calm is merely a semblance. The seed of these contestations, rooted in the very nature of human reason, has to be eradicated ; yet how are we to eradicate it unless we allow it liberty, and indeed even feed it, so that it may put forth its foliage, reveal itself by that means, and then be uprooted altogether? So think up for yourselves objections that no adversary has yet lit upon, and go so far as to hand him weapons, or concede to him the most advantageous ground he could ever desire! There is in all this nothing whatever to be dreaded, but much rather to be hoped—namely, that you will procure for yourselves a possession never again to be contested throughout all time to come.

To your full array of arms there now also belong the hypotheses of pure reason, which, though no better than leaden weapons (steeled by no law of experience), can nonetheless always accomplish as much as any that an adversary might wield against you. So if, opposing the soul's immaterial nature—assumed on some other, non-speculative ground and exempt from all bodily alteration—the difficulty arises that experience nevertheless appears to demonstrate the heightening no less than the disordering of our powers of mind to be nothing more than diverse modifications of our organs: you may blunt the force of that demonstration by supposing our body to be merely the foundational appearance upon which, as its condition, the whole capacity of sensibility and with it all thought rests in the present state (during life). Departure from the body would mark the termination of this sensible use to which your cognitive power is put, and the inauguration of its intellectual use. The body, on this view, would not be what causes thought, but only a condition that restricts it, so that, while it must count as promoting sensible and animal life, it must all the more count as a hindrance to pure and spiritual life; and the reliance of the one upon the body's constitution would establish nothing about the reliance of life in its entirety upon the condition of our organs. You are able, however, to press yet further and even to discover fresh doubts, whether not yet raised at all or not pushed far enough.

The contingency of procreations—which in human beings, as in creatures devoid of reason, hangs upon opportunity, and moreover often upon sustenance, upon governance with its moods and caprices, indeed often even upon vice—poses a formidable difficulty against the opinion of a persistence, reaching out into eternities, of a creature whose life first got under way amid circumstances so inconsequential and so utterly abandoned to our freedom. So far as the persistence of the whole kind (here upon earth) goes, the difficulty in respect of it weighs but little, since the chance operative in the single case is none the less subject to a rule in the aggregate; but to look, in respect of every individual, for so potent an effect from causes so slight does certainly seem precarious. In opposition to this, however, you are able to marshal a transcendental hypothesis: that all life, properly speaking, is only intelligible, in no way subordinate to the alterations of time, having neither commenced with birth nor destined to close with death; that this life amounts to no more than an appearance—i.e. a sensible representation of the pure spiritual life—and that the entire sensible world is but an image hovering before our present mode of cognition, one that, dreamlike, possesses in itself no objective reality; that, were we to intuit both things and our own selves as they are, we should find ourselves set within a realm of spiritual natures, our one genuine community with which neither took its start through birth nor will terminate through the death of the body (these being mere appearances), etc.

Now although, of everything we here advance hypothetically to fend off the assault, we neither know the slightest part nor seriously maintain it—the whole being not so much as an idea of reason, but merely a concept devised for the sake of counter-defense—we proceed in all this quite rationally, inasmuch as, to the adversary who fancies he has exhausted every possibility, passing off the want of its empirical conditions falsely as a proof that what we believe is utterly impossible, we do no more than show him: that he is as little able, by mere laws of experience, to span the entire range of things possible in themselves, as we are able, beyond experience, to gain anything for our reason in a well-grounded fashion. Whoever puts such hypothetical counter-remedies in place against the presumptions of the brazenly denying adversary must not be supposed to want to appropriate them as his own genuine opinions. He lets them go the moment he has disposed of the adversary's dogmatic self-conceit. For however modest and restrained it may appear when someone conducts himself, in respect of others' assertions, in a merely refusing and negating way, the pretension is nonetheless, the moment he sets out to press these objections of his as proofs of the contrary, no less haughty and self-important than had he sided with the affirming party and taken up its assertion.

From all this it becomes evident that, in reason's speculative employment, hypotheses possess no validity as opinions taken in their own right, but hold good only in relation to the opposing transcendent pretensions set against them. For stretching the principles that govern possible experience out over the possibility of things as such is no less transcendent than claiming objective reality for concepts of a kind whose objects can be met with nowhere save beyond the limit of all possible experience. Whatever pure reason pronounces assertorically must—as with everything reason cognizes—be necessary, or it is nothing whatsoever. Consequently it harbors, in truth, no opinions at all. The hypotheses under discussion, though, are nothing but problematic judgments which at any rate cannot be refuted, even if, to be sure, nothing can prove them, and are therefore strictly private opinions, of which one nonetheless cannot properly divest oneself (even for the sake of inner calm) in the face of scruples that stir within. In that character, however, they must be kept, and one must scrupulously prevent them from coming forward as self-authenticated and possessed of any absolute validity, thereby drowning reason beneath fabrications and delusions.

Section 4. The discipline of pure reason in respect of its proofs

What sets the proofs of transcendental and synthetic propositions apart from all other proofs of a synthetic cognition a priori is the following peculiarity: in them reason is not permitted to address the object outright through its concepts, but has first to demonstrate a priori both that the concepts are objectively valid and that their synthesis is possible. This is no mere rule of prudence that one happens to need; it goes to the very essence of the proofs and to whether they are possible at all. Should I have to pass beyond the concept of an object a priori, that cannot be done without a particular clue that lies outside the concept in question. In mathematics this guiding clue is a priori intuition, which steers my synthesis, so that every inference may be drawn there straight from pure intuition. Within transcendental cognition, as long as nothing but concepts of the understanding is at stake, the standard that serves this purpose is possible experience. The proof, that is, does not demonstrate that a given concept (say, of what happens) points straightaway to a further concept (that of a cause)—for a transition of that sort would be an unwarrantable leap—but demonstrates instead that experience, and with it the object of experience, could not exist at all were such a linkage absent. So the proof had, in one and the same move, to make evident that one can reach synthetically and a priori a certain cognition of things which lay nowhere in the concept one had of them. Lacking such vigilance, proofs go careering off wildly across open country, like a flood that has broken its banks, driven to whatever point the slope of some concealed association chances to carry them. A show of conviction resting on association's subjective causes, and mistaken for insight into a natural affinity, can in no way balance out the reservations that must, in all fairness, arise in the face of such hazardous steps. This is why every effort to prove the principle of sufficient reason has, as the connoisseurs generally concede, come to nothing; and until transcendental critique arrived on the scene, thinkers—unable, after all, to give the principle up—chose rather to fall back defiantly on sound common sense (a recourse that is invariably a sign that reason's cause is lost) than to hazard fresh dogmatic proofs.

If, however, the proposition to be proved happens to be a claim of pure reason, and if I mean, through mere ideas no less, to venture past my empirical concepts, then that proof would need, still more urgently, to carry within it the vindication of such a synthetic step (assuming one were possible) as an indispensable condition of its power to prove anything. So, no matter how convincing the alleged proof of the simplicity of our thinking substance may look when drawn from the unity of apperception, one reservation blocks it irremovably: since absolute simplicity is, after all, not a concept that could be tied straight to a perception but has to be reached merely as an inferred idea, one cannot in the least see how the bare consciousness which is—or can at any rate be—contained in all thinking (granting that, to that degree, it is a simple representation) is supposed to deliver me over to the consciousness and cognizance of a thing in which thought alone can reside. For when I picture to myself my body's force in motion, then, so far as that goes, it is an absolute unity for me, and my representation of it is simple; and this lets me express it, too, by the movement of a single point, since here its volume contributes nothing and, with no loss of force, may be conceived as tiny as one pleases—hence as seated in a point as well. Even so, I shall not draw from this the conclusion that a body, when nothing but its moving force is given to me, may be conceived as a simple substance merely because the representation of it leaves aside every magnitude of spatial content and is on that account simple. And it is just here—in the fact that the simple met with in abstraction differs completely from the simple met with in the object, and that the I, which taken the first way holds no manifold at all within itself, taken the second way, where it stands for the soul itself, may prove a highly composite concept, one that holds and marks out a great many things under itself—that I catch sight of a paralogism. But to sense this in advance (for absent some such preliminary surmise nobody would ever grow suspicious of the proof), it is indispensable to keep constantly at hand a criterion for whether synthetic propositions of this kind—ones meant to prove more than experience is able to yield—are so much as possible: a criterion that amounts to this, that the proof proceed not straight to the predicate one is after, but solely by way of a principle for expanding our given concept a priori up to ideas and giving those ideas reality. Where this caution is unfailingly observed, where, prior to any attempt at the proof, one first prudently deliberates with oneself about how, and on what grounds of hope, such an expansion by pure reason might be looked for, and from what source, in a case of this kind, one proposes to fetch insights that admit neither of being unfolded from concepts nor of being anticipated with reference to possible experience—there one may be spared a great deal of laborious yet barren toil, since one then asks of reason nothing that manifestly outruns its power, or rather brings reason, which in the grip of its speculative itch for expansion submits reluctantly to any limit, under the discipline of restraint.

The first rule, accordingly, runs thus: undertake no transcendental proofs until you have thought through, and given an account to yourself of, the source from which you propose to draw the principles you plan to raise them upon, and the right by which you may look to those principles for a sound outcome of your inferences. Where they are principles of the understanding (causality, say), it is pointless to reach ideas of pure reason by their means, for such principles are valid only of objects of a possible experience. Where they are meant to be principles drawn from pure reason, once again the whole effort is wasted. Reason does possess principles of that kind, true enough, but taken as objective principles they are dialectical throughout, and can hold good, if at all, only in the manner of regulative principles governing the systematically connected empirical use. Yet where supposed proofs of this description are already before you, meet the fraudulent conviction with the non liquet of your seasoned power of judgment; and even if you cannot as yet see through the deception it works, you are still fully entitled to require a deduction of the principles it puts to use—a deduction that can never be supplied to you if those principles are alleged to issue from pure reason alone. And so you are not even obliged to trouble yourselves with unfolding and rebutting every baseless show one by one; you may instead throw out, in whole heaps and all at once, the entire dialectic, inexhaustible in its tricks, at the bar of a critical reason that insists on laws.

The second distinctive trait of transcendental proofs is this: for every transcendental proposition there is but a single proof to be had. If my inference is to proceed not from concepts but from the intuition answering to a concept—whether a pure intuition, as in mathematics, or an empirical one, as in natural science—then the intuition put at the basis furnishes me with a manifold of material for synthetic propositions that I can combine in more than one fashion and, being free to begin from more than one starting point, can reach the same proposition along several paths.

Now any transcendental proposition whatever sets out from one concept only, and pronounces the synthetic condition under which the object is possible according to that concept. There can accordingly be no more than one ground of proof, for apart from this concept nothing else is present through which the object might be determined, so that the proof can hold nothing beyond the determining of an object as such according to this concept—itself, again, only one. Thus in the transcendental analytic we derived the principle that whatever happens has a cause from the one and only condition of the objective possibility of a concept of what happens at all, namely: that an event's determination in time—and hence that event, as something belonging to experience—could not be, unless it were placed under a dynamical rule of this kind. And this, too, is the sole ground of proof there can be; for the represented event acquires objective validity—that is, truth—only in that, through the causal law, an object comes to be determined for the concept. Other proofs of the principle have of course been tried—one from contingency, for instance—but examine that one in broad daylight and no token of contingency turns up except happening itself, i.e., an existence ahead of which there runs a non-being of the object, so that one lands right back at the identical ground of proof. When the proposition to be established is that whatever thinks is simple, one does not linger over the manifold in thinking, but keeps solely to the concept of the I, itself a simple concept and the one back to which all thought is traced. The transcendental proof of God's existence stands on just the same footing: it turns solely on the reciprocability of the concepts of the most real and the necessary being, and admits of being looked for in no other quarter.

Through this cautionary observation, the critique of reason's assertions is narrowed down to very small compass. Wherever reason transacts its affairs by way of bare concepts, one proof and one alone is possible—if, that is, any proof is possible at all. So, once you observe the dogmatist stepping forward with ten proofs in hand, you may confidently conclude that he has not a single one. For, possessed of one that demonstrated apodictically—as, in matters of pure reason, it is bound to—what use would he have for the others? His purpose is nothing but that of the well-known barrister before parliament: this argument suits the one man, that argument the next—the object being to turn the frailty of his judges to account, judges who, rather than enter deeply into things and eager to have done with the affair, snatch at whatever first catches their eye and rule on that basis.

The third rule peculiar to pure reason, once it is placed under a discipline touching transcendental proofs, is that its proofs may at no time be apagogic but must always be ostensive. In every sort of cognition the direct or ostensive proof is the one that unites conviction of the truth with an insight into where that truth springs from; the apagogic proof, by contrast, is able to yield certainty, yet not an understanding of the truth as regards how it hangs together with the grounds that make it possible . The apagogic sort are therefore more of a stopgap than a procedure that meets all of reason's purposes. Still, they hold one edge in self-evidence over the direct proofs: a contradiction always brings more clarity to the representation than the finest connection can, and thereby draws nearer to the intuitiveness of a demonstration.

The genuine reason for resorting to apagogic proofs across the various sciences is presumably the following. When the grounds from which some cognition is to be derived lie either too various or too deeply buried, one puts it to the test whether the cognition might not be gotten at by its consequences instead. Now the modus ponens—arriving at a cognition's truth from the truth of its consequences—would be legitimate only where every possible consequence of it is true; for then, and only then, is a single ground possible for those consequences, and that ground is the true one. This way of proceeding, however, is not feasible, since surveying every possible consequence of some assumed proposition surpasses our powers; and yet one does resort to this manner of concluding—albeit, to be sure, with a certain leniency—whenever the task is only to establish something as a hypothesis, conceding the inference by analogy that if as many consequences as one has so far tried square nicely with an assumed ground, all the rest that are possible will fall into line with it as well. That is precisely why no hypothesis can ever be turned, along this route, into demonstrated truth. The modus tollens of rational inferences, which conclude from the consequences back to the grounds, proves not only with entire stringency but also with the greatest of ease. For should even one false consequence be derivable from a proposition, that proposition is thereby false. Rather than travel the entire chain of grounds within an ostensive proof—the route that can bring one to a cognition's truth by a thorough insight into how it is possible—one has merely to detect a single false consequence among those issuing from its contrary, whereupon that contrary is false as well, and the cognition one set out to prove is accordingly true.

The apagogic manner of proof, however, is admissible only in those sciences where it is out of the question, in the place of the objective—namely of the cognition of what belongs to the object— to foist the subjective side of our representations. But where that objective side has the upper hand, it must happen again and again that the contrary of a given proposition either clashes merely with the subjective conditions of thinking and not with the object, or else that the two propositions clash only under a subjective condition wrongly held to be objective, so that, the condition being false, both may be false together, with no warrant for concluding from the falsehood of the one to the truth of the other.

In mathematics such a subreption cannot occur, which is why apagogic proofs find their proper home precisely there. In natural science, where everything rests on empirical intuitions, that same act of surreptition can for the most part be forestalled by comparing many observations; but even there this kind of proof is, on the whole, of slight moment. The transcendental undertakings of pure reason, however, are without exception carried out inside the very element of dialectical semblance—that is, inside the subjective, which presents itself to reason among its premises as objective, or indeed presses itself on reason as such. Here, then, where synthetic propositions are concerned, one is by no means at liberty to make good one's assertions by disproving the contrary. For either this disproof amounts to nothing more than exhibiting the clash of the opposing opinion with the subjective conditions under which our reason can comprehend anything—which does nothing whatever to warrant discarding the matter itself on that score (much as, for example, the unconditioned necessity in a being's existence simply cannot be grasped by us, and hence subjectively sets itself, and rightly so, against any speculative proof of a necessary highest being, though it sets itself in itself and wrongly against the very possibility of such an original being); or else both sides, the affirming party and the denying alike, misled by the transcendental semblance, place beneath their case an impossible concept of the object, and here the rule obtains: non entis nulla sunt praedicata—that is, whatever was asserted of the object, be it affirmed or denied, is in both cases wrong, and there is no arriving apagogically at cognition of the truth by refuting the contrary. Take, for instance, the supposition that the world of sense is given in itself in its totality: it is then false that this world must be either infinite in respect of space or else finite and bounded—false, that is, for the reason that each alternative is false. For appearances (being mere representations) that were nonetheless supposed to be given in themselves (as objects) are something impossible, and the infinitude of this fancied whole, though it would indeed be unconditioned, would nevertheless run counter (since in appearances everything is conditioned) to that unconditioned determination of magnitude which the concept for its part presupposes.

The apagogic manner of proof is, besides, the very piece of trickery by which the admirers of our dogmatic reasoners' rigor have always been strung along: it plays, so to speak, the part of the champion who sets out to establish the honor and the unquestionable right of the side he has espoused by undertaking to come to blows with anyone who should care to call it in question—though bluster of this sort settles nothing about the issue itself, only about the relative strength of the combatants, and even that only on the side of whoever is on the attack. The onlookers, watching how each man is by turns victorious and defeated in his round, frequently find in this a reason to grow skeptically doubtful of the very object under dispute. They have, however, no ground for it, and one need only cry to them: non defensoribus istis tempus eget. Each party has to plead its cause by a rightful proof conducted through a transcendental deduction of the grounds of proof, that is, directly, so that it may be seen what its claims on behalf of reason can urge in their own support. For if his adversary props himself on subjective grounds, he is admittedly refuted with ease, yet to no profit for the dogmatist, who as a rule leans just as heavily on the subjective causes of judgment and can be cornered by his adversary in exactly the same way. But let both parties proceed by direct means alone, and they will either come of their own accord to notice the difficulty—indeed the impossibility—of tracing out the title to their assertions, and be left in the end with nothing but an appeal to long possession, or else critique will readily lay bare the dogmatic semblance and force pure reason to abandon the pretensions it has pitched too high in speculative use and to fall back within the confines of its own proper ground, namely practical principles.

Chapter 2. The Canon of Pure Reason

It is humbling for human reason that in its pure use it achieves nothing and even requires a discipline to rein in its extravagances and to prevent the illusions that befall it. Yet on the other hand this once again elevates reason and gives it a confidence in itself, that it can and must exercise this discipline of its own accord, without permitting any other censorship over itself; likewise that the boundaries it is compelled to set to its speculative use at the same time restrict the sophistical pretensions of every opponent, and can thereby secure against all attacks whatever might still remain to it of its formerly overblown demands. The greatest, and perhaps the only, utility that the entire philosophy of pure reason affords is thus in all likelihood merely negative: since it functions not as an organon for extension but as a discipline for fixing its limits, and, in place of uncovering truth, possesses only the unobtrusive merit of averting errors.

Yet there must, somewhere, be a wellspring of positive cognitions belonging within the province of pure reason, ones that perhaps occasion errors only by being misunderstood, though they truly make up the very aim of reason's zealous pursuit. For to what cause else should the insuppressible craving to gain a firm foothold somewhere entirely beyond the boundary of experience be ascribed? It has a presentiment of objects that carry with them a great interest of their own. To draw near to them it embarks on the route of mere speculation; but these take flight before it. Presumably better fortune is to be hoped for it upon the only path still left to it, namely that of practical use.

By a canon I mean the totality of the a priori principles for the proper employment of certain faculties of cognition as such. Accordingly, general logic, in its analytic portion, amounts to a canon for the understanding and for reason as such, though merely with respect to form, since it leaves all content out of account. In the same way, the transcendental analytic proved to be the canon of the pure understanding; for the understanding alone can achieve genuine synthetic cognitions a priori. Yet wherever no proper employment of a cognitive power is possible, no canon exists at all. Now, by every proof marshalled up to this point, pure reason in its speculative employment is wholly incapable of any synthetic cognition. There is therefore no canon whatever for its speculative employment (this being dialectical through and through); rather, in this regard the whole of transcendental logic is nothing more than discipline. Consequently, should there be anywhere a proper employment of pure reason — in which event a canon for it would likewise have to exist — such a canon will bear not on the speculative but on the practical use of reason, which we accordingly now propose to examine.

Section 1. On the ultimate end of the pure use of our reason

A propensity in its very nature drives reason to press beyond its use in experience, to hazard—in a pure use, and by way of mere ideas—an advance to the utmost limits of all cognition, and to come to rest only once its circuit is complete, in a systematic whole subsisting on its own. Now, is this striving founded merely upon reason's speculative interest, or instead wholly and only upon its practical one?

I shall leave aside for now the fortune that pure reason enjoys in its speculative undertaking, and inquire solely into those problems whose resolution constitutes its ultimate end—reach it or not—and beside which every other problem carries only the worth of a means. By the very nature of reason, these supreme ends will once more have to form a unity, so that the interest of humanity subordinate to no higher interest may be furthered as one.

The concluding aim at which reason's speculation, in its transcendental use, finally arrives bears on three objects: the will's freedom, the soul's immortality, and God's existence. As to all three, reason's purely speculative interest is but slight, and it is hardly for its sake that anyone would take up the exhausting toil of transcendental research, forever contending with obstacles, seeing that not one of the discoveries conceivably to be made here admits of a use that would demonstrate its worth in concreto, that is, within the study of nature. Grant that the will is free—even so, this can bear only on the intelligible cause of our willing. For where the phenomena of its manifestations are concerned, namely the actions, an inviolable ground-maxim—lacking which no reason could be exercised in an empirical use—obliges us to explain them exactly as we explain every other appearance of nature, that is, by nature's unchangeable laws. Suppose, secondly, that the soul's spiritual nature (and with it its immortality) admitted of insight—still, nothing can be built on this, neither as a ground of explanation touching the appearances of the present life, nor touching the special makeup of the state to come, for our concept of an incorporeal nature is nothing but negative, in no degree extending our cognition, and furnishing no serviceable material for inferences save such as could pass only as inventions, which philosophy disallows. Suppose, thirdly, that the existence of a supreme intelligence had been demonstrated: we would then indeed render comprehensible to ourselves the purposiveness in the world's contrivance and order taken generally, yet by no means be warranted to draw from it any specific institution and order, or, where such is not observed, to conclude to it audaciously; for a necessary rule of reason's speculative use forbids us to pass over natural causes and to relinquish what experience can teach us, so as to derive something we do know from what utterly exceeds all our acquaintance. In short, these three propositions stay, for speculative reason, transcendent throughout, and possess no immanent use whatever—none, that is, admissible for objects of experience and thereby in any manner useful to us—being rather, taken by themselves, wholly futile and, on top of that, extremely laborious strainings of our reason.

If, accordingly, these three cardinal propositions are in no way necessary to us for knowledge, and yet are pressed upon us insistently by our reason: then their significance can properly bear only on the practical.

Practical is whatever is possible through freedom. But when the conditions under which our free choice is exercised are empirical, reason can there have no use save a regulative one, serving merely to produce the unity of empirical laws; thus, for instance, in the doctrine of prudence reason's entire task lies in bringing together all the ends prescribed to us by our inclinations into the one end, happiness, and in making the means to it accord—so that reason can thereupon deliver no laws of free conduct except pragmatic ones, directed at attaining the ends the senses commend to us, and thus no pure laws determined wholly a priori. Pure practical laws, on the other hand—laws whose end reason supplies entirely a priori, and which do not command under empirical conditions but unconditionally—would be products of pure reason. Of just this sort are the moral laws; and so it is these alone that pertain to the practical use of pure reason and allow of a canon.

Thus the whole equipment of reason, in the enterprise one may name pure philosophy, is directed in truth only upon the three problems already considered. Yet these, for their part, look beyond themselves to a still more distant intent, namely what is to be done, supposing the will free, supposing there be a God and a world to come. Since what is here at issue is our behavior with a view to the highest end, the final purpose of the nature that so wisely provides for us, in fashioning our reason, is properly set upon the moral alone.

Caution, however, is called for: since we are turning our regard to an object foreign⁷² to transcendental philosophy, we must neither digress into episodes and so damage the unity of the system, nor, on the other side, by saying too little of this fresh material, let it come up short in distinctness or in conviction. I hope to achieve both by holding myself as closely as I can to the transcendental, and by putting wholly to one side whatever here might be psychological, that is, empirical.

And here the first thing to remark is that, for the present, I shall use the concept of freedom only in its practical sense, while the concept in its transcendental import—which cannot, as a ground of explanation of the appearances, be posited empirically, but is itself a problem for reason—I here set aside as already disposed of above. A power of choice, namely, is merely animal (arbitrium brutum) when nothing but sensible impulses can determine it, that is, pathologically. The power of choice, by contrast, that can be determined apart from sensible impulses, and thus by moving causes which reason alone represents, is termed free choice (arbitrium liberum); and whatever hangs together with it, be it as ground or as consequence, is called practical. Practical freedom can be proved through experience. For the human power of choice is determined not solely by what allures, that is, what affects the senses directly; rather, we possess a capacity to master the impressions on our sensible faculty of desire through representations of what, even in a more remote fashion, is beneficial or harmful; and these considerations of what is worth desiring with a view to our whole condition, that is, what is good and beneficial, rest upon reason. Reason accordingly issues laws too—imperatives, that is, objective laws of freedom—which pronounce what ought to happen, though perhaps it never does, and which are thereby marked off from laws of nature, whose sole concern is what does happen; and for this reason they are likewise named practical laws.

But whether reason itself, in these acts by which it prescribes laws, is not once more determined by influences of another kind, and whether what, with respect to sensible impulses, bears the name of freedom may not, with respect to higher and more remotely operating causes, once again be nature—that does not concern us in the practical domain, where we interrogate reason at first only for the precept of conduct; it is instead a purely speculative question, one we may lay aside so long as our concern is directed to acting or forbearing. Practical freedom, then, we come to know through experience as one among the natural causes, namely a causality that reason exercises in determining the will, while transcendental freedom asks for an independence of this reason itself (as regards its causality in beginning a series of appearances) from every determining cause of the sensible world, and to that extent appears to contradict the law of nature, and so all possible experience, thus remaining a problem. For reason in its practical use, however, this problem has no place; and so, within a canon of pure reason, we are occupied with just two questions bearing on the practical interest of pure reason, questions for which a canon of its use must be feasible, namely: is there a God? is there a life to come? The question regarding transcendental freedom touches merely speculative knowledge, and this we may set to one side as entirely a matter of indifference when the practical is at stake—a question, moreover, on which the antinomy of pure reason already affords discussion enough.

Section 2. On the ideal of the highest good, as a ground determining the ultimate end of pure reason

Reason, in its speculative employment, conducted us across the terrain of experience, and then—since it can nowhere find full satisfaction there—onward to speculative ideas; yet these in the end steered us back to experience once more, so that reason accomplished its purpose in a way that, however useful, fell quite short of what we had expected. One trial yet remains for us: whether pure reason may also be found at work in its practical employment; whether therein it conducts us to the ideas that reach those supreme ends of pure reason just enumerated above; and whether, viewed from the angle of its practical concern, it can after all bestow on us precisely what, on the speculative side, it denies us altogether.

Every concern of my reason, the speculative no less than the practical, converges upon the three following questions: 1. What can I know? 2. What ought I to do? 3. What am I permitted to hope?

The first of these is purely speculative. As I flatter myself, we have run through every answer that it admits of and have finally lit upon the one at which reason must indeed come to rest and, provided it keeps its gaze off the practical, has good ground to feel content; yet we stand as remote as ever from the two great ends at which this whole striving of pure reason was really aimed—as remote as if we had, from sheer love of comfort, refused the task at the very start. If, then, what we are after is knowledge, this much at any rate stands firm and beyond dispute: that in regard to those two tasks it can never become ours.

The second question is purely practical. As such a question it may well fall to pure reason, and yet in that case it is not transcendental but moral, so that it cannot be a business for our critique taken by itself.

The third question—namely, if I now do what I ought, what am I then entitled to hope? is at once practical and theoretical, in such a way that the practical merely serves as a thread by which we arrive at the theoretical, and, where this reaches high, the speculative question. For all hoping aims at happiness, and, as concerns the practical and the moral law, it is exactly what knowledge and the law of nature are as concerns the theoretical cognition of things. The former issues at last in the inference that something is (that which fixes the final possible end) because something ought to happen; the second, that something is (that which operates as supreme cause) because something happens.

Happiness is the gratification of all our inclinations (whether extensive, in respect of their manifoldness, or intensive, in respect of degree, or again protensive, in respect of duration). A practical law whose moving ground is happiness I term pragmatic (a rule of prudence); but one—should any such exist—that takes for its moving ground nothing beyond the worthiness to be happy I term moral (the moral law). The first counsels what must be done if we would have a share in happiness; the second dictates how we must bear ourselves so as merely to grow worthy of it. The first is founded on empirical principles; for apart from the mediation of experience I have no way of knowing either which inclinations exist that press for satisfaction, or what the natural causes are through which their satisfaction might be brought about. The second leaves out of account both the inclinations and the natural means of gratifying them, attending solely to the freedom of a rational being as such together with the necessary conditions under which that freedom, and it alone, accords with a distribution of happiness by principles, and therefore it can at the least rest upon bare ideas of pure reason and admit of being cognized a priori.

I take it that there genuinely exist pure moral laws which, wholly a priori (with no regard to empirical moving grounds, that is, to happiness), settle what is to be done and left undone, that is, govern how the freedom of a rational being in general is exercised, and that such laws command absolutely (not merely conditionally, on the supposition of further empirical ends) and are on that account necessary in every respect. This proposition I am entitled to lay down in advance, invoking not merely the demonstrations of the most enlightened among moralists, but the ethical judgment of any human being whatever, once he sets himself to conceive such a law with clarity.

Pure reason accordingly harbors—not in its speculative use, to be sure, but nonetheless in a certain practical, namely the moral, use—principles of the possibility of experience, that is, of such deeds as could, in keeping with ethical precepts, come to be found in the history of humankind. For inasmuch as it commands that such deeds ought to come about, they must also be capable of coming about, and hence a distinctive kind of systematic unity—the moral kind—has to be possible, while the systematic unity of nature could not be established on speculative principles of reason, since reason wields causality in the matter of freedom at large yet not in the matter of nature taken as a whole, and moral principles of reason are able to give rise to free deeds but not to laws of nature. In consequence, the principles of pure reason possess objective reality in their practical, and above all in their moral, use.

A world, to the extent that it should stand in accord with all ethical laws (as, by virtue of the freedom of rational beings, it can stand, and, by virtue of the necessary laws of morality, it ought to stand), I name a moral world. So far forth it is conceived merely as an intelligible world, because within it one leaves aside all conditions (ends) and even every impediment to morality therein (the frailty or impurity of human nature). To that degree, then, it is a mere idea, though a practical one, which really can and should exert its influence upon the sensible world, in order to bring the latter into accord with this idea as far as may be. The idea of a moral world therefore possesses objective reality, not as though it bore upon an object of some intelligible intuition (a thing we are wholly unable to conceive), but as bearing upon the sensible world—though as an object belonging to pure reason in its practical exercise and as a corpus mysticum of the rational beings within that world, in that their free choice, under moral laws, carries in itself a thoroughgoing systematic unity alike with its own self and with the freedom of each of the rest.

That constituted the reply to the earlier of the two questions that pure reason raised touching the practical concern: Do that through which you make yourself worthy to be happy. The second now inquires: given that I so bear myself as not to be undeserving of happiness, may I likewise hope by that means to become capable of sharing in it? Everything, in answering it, turns on whether the principles of pure reason that lay down the law a priori likewise bind up this hope with it of necessity.

My claim, then, is this: that precisely as the moral principles are necessary according to reason in its practical use, so it is no less necessary, according to reason in its theoretical use, to grant that each person has ground to hope for happiness to just the degree in which he has, by his conduct, rendered himself worthy of it, and hence that the system of ethical life is knit together with that of happiness indissolubly, though only within the idea of pure reason.

Now within an intelligible, that is, a moral, world—in the concept of which we set aside every impediment to ethical life (the inclinations)—such a system, wherein a proportioned happiness is joined to morality, admits of being thought as necessary as well, for freedom, in part impelled and in part curbed by ethical laws, would be the very source of the universal happiness, so that rational beings, guided by principles of this sort, would themselves author both their own lasting welfare and that of others at once. But this system of a self-recompensing morality is no more than an idea, the carrying-out of which hinges on the condition that each and all do as they ought—that is, that every deed of rational beings unfold as if it had issued from a sovereign will that gathers all private choice within or beneath itself. But since the bindingness that flows from the moral law holds good for every particular exercise of freedom, even where others should fail to conduct themselves in keeping with that law, nothing in the nature of the world's things, nor in the causality of the actions themselves and their bearing on ethical life, settles how their upshot will stand toward happiness; and the necessary linkage already noted—between the hope of being happy and the ceaseless endeavor to render oneself worthy of happiness—cannot be cognized by reason so long as one takes bare nature for one's foundation, but may only be hoped for once a supreme reason, commanding in accordance with moral laws, is taken as at the same time the ground of nature.

The idea of such an intelligence—one in which a will of the utmost moral perfection, conjoined with the highest bliss, is the origin of all the happiness in the world, so far as that happiness stands in precise proportion to ethical life (as the worthiness to be happy)—this idea I name the ideal of the highest good. Hence it is only within the ideal of that highest original good that pure reason can come upon the ground of the practically necessary linkage of the two constituents of the highest derived good—namely, an intelligible, that is, moral, world. Since we are now bound, through reason, to picture ourselves as belonging to such a world, even though the senses set before us nothing but a world of appearances, we shall have to take that world to be a sequel of our conduct in the sensible world and—because the latter presents us with no such linkage—to be a world still to come for us. God, then, and a life to come are two suppositions that, by the principles of that very reason, cannot be sundered from the bindingness which pure reason lays upon us.

Ethical life taken by itself makes up a system, but happiness does not, save to the extent that it is meted out in exact fitness to morality. This, however, is possible solely within the intelligible world, beneath a wise originator and governor. Reason finds itself constrained to assume such an originator, along with life in such a world—one we must look upon as yet to come—or else to treat the moral laws as hollow chimeras of the mind, since the necessary success that this same reason ties to them would inevitably lapse were that supposition wanting. This is likewise why everyone looks upon the moral laws as commands, which they could not be did they not, a priori, attach fitting consequences to their rule and thus carry promises and threats along with them. Yet even this they cannot do unless they have their seat in a necessary being—the highest good—that alone can make such a purposive unity possible.

Leibniz gave the world—so far as one heeds in it only the rational beings and their interconnection under moral laws beneath the government of the highest good—the name realm of grace, marking it off from the realm of nature, in which these same beings do indeed stand under moral laws yet look for no results of their conduct other than those that follow the ordinary course of nature in our sensible world. Thus to behold oneself within the realm of grace, where the whole of happiness lies in wait for us—save in so far as we ourselves cut down our share of it by an unworthiness to be happy—is an idea of reason that is practically necessary.

Practical laws, in so far as they come to be at the same time subjective grounds of the actions—that is, subjective principles—are termed maxims. The assessment of ethical conduct as to its purity and its consequences takes place by ideas; the following of its laws, by maxims.

It is necessary that the whole conduct of our life be placed under ethical maxims; and yet it is at the same time impossible for this to happen unless reason attaches, to the moral law—which is a bare idea—an operative cause that assigns to conduct governed by that law an outcome answering exactly to our highest ends, be it in this life or in some other. Absent a God, then, and a world unseen by us at present but hoped for, the splendid ideas of ethical life are indeed objects of applause and wonder, but not springs of resolve and performance, for they do not fulfil the whole end which is native to every rational being and which that very same pure reason fixes and makes necessary a priori.

Happiness on its own is, in the eyes of our reason, very far from the complete good. Reason gives it no sanction (however keenly inclination may crave it) so long as it is not wedded to the worthiness to be happy, that is, to good ethical conduct. But morality on its own, and with it the mere worthiness to be happy, likewise falls well short of being the complete good. For this to be brought to completion, whoever has borne himself as not undeserving of happiness must be in a position to hope for a share in it. Even a reason liberated from every private aim, were it—taking no interest of its own into the reckoning—to place itself in the position of a being charged with apportioning all happiness to others, could reach no other verdict; for in the practical idea the two components are bound together essentially, though in such wise that the moral disposition, functioning as condition, is what first makes possible the share in happiness, and not the reverse—that the prospect of happiness should be what first renders the moral disposition possible. For in the latter case it would fail to be moral, and hence unworthy also of that entire happiness which, in the sight of reason, acknowledges no restriction other than the one springing from our own unethical conduct.

Happiness, then, in precise commensuration with the ethical worth of rational beings, whereby they are worthy of it, is what alone makes up the highest good belonging to a world into which we are wholly obliged to transport ourselves by the precepts of pure yet practical reason—a world that is, admittedly, no more than intelligible, since the sensible world holds out to us, from the nature of things, no such systematic unity of ends, and whose reality can moreover be founded on nothing else than the supposition of a highest original good, wherein a self-standing reason, furnished with all the sufficiency of a supreme cause, in keeping with the most consummate purposiveness founds, sustains, and brings to completion the universal order of things, though one hidden deep from us in the sensible world.

This moral theology enjoys, now, the singular advantage over the speculative kind that it leads without fail to the concept of a single, most perfect of all, and rational primordial being—something toward which speculative theology, arguing from objective grounds, does not so much as direct us, still less could it persuade us of it. For neither in transcendental nor in natural theology, however far reason may carry us within them, do we come upon any weighty ground for positing so much as a single being that we might set over all natural causes and upon which we might have cause enough to make those causes dependent through and through. If, on the other hand, we weigh—from the vantage of ethical unity as a necessary law of the world—the cause that can lend this unity its fitting effect and therewith a force binding upon us, then it must be one sole supreme will that holds all these laws together within itself. For how could a complete unity of ends ever be found among a plurality of wills? This will must be all-powerful, so that the whole of nature, together with its bearing on ethical life in the world, may lie subject to it; all-knowing, so that it may cognize the inmost of the dispositions and their moral worth; everywhere present, so that it may stand immediately near to every need that the world's supreme good demands; everlasting, so that at no time may this concord of nature and freedom fall short, and so on.

But this systematic unity of ends within the said world of intelligences—which, taken as mere nature, amounts only to a world of sense, whereas as a system of freedom it may be styled an intelligible, that is, moral, world (regnum gratiae)—leads without fail to a purposive unity of all the things that compose this vast whole by universal laws of nature, exactly as the former unity does by universal and necessary ethical laws, and it fuses practical reason with the speculative. The world must be pictured as having sprung from an idea, if it is to fall into accord with that employment of reason apart from which we should count ourselves unworthy of reason—namely the moral employment, resting as it does wholly on the idea of the highest good. By this means every inquiry into nature receives a bent toward the form of a system of ends, and, at its widest reach, turns into physico-theology. This latter, however—since it set out, after all, from ethical order as a unity grounded in the very essence of freedom and not contingently instituted by outward commands—carries the purposiveness of nature back to grounds that must be a priori and inseparably tied to the inner possibility of things, and thereby to a transcendental theology which fastens upon the ideal of the highest ontological perfection as its principle of systematic unity—a principle binding all things by universal and necessary laws of nature, since one and all they take their origin in the absolute necessity of a single primordial being.

What use are we to make of our understanding, even where experience is concerned, if we set ourselves no ends? But the loftiest ends are those of morality, and these it is pure reason alone that can bring us to cognize. Equipped with these ends now and led by their thread, we can put the knowledge of nature itself to no purposive use as regards cognition wherever nature has not herself laid down a purposive unity; for lacking this we should not so much as possess a reason of our own, since we would be without any school for it and without any cultivation by way of objects that might furnish the material for concepts of the kind. That purposive unity, however, is necessary and takes its ground in the very essence of free choice, and so the latter—holding, as it does, the condition for applying that unity in concreto—must be necessary too; and thus the transcendental heightening of our rational cognition would prove to be, not the cause, but merely the effect of the practical purposiveness that pure reason lays upon us.

We therefore likewise discover, in the history of human reason: that until the moral concepts had been purified and made determinate enough, and until the systematic unity of ends conforming to them had been grasped—and grasped, indeed, from necessary principles—the knowledge of nature, and even a respectable degree of cultivation of reason across a number of other sciences, was able in part to bring forth none but crude and roving concepts of the deity, and in part left standing an astonishing indifference toward this question altogether. A fuller working-out of moral ideas, rendered necessary by the utterly pure moral law of our religion, whetted reason upon the object through the interest it obliged reason to take therein; and without any contribution either from an enlarged acquaintance with nature or from sound and trustworthy transcendental insights (of which sort there has at every period been a dearth), these ideas brought to pass a concept of the divine being that we now regard as the right one—not because speculative reason persuades us of its rightness, but because it chimes perfectly with the moral principles of reason. And so, when all is said, it is ever only pure reason, though solely in its practical employment, that has the credit of binding to our highest concern a cognition which bare speculation may merely surmise yet cannot make good, and of thereby raising it—not, to be sure, into a demonstrated dogma, but nonetheless into a wholly indispensable supposition attaching to reason's most essential ends.

But now that practical reason has attained this lofty vantage—the concept, namely, of a single primordial being as the highest good—it may in no way take the liberty, as though it had lifted itself above all the empirical conditions of that concept's application and soared up to an immediate acquaintance with fresh objects, of setting out from this concept and deducing the moral laws themselves from it. For it was these very laws whose inner practical necessity drove us to the supposition of a self-standing cause, or of a wise governor of the world, so as to lend those laws effect; and for that reason we cannot, following upon this, turn round and regard them as contingent and drawn from a mere will—least of all from a will of which we should have no concept whatever, had we not shaped it in conformity with those very laws. So far as practical reason is entitled to lead us, we shall deem actions binding not on the ground that they are God's commands, but shall instead look on them as divine commands on the ground that we stand inwardly bound to them. We shall study freedom beneath the purposive unity by the principles of reason, and shall believe ourselves in accord with the divine will only to the extent that we hold sacred the moral law which reason teaches us out of the very nature of actions, and shall believe that we serve that will by this alone—that we further the world's good in ourselves and in others. Moral theology is thus of an immanent use only—namely, to discharge our vocation here in the world by fitting ourselves into the system of all ends—and not, in a rapturous or perhaps even sacrilegious spirit, to forsake the thread of a morally legislative reason within a good course of life in order to tie it directly onto the idea of that highest being—an idea whose adoption would furnish a transcendent use that, just like the use of bare speculation, cannot but pervert and thwart the ultimate ends of reason.

Third Section. On opining, knowing, and believing

Assent is an event within our understanding, one that may indeed rest on objective grounds while also requiring subjective causes in the mind of whoever is judging. Should it hold good for everyone, so far as he but possesses reason, then its ground is objectively sufficient, and the assent is at that point termed conviction. Should its ground lie merely in the special character of the subject, it is termed persuasion.

Persuasion is nothing but a semblance, since the ground of the judgment, residing purely in the subject, is held to be objective. For that reason such a judgment likewise carries only private validity, and the assent admits of no communication. Truth, by contrast, reposes on accordance with the object, in regard to which the judgments of every understanding must accordingly agree (consentientia uni tertio consentiunt inter se). Whether an assent amounts to conviction or to mere persuasion has, then, its outward touchstone in whether it can be shared and found valid for the reason of every human being; for at that point there is at any rate a surmise that the ground of the concurrence of all judgments, in spite of the differences among the subjects themselves, will lie in the common ground, that is, the object, with which they therefore one and all harmonize and so establish the truth of the judgment.

Persuasion, then, admittedly cannot be told apart subjectively from conviction whenever the subject keeps the assent in view merely as an appearance of its own mind; yet the trial one runs by applying the grounds of it, valid for us, to the understanding of another—to see whether upon a foreign reason they work exactly the effect they work upon ours—is nonetheless a means, subjective though it remains, not indeed of producing conviction, but of laying bare the sheer private validity of the judgment, that is, something in it that is nothing but persuasion.

If, over and above this, we are able to unfold the subjective causes of the judgment that we mistake for its objective grounds, and can thereby account for the deceptive assent as an event in our mind without requiring for it the character of the object: then we strip the semblance bare and are on that account no longer taken in, though still to some degree tempted so long as the subjective cause of the semblance cleaves to our nature.

I am able to assert nothing—in other words, to enunciate as a judgment binding for everyone of necessity—save what produces conviction. A persuasion I may retain for myself if I find it agreeable, yet I can neither, nor ought I to wish to, make it count outside myself.

Assent, or the subjective validity of a judgment in relation to conviction (which holds objectively at the same time), possesses the following three grades: opining, believing, and knowing. Opining is an assent consciously deficient both subjectively and objectively. Where the latter is merely sufficient subjectively while being reckoned objectively deficient, it bears the name believing. Lastly, an assent sufficient subjectively as well as objectively bears the name knowing. Sufficiency on the subjective side is termed conviction (for myself), sufficiency on the objective side certainty (for everyone). I shall not linger over the clarification of concepts as easy to grasp as these.

I dare never presume to opine unless I know at least something whereby the judgment, in itself no more than problematic, gains a link with truth which, incomplete though it be, still amounts to more than a capricious fabrication. Beyond this, the law governing such a link must be certain. For if in regard to it I too have nothing beyond opinion, then the whole is but a game of imagination lacking the least bearing on truth. Within judgments drawn from pure reason there is no leave whatever to opine. For inasmuch as they draw no support from grounds of experience but everything is meant to be cognized a priori, where all is necessary, the principle of the linkage calls for universality and necessity, and thus for entire certainty, in default of which no lead toward truth is to be had at all. Hence it is preposterous to opine in pure mathematics; one must know, or else abstain from judging altogether. Matters stand the same way with the principles of morality, since one dare not risk an action on the bare opinion that something is permitted, but has to know it.

In the transcendental employment of reason, on the other hand, opining is naturally too meager, yet knowing likewise too much. With a purely speculative aim, then, we cannot judge here at all: for subjective grounds of assent, such as can bring about belief, merit no approbation in speculative questions, since they neither keep themselves clear of every empirical aid nor allow of being conveyed to others to the same degree.

It is solely within a practical relation, however, that a theoretically deficient assent can ever be called belief. This practical aim is now either the aim of skill or that of morality, the former bearing on arbitrary and contingent purposes, the latter, however, on purposes utterly necessary.

The moment an end is laid down, the conditions for reaching it become hypothetically necessary. This necessity is subjective, yet no more than comparatively sufficient, in case I am aware of no other conditions whatever under which the end might be reached; but it is unqualifiedly and universally sufficient once I know for certain that no one could be acquainted with other conditions leading to the end laid down. In the former case my supposition, together with the assent to certain conditions, is a merely contingent belief, whereas in the latter it is a necessary one. A physician confronted with a patient in danger has to do something, yet does not recognize the disease. He attends to the symptoms and concludes, for want of anything better, that it is consumption. His belief is, even by his own verdict, merely contingent; someone else might well hit the mark more accurately. Such contingent belief, which nevertheless underlies the real employment of the means toward certain actions, I call pragmatic belief.

The customary touchstone for telling whether what someone maintains is bare persuasion, or at any rate subjective conviction—that is, firm belief—is wagering. Not seldom a person delivers his propositions with so assured and intractable an obstinacy that he appears to have shed every worry about error. A wager pulls him up short. At times it emerges that his persuasion, while worth staking a single ducat, does not extend to ten. The one he will still hazard readily enough, but faced with ten he suddenly grows aware of what had escaped him before, namely that he may, after all, quite possibly have gone wrong. Let a person picture to himself that he is to wager the fortune of his entire life upon it, and his triumphant verdict shrinks drastically, he turns exceedingly diffident, and only then does it dawn on him that his belief does not carry so far. Pragmatic belief, accordingly, has but a degree, which—depending on how large the interest in play may be—can prove great or else small.

But since—granting that we can set nothing whatever afoot with respect to an object, so that the assent stays merely theoretical—we can nonetheless in many instances entertain and picture an enterprise for which we fancy ourselves to hold adequate grounds, supposing there were some means of settling the certainty of the thing, there arises in purely theoretical judgments an analogue of practical ones, to whose assent the word belief is suited, and which we may christen doctrinal belief. Were it feasible to settle the point through any experience at all, I would readily stake everything I own upon it that inhabitants exist on at least one or another of the planets within our sight. For that reason I declare it to be no mere opinion but a robust belief (on whose rightness I would already hazard many of life's benefits) that dwellers in other worlds exist as well.

We must now own that the doctrine of God's existence pertains to doctrinal belief. For although, as regards the theoretical knowledge of the world, I have nothing to dispose of that would of necessity presuppose this thought as a condition of my explanations of the world's appearances, being obliged rather to employ my reason as though everything were mere nature: the purposive unity is for all that so weighty a condition of the application of reason to nature that I—experience furnishing me, besides, abundant instances of it—can by no means pass it over. For this unity, however, I am acquainted with no other condition that would render it my clue for the study of nature than to presuppose that a supreme intelligence has arranged all things after the wisest ends. It follows that presupposing a wise author of the world is a condition of an aim which, though contingent, is nonetheless far from trivial—namely, that of having a guide in the investigation of nature. The upshot of my inquiries so frequently corroborates the serviceability of this presupposition, while nothing can be brought decisively against it, that I would be saying far too little were I to call my assent a mere opining; rather, even within this theoretical bearing it may be said that I steadfastly believe in a God; yet in that case this belief, taken strictly, is nonetheless not a practical one, but has to be termed a doctrinal belief, such as the theology of nature (physico-theology) must of necessity generate at every turn. In view of that very wisdom, considering the superb outfitting of human nature together with the shortness of life so ill-fitted to it, there is likewise ample ground to be met with for a doctrinal belief in the future life of the human soul.

In such cases the profession of belief is a profession of modesty on the objective side, yet at once of steadfast confidence on the subjective. Were I to call the merely theoretical assent here so much as a hypothesis that I should be entitled to adopt, I would thereby be pledging myself already to command a fuller concept of the makeup of a world-cause and of another world than I am truly able to set forth; for of anything I adopt even only as a hypothesis I must be acquainted at least with enough of its properties that I may fabricate not its concept but only its existence. The word belief, however, bears solely upon the guidance an idea affords me and upon the subjective influence toward furthering my operations of reason, which keeps me holding fast to that idea, even though I am unable to render account of it with a speculative aim.

But merely doctrinal belief harbors something wavering in itself; one is often unseated from it by difficulties cropping up in speculation, though one unfailingly comes back to it time and again.

With moral belief the case stands quite differently. For here it is downright necessary that something come to pass, namely that I render obedience to the moral law in every particular. The end is here fixed beyond escape, and by all my insight only one solitary condition is possible under which this end hangs together with the sum of all ends and thereby holds practical validity—namely, that a God and a world to come exist; I know, moreover, with full certainty that no one is acquainted with other conditions conducting to the same unity of ends beneath the moral law. But since, then, the moral precept is at once my maxim (reason, indeed, enjoining that it be so), I shall unfailingly believe in an existence of God and in a life to come, and I rest assured that nothing can set this belief tottering, seeing that thereby my very moral principles would be toppled, principles I cannot forswear without becoming loathsome in my own eyes.

In this manner, once all the ambitious designs of a reason roving past the frontiers of every experience have been thwarted, there yet remains enough for us to have reason to rest content with it for practical purposes. Admittedly no one, to be sure, will be in a position to plume himself that he knows there to be a God and there to be a life to come; for if he knows this, he is precisely the man I have long been in search of. Every piece of knowledge (where it concerns an object of mere reason) admits of communication, and I might therefore even hope, through his tuition, to behold my own knowledge stretched to so marvelous an extent. No—the conviction is not a logical but a moral certainty, and because it reposes on subjective grounds (those of the moral cast of mind), I must not so much as declare: it is morally certain that a God exists, etc., but instead: I am morally certain, etc. Which is to say: my belief in a God and in another world is woven together with my moral cast of mind so tightly that, just as little as I stand in danger of forfeiting the latter, so little do I fear that the former could ever be torn from me.

The one misgiving that presents itself in all this is that this belief of reason props itself upon the presupposition of moral dispositions. Should we set this aside and take up someone utterly indifferent toward moral laws, then the question reason throws up turns into a mere problem for speculation and can at that point be shored up, to be sure, with forceful grounds drawn from analogy, yet not with such as the most obstinate craving for doubt would have to yield to.⁷³ There is, however, no human being free of all interest where these questions are concerned. For though a lack of good dispositions may sever him from the moral, still even in this case enough is left over to make him dread a divine existence and a hereafter. For nothing further is called for here than that he be at the very least incapable of pretending to any certainty that no such being and no life to come are to be found—which, since it would have to be proved by pure reason and thus apodictically, would oblige him to establish the impossibility of both, a thing that assuredly no reasonable person can shoulder. This would be a negative belief, one able to bring about not indeed morality and good dispositions, but nonetheless the analogue of them—that is, forcibly to hold in check the eruption of the evil ones.

But is this the whole of it, someone will say, that pure reason brings off in throwing open vistas past the bounds of experience? no more than a pair of articles of belief? So much as this even ordinary understanding could well have brought off, without calling the philosophers into consultation over it!

I have no wish here to vaunt the merit that philosophy possesses, through the toilsome exertion of its critique, on behalf of human reason; suppose its issue were even found to be merely negative; for something on that head will still come up in the following section. But do you really insist that a cognition bearing on all human beings should outstrip ordinary understanding and be unveiled to you by philosophers alone? This very thing you find fault with is the finest corroboration of the soundness of the assertions advanced hitherto, inasmuch as it brings to light what could not be foreseen at the outset—namely, that nature, in matters of concern to human beings without distinction, is not to be accused of any partial parceling out of her gifts, and that the loftiest philosophy, when it comes to the essential ends of human nature, can carry things no further than the guidance she has vouchsafed even to the most ordinary understanding.

Chapter 3. The Architectonic of Pure Reason

What I mean by an architectonic is the art proper to systems. It is systematic unity that first elevates ordinary cognition into a science — that turns a mere aggregate of it into a system — and for this reason the architectonic is the teaching about whatever is scientific in our cognition taken as a whole, so that it belongs of necessity to the doctrine of method.

Where reason holds sway, our cognitions are not permitted to form any rhapsody whatever; they are required instead to make up a system, since only within one can they lend support to reason's essential ends and carry them forward. And by a system I mean the unity of manifold cognitions brought together under one idea. Such an idea is the rational concept of the form of a whole, to the extent that this concept fixes a priori both how far the manifold extends and where the several parts stand in relation to one another . Hence this scientific concept of reason holds within it the end together with the form of that whole which answers to it. Because the end is one — and all the parts refer to it, and, within its idea, to one another as well — it comes about that any part may be found wanting once the others are known, and that no chance addition occurs, nor any indeterminate magnitude of perfection lacking the boundaries fixed for it a priori. The whole is therefore jointed (articulatio) rather than piled up (coacervatio); it may grow from within (per intussusceptionem), though never from without (per appositionem), just as an animal body grows without gaining a single limb, its growth leaving the proportions untouched while rendering each part stronger and fitter for its ends.

To be carried out, the idea stands in need of a schema, that is, of an essential manifoldness and arrangement of the parts, both fixed a priori out of the principle of the end. Where a schema is sketched not from an idea — that is, not from reason's principal end — but empirically, following intentions that happen to turn up (whose sum no one can foresee), it delivers technical unity; where, by contrast, it springs solely in consequence of an idea (reason here assigning the ends a priori rather than waiting on experience for them), it founds architectonic unity. What we name a science can arise not technically — through some resemblance among the manifold, or through a chance employment of cognition in concreto toward any external ends one pleases — but only architectonically, by virtue of the kinship and the descent from one sole supreme and inner end that alone renders the whole possible; and the schema of such a science must set out the contour (monogramma) as well as the partition of the whole into members conformably to the idea, that is, a priori, and must mark it off with certainty and on principles from all the rest.

No one sets out to establish a science unless some idea underlies his effort. Yet as he works it out, the schema — indeed even the definition he offers of his science at the very start — seldom matches his idea; for the idea rests in reason after the fashion of a seed, within which every part still lies tightly folded and so hidden as to be barely discernible even under microscopic scrutiny. On that account, seeing that all sciences are conceived from the vantage of some general interest, one ought to expound and delimit them not by the description their originator supplies of them, but by the idea that one discovers grounded in reason itself, an idea drawn from the natural unity of the parts he has brought together. For it will emerge in that case that the originator, and frequently his latest heirs as well, grope about an idea they have never managed to make plain to themselves, and are therefore unable to pin down the distinctive content, the articulation (systematic unity), and the limits of the science.

It is a sorry thing that only once we have, over a long stretch and at the prompting of an idea concealed within us, gathered up in rhapsodic fashion a mass of pertinent cognitions to serve as building stock — indeed only once we have for lengthy spans of time fitted them together technically — does it at last become possible for us to catch sight of the idea in a brighter light and to lay out a whole architectonically in keeping with the ends of reason. Systems have the look of worms, sprung by a generatio aequivoca from the sheer running-together of amassed concepts — misshapen at first and, with time, brought to completion — even though one and all they held their schema as the original seed within a reason that merely unfolds itself, so that each is not only jointed on its own according to an idea, but the whole set are, beyond that, joined purposefully to one another, standing once more as limbs of one body within a system of human cognition, and thus make room for an architectonic of all human knowledge which, in our own day — when material lies gathered already in such quantity, or may be retrieved from the rubble of old edifices that have caved in — would prove not merely attainable but hardly even difficult. For our part we rest content with finishing the task before us, which is simply to lay out the architectonic of all cognition that issues from pure reason, and we take our start only from that juncture at which the common root of our cognitive power splits and sends up two trunks, one being reason. Here, though, by reason I mean the whole of the higher faculty of cognition, thereby setting the rational over against the empirical.

Should I set aside the entire content of cognition, regarded objectively, then, on the subjective side, all cognition is either historical or rational. Historical cognition amounts to cognitio ex datis, the rational to cognitio ex principiis. However a cognition may first have been supplied, and from whatever quarter, it remains, for whoever holds it, historical, provided he cognizes only to the measure and the amount handed to him from without; and this handing-over may reach him through firsthand experience, through report, or else through instruction (in general cognitions). Thus a man who has genuinely learned a philosophical system — the Wolffian, say — even were he to carry in his head all its principles, its explications and demonstrations, along with the layout of the entire doctrinal structure, and could tick every item off on his fingers, still possesses none but a complete historical cognition of the Wolffian philosophy; he knows and adjudges no more than was consigned to him. Let a definition be contested against him, and he is at a loss where to procure another. He shaped himself upon another's reason, yet the faculty that copies is not the faculty that generates — that is, in him the cognition did not well up out of reason — and although objectively it was indeed a cognition of reason, on the subjective side it stays merely historical. He apprehended well and held fast, that is, he learned, and he is a plaster impression taken from a living man. Cognitions of reason that are so objectively (in that they can, to begin with, well up only from the human being's own reason) are entitled to carry this name subjectively too, but only where they have been drawn from reason's universal wellsprings — the very source from which criticism, and even the repudiation of what was learned, may equally proceed — in short, from principles.

Every cognition of reason is at this point either one derived from concepts or one derived from the construction of concepts; the first we term philosophical, the second mathematical. The inner difference between the two I have already dealt with in the first chapter. A cognition may thus be philosophical objectively and yet historical subjectively, as happens with the majority of pupils and with all who never look past the schoolroom and stay pupils for life. It is curious, all the same, that mathematical cognition, precisely as one has picked it up, can pass subjectively for cognition of reason as well, so that the sort of split found in the philosophical case does not arise for it. The reason lies in this: the springs of cognition on which the teacher alone can draw are situated nowhere but in the essential and authentic principles of reason, and so cannot be fetched by the pupil from any other quarter, nor indeed contested; and this holds because here reason is exercised only in concreto, yet still a priori — namely upon the pure and for that very reason faultless intuition — and thereby shuts out all illusion and error. Among all the rational sciences (a priori), then, mathematics alone can be learned, philosophy never (save historically); where reason itself is concerned, the most one can learn is to philosophize.

The system embracing all philosophical cognition is precisely philosophy. One is bound to take it objectively when one means by it the prototype against which every attempt at philosophizing is to be measured, a prototype serving to appraise each subjective philosophy, whose structures are so often varied and so often shifting. Taken this way, philosophy is a mere idea of a science that might be, nowhere handed to us in concreto, though one strives to draw near it along sundry routes until the sole footpath — badly overgrown by sensibility — comes to light and the hitherto botched copy is made, so far as is granted to human beings, to match the prototype. Until that point no philosophy can be learned; for where does it reside, who has it in hand, and by what marks is it to be known? One can learn only to philosophize — that is, to train reason's talent by having it follow its universal principles across certain attempts already at hand, though always keeping in reserve reason's right to probe those principles at their sources and to uphold or discard them.

Up to that point, however, the concept of philosophy is nothing beyond a scholastic concept, namely of a system of cognition pursued solely as a science, aiming at nothing further than the systematic unity of this knowledge and thus at the logical completeness of cognition. But there is besides a cosmic concept (conceptus cosmicus) that has at all times lain beneath this label, above all whenever one personified it, as it were, and pictured it as a prototype in the ideal of the philosopher. On this understanding, philosophy is the science that treats how all cognition bears on the essential ends of human reason (teleologia rationis humanae), and the philosopher is no craftsman of reason but the lawgiver of human reason. In that sense it would be great presumption to style oneself a philosopher and to lay claim to having matched the prototype, which resides in the idea alone.

The mathematician, the natural scientist, the logician — however splendid the progress the former may make in cognition of reason at large, and the latter above all in philosophical cognition — remain for all that mere craftsmen of reason. There is besides a teacher in the ideal who deploys them all, turning them into tools for advancing the essential ends of human reason. Him alone ought we to call the philosopher; but since he is nowhere to be encountered, while the idea of his lawgiving is encountered everywhere, in every human reason, we shall confine ourselves to the latter and settle more closely what systematic unity philosophy, taken by this cosmic concept,⁷⁴ lays down from the vantage of ends.

Essential ends are not on that account already the highest, of which (once reason attains perfect systematic unity) there can be but one. They are accordingly either the final end or subordinate ends that necessarily attach to it as means. The former is nothing else than the whole vocation of the human being, and the philosophy bearing on it we call morals. Because of this precedence that moral philosophy enjoys over every other pursuit of reason, the ancients too, under the name of philosopher, always meant at once and by preference the moralist; and even now the outward appearance of governing oneself through reason is what leads us, by a kind of analogy, to call a person a philosopher despite the narrowness of his knowledge.

The lawgiving of human reason (philosophy) has, then, two objects, nature and freedom, and so comprises the law of nature no less than the law of morals — housed first in two distinct systems, but in the end within one philosophical system alone. The philosophy of nature reaches to all that is, that of morals only to what ought to be.

All philosophy, though, is either cognition sprung from pure reason or cognition of reason resting on empirical principles. The first we call pure philosophy, the second empirical.

The philosophy of pure reason is now either propaedeutic (a preparatory drill), which examines reason's capacity with regard to all pure cognition a priori and bears the name critique, or, secondly, the system of pure reason (as a science), the entire body of philosophical cognition from pure reason — true and apparent alike — in systematic coherence, bearing the name metaphysics; though this last name may equally be conferred on the whole of pure philosophy, critique included, so as to gather up both the inquiry into everything that can ever be cognized a priori and the exposition of whatever makes up a system of pure philosophical cognitions of this sort, marked off, however, from all empirical and likewise from the mathematical use of reason.

Metaphysics splits into a metaphysics of the speculative and one of the practical use of pure reason, and is thus either a metaphysics of nature or a metaphysics of morals. The former holds all the pure principles of reason drawn from concepts alone (mathematics thereby excluded) that govern the theoretical cognition of all things; the latter holds the principles that fix what is to be done and left undone a priori and render it necessary. Now morality is the sole conformity-to-law of actions that admits of being derived wholly a priori from principles. The metaphysics of morals is therefore, strictly, pure morality, one that rests on no anthropology (no empirical condition) as its foundation. The metaphysics of speculative reason is what one customarily labels metaphysics in the narrower sense; but since pure moral doctrine belongs nonetheless to that special stem of human — indeed philosophical — cognition out of pure reason, we mean to keep that title for it, even while we set it aside here as not pertaining to our purpose just now.

It matters in the highest degree to isolate cognitions that stand apart from others in kind and in origin, and to take careful precaution that they do not merge into a blend with those to which, in use, they are ordinarily tied. What the chemist does in parting substances, and the mathematician in his pure theory of quantity, falls upon the philosopher still more heavily, so that he may pin down with assurance the portion that a distinct species of cognition contributes to the stray use of the understanding, and thereby its peculiar worth and influence. For this reason human reason, ever since it began to think — or rather to reflect — has at no time gone without a metaphysics, and yet has never been able to set it forth cleansed sufficiently of everything alien to it. The idea of a science of this kind runs back as far as speculative human reason itself; and what reason does not speculate, be it in a scholastic or in a popular vein? One must grant, meanwhile, that the separation of the two elements of our cognition — the one sort wholly within our command a priori, the other to be had only a posteriori from experience — stayed exceedingly murky even among thinkers by trade, and could on that account never accomplish the bounding-off of a distinct species of cognition, and hence never the genuine idea of a science that has so long and so keenly engaged human reason. Were one to say that metaphysics is that science which handles the first principles of human cognition, one would thereby single out not a wholly distinct species but merely a rank as regards generality, so that on this footing it could not be told apart in any recognizable way from the empirical; for among empirical principles too some are broader and hence loftier than others; and along the sequence of such a subordination (given that one does not part what is wholly a priori from what is cognized only a posteriori): at what point is the cut to be made that would sever the first portion and the topmost members from the last and the ones ranked beneath? What would be said if chronology could mark off the epochs of the world only in this manner, that it divided them into the first centuries and those coming afterward? Does the fifth, the tenth, etc. century likewise count among the first? one would ask; and in the same way I ask: Does the concept of the extended fall under metaphysics? You reply: Yes! Ah, but that of body as well? Yes! And that of the fluid body? You falter, for if things run on in this way, then everything will fall under metaphysics. From this it is plain that the bare degree of subordination (the particular set beneath the general) cannot mark out the boundaries of a science, but rather, in our case, the utter dissimilarity and diversity of origin. What further clouded the root idea of metaphysics on yet another side was that, being cognition a priori, it displays a certain kinship with mathematics — a kinship that, so far as the a priori origin goes, does make the two akin; but so far as concerns the manner of cognizing from concepts in the one, set against the manner of judging simply through the construction of concepts a priori in the other, and thus the difference between a philosophical cognition and a mathematical one, there stands revealed a heterogeneity so pronounced that, though one always somehow sensed it, one could never reduce it to distinct criteria. It has thereby come to pass that, philosophers having themselves gone astray in unfolding the idea of their science, the working of it could possess no fixed aim and no reliable measuring-line, and that, saddled with so arbitrary a draft, in the dark as to the road they should take, and forever quarreling among themselves over the discoveries each insisted he had made along his own, they dragged their science first into others' contempt and in the end even into their own.

All pure cognition a priori thereby forms, in virtue of the particular cognitive faculty within which alone it can be lodged, a unity of its own, and metaphysics is that philosophy whose task is to set forth this cognition in such systematic unity. Its speculative part, which has claimed this title for itself above all — the part we call the metaphysics of nature, which weighs everything, insofar as it is (not what ought to be), out of concepts a priori — is now partitioned as follows.

Metaphysics in the narrower sense, so named, is made up of two parts: the transcendental philosophy and the physiology of pure reason. The first of these attends solely to the understanding and to reason as such within a system comprising all those concepts and principles that bear upon objects as such, positing no objects that would be given (Ontologia); the second attends to nature, that is, to the totality of given objects (be they given to the senses or, should one wish, to some other manner of intuition), and it is accordingly physiology (albeit only rationalis). Now within this rational contemplation of nature reason may be put to use in a manner either physical or hyperphysical — or, to phrase it better, either immanent or transcendent. The first bears upon nature to the extent that cognition of it admits of application within experience (in concreto); the second bears upon that linkage among the objects of experience which oversteps experience altogether. This transcendent physiology thus takes for its object either an inner linkage or an outer one, both of which, though, run past possible experience; the first is the physiology of the whole of nature, that is, transcendental cognition of the world, the second that of the whole of nature's tie with a being above nature, that is, transcendental cognition of God.

Immanent physiology, on the other hand, views nature as the totality of all objects of the senses, and hence as it is given to us, though solely under those conditions a priori on which it can be given to us at all. Its objects, however, are of just two sorts: 1. Those belonging to the outer senses, and so the totality of them, corporeal nature. 2. The object of the inner sense, the soul, and, by its basic concepts generally, thinking nature. The metaphysics of corporeal nature is termed physics — but, since it is meant to hold only the a priori principles of its cognition, rational physics. The metaphysics of thinking nature is termed psychology, and for the cause just adduced only its rational cognition is here to be understood.

The full system of metaphysics accordingly rests on four principal parts: 1. The ontology. 2. The rational physiology. 3. The rational cosmology. 4. The rational theology. The second part — namely the doctrine of nature belonging to pure reason — embraces two subdivisions, the physica rationalis⁷⁵ and the psychologia rationalis.

The primordial idea of a philosophy of pure reason itself dictates this partition; the partition is therefore architectonic, answering to its essential ends, and not merely technical, arranged by kinships noticed at random and, so to say, on a gamble — and just for that reason it is also unalterable and legislative. Yet several points crop up here that stir misgiving and might sap one's conviction of its lawfulness.

In the first place, how am I to look for a cognition a priori, and so a metaphysics, of objects insofar as they are handed to our senses and thus a posteriori? and how can it be done, to cognize the nature of things by principles a priori and to reach a rational physiology ? The reply runs thus: from experience we borrow nothing beyond what is needed in order to give ourselves an object, partly of the outer, partly of the inner sense. The one comes about by the bare concept of matter (impenetrable, lifeless extension), the other by the concept of a thinking being (within the empirical inner representation: I think). For the rest, throughout the entire metaphysics of these objects we should have to hold ourselves back wholly from any empirical principle that might tack some further experience onto the concept so as to draw from it a judgment about these objects.

In the second place: what then becomes of empirical psychology, which from of old has held its ground within metaphysics, and from which, in our times, so much has been anticipated toward illuminating it, once the hope of accomplishing anything usable a priori was abandoned? My reply: it must be assigned there where the proper (empirical) doctrine of nature has its place — that is, on the flank of applied philosophy, to which pure philosophy contributes the principles a priori, so that the former must be bound up with it, yet not commingled. Empirical psychology must therefore be banished outright from metaphysics, and by the very idea of metaphysics it already stands wholly shut out. All the same, in keeping with scholastic practice one will yet still have to concede it a small corner there (albeit only by way of episode), and that on grounds of economy, since it is not yet rich enough to constitute a study on its own, and yet too weighty to be thrown out altogether or fastened somewhere else, where it would find even less affinity than in metaphysics. It is thus no more than a stranger lodged for the time being, granted a stay for a while, until in a full-scale anthropology (the counterpart to the empirical doctrine of nature) he can take up quarters of his own.

Such, then, is the general idea of metaphysics, which — because more was at first expected of it than can in fairness be demanded, and because for a while people indulged themselves with pleasant expectations — sank in the end into general disdain, once they found their hope betrayed. From the whole run of our critique one will by now be amply persuaded of this: that, granted metaphysics cannot serve as the bedrock of religion, it must nevertheless remain at all times as its rampart , and that human reason — dialectical already through the bent of its own nature — can never dispense with a science of this kind, one that curbs it and, by means of a scientific and perfectly luminous self-knowledge, holds off the ravages that an unbridled speculative reason would otherwise, quite without fail, work upon morals as well as religion. One may thus be assured — however aloof or dismissive those carry on who know how to appraise a science not by its nature but purely by its incidental effects — that we shall time and again come back to it as to a beloved from whom we have been estranged, for reason, where essential ends are here in question, is bound to labor without rest either toward searching insight or toward the wrecking of sound insights already possessed.

Metaphysics, then — of nature as much as of morals — and above all the critique of a reason that dares to fly on its own wings, which runs ahead by way of preliminary exercise (propaedeutically), is really the one thing that alone constitutes what we can, in the true sense, call philosophy. Philosophy so understood refers everything to wisdom, but by the road of science — the only road which, once it has been opened, never grows over again and suffers no wanderings astray. Mathematics, natural science, and even the empirical acquaintance with the human being carry a high worth as means — for the most part toward contingent, but in the last resort toward necessary and essential ends of mankind — yet only then through the mediation of a cognition of reason out of bare concepts, which, call it what you will, is at bottom nothing but metaphysics.

For precisely this reason metaphysics is likewise the crowning of every cultivation of human reason, indispensable even should one leave out of account its bearing as a science upon certain determinate ends. For it examines reason in respect of its elements and supreme maxims, which must themselves underlie the possibility of certain sciences and the use of them all. That, as mere speculation, it does more to fend off errors than to widen cognition detracts nothing from its worth; on the contrary, it lends it dignity and standing through the censorial office, which safeguards the general order and harmony — indeed the prosperity — of the scientific commonwealth and keeps its daring and fertile labors from drifting away from the chief end, the happiness of all.

Chapter 4. The History of Pure Reason

This title stands here merely to designate a place that is left vacant in the system and will have to be supplied at some future point. I content myself with casting, from a purely transcendental vantage point—namely the nature of pure reason—a fleeting glance over the whole of the treatments it has so far received, which to my eye admittedly presents edifices, yet only ones lying in ruins.

It is remarkable enough—though in the nature of things it could not have been otherwise—that human beings, in the childhood of philosophy, set out from precisely where we would now rather come to rest, namely by first taking up the cognition of God, together with the hope—or even the makeup—of a world beyond. Whatever crude religious concepts the ancient usages, surviving from a time even prior to the peoples' rude condition, may have brought in, this did not keep the more enlightened part from dedicating themselves to free inquiry into this object, and it was easy to see that no more solid and trustworthy way of pleasing the invisible power that rules the world—so as to be happy at least in another world—could be found than a good conduct of life. Theology and morals were on that account the two mainsprings—or better, the two points of reference—for all those abstracted inquiries of reason to which people have ever since given themselves. The former, meanwhile, was really what drew merely speculative reason, little by little, into that business which subsequently grew so famous under the title of metaphysics.

I will not now separate out the periods on which this or that transformation of metaphysics happened to fall, but only present, in a rapid outline, the difference of idea that prompted its principal revolutions. And there I find a threefold aim under which the most significant transformations were founded upon this stage of controversy.

1. As regards the object to which all our cognitions of reason refer, some were merely sensual-, others merely intellectual philosophers. Epicurus can be called the foremost philosopher of sensibility, Plato that of the intellectual realm. This distinction between the schools, however subtle it may be, dates back to the very earliest times and long persisted without a break. The adherents of the former maintained that actuality resides solely in the objects of the senses and that all the rest is fancy; the adherents of the second held, on the contrary: within the senses nothing is found but semblance, and the understanding alone cognizes what is true. On that account the former did not, for all that, deny reality to the concepts of the understanding, yet in their hands this reality was only logical, while in the hands of the others it was mystical. The former, while granting intellectual concepts, took only sensible objects to be given. The latter, by contrast, held the true objects to be merely intelligible and posited an intuition carried out through the pure understanding—one attended by no senses and, on their view, only thrown into confusion by them.

2. As concerns the origin of pure cognitions of reason—as to whether they are drawn from experience or, independently of it, find their source in reason. Aristotle can be taken as the leader of the empiricists, and Plato as that of the noologists. Locke, who in more recent days took the side of the former, and Leibniz, who took that of the latter (albeit at a sufficient distance from the latter's mystical system), have all the same proved unable to bring this quarrel to any decision. At least Epicurus, for his part, went about his sensual system far more consistently (for in his inferences he never once passed beyond the frontier of experience) than did Aristotle and Locke (but above all the latter), who, having drawn every concept and principle from experience, presses their use so far as to hold that God's existence and the immortality of the soul (although both objects lie wholly beyond the limits of possible experience) can be demonstrated every bit as evidently as some theorem of mathematics.

3. As to method. If anything at all is to bear the name of method, it must be a procedure conducted according to principles. Now the method presently dominant in this branch of investigation admits of a division into the naturalistic and the scientific. The naturalist where pure reason is concerned adopts as his principle: that on the loftiest questions making up the task of metaphysics more is to be achieved by ordinary reason without science (which he styles sound reason) than by way of speculation. He thus asserts that the size and remoteness of the moon can be settled with more assurance by the estimate of the eye than through mathematical detours. It is sheer misology raised to principles and—what is more preposterous than anything—the disregard of all artful means, trumpeted as a distinctive method for broadening one's cognition. For as far as those naturalists are concerned who act from a want of fuller insight, nothing can with good ground be charged against them. They keep to ordinary reason without parading their ignorance as a method that is supposed to hold the secret of drawing truth up from Democritus's deep well. Quod sapio, satis est mihi, non ego curo esse quod Arcesilas aerumnosique Solones (Pers.) is their watchword, under which they may, content and worthy of approval, pass their days without troubling over science or throwing its business into disarray.

As for those who observe a scientific method, they are here free to proceed either dogmatically or skeptically, though under every circumstance bound to proceed systematically. If for the first of these I here name the celebrated Wolff, and for the second David Hume, I may, consistent with my present aim, leave the others unnamed. The critical path alone still lies open. If the reader has shown the good will and patience to walk through it in my company, he may now judge whether—should he care to add his own contribution toward turning this footpath into a highroad—what many centuries were unable to accomplish might not be reached before the present one has run its course: that is, to grant human reason full contentment in the very matter that has forever engaged its craving to know, though thus far to no avail.