These Prolegomena are not designed for the use of pupils, but of future teachers, and even for the latter should serve not so much to regulate the exposition of an already existing science, as for the discovery of such a science.
There are scholars with whom the history of philosophy (ancient no less than modern) constitutes their own philosophy; for these the present Prolegomena are not written. They must wait till those, who are endeavouring to construct one out of the resources of Reason, have completed their work, and it will then be their turn to give an acount of what has already taken place. Otherwise nothing can be said which, in their opinion, has not been said before, and in fact this may pass as an infallible prophecy for all future time; inasmuch as the human understanding having speculated on countless subjects through so many centuries, in so many ways, it can scarcely fail that for every new idea an old one should be found having some affinity with it.
My purpose is, to convince all those who care to trouble themselves with metaphysics, that it is indispensably necessary for the present to suspend their work, to look upon all that is gone before as non-existent, and, above all things, first to propose the question “Whether such a thing as metaphysics be even possible at all?”
If it be a science, how comes it that it cannot like other sciences win for itself a universal and lasting recognition? If it be not one, how is it that under the semblance of a science it is ceaselessly boasting and holding out to the human understanding hopes that are never extinguished and never fulfilled? Something must be definitely decided respecting the nature of this assumed science, whether it be to demonstrate our knowledge or our ignorance; for it is impossible that it should remain longer on the same footing as heretofore. It seems well-nigh ridiculous, while every other science ceaselessly progresses, that this which is supposed to be wisdom itself, whose oracle every one interrogates, is continually turning round on the same spot, without moving a step in advance. Its votaries have also much decreased, and we do not see those who feel themselves strong enough to shine in other sciences, willing to risk their fame in this, where every one, ignorant though he be in all else, ventures upon a decided opinion, because forsooth in this sphere there is no certain weight and measure at hand by which to distinguish profundity from worthless jargon.
It is, however, nothing unheard of, after lengthened treatment of a science, when wonders are thought as to the progress made in it, that some one lets fall the question: Whether and how such a science is possible at all? For the human Reason is so fond of building, that it has many times reared up a lofty tower and afterwards pulled it down again, to see how its foundation was laid. It is never too late to become reasonable and wise; but it is always more difficult when the knowledge comes late to bring it into working order.
To ask, whether a science is possible, presupposes a doubt as to its reality. But such a doubt must offend all those whose whole fortune, perhaps, consists in this supposed treasure; any one who starts such a doubt may always make up his mind then for resistance on all sides. Some, in the proud consciousness of their old and therefore, as they think, legitimate possession, with their metaphysical compendiums in their hands, will look down upon it with contempt. Others, who never see anything anywhere that does not coincide with what they have elsewhere previously seen, will not understand it, and everything will remain for some time as though nothing at all had happened to prepare or to admit the hope of a near change.
At the same time, I may confidently predict that the self-thinking reader of these Prolegomena will not merely doubt his previous science, but in the end will be quite convinced, that there cannot exist such a science without the demands here made being satisfied, upon which its possibility rests, and that inasmuch as this has never happened, that there is as yet no such thing as metaphysics at all. But as notwithstanding the search after it can never lose its interest, 1 because the interests of the universal human Reason are so intimately bound up with it, he will confess that a complete reform, or rather a new birth according to a plan hitherto quite unknown, is inevitable, however much it may be striven against for a time.
Since the attempts of Locke and Leibnitz, or rather since the first rise of metaphysics as far as its history will reach, no event has occurred that in view of the fortunes of the science could be more decisive than the attack made upon it by David Hume. He, indeed, threw no light upon this order of knowledge, but he struck a spark by which a light might have been kindled, had it touched a receptive substance, to have preserved and enlarged its glimmer.
Hume took for his starting-point, mainly, a single but important conception of metaphysics, namely, that of the connection of Cause and Effect (together with the derivative conceptions of Force and Action, c.) and required of the Reason which professes to have given it birth a rigid justification of its right, to think, that something is so constructed that on its being posited something else is therewith necessarily also posited; for so much is contained in the conception of Cause. He proved irrefutably that it is quite impossible for the Reason à priori, out of mere conceptions, to cogitate this connection, since it involves necessity; but the problem nevertheless was not to be overlooked, how that, because something exists, something else must necessarily also exist, and thus how the conception of such a connection can be regarded as à priori. Hence he concluded that the Reason completely deceived itself with this conception, that it falsely claimed it as its own child, while it was nothing more than a bastard of the imagination, which, impregnated by experience, had brought certain presentations under the law of association, and had substituted a subjective necessity arising thence, i.e., from habit, for an objective one founded on insight. From this he concluded that the Reason possessed no faculty of cogitating such connections even in general, because its conceptions would then be mere inventions, and all its pretended à priori cognitions nothing but common experiences mislabelled; which is as much as to say, no such thing as metaphysics exists at all, and there is no possibility of its ever existing. 1
However hasty and incorrect his conclusion may have been, it was at least based on investigation, and it would have been well worth while if the good heads of his time had united to solve the problem in the sense in which he had stated it, if as far as possible with happier results; the consequence of which must have been a speedy and complete reform of the science.
But the always unfavourable fate of metaphysics, willed that he should be understood by no one. It cannot be without feeling a certain regret that one sees how completely his opponents, Reid, Oswald, Beattie, and, lastly, Priestley, missed the point of his problem in taking that for granted which was precisely what he doubted, and on the other hand in proving with warmth, and in most cases great immodesty, what it had never entered his head to question, and as a result in so completely mistaking his reforming hint that everything remained in the same state as though nothing had happened. It was not the question whether the conception of Cause was correct and useful, and in view of the whole knowledge of Nature, indispensable, for upon this Hume had never cast a doubt, but whether it could be cogitated à priori by the Reason in such a manner as to constitute an inward truth independent of all experience, and therefore of a more extended use than that of being solely applied to the objects of experience; it was upon this that Hume desired enlightenment. The question was as to the origin of the idea, not as to its practical necessity in use; were the former ascertained, the conditions of its use and the extent in which it is valid would have been sufficiently obvious.
The opponents of this celebrated man, to have done the problem full justice, must have penetrated deeply into the nature of the Reason, in so far as it is occupied solely with pure thought, a thing which was inconvenient for them. They invented therefore a more convenient means, by which, without any insight, they might defy him, namely, the appeal to the common sense of mankind. It is indeed a great natural gift to possess, straightforward (or, as it has been recently called, plain) common sense. But it must be proved by deeds, by the thoughtfulness and rationality of what one thinks and says, and not by appealing to it as an oracle, when one has nothing wise to adduce in one’s justification. When insight and science are at a low ebb, then and not before to appeal to common sense is one of the subtle inventions of modern times, by which the emptiest talker may coolly confront the profoundest thinker and hold out against him. But so long as there is a small remnant of insight left, one will be cautious of clutching at this straw. And seen in its true light, the argument is nothing better than an appeal to the verdict of the multitude; a clamour before which the philosopher blushes, and the popular witling scornfully triumphs. But I should think that Hume can make as good claim to the possession of common sense as Beattie, and in addition, to something the latter certainly did not possess, namely, a critical Reason, to hold common sense within bounds in order not to let it overreach itself in speculations; or if we are merely concerned with the latter, not to require it to decide, seeing that it is incompetent to deal with matters outside its own axioms; for only in this way will it remain a healthy common sense. Chisel and hammer are quite sufficient to shape a piece of deal, but for copper-engraving an etching-needle is necessary. In the same way, common, no less than speculative understanding, is useful in its kind; the former when we have to do with judgments having an immediate bearing on experience, but the latter, where we have to judge, universally, out of mere conceptions, as for instance in metaphysics, where the self-styling (though often per antiphrasin ) healthy understanding is capable of no judgment at all.
I readily confess, the reminder of David Hume was what many years ago first broke my dogmatic slumber, and gave my researches in the field of speculative philosophy quite a different direction. I was far enough removed from giving him an ear so far as his consequences were concerned, the latter resulting merely from his not having placed his problem fully before him, but only attacking a part of it, which, without taking the whole into consideration, could not possibly afford a solution. When one starts from a well-founded, though undeveloped, idea that a predecessor has left, one may well hope, by increased reflection, to bring it further than was possible for the acute man one has to thank for the original sparks of its light.
First of all, I tried whether Hume’s observation could not be made general, and soon found that the conception of the connection of cause and effect was not by a long way the only one by which the understanding cogitates à priori the connections of things, but that metaphysics consists entirely of such. I endeavoured to ascertain their number, and as I succeeded in doing this to my satisfaction, namely, out of a single principle, I proceeded to the deduction of these conceptions, which I was now assured could not, as Hume had pretended, be derived from experience but must have originated in the pure understanding. This deduction, that seemed impossible to my acute predecessor, that had not even occurred to any one except him, although every one unconcernedly used the conception (without asking on what its objective validity rested); this, I say, was the most difficult problem that could ever be undertaken in the interests of metaphysics, and the worst of it was, that metaphysics, so far as it anywhere exists at present, could not afford me the least help, because the above deduction had in the first place to make metaphysics possible. Having now succeeded in the solution of Hume’s problem, not in one particular case only, but in respect of the whole capacity of the pure Reason, I could at least more surely, though still only by slow steps, determine the whole range of the pure Reason, in its limits as well as in its content, completely according to universal principles, which was what metaphysics required, in order to construct its system on an assured plan.
I am afraid, however, lest the carrying out of the problem of Hume in its greatest possible development (namely, in the Critique of the Pure Reason) should fare as the problem itself fared when it was first stated. It will be falsely judged, because it is misunderstood; it will be misunderstood, because people, though they may care to turn over the leaves of the book, will not care to think it out; and they will be unwilling to expend this trouble upon it because the work is dry, obscure, and opposed to all accustomed conceptions, besides being diffuse. But I must confess, it was quite unexpected for me to hear from a philosopher complaints as to its want of popularity, entertainingness, and agreeable arrangement, when the question was of a branch of knowledge highly prized and indispensable to humanity, and which cannot be treated otherwise than according to the most strict rules of scholastic precision; whereby popularity may indeed follow in time, but can never be expected at the commencement. As regards a certain obscurity, however, arising partly from the diffuseness of the plan, in consequence of which the main points of the investigation are not so readily grasped, the grievance must be admitted, and this it is the task of the present Prolegomena to remove.
The above work, which presents the capacity of the pure Reason in its whole range and boundaries, always remains the foundation to which the Prolegomena are only preparatory; for the Critique must, as science, stand complete and systematic even down to the smallest detail, before we can so much as think of the rise of metaphysics, or even allow ourselves the most distant hope in this direction.
We have been long accustomed to see old and worn-out branches of knowledge receive a new support, by being taken out of their former coverings, and suited with a systematic garment according to our own approved style, but under new titles; and the great majority of readers will expect nothing different from our Critique. But these Prolegomena will convince him that it is quite a new science, of which no one previously had had the smallest conception, of which even the idea was unknown, and with reference to which all hitherto received knowledge was unavailable, with the exception of the hint afforded by Hume’s doubt. But Hume never dreamt of a possible formal science of this nature, and in order to land his ship in safety, ran it aground on the shore of scepticism, where it might lie and rot; instead of which, it is my purpose to furnish a pilot, who, according to certain principles of seamanship, derived from a knowledge of the globe, and supplied with a complete map and compass, may steer the ship with safety wherever it seems good to him.
In a new science, which is wholly isolated and single of its kind, we should achieve nothing were we to start with the prejudice that we could judge of things by means of our previously acquired knowledge, which is precisely what has first to be called in question. For were we to do this, we should only fancy we saw everywhere what we had already known, the expressions, having a similar sound, only that all would appear utterly metamorphosed, senseless and unintelligible, because we should have as a foundation our own notions, made by long habit a second nature, instead of the author’s. But the diffuseness of the work, founded as it is on science (of which an unavoidable dryness and scholastic precision are characteristics) rather than on style, however advantageous it may be to the subject, is undoubtedly disadvantageous to the book.
It is indeed not given to every one to write as subtly and at the same time as fascinatingly as David Hume, or as profoundly and as elegantly as Moses Mendelssohn; but I flatter myself I might have rendered my style popular, if I had only had to sketch a plan, and to leave its completion to others, and not had the well-being of the science, with which I had been so long occupied, so much at heart; for it requires considerable endurance and not a little self-denial to choose a late but enduring fame, in preference to the allurement of a speedy and favourable reception.
Plan-making is often a luxurious and pretentious mental occupation, whereby the reputation of a creative genius is acquired by demanding what one cannot achieve oneself, censuring what one cannot improve, and proposing what one does not know where to find. But to a thorough plan of the general Critique of the Reason something more is necessary, as may be well supposed, if it is not to be, as usual, a mere declamation of pious wishes. For pure Reason is so isolated, and in itself so intimately connected a sphere, that no part of it can be touched upon without affecting the rest. We can accomplish nothing, therefore, without determining the position and influence of each part with regard to the others, because there is nothing external to it by which our judgment can be corrected as to its inner character. The validity and use of every part depends upon the relations in which it stands toward the rest witin the Reason, and as in the construction of an organised body, the purpose of each member can only be deduced from a complete conception of the whole. It may therefore be said of such a critique that it is never reliable, unless it be quite complete, down to the least of the elements of pure Reason; and that in the sphere of this faculty, one must determine and expound either everything or nothing.
Yet although a mere plan, if it preceded the critique, would be incomprehensible, unreliable and useless, it is so much the more useful when it follows it. For one is then in a position to view the whole, to test the main points upon which the science rests piecemeal, and to render the style better than was possible on the first execution of the work.
The following is such a plan, which as the work is complete may be presented in an analytical manner, whereas the work itself was obliged to be constructed throughout on a synthetic method, in order that the science might exhibit all its articulations in there natural connection as the organisation of a special faculty of knowledge. Should, on the other hand, any one find this plan, put forward by me as Prolegomena to any future system of metaphysics, itself obscure, he must bear in mind that it is not necessary for every one to study metaphysics; that there is much talent, perfectly adequate to the investigation of thorough and even deep sciences, lying more in the region of intuition, which is unsuccessful in a species of research based solely on abstract conceptions, and that, in such a case, mental abilities should be turned in another direction. But he who undertakes to judge a system of metaphysics or to construct one, must in every way satisfy the demands that will here be made. It may so happen, either that he accepts my solution, or that he utterly refutes it and offers another in its stead—evade it, he cannot; and that, finally, the so-much decried obscurity (though a frequent covering for indolence and stupidity) may have its uses, since those who in respect of other sciences maintain a judicious silence, in questions of metaphysics speak and decide in a dictatorial tone, because here their ignorance does not distinctly clash with the knowledge of other people, though not the less with the axioms of a sound criticism; of which one may say, ignavum fucos, pecus a prœsepibus arcent. Virg.’ (they keep off, from the hives, the lazy swarm of drones).
In presenting a branch of knowledge as science, it is necessary to be able to define with precision its distinguishing characteristic, that which it possesses in common with no other branch, and which is therefore special to itself; when this is not the case the boundaries of all sciences run into one another, and no one of them can be thoroughly treated of, according to its own nature.
Now this speciality may consist in the distinction of its object, of its sources of cognition, of its mode of cognition, or lastly, of several if not all these points taken together, on which the idea of a possible science and of its territory primarily rests.
Firstly, as regards the sources of metaphysical knowledge, the very conception of the latter shows that these cannot be empirical. Its principles (under which not merely its axioms, but also its fundamental conceptions are included) must consequently never be derived from experience; since it is not physical but metaphysical knowledge, i.e., knowledge beyond experience, that is wanted. Thus neither external experience, the source of physical science proper, nor internal experience, the groundwork of empirical psychology, will suffice for its foundation. It consists, then, in knowledge à priori, that is, knowledge derived from pure understanding and pure reason.
But in this, there is nothing to distinguish it from pure mathematics; it must be defined, therefore, as pure philosophical knowledge; respecting the meaning of which expression, I must refer the reader to the Critique of Pure Reason, (Bohn’s Ed. p. 435,) where the distinction between these two modes of the Reason’s use are clearly and exhaustively expounded. So much as to the sources of metaphysical knowledge.
Metaphysical knowledge must contain simply judgments à priori, so much is demanded by the speciality of its sources. But judgments, let them have what origin they may, or let them even as regards logical form be constituted as they may, possess a distinction according to their content, by virtue of which they are either simply explanatory and contribute nothing to the content of a cognition, or they are extensive, and enlarge the given cognition; the first may be termed analytic, and the second synthetic judgments.
Analytic judgments say nothing in the predicate, but what was already cogitated in the conception of the subject, though perhaps not so clearly, or with the same degree of consciousness. When I say, all bodies are extended, I do not thereby enlarge my conception of a body in the least, but simply analyse it, inasmuch as extension, although not expressly stated, was already cogitated in that conception; the judgment is, in other words, analytic. On the other hand, the proposition, some bodies are heavy, contains something in the predicate which was not already cogitated in the general conception of a body; it enlarges, that is to say, my knowledge, in so far as it adds something to my conception; and must therefore be termed a synthetic judgment.
All analytic judgments are based entirely on the principle of contradiction, and are by their nature cognitions à priori, whether the conceptions serving as their matter be empirical or not. For inasmuch as the predicate of an affirmative analytic judgment is previously cogitated in the conception of the subject, it cannot without contradiction be denied of it; in the same way, its contrary, in a negative analytic judgment, must necessarily be denied of the subject, likewise in accordance with the principle of contradiction. It is thus with the propositions—every body is extended; no body is unextended (simple). For this reason all analytic propositions are judgments à priori, although their conceptions may be empirical. Let us take as an instance the proposition, gold is a yellow metal. Now, to know this, I require no further experience beyond my conception of gold, which contains the propositions that this body is yellow and a metal; for this constitutes precisely my conception, and therefore I have only to dissect it, without needing to look around for anything elsewhere.
There are synthetic judgments à posteriori whose origin is empirical; but there are also others of an à priori certainty, that spring from the Understanding and the Reason. But both are alike in this, that they can never have their source solely in the axiom of analysis, viz., the principle of contradiction; they require an altogether different principle, notwithstanding that whatever principle they may be deduced from, they must always conform to the principle of contradiction, for nothing can be opposed to this principle, although not everything can be deduced from it. I will first of all bring synthetic judgments under certain classes.
(1) Judgments of experience are always synthetic. It would be absurd to found an analytic judgment on experience, as it is unnecessary to go beyond my own conception in order to construct the judgment, and therefore the confirmation of experience is unnecessary to it. That a body is extended is a proposition possessing à priori certainty, and no judgment of experience. For before I go to experience I have all the conditions of my judgment already present in the conception, out of which I simply draw the predicate in accordance with the principle of contradiction, and thereby at the same time the necessity of the judgment may be known, a point which experience could never teach me.
(2) Mathematical judgments are in their entirety synthetic. This truth seems hitherto to have altogether escaped the analysts of human Reason; indeed, to be directly opposed to all their suppositions, although it is indisputably certain and very important in its consequences. For, because it was found that the conclusions of mathematicians all proceed according to the principle of contradiction (which the nature of every apodictic certainty demands), it was concluded that the axioms were also known through the principle of contradiction, which was a great error; for though a synthetic proposition can be viewed in the light of the above principle, it can only be so by presupposing another synthetic proposition from which it is derived, but never by itself.
It must be first of all remarked that essentially mathematical propositions are always à priori, and never empirical, because they involve necessity, which cannot be inferred from experience. Should any one be unwilling to admit this, I will limit my assertion to pure mathematics, the very conception of which itself brings with it the fact that it contains nothing empirical, but simply pure knowledge à priori.
At first sight, one might be disposed to think the proposition 7+5 = 12 merely analytic, resulting from the conception of a sum of seven and five, according to the principle of contradiction. But more closely considered it will be found that the conception of the sum of 7 and 5 comprises nothing beyond the union of two numbers in a single one, and that therein nothing whatever is cogitated as to what this single number is, that comprehends both the others. The conception of twelve is by no means already cogitated, when I think merely of the union of seven and five, and I may dissect my conception of such a possible sum as long as I please, without discovering therein the number twelve. One must leave these conceptions, and call to one’s aid an intuition corresponding to one or other of them, as for instance one’s five fingers (or, like Segner in his Arithmetic, five points), and so gradually add the units of the five given in intuition to the conception of the seven. One’s conception is therefore really enlarged by the proposition 7+5 = 12; to the first a new one being added, that was in nowise cogitated in the former; in other words, arithmetical propositions are always synthetic, a truth which is more apparent when we take rather larger numbers, for we must then be clearly convinced, that turn and twist our conceptions as we may, without calling intuition to our aid, we shall never find the sum required, by the mere dissection of them.
Just as little is any axiom of pure geometry analytic. That a straight line is the shortest between two points, is a synthetic proposition. For my conception of straight, has no reference to size, but only to quality. The conception of the “shortest” therefore is quite additional, and cannot be drawn from any analysis of the conception of a straight line. Intuition must therefore again be taken to our aid, by means of which alone the synthesis is possible.
Certain other axioms, postulated by geometricians, are indeed really analytic and rest on the principle of contradiction, but they only serve, like identical propositions, as links in the chain of method, and not themselves as principles; as for instance a = a, the whole is equal to itself, or ( a+b )≻ a, i.e., the whole is greater than its part. But even these, although they are contained in mere conceptions, are only admitted in mathematics because they can be presented in intuition. What produces the common belief that the predicate of such apodictic judgments lies already in our conception, and that the judgment is therefore analytic, is merely the ambiguity of expression. We ought, namely, to cogitate a certain predicate to a given conception, and this necessity adheres even to the conceptions themselves. But the question is not what we ought to, but what we actually do, although obscurely, cogitate in them; this shows us that the predicate of those conceptions is dependent indeed necessarily, though not immediately (but by means of an added intuition), upon its subject.
This division is in view of the Critique of human understanding indispensable, and deserves therefore to be classic in this department; though I am not aware of any other in which it has any important use. And here I also find the cause why dogmatic philosophers who looked for the sources of metaphysical judgments in metaphysics itself (rather than outside of it, in the laws of the pure Reason in general), have always neglected this division, that seems so naturally to offer itself, and like the celebrated Wolff, or the acute Baumgarten, who followed in his steps, have sought the proof of the principle of sufficient reason, which is obviously synthetic, in that of contradiction. On the other hand, I can trace already in “Locke’s Essays on the Human Understanding” a notion of this division. For in the third chapter of the fourth book, (Chap. III. § 9 et seq., ) after he has spoken of the connection of different presentations in judgments, and of their sources, one of which he places in identity or contradiction (analytic judgments), and the other in the existence of presentations in a subject (synthetic judgments), he confesses, § 10, that our knowledge ( à priori ) of the last is very limited, amounting almost to nothing. But there is so little that is definite and reduced to rule in what he says respecting this kind of knowledge, that one cannot wonder that nobody, strange to say, not excepting Hume, was induced thereby to institute investigations into the class of propositions in question. For universal yet definite principles like these, are not easily learnt from other men, to whom they have been only dimly discernible. One must, first of all, have come upon them through one’s own reflection, and one will then find them elsewhere, in places where otherwise they would certainly not have been discovered; since not even the authors knew that such an idea lay at the foundation of their own remarks. Those who do not think for themselves, possess notwithstanding the sharpness of insight to detect everything after it has already been shown them, in what has previously been said, where no one could before see it.
Were metaphysics actually present as a science, one might say: Here is metaphysics, you only require to learn it, and it will convince you permanently and irresistibly of its truth. In that case the present question would be unnecessary, and there would only remain one which would more concern a testing of our acuteness, than a proof of the existence of the thing itself; namely, the question, How is it possible, and how is the Reason to set about attaining it? Unfortunately, in this case, human Reason is not in such a happy position. There is no single book that can be shown, like for instance Euclid, of which it can be said: This is metaphysics, herein is to be found the chief end of the science, the knowledge of a Supreme Being and of a future world, demonstrated upon principles of the pure Reason. It is possible, doubtless, to bring forward many propositions that are apodictically certain, and that have never been contested; but these are in their entirety analytic, and concern more the materials and the elements of construction, than the extension of knowledge, which is our special object in the present case. But even when synthetic propositions are produced (such as the principle of sufficient Reason), which though they have never been proved from mere Reason, that is, à priori, as they ought to have been, are willingly admitted; even then, whenever it is attempted to make use of them for the main purpose, one is landed in such unstable and doubtful assertions, that it has always happened that one system of metaphysics has contradicted another, either in respect of the assertions themselves or their proofs, and has thus destroyed all claim to a lasting recognition. The very attempts made to establish the science have without doubt been the primary cause of the scepticism that so early arose, a mode of thought in which the Reason treats itself with such violence, that it would never have arisen but from the latter’s utter despair of satisfying its chief aspirations. For long before man began methodically to question Nature, he interrogated his own isolated Reason, already practised, in a measure by common experience; because Reason is always present, while the laws of Nature generally require to be laboriously sought out. And so metaphysics floated to the surface like foam, and like foam, too, no sooner was it gathered up than it dissolved, while another mass of it appeared upon the scene which some were always found eager to grasp; while others, instead of seeking to penetrate the cause of the phenomenon in question, thought themselves wise in laughing at the futile exertions of the former.
The essential feature distinguishing pure mathematical knowledge from all other knowledge à priori, is that it does not proceed from conceptions themselves, but always through the construction of conceptions. (Critique, p. 435.) Since, therefore, in its propositions it must pass out of the conception to that containing the corresponding intuition, these can and ought never to arise from the dissection of conceptions, that is, analytically; in other words, they are, in their entirety, synthetic.
I cannot refrain from remarking on the disadvantage resulting to philosophy from a neglect of this simple and apparently insignificant observation. Hume, indeed, feeling it a task worthy of a philosopher, cast his eye over the whole field of pure knowledge à priori in which the human understanding claims such extensive possession. He, however, inconsiderately severed from it an entire, and indeed the most important, province, namely, that of pure mathematics, under the impression that its nature, and, so to speak, its constitution, rested on totally different principles, that is, solely on the principle of contradiction; and although he did not make such a formal and universal division of propositions as is here done by me, or under the same name, yet it was as good as saying, pure mathematics contains simply analytic judgments, but metaphysics, synthetic judgments à priori. Now in this he made a great mistake, and this mistake had decidedly injurious consequences on his whole conception. For if he had not made it, he would have extended his question respecting the origin of our synthetic judgments far beyond his metaphysical conception of causality, and comprehended therein the possibility of mathematics à priori; for he must have regarded this as equally synthetic. But in the latter case he could, under no circumstances, have based his metaphysical propositions on mere experience, as he would then have been obliged to have subordinated the axioms of pure mathematics themselves to experience, a proceeding for which he was much too penetrating.
The good company into which metaphysics would then have been brought must have ensured it against contemptuous treatment; for the strokes aimed at the latter must have also hit the former, and this neither was nor could have been his intention. The result must have been to lead the acute man to considerations similar to those with which we are now occupied, but which must have gained infinitely by his inimitable style.
Essentially metaphysical judgments are, in their entirety, synthetic. We must distinguish between judgments belonging to metaphysics from metaphysical judgments proper. Among the former are comprised many that are analytic, but they only furnish the means for metaphysical judgments, these forming the entire purpose of the science, and being all synthetic. For when conceptions belong to metaphysics, as, for instance, that of substance, the judgments arising from their dissection belong also to metaphysics; e.g., substance is that which only exists as subject, c., and many more similar analytic judgments, by means of which an en leavour is made to approach the definition of the conception. Since, however, the analysis of a pure conception of the understanding (such as those metaphysics contains) cannot proceed differently from the analysis of any other conception (even an empirical one) not belonging to metaphysics (e.g., air is an elastic fluid, the elasticity of which is not destroyed by any known degree of cold), it follows that the conception but not the analytic judgment, is properly metaphysical. The science in question has something special and peculiar in the production of its cognitions à priori, which must be distinguished from what it has in common with all other cognitions of the understanding; so, for instance, the proposition, “all that is substance in things is permanent,” is a synthetic and properly metaphysical judgment.
When the conceptions à priori constituting the materials of metaphysics have been previously collected according to fixed principles, the dissection of these conceptions is of great value. They can be then presented as a special department (as it were a philosophia definitiva ), containing solely analytic propositions relating to metaphysics, though quite distinct from the synthetic, which constitute metaphysics itself. For, indeed, these analyses have nowhere any important use, except in metaphysics, that is, in reference to the synthetic propositions, to be generated from these dissected conceptions.
The conclusion drawn in this section is then, that metaphysics is properly concerned with synthetic propositions à priori, and that these alone constitute its purpose, but that, in addition to this, it requires frequent dissections of its conceptions, or analytic judgments, the procedure in this respect being only the same as in other departments of knowledge, where conceptions are sought to be made plain by analysis. But the generation of knowledge à priori, as much in intuition as in conceptions, in fine, synthetic propositions à priori in philosophical cognitions, make up the essential content of metaphysics.
Wearied, then, of the dogmatism that teaches us nothing, as well as of the scepticism that promises us nothing, not even the rest of a permissible ignorance, led on by the importance of the knowledge we need, rendered mistrustful by a long experience, of all we believe ourselves to possess, or that offers itself in the name of pure Reason, there only remains one critical question, the answer to which must regulate our future procedure— Is metaphysics possible at all? But this question must not be answered by sceptical objections to particular assertions of any actual system of metaphysics (for we do not admit any at present), but from the, as yet, only problematical conception of such a science.
In the ‘Critique of Pure Reason,’ I went synthetically to work in respect of this question, in instituting researches into the pure Reason itself, and in this source endeavoured to determine the elements, as well as the laws of its pure use, according to principles. The task is difficult, and demands a resolute reader, gradually to think out a system, having no datum other than the Reason itself, and which, therefore, without supporting itself on any fact, seeks to unfold knowledge from its original germs. Prolegomena should, on the contrary, be preparatory exercises, designed more to show what has to be done, to realise a science as far as is possible, than to expound one. They must, therefore, rely on something known as trustworthy, from which we may with confidence proceed, and ascend to its sources, as yet unknown to us, and the discovery of which will not only explain what we already knew, but at the same time exhibit to us a range of many cognitions, all arising from these same sources. The methodical procedure of Prolegomena, especially of those destined to prepare a future system of metaphysics, will therefore be analytic.
Now it fortunately happens that, although we cannot accept metaphysics as a real science, we may assert with confidence that certain pure synthetic cognitions are really given à priori, namely, pure mathematics and pure natural science, for both contain propositions, partly apodictically certain through mere Reason, and partly recognised by universal consent as coming from experience, and yet as completely independent of it.
We have, then, at least some uncontested, synthetic knowledge à priori, and do not require to ask whether this is possible, since it is actual, but only— How it is possible, in order to be able to deduce from the principle, rendering possible what is already given, the possibility of all the rest.
We have already seen the important distinction between analytic and synthetic judgments. The possibility of analytic propositions can be very easily conceived, for they are based simply on the principle of contradiction. The possibility of synthetic propositions à posteriori, i.e., of such as are derived from experience, requires no particular explanation, for experience is nothing more than a continual adding together (synthesis) of perceptions. There remains, then, only synthetic propositions à priori, the possibility of which has yet to be sought for, or examined, because it must rest on other principles than that of contradiction.
But we do not require to search out the possibility of such propositions, that is, to ask whether they are possible, for there are enough of them, actually given, and with unquestionable certainty; and as the method we are here following is analytic, we shall assume at the outset that such synthetic but pure knowledge from the Reason, is real; but thereupon we must investigate the ground of this possibility and proceed to ask—How is this knowledge possible? in order that, from the principles of its possibility, we may be in a position to determine the conditions, the scope, and limits of its use. The proper problem, on which everything turns, when expressed with scholastic precision, will accordingly stand thus— How are synthetic propositions à priori possible ?
In the above, for the sake of popularity, I have expressed the question somewhat differently, namely, as an inquiry after knowledge from pure Reason, which I could do on this occasion without detriment to the desired insight. For as we are here simply concerned with metaphysics and its sources, I hope, after the above remarks, readers will constantly bear in mind that, when we here speak of knowledge from pure Reason, we invariably refer to synthetic and never to analytic knowledge. 1 Upon the solution of this problem, the standing or falling of metaphysics, in other words, its very existence, entirely lepends. Let any one lay down assertions, however plausible, with regard to it, pile up conclusions upon conclusions to the point of overwhelming, if he has not been able first to answer satisfactorily the above question, I have a right to say: It is all vain, baseless philosophy, and false wisdom. You speak through pure Reason, and claim to create à priori cognitions, inasmuch as you pretend not merely to dissect given conceptions but new connections which do not rest on the principle of contradiction, and which you think you conceive quite independently of all experience. How do you arrive at them, and how will you justify yourself in such pretensions? To appeal to the concurrence of the general common sense of mankind you cannot be allowed, for that is a witness whose reputation rests only on vulgar report.
But indispensable as is the answer to this question, it is at the same time no less difficult, and although the chief cause why men have not long ago endeavoured to answer it, lies in the fact of its never having occurred to them that anything of the kind could be asked; there is a second cause, in that the satisfactory answer to this one question demands a more persistent, a deeper and more laborious reflection than the most diffuse work, on metaphysics, the first appearance of which has given promise of immortal fame to its author. And every thoughtful reader, on attentively considering the requirement of this problem, frightened at the outset by its difficulty, would regard it as insoluble; and indeed, were it not for the actual existence of such pure synthetic cognitions à priori, as altogether impossible. This happened in the case of David Hume, although he did not place the problem before him in such generality by far as is here done, and as must be done if the answer is to be decisive for the whole of metaphysics. For how is it possible, said the acute man, that when a conception is given me, I can pass out of it, and connect it with another, which is not contained in the former, and indeed in such a manner as if it necessarily belonged to it? Only experience can present us with such connections (this he concluded from the difficulty which he mistook for an impossibility), and all this imagined necessity, or, what is the same thing, knowledge assumed to be à priori, is nothing but a long habit of finding something true, and thence of holding the subjective necessity for objective. If the reader complains of the difficulty and trouble I shall give him in the solution of this problem, let him only set about the attempt to solve it in an easier way. He will then perhaps feel obliged to one who has undertaken for him the labour of such deep research, and rather show some surprise at the facility with which the solution has been able to be given, when the nature of the subject is taken into account. It has cost years of trouble to solve this problem in its whole universality (in the sense in which mathematicians use this word, namely, as sufficient for all cases), and to be able finally to present it in analytic form, such as the reader will here find.
All metaphysicians are therefore solemnly and lawfully suspended from their occupations, till they shall have adequately answered the question— How are synthetic cognitions à priori possible? for in their answer alone consists the credentials they must produce, if they have aught to bring us in the name of pure Reason; in default of this, they can expect nothing else, than to be rejected, without any further inquiry as to their productions, by sensible people who have been so often deceived.
If, on the other hand, they carry on their business not as a science, but as an art of wholesome persuasion, suitable to the general common sense of mankind, this calling cannot in fairness be denied them. In that case they will only use the modest language of a rational belief; they will admit that it is not allowed them even to conjecture, much less to know, anything, respecting that which lies beyond the boundaries of all possible experience, but merely to assume (not indeed for speculative use, for this they must renounce, but for purely practical purposes) what is possible and even indispensable for the direction of the understanding and will, in life. In this way alone can they possibly carry the reputation of wise and useful men, and they will do so the more in proportion as they renounce that of metaphysicians. For the object of the latter is to be speculative philosophers, and inasmuch as when we are concerned with judgments à priori, bare probabilities are not to be relied on (for what on its assumption is known à priori, is thereby announced as necessary), it cannot be allowed them to play with conjectures, but their assertions must be either science, or they are nothing at all.
It may be said that the whole transcendental philosophy which necessarily precedes all metaphysics is itself nothing more than the full solution in systematic order and completeness of the question here propounded, and that therefore as yet we have no transcendental philosophy. For what bears its name is properly a part of metaphysics, but the former science must first constitute the possibility of the latter, and must therefore precede all metaphysics. Considering, then, that a complete and in itself entirely new science, and one respecting which no aid is to be derived from other sciences, is necessary before a single question can be adequately answered, it is not to be wondered at if the solution of the same is attended with trouble and difficulty, and even perhaps with some degree of obscurity.
As we now proceed to this solution according to analytic method, in which we presuppose that such cognitions from pure Reason are real, we can only call to our aid two sciences of theoretic knowledge (with which alone we are here concerned), namely, pure mathematics and pure natural science, for only these can present to us objects in intuition, and therefore (if a cognition à priori should occur in them) show their truth or agreement with the object in concreto, i.e., their reality; from which to the ground of their possibility we can proceed on the analytic road. This facilitates the matter very much, as the universal considerations are not merely applied to facts but even start from them, rather than as in synthetic procedure, being obliged to be derived, wholly in abstracto, from conceptions.
But from these real and at the same time well-grounded pure cognitions à priori, to rise to a possible one such as we are seeking, namely, to metaphysics as a science, we must needs embrace under our main question that which occasions it, to wit, the naturally given, though as regards its truth not unsuspicious, knowledge à priori lying at its foundation, and the working out of which, without any critical examination of its possibility, is now usually called metaphysics—in a word, the natural tendency to such a science; and thus the transcendental main question, divided into four other questions, will be answered step by step:—
It will be seen, that although the solution of these problems is chiefly meant to illustrate the essential contents of the Critique, it has nevertheless something special, which is of itself worthy of attention, namely, to seek the sources of given sciences in the Reason, in order to investigate and measure this, their faculty of knowing something à priori, by means of the act itself. In this way the particular science itself must gain, if not in respect of its content, at least as regards its right employment, and while it throws light on the higher question of its common origin, at the same time give occasion to better elucidating its own nature.
Here is a great and established branch of knowledge, already of remarkable compass, and promising unbounded extension in the future, carrying with it a thorough apodictic certainty, i.e., absolute necessity, and thus resting on no empirical grounds, but being a pure product of the Reason, besides thoroughly synthetic. “How is it possible for the human Reason to bring about such a branch of knowledge entirely à priori? ” Does not this capacity, as it does not and cannot stand on experience, presuppose some ground of knowledge à priori, lying deep-hidden, but which might reveal itself through these its effects, if their first beginnings were only diligently searched for?
But we find that all mathematical knowledge has this speciality, that it must present its conception previously in intuition, and indeed à priori, that is, in an intuition that is not empirical but pure, without which means it cannot make a single step; its judgments therefore are always intuitive, whereas philosophy must be satisfied with discursive judgments out of mere conceptions; for though it can explain its apodictic doctrines by intuition, these can never be derived from such a source. This observation respecting the nature of mathematics, itself furnishes us with a guide as to the first and foremost condition of its possibility, namely, that some pure intuition must be at its foundation, wherein it can present all its conceptions in concreto and à priori at the same time, or as it is termed, construct them. If we can find out this pure intuition together with its possibility, it will be readily explicable how synthetic propositions à priori are possible in pure mathematics, and therefore, also, how this science is itself possible. For just as empirical intuition enables us, without difficulty, to extend synthetically in experience the conception we form of an object of intuition, by new predicates, themselves afforded us by intuition, so will the pure intuition, only with this difference: that in the last case the synthetic judgment à priori is certain and apodictic, while in the first case it is no more than à posteriori and empirically certain, because the latter only contains what is met with in chance empirical intuition, but the former what is necessarily met with in the pure intuition, inasmuch as being intuition à priori, it is indissolubly bound up with the conception before all experience or perception of individual things.
But the difficulty seems rather to increase than to diminish by this step. For the question is now: How is it possible to intuite anything à priori? Intuition is a presentation, as it would immediately depend on the presence of the object. It seems therefore impossible to intuite originally à priori, because the intuition must then take place without either a previous or present object to which it could refer, and hence could not be intuition. Conceptions are indeed of a nature that some of them, namely, those containing only the thought of an object in general, may be very well formed à priori, without our being in immediate relation to the object (e.g., the conceptions of quantity, of cause, c.), but even these require a certain use in concreto, i.e., an application to some intuition, if they are to acquire sense and meaning, whereby an object of them is to be given us. But how can intuition of an object precede the object itself?
Were our intuition of such a nature as to present things as they are in themselves, no intuition à priori would take place at all, but it would always be empirical. For what is contained in the object in itself, I can only know when it is given and present to me. It is surely then inconceivable how the intuition of a present thing should enable me to know it as it is in itself, seeing that its properties cannot pass over into my presentative faculty. But granting the possibility of this, the said intuition would not take place à priori, that is, before the object was presented to me, for without it no ground of connection between my presentation and the object could be imagined; in which case it must rest on inspiration ( Eingebung ). Hence there is only one way possible, by which my intuition can precede the reality of the object and take place as knowledge à priori, and that is, if it contain nothing else but that form of sensibility which precedes in my subject all real impressions, by which I am affected by objects. For, that objects of sense can only be intuited in accordance with this form of sensibility, is a fact I can know à priori. From this it follows, that propositions merely concerning the form of sensible intuition, will be valid and possible for all objects of sense; and conversely, that intuitions possible à priori, can never concern other things than objects of our sense.
Hence, it is only by means of the form of sensuous intuition that we can intuite things à priori, but in this way we intuite the objects only as they appear to our senses, not as they may be in themselves; an assumption absolutely necessary if synthetic propositions à priori are to be admitted as possible, or in the event of their being actually met with, if their possibility is to be conceived and defined beforehand.
Now, such intuitions are space and time, and these lie at the basis of all the cognitions and judgments of pure mathematics, exhibiting themselves at once as apodictic and necessary. For mathematics must present all its conceptions primarily in intuition, and pure mathematics in pure intuition, i.e., it must construct them. For without this it is impossible to make a single step, so long, that is to say, as a pure intuition is wanting, in which alone the matter of synthetic judgments à priori can be given; because it cannot proceed analytically, that is, by the dissection of conceptions, but is obliged to proceed synthetically. The pure intuition of space constitutes the basis of geometry—even arithmetic brings about its numerical conceptions by the successive addition of units in time; but above all, pure mechanics can evolve its conception of motion solely with the aid of the presentation of time. Both presentations, however, are mere intuitions; for when all that is empirical, namely, that belongs to feeling, is left out of the empirical intuitions of bodies and their changes (motion), space and time still remain over, and are therefore pure intuitions, lying à priori at the foundation of the former. For this reason, they can never be left out, but being pure intuitions à priori, prove that they are the bare forms of our sensibility, which must precede all empirical intuition, i.e., the perception of real objects, and in accordance with which objects can be known à priori, though only as they appear to us.
The problem of the present section is therefore solved. Pure mathematics is only possible as synthetic knowledge à priori, in so far as it refers simply to objects of sense, whose empirical intuition has for its foundation a pure intuition à priori (that of time and space), which intuition is able to serve as a foundation, because it is nothing more than the pure form of sensibility itself, that precedes the real appearance of objects, in that it makes them in the first place possible. Yet this faculty of intuiting à priori does not concern the matter of the phenomenon, i.e., that which is feeling ( Empfindung ) in the latter, for this constitutes the empirical element therein; but only its form, space and time. Should anybody cast the least doubt on the fact that neither of them are conditions of things in themselves, but only dependent on their relation to sensibility. I should be glad to be informed how he deems it possible to know à priori, and therefore before all acquaintance with the things, that is, before they are given us, how their intuition must be constructed, as is here the case with space and time. Yet this is quite conceivable, as soon as they both count for nothing more than formal determinations of our sensibility, and the objects merely as phenomena, for in that case the form of the phenomenon, that is, the pure intuition, can be conceived as coming from ourselves, in other words, as à priori.
To contribute something to the explanation and confirmation of the above, we have only to consider the ordinary and necessary procedure of geometricians. All the proofs of complete likeness between two given figures, turn at last upon the fact of their covering each other; in other words, of the possibility of substituting one, in every point, for the other, which is obviously nothing else but a synthetic proposition resting on immediate intuition. Now this intuition must be given pure and à priori, for otherwise the proposition in question could not count as apodictically certain, but would possess only empirical certainty. We could only say in that case, it has been always so observed, or it is valid so far as our perception has hitherto extended. That complete space, itself no boundary of a further space, has three dimensions, and that no space can have more than this number, is founded on the proposition that not more than three lines can bisect each other at right angles in a single point. But this proposition cannot be presented from conceptions, but rests immediately on intuition, and indeed on pure à priori intuition, because it is apodictically certain that we can require a line to be drawn out to infinity ( in indefinitum ), or that a series of changes (e.g., spaces passed through by motion) shall be continued to infinity, and this presupposes a presentation of space and time, merely dependent on intuition, namely, so far as in itself, it is bounded by nothing, for from conceptions it could never be concluded. Pure intuitions à priori, then, really lie at the foundation of mathematics, and these make its synthetic and apodictically valid propositions possible, and hence our transcendental deduction of conceptions in space and time explains at the same time the possibility of pure mathematics, which without such a deduction, and without our assuming that “all which can be given to oursenses (the outer in space, the inner in time) is only intuited by us, as it appears to us, and not as it is in itself,” might indeed be conceded, but could in nowise be understood
Those who are unable to free themselves from the notion, that space and time are real qualities ( Beschaffenheiten ) appertaining to the things in themselves, may exercise their wits on the following paradoxes, and when they have in vain attempted their solution, may suppose, being freed from their prejudices at least for a few moments, that perhaps the degradation of space and time to the position of mere forms of our sensible intuition, may have some foundation.
When two things are exactly alike [equal] in all points that can be cognised in each by itself (i.e., in all respecting quantity or quality), it must follow, that one can in all cases and relations be put in the place of the other, without this substitution occasioning the least cognisable difference. This indeed applies to plane figures in geometry; but there are many spherical figures, which in spite of this complete internal agreement exhibit in their external relations an agreement falling short of admitting one to be put in the place of the other.
For instance, two spherical triangles on opposite hemispheres, having an arc of the equator as a common base, are perfectly equal both in respect of their sides and their angles, so that in neither of them, if separately and at the same time completely described, would anything be found which was not equally present in the other; and yet notwithstanding this, one cannot be put in the place of the other, i.e., on the opposite hemisphere, and herein consists the internal difference of both triangles, that no understanding can indicate as internal, but which reveals itself only by means of the external relation in space. I will now adduce some more ordinary cases taken from common life.
What can more resemble my hand or my ear, and be in all points more like, than its image in the looking-glass? And yet I cannot put such a hand as I see in the glass in the place of its original; for when the latter is a right hand, the one in the glass is a left hand, and the image of the right ear is a left one, which can never take the place of the former. Now, here there are no internal differences that could be imagined by any understanding. And yet the differences are internal, so far as the senses teach us, for the left hand cannot, despite all equality and similarity, be enclosed within the same bounds as the right (they are not congruent); the glove of one hand cannot be used for the other. What then is the solution? These objects are not presentations of things as they are in themselves, and as the pure understanding would cognise them, but they are sensuous intuitions, i.e., phenomena, the possibility of which rests on the relations of certain unknown things in themselves to something else, namely, to our sensibility. Now, space is the form of the outward intuition of these, and the inward determination of every space is only possible through the determination of outward relations to the whole space, of which each [separate] space is a part (i.e., by its relation to the outward sense); in other words, the part is only possible through the whole, which though it could never be the case with things in themselves, namely, with objects of the mere understanding, can very well be so with mere phenomena. Hence we can render the difference of similar and equal, though incongruent things (e.g., spirals winding opposite ways 1 ) intelligible by no single conception, but only by the relation of the right and left hands, which refers immediately to intuition.
Pure mathematics, and especially pure geometry, can only possess objective reality under the condition that they merely refer to objects of sense, in view of which, however, the axiom holds good that our sensuous presentation is in nowise a presentation of things in themselves, but only of the manner wherein they appear to us. Hence it follows that the propositions of geometry are not the mere determinations of a creation of our poetic fancy, which therefore cannot be referred with confidence to real objects, but that they are necessarily valid of space, and consequently of everything that may be found in space; because space is nothing more than the form of all external phenomena, under which alone objects of sense can be given us. Sensibility, the form of which lies at the foundation of geometry, is that whereon the possibility of external phenomena rests; so these can never contain anything but what geometry prescribes for them. It would be quite different if the senses had to present the objects as they are in themselves. For in that case it would by no means follow from the presentation of space (which the geometrician posits with all its properties as an à priori basis), that all this, together with what is deduced therefrom, is exactly so constituted in Nature. The space of the geometrician would be regarded as a mere fiction, and no objective validity ascribed to it, because we do not see why things must necessarily conform to the image that we make of them spontaneously and beforehand. But when this image, or rather this formal intuition, is the essential property of our sensibility by means of which alone objects are presented to us; and yet this sensibility presents not things in themselves, but only their appearances, it is quite easy to conceive, and at the same time incontrovertibly proved, that all the external objects of our sense-world must necessarily conform with the most complete accuracy to the propositions of geometry. For sensibility, by its form of external intuition (space) with which the geometrician is occupied, makes those objects themselves (though as mere appearances) primarily possible. It will always remain a remarkable phenomenon in the history of philosophy that there has been a time when even mathematicians who were also philosophers began to doubt, not indeed of the correctness of their propositions in so far as they concerned space, but of the objective validity and application of this conception, with all its geometrical determinations, to Nature. They were concerned lest a line in Nature might consist of physical points, and the true space in the object, accordingly of simple parts, whereas the space the geometrician has in his mind can never consist of such. They did not recognise that this space in thought makes the physical space, i.e., the extension of matter, itself possible; that the latter is no quality of things in themselves, but only a form of our sensible faculty of presentation; that all objects in space are mere phenomena, i.e., are not things in themselves, but presentations of our sensuous intuition; and hence that space, as the geometrician thinks it, is exactly the form of sensuous intuition we find à priori in ourselves, containing the ground of possibility of all external phenomena (as regards their form); and that these must necessarily and in the most exact manner agree with the propositions of the geometrician, which he draws from no fictious conception, but from the subjective foundation of all external phenomena, namely, the sensibility itself. In such and no other manner can the geometrician be ensured as to the indubitable objective reality of his propositions against all the cavils of an arid metaphysics, however strange it may seem to him, owing to his not having reverted to the sources of his conceptions.
All that is given us as object, must be given us in intuition. But all our intuition takes place by means of the senses alone; the understanding intuites nothing, but only reflects. Inasmuch then as the senses, according to what is above observed, never enable us to cognise, not even in one single point, the things in themselves, but only their phenomena, while these are mere presentations of sensibility, “all bodies, together with the space in which they are found, must be held to be nothing but mere presentations, existing nowhere but in our thoughts.” Now is this not the plainest idealism?
Idealism consists in the assertion that there exist none but thinking entities; the other things we think we perceive in intuition, being only presentations of the thinking entity, to which no object outside the latter can be found to correspond. I say, on the contrary, things are given as objects discoverable by our senses, external to us, but of what they may be in themselves we know nothing; we know only their phenomena, i.e., the presentations they produce in us as they affect our senses. I therefore certainly admit that there are bodies outside us, that is, things, which although they are wholly unknown to us, as to what they may be in themselves, we cognise through presentations, obtained by means of their influence on our sensibility. To these we give the designation of body, a word signifying merely the phenomenon of that to us unknown, but not the less real, object. Can this be termed idealism? It is indeed rather the contrary thereof.
That without calling in question the existence of external things, it may be said of a number of their predicates that they do not belong to the things in themselves, but only to their phenomena, and have no self-existence outside our presentation, is what had been generally accepted and admitted long before Locke’s time, but more than ever since then. To these belong heat, colour, taste, c. No one can adduce the least ground for saying that it is inadmissible on my part, when for important reasons I count in addition the remaining qualities of bodies called primarias, such as extension, place, and more especially space, together with what is dependent thereon (impenetrability or materiality, figure, c.) amongst the number of these phenomena. And just as little as the man who will not admit colours to be properties of the object in itself, but only to pertain as modifications to the sense of sight, is on that account called an idealist, so little can my conception be termed idealistic because I find in addition that all properties which make up the intuition of a body belong merely to its appearance. For the existence of a thing, which appears, is not thereby abolished as with real idealism, but it is only shown that we cannot cognise it, as it is in itself, through the senses.
I should like to know how my assertions must be fashioned, if they are not to contain an idealism. I should doubtless have to say, that the presentation of space is not alone completely in accordance with the relation of our sensibility to objects, for that I have already said, but that it is exactly similar to the object itself; an assertion to which no sense can be attached, just as little as that the feeling of red has a similarity with the cinnabar producing this feeling in me.
Hence we may readily set aside an easily foreseen but pointless objection: namely, that through the ideality of space and time, the whole sense-world would be changed to sheer illusion. All philosophical insight into the nature of sensuous cognition was ruined from the first by making sensibility to consist simply in a confused mode of presentation, by which we cognise the things as they are, without having the capacity to bring everything in this, our cognition, to clear consciousness. On the other hand, it has been proved by us that sensibility does not consist in this logical distinction of clearness and obscurity, but in the genetic distinction of the origin of knowledge itself, since sensuous cognition does not present the things as they are, but only the manner in which they affect our senses; and that therefore through them mere phenomena, and not the things themselves, are given to the understanding for reflection. After this necessary correction, a consideration presents itself, arising from an inexcusable and almost purposeless misapplication, as though my doctrine changed all the objects of sense into mere illusion.
When an appearance is given us we are quite free as to what we thence infer with regard to the matter. The former, namely, the appearance, rests on the senses, but the judgment on the understanding; and the only question is, whether or not there is truth in the determination of the object. But the distinction between truth and dream is not decided by the construction of the presentations, which are referred to objects, for they are alike in both, but by the connection of the same according to the rules determining the coherence of presentations in the conception of an object, and by whether they can stand together in an experience or not. Hence the fault does not lie with the phenomena, if our cognition takes the illusion for truth, i.e., if an intuition, whereby an object is given, is held to be the conception of the object or its existence, which the understanding alone can cogitate. The senses present to us the course of the planets as first forwards and then backwards, and in this there is neither falsehood nor truth, because so long as it is considered as an appearance only, no judgment is yet formed as to the objective character of their motion. But inasmuch as when the understanding does not take great care lest this subjective mode of presentation be held for objective, a false judgment may easily arise; it is said, they seem to go back; the illusion, however, is not to be laid to the account of the senses, but of the understanding, whose province alone it is to form an objective judgment on the phenomenon.
In this manner, even if we did not reflect on the origin of our presentations, and let our intuitions of sense contain what they may, if it be but connected according to the coherence of all knowledge in an experience, [we shall find that] deceptive illusion or truth will arise according as we are negligent or careful; for it concerns solely the use of sensuous presentations in the understanding, and not their origin. In the same way, if I hold all presentations of sense together with their form, namely, space and time, to be nothing but phenomena, and the latter to be a mere form of sensibility not present in the objects external to it, and I make use of these presentations only in reference to a possible experience, there is not therein the least temptation to error, neither is there an illusion implied in my regarding them as mere appearances; for in spite of this they can rightly cohere according to the rules of truth in an experience. In such wise all the propositions of geometry respecting space are valid just as much of all the objects of sense, and therefore in respect of all possible experience, whether I regard space as a mere form of sensibility or as something inhering in the things themselves. But in the first case alone can I conceive how it is possible to know à priori the above propositions concerning objects of external intuition. Otherwise everything remains in respect to all merely possible experience just as though I had never undertaken this departure from the popular judgment.
But, let me only venture with my conceptions of space and time beyond all possible experience, which is unavoidable if I give them out as qualities appertaining to the things in themselves (for what should prevent me from assuming them as valid of these same things, even though my senses were differently constructed, and whether they were suited to them or not?) then a serious error may arise, resting on an illusion giving out as universally valid what is a mere condition of the intuition of things pertaining to my subject (certain for all the objects of sense, and thereby for all possible experience), because I refer them to things in themselves and fail to limit them to the conditions of experience.
So far, then, from my doctrine of the ideality of space and time reducing the whole sense-world to mere illusion, it is rather the only means of ensuring the application of some of the most important cognitions, namely, those propounded à priori by mathematics, to real objects, and of guarding them from being held as illusion. For without this observation it would be quite impossible to ascertain whether the intuitions of space and time we borrow from no experience, but which nevertheless lie à priori in our faculty of presentation, were not mere self-made cobwebs of the brain, to which no object, or at least no adequate object, corresponded, and geometry itself therefore a mere illusion; instead of which, its incontestable validity in respect of all objects of the sense-world, owing to these being simply phenomena, has been able to be demonstrated by us.
Secondly, so far from my principles, because they reduce the presentations of the senses to phenomena, turning the truth of experience into illusion, they are rather the only means of guarding against the transcendental illusion, whereby metaphysics has always been deceived and misled into childish endeavours to grasp at soap-bubbles, by taking phenomena, which are mere presentations, for things in themselves; whence have resulted the remarkable assumptions of the antinomy of the Reason, of which I shall make mention farther on, and which are abolished by the single observation that appearance, as long as it is used simply in experience, produces truth, but as soon as it passes beyond the bounds of the latter and becomes transcendent, nothing but pure illusion.
Inasmuch, then, as I leave their reality to the things we intuite to ourselves through the senses, and only limit our sensuous intuition of those things in that they in no particular, not even in the pure intuitions of space and time, represent more than the appearance of the above things, and never their constitution as they are in themselves; this is no thorough-going illusion of my own invention [applied to] Nature. My protestation against all supposition of an idealism is so decisive and clear, that it might seem superfluous were it not for incompetent judges, who like to have an old name for every departure from their distorted although common opinion, and who never judge of the spirit of philosophical terminology, but cling simply to the letter, being ready to put their own delusion in the place of well-defined perceptions, and so to distort and deform them. For the fact of my having myself given my theory the name of transcendental idealism, can justify no one in confounding it with the idealism of Descartes (though this was only a problem, on account of whose insolubility every one was free, in the opinion of Descartes, to deny the existence of the bodily world, because it could never be satisfactorily solved), or with the mystical and visionary idealism of Berkeley, against which and other similar cobwebs of the brain our Critique rather contains the best specific. For what is by me termed idealism, does not touch the existence of things (the doubt of the same being what properly constitutes idealism in the opposite sense), for to doubt them has never entered my head, but simply concerns the sensuous presentation of things, to which space and time chiefly belong; and of these and of all phenomena I have only shown that they are neither things (but only modes of presentation), nor determinations belonging to things in themselves. But the word transcendental, which with me never implies a reference to our knowledge of things, but only to our faculty of knowledge ( Erkenntnissvermogen ) should guard against this misconception. Rather, however, than occasion its further continuance, I prefer to withdraw the expression, and let it be known as critical (idealism). If it be indeed an objectionable idealism, to change into mere presentations real things (not phenomena), what name shall be applied to that which conversely turns mere presentations into things? I think we may term it the dreaming idealism, in contradistinction to the foregoing, that may be termed the visionary, but both of which ought to have been obviated by my elsewhere so-called transcendental, but better, critical, idealism.
Nature is the existence of things, in so far as it is determined according to universal laws. If Nature signified the existence of things in themselves, we could never know it either à priori or à posteriori. Not à priori, for how shall we know what applies to things in themselves? since this can never be done by the dissection of our conceptions (analytic propositions). For what I want to know, is not what is contained in my conception of a thing (for that concerns its logical nature), but what in the reality of the thing is superadded to this conception, by which the thing itself is determined outside my conception. My understanding and the conditions under which alone it can connect the determination of things in their existence, prescribes no rules for the things in themselves; these do not conform themselves to my understanding, but my understanding conforms itself to them. They must therefore be previously given me, in order for these determinations to be discovered in them; and in this case they would not be known à priori.
But à posteriori such a knowledge of the nature of things in themselves would be equally impossible. For if experience is to teach me laws to which the existence of things is subordinated, these must, in so far as they concern things in themselves, of necessity also apply to them outside my experience. Now experience teaches me, indeed, what exists and how it exists, but never that it exists necessarily in such a manner and no other. It can never, therefore, teach the nature of things in themselves.
We are nevertheless really in possession of a pure natural science, which à priori and with all the necessity requisite to apodictic propositions, puts forward laws to which Nature is subordinated. I only require here to call to witness that propaedeutic, which, under the title of universal natural science, precedes all physical scienco based on empirical principles. Therein we find mathematics applied to phenomena, also those discursive principles (from conceptions) constituting the philosophical part of pure natural knowledge. But the latter also contains much that is not pure, and independent of the sources of experience, as the conception of motion, of impenetrability (on which the empirical conception of matter rests), of inertia and others, which prevent its being called a perfectly pure natural science. Besides, it is only concerned with the objects of the external sense, and thus furnishes no example of a pure natural science in its strictest meaning; for this would have to bring Nature generally under universal laws, irrespective of whether it concerned the object of the outer or of the inner sense of physical science, or of psychology. But among the principles of the above universal physical science are to be found some that really possess the universality we require, as the proposition that substance continues and is permanent, and that all which happens is at all times previously determined by a cause, according to fixed laws. These are really universal natural laws, existing completely à priori. There is then in fact a pure natural science, and now the question arises— how is it possible?
The word Nature further assumes another meaning, which defines the object, whereas in the above meaning the mere regularity of the existence of the determinations of things generally, is denoted. Nature considered materialiter is the sum-total of all the objects of experience. With this we are alone concerned at present, for things which could never be objects of an experience were they to be known according to their nature, would necessitate us to form conceptions, to which meaning could never be given in concreto (in any example from a possible experience), and of the nature of which we should be obliged to make conceptions alone, whose reality, that is, whether they really referred to objects or were mere figments of thought, could never be decided. With that which cannot be an object of experience, the knowledge of which would be hyperphysical, or anything like it, we have here nothing at all to do, but only with the natural knowledge whose reality can be confirmed by experience, notwithstanding its being à priori possible, and preceding all experience.
The formal in Nature, in this narrower signification, is then the regularity of all the objects of experience, and in so far as they are known à priori, their necessary regularity. But it has been just demonstrated that the laws of Nature can never be known à priori in objects, in so far as they are considered not as the objects of a possible experience but as things in themselves. We are not here concerned with things in themselves (the qualities of which we put on one side), but merely with things as the objects of a possible experience, and the sum-total of which is properly what we call Nature. And I now ask, whether, if the question be as to the possibility of a cognition of Nature à priori, it would be better to formulate the problem, as follows: How is it possible to cognise à priori the necessary regularity of things as objects of experience? or, How is the necessary regularity of experience itself in respect of all its objects, generally [possible to be cognised à priori ]?
Seen in its true light, the solution of the problem, whether presented in the one or in the other form, in respect of the pure cognition of Nature (which constitutes the real point of the question) is in the end altogether the same. For the subjective laws under which alone an experiential cognition of things is possible, are valid also of those things as objects of a possible experience (though not indeed as things in themselves; but the latter we are not here considering). It is quite the same, then, whether I say: Without the law—that on an event being perceived, it must invariably be referred to something preceding it, upon which it follows according to a universal rule—a judgment of perception can never avail as experience; or whether I express myself thus: Everything that experience teaches us, happens, must have a cause.
It is, however, advisable to choose the first formula. For as we can have a knowledge à priori and before all given objects, of those conditions under which alone an experience in respect of them is possible, but never of what laws, they, without reference, to a possible experience, are subordinated to, in themselves; we shall not be able to study the nature of things à priori, otherwise than by investigating the conditions and universal (although subjective) laws, under which such a knowledge is alone possible (in respect of mere form), as experience, and in accordance therewith determine the possibility of things as objects of experience. Were I to choose the second mode of expression and seek the conditions à priori under which Nature is possible as an object of experience, I should easily be led into misunderstanding, and fancy I had to explain Nature as a thing in itself, and I should then be fruitlessly involved in endless endeavours to seek laws for things of which nothing is given me.
We shall here, therefore, be simply concerned with experience, and the universal and à priori given conditions of its possibility, and thence determine Nature as the complete object of all possible experience. I think it will be understood, that I do not refer to the rules for the observation of a nature already given, which presuppose experience, or how through experience we can arrive at the laws of Nature, for these would not then be laws à priori, and would give no pure science of Nature; but how the conditions à priori of the possibility of experience are at the same time the sources from which all the universal laws of Nature must be derived.
We must first of all observe then, that, although all the judgments of experience are empirical, i.e., have their ground in the immediate perception of sense, yet on the other hand all empirical judgments are not judgments of experience, but that beyond the empirical, and beyond the given sensuous intuition generally, special conceptions must be superadded, having their origin entirely à priori in the pure understanding, under which every perception is primarily subsumed, and by means of which only it can be transformed into experience.
Empirical judgments, in so far as they have objective validity, are judgments of experience; but those which are merely subjectively valid I call judgments of perception. The last require no pure conception of the understanding; but only the logical connection of perception in a thinking subject. But the first demand, above the presentations of sensuous intuition, special conceptions originally generated in the understanding, which make the judgment of experience objectively valid.
All our judgments are at first mere judgments of perception; they are valid simply for us, namely, for our subject. It is only subsequently that we give them a new reference, namely, to an object, and insist that they shall be valid for us always, as well as for every one else. For when a judgment coincides with an object, all judgments must both coincide with the same object and with one another, and thus the objective validity of the judgment of experience implies nothing more than the necessary universal validity of the same. But, on the other hand, when we see reason to hold a judgment of necessity universally valid (which never hinges on the perception itself, but on the pure conception of the understanding under which the perception is subsumed), we are obliged to regard it as objective, i.e., as expressing not merely the reference of the perception to a subject but a quality of the object; for there would be no reason why the judgments of other persons must necessarily coincide with mine, if it were not that the unity of the object to which they all refer, and with which they coincide, necessitates them all agreeing with one another.
Objective validity and necessary universality (for every one) are therefore exchangeable notions, and although we do not know the object in itself, yet when we regard a judgment as at once universal and necessary, objective validity is therewith understood. We cognise in this judgment the object (though it remain unknown what it is in itself) by the universal and necessary connection of given perceptions, and as this is the case with all objects of sense, judgments of experience owe their objective validity not to the immediate cognition of the object (for this is impossible), but merely to the condition of universality in the empirical judgment, which, as has been said, never rests on empirical, or on any sensuous conditions, but on a pure conception of the understanding. The object in itself always remains unknown; but when through the conception of the understanding, the connection of the presentations given to our sensibility by the latter is determined as universally valid, the object is determined by this relation, and the judgment is objective.
We will explain this; that the room is warm, 1 the sugar sweet, the wormwood bitter, are merely subjectively valid judgments. I do not expect that I shall always, or that every other person, will find them as I do now. They only express a reference of two sensations to the same subject, namely, myself, and that only in my present state of perception, and are not therefore valid of objects. I call these judgments of perception. With judgments of experience the case is altogether different. What experience teaches me under certain circumstances, it must teach me at all times, and every other person as well; its validity is not limited to the subject or to the state of the latter at a particular time. I pronounce, therefore, all such judgments to be objectively valid. For instance when I say—the air is elastic, this judgment is immediately a judgment of perception, since I only refer the feelings in my senses to one another. If I insist it shall be called a judgment of experience, I expect this connection to stand under a condition making it universally valid. I insist, that is, that I at all times and every other person, shall necessarily so combine the same perceptions, under the same circumstances.
We must therefore dissect experience, in order to see what is contained in this product of sense and understanding, and how the judgment of experience itself is possible. The intuition of which I am conscious, namely, perception ( perceptio ), which merely belongs to the senses, lies at its foundation. But secondly, judgment (which pertains solely to the understanding) also belongs to it. This [act of] judgment may be twofold; firstly, I may simply compare the perceptions in a particular state of my own consciousness; or secondly, I may combine them in a consciousness in general. The first judgment is a simple judgment of perception, and has therefore only subjective validity, being the mere connection of perceptions in my mental state, without reference to the object. Hence it is not sufficient for experience, as is commonly imagined, to compare perceptions and to connect them in a consciousness by means of the judgment. No universality and necessity in the judgment can arise therefrom, by means of which alone it can be objectively valid, and experience.
There is another and quite a different judgment presupposed, before perception can become experience. The given intuition must be subsumed under a conception determining the form of the judgment generally in respect of the intuition, connecting the empirical consciousness of the last in a consciousness in general, and thereby obtaining universality for the empirical judgment; such a conception is a pure à priori conception of the understanding, that does nothing but determine for an intuition the general manner in which it can serve for judgment. Should the conception be that of cause, it determines the intuition subsumed under it in respect of judgment generally; for instance, in the case of air, that in respect of expansion, it stands in the relation of antecedent to consequent, in a hypothetical judgment. The conception of cause is then a pure conception of the understanding, entirely distinct from all possible perception, and only serves to determine that presentation contained under it, in respect of judgment generally, in short, to make a universally valid judgment possible.
Now, before a judgment of perception can become a judgment of experience, it is first of all necessary that the perception be subsumed under these conceptions of the understanding. For instance, air belongs to the conception of causes, which determines the judgment regarding its extension, as hypothetical. 1 In this way, the extension is represented not merely as belonging to my perception of air in my particular state, or in many of my states, or in a particular state of the perception of others, but as necessarily belonging thereto; and the judgment, the air is elastic, becomes universally valid, and therefore a judgment of experience, preceded by certain judgments, which subsume the intuition of air under the conception of cause and effect, and thereby the perceptions, not merely with respect to one another in my subject, but relatively to the form of judgment generally (here the hypothetical), and thus make the empirical judgment universally valid.
If we dissect all our synthetic judgments, in so far as they are valid objectively, we shall find that they never consist of mere intuitions, connected (as is commonly believed) through comparison in a judgment, but that they would be impossible were there not beyond the conceptions drawn from experience, a pure conception of the understanding, under which the former conceptions are subsumed, and in this way only, connected in an objectively valid judgment. Even the judgments of pure mathematics in their simplest axioms, are not excepted from this condition. The axiom, the straight line is the shortest way between two points, presupposes that the line be subsumed under the conception of quantity, which is assuredly no intuition, but has its seat in the understanding, and serves to determine the intuition (the line) in the reference of the judgment that may be made regarding it, in respect of its quantity, namely, of plurality (as judicia plurativa ), 1 inasmuch as it is thereby understood that in a given intuition, many homogeneous parts are contained.
In order to demonstrate the possibility of experience, in so far as it rests on pure à priori conceptions of the understanding, we must first present what belongs to judgment generally, and the various momenta of the understanding in the same, in a complete table, for the pure conceptions of the understanding, which are nothing more than conceptions of intuitions in general, in so far as these are determined in themselves by one or other of these momenta of judgment, that is, are necessarily and universally valid, must run exactly parallel to them [viz., these momenta]. In this way, the axioms à priori of the possibility of all experience as an objectively valid empirical cognition, are precisely determined. For they are nothing but propositions, subsuming all perception (in accordance with certain universal conditions of perception), under the above pure conceptions of the understanding.
| L OGICAL T ABLE OF THE J UDGMENTS. | |
|---|---|
| 1. | 2. |
| According to Quantity. | According to Quality |
| Universal. | Affirmative. |
| Particular. | Negative. |
| Singular. | Infinite. |
| 3. | 4. |
| According to Relation. | According to Modality. |
| Categorical. | Problematical. |
| Hypothetical. | Assertorical. |
| Disjunctive. | Apodictic. |
| T RANSCENDENTAL T ABLE OF THE C ONCEPTIONS OF THE U NDERSTANDING. | |
|---|---|
| 1. | 2. |
| According to Quantity. | According to Quality. |
| Unity (the measure). | Reality. |
| Plurality (the amount). | Negation. |
| Totality (the whole). | Limitation. |
| 3. | 4. |
| According to Relation. | According to Modality. |
| Substance. | Possibility. |
| Cause. | Actuality. |
| Reciprocity. | Necessity. |
| P URE P HYSIOLOGICAL T ABLE OF THE U NIVERSAL P RINCIPLES OF N ATURAL S CIENCE. | ||
|---|---|---|
| 1. | ||
| Axioms of Intuition. | ||
| 2. | 3. | |
| Anticipations of Perception. | Analogies of Experience. | |
| 4. | ||
| Postulates of Empirical Thought in general. | ||
In order to grasp the preceding in a single notion, it is necessary to remind the reader that we are not here speaking of the origin of experience, but of that which lies within it. The first belongs to empirical psychology, and would exist without the second, which belongs to the critique of cognition, and especially to that of the understanding, and can never be sufficiently developed.
Experience consists of intuitions, belonging to sensibility, and of judgments which are entirely the work of the understanding. But the judgments the understanding constructs merely out of sensuous intuitions, are not, by far, judgments of experience. For in the one case the judgment simply connects the perceptions, as they are given in sensuous intuition; but in the other, the judgments must say what experience generally contains, and not what the mere perception, the validity of which is purely subjective, contains. The judgment of experience must add something to a judgment, over and above the sensuous intuition, and the logical connection of the same (after it has been made universal by comparison), something that determines the synthetic judgment, as at once necessary and thereby universally valid; and this can be nothing else but that conception which presents the intuition as determined in itself, in respect to one form of judgment rather than another, i.e., a conception of that synthetic unity of intuitions, which can only be presented through a given logical function of the judgment.
The sum of the above is this: the business of the senses is to intuite, that of the understanding to think. But to think is to unite presentations in a consciousness. This union is either merely relative to the subject, and is contingent and subjective, or is given unconditionally, and is necessary or objective. The union of presentations in a consciousness is judgment. Thinking, then, is the same as judging, or referring presentations to judgments in general. Hence judgments are either entirely subjective when presentations are solely referred to a consciousness in one subject, and are therein united, or they are objective when they are united in a consciousness in general, that is, are necessarily united therein. The logical momenta of all judgments are so many possible modes of uniting presentations in a consciousness. But if they serve as conceptions, they are conceptions of the necessary union of the same in a consciousness, and therefore principles of objectively valid judgments. This union in a consciousness is either analytic by identity, or synthetic by the combination and addition of different presentations to one another. Experience consists in the synthetic connection of phenomena (perceptions) in a consciousness, in so far as this is necessary. Hence pure conceptions of the understanding are those under which all perceptions must be previously subsumed, before they can serve as judgments of experience, in which the synthetic unity of perceptions is presented as necessary and universal. 1
Judgments, considered merely as the union of given presentations in a consciousness, are rules. These rules, in so far as they present the union as necessary, are rules à priori, and in so far as there are none beyond them from which they can be derived, they are axioms. Since, then, in respect of the possibility of all experience, when viewed as the mere form of thought, there are no conditions of the judgments of experience beyond those which bring the phenomena in the various forms of their intuition under the pure conceptions of the understanding which make the empirical judgment objectively valid, these must be the à priori axioms of all possible experience.
The axioms of possible experience are at the same time the universal laws of Nature as known à priori. And thus the problem contained in our present second question— How is pure natural science possible? is solved. For the systematic character required by the form of a science is met with here in completeness, since beyond the above-named formal conditions of all judgments in general, that is, of all the general rules to be found in logic, there are none possible, and these constitute a logical system; while the conceptions founded upon them, containing the conditions à priori of all synthetic and necessary judgments, [constitute] in the same way a transcendental system, and finally the axioms, by means of which all phenomena are subsumed under these conceptions, [constitute] a physiological 1 system, i.e., a system of nature, preceding all empirical knowledge of nature, rendering this in the first place possible, and therefore to be properly termed the universal and pure natural science.
The first of the above physiological 2 axioms subsumes all phenomena, as intuitions in space and time, under the conception of quantity, and is so far a principle of the application of mathematics to experience. The second subsumes the properly empirical, namely, the feeling, which denotes the reality of intuitions, not precisely under the conception of quantity, because feeling is no intuition, contained in space and time, although it places its corresponding object in both. But between reality (presentation of feeling) and zero, i.e., the complete emptiness of intuition in time, there is a difference which has a quantity. For between each given degree of light and darkness, between each degree of heat, and complete coldness, each degree of weight and of absolute lightness, each degree of the containing of space and of totally empty space, progressively smaller degrees can be thought of, and similarly between consciousness and complete unconsciousness (psychological darkness) continually smaller [degrees] exist. Hence no perception is possible that would prove an absolute void; for instance, no psychological darkness that could be viewed otherwise than as a consciousness, which is but surpassed by another stronger consciousness, and the same in all cases of feeling. In this way the understanding can even anticipate feelings which constitute the proper quality of empirical presentations (phenomena), by means of the axiom that they all (that is, the real of every phenomenon) have a degree, and this is the second application of mathematics ( mathesis intensorum ) to natural science.
As regards the relation of phenomena, and indeed simply as to their existence, the determination of this relation is not mathematic but dynamic, and can never be valid objectively, and therefore adequate to an experience, if it be not subordinated to principles à priori rendering the cognition of experience regarding them in the first place possible. Hence phenomena must be subsumed under the conception of substance, which lies at the foundation of all determination of existence as a conception of the thing itself; or secondly, in so far as a succession, that is, an event, is met with among the phenomena, under the conception of an effect in reference to cause; or in so far as co-existence is to be cognised objectively, that is, through a judgment of experience, under the conception of community (reciprocal action); and these principles à priori lie at the foundation of objectively valid although empirical judgments, that is, the possibility of experience in so far as it is to connect the existence of objects in Nature. These principles are the particular laws of Nature, which may be termed dynamic.
There belongs, finally, to the judgments of experience the cognition of the agreement and connection, not so much of phenomena among one another in experience, as of their relation to experience generally, which unites either their agreement with the formal conditions cognised by the understanding or their coherence with the material of sense and of perception, or both, in one conception, and consequently contains possibility, reality and necessity, according to universal natural laws, thereby constituting the physiological doctrine of method, the distinction between truth and hypotheses, and the limits of the reliability of the latter.
Although the third table of the principles drawn from the nature of the understanding on the critical method, shows a completeness in itself, which raises it far above every other that has been vainly attempted or may be attempted in the future [to be drawn] from the nature of the thing itself, in a dogmatic way, inasmuch as therein all synthetic axioms à priori have been produced in accordance with a principle, that is, the possibility of judgment in general, which constitutes the essence of experience, in reference to the understanding, in such a manner that one may be certain there are no more such axioms (a satisfaction never to be obtained from the dogmatic method)—yet this is by far not its greatest service.
Attention must be paid to the ground of proof, which discovers the possibility of this knowledge à priori, and limits at the same time all such axioms by a condition, that must never be overlooked, if they are not to be misunderstood, and extended farther in use than the original sense attached to them by the understanding will admit of: namely, that they only contain the conditions of possible experience in general, in so far as it is subordinated to laws à priori. Thus I do not say that things in themselves contain a quantity, their reality, a degree, their existence, connection of accidents in a substance, c.; for this no one can prove, because such a synthetic connection is simply impossible out of mere conceptions, where all reference to sensuous intuition on the one hand, and all connection of the same in a possible experience on the other, is wanting. The essential limitation of conceptions in these axioms is, therefore, that all things only stand under the above-mentioned conditions à priori as objects of experience.
From this there follows, in the second place, a special and peculiar mode of proof of the foregoing: that the axioms in question do not refer directly to phenomena and their relation, but to the possibility of experience of which phenomena constitute the matter but not the form, i.e., to objective and universally valid synthetic propositions, wherein judgments of experience are distinguished from mere judgments of perception. This happens in that the phenomena as mere intuitions, taking in a portion of space and time, are subordinated to the conception of quantity, which unites the manifold in the same synthetically in accordance with à priori rules; and that in so far as the perception contains feeling as well as intuition, between which and zero, namely, its total disappearance, a progression by diminution always takes place, the real of the phenomena must have a basis, seeing that in itself it takes in no portion of space or time. 1 But this progression towards it [viz., reality] from empty time or space, is only possible in time. Consequently, although feeling as the quality of empirical intuition can never be known à priori in respect of that wherein it is specifically distinguished from other feelings, it can nevertheless be distinguished in a possible experience generally, as quantity of perception intensively [distinct] from every other of the same kind; which means the application of mathematics to Nature in respect of the sensuous intuition, by which the former is given us, and by which it becomes in the first place possible and definite.
But the reader must give the greatest attention to the mode of proof of the principles coming under the name of analogies of experience. For inasmuch as these do not, like the principles of the application of mathematics to natural science generally, concern the generation of intuitions, but the connection of their existence in an experience, this can be nothing but the determination of existence in time according to necessary laws, under which alone they are objectively valid, and therefore experience. Thus the proof of synthetic unity does not turn on the connection of things in themselves, but of perceptions, and even of these, not in respect of their content but of their determination in time, and of the relation of existence thereto, according to universal laws. These universal laws contain, therefore, the necessity of the determination of existence in time generally (consequently, according to a rule of the understanding, à priori ) when the empirical determination in the relative time is to be objectively valid, that is, experience. I cannot enter further into the matter here, in Prolegomena, than to recommend the reader who has been long accustomed to regard experience as a mere empirical aggregation of perceptions, and hence does not reflect that it greatly exceeds the sphere of these, that it gives, namely, to empirical judgments, universal validity, and that for this a pure unity of the understanding is necessary to precede à priori, [to recommend him] to give attention to this distinction of experience from a mere aggregrate of perceptions, and to judge the manner of proof from this point of view.
It is here the place to raze Hume’s doubt from its foundation. He maintained justly that we can in nowise discern through the Reason the possibility of causation, namely, the reference of the existence of one thing to the existence of some other thing posited by the former. I may add to this, that we can just as little discern the conception of subsistence, i.e., the necessity contained therein, that a subject must lie at the basis of the existence of a thing, and itself be no predicate of any other thing. [I would say even] that we can form no conception of the possibility of such a thing (though we can point out examples of its use in experience). In the same way this inconceivability attaches even to the community of things, since it is not discernible how, from the state of one thing, a consequence can be drawn as to the state of some totally different thing, external to it, and vice versâ; and how substances of which each has its own separate existence, are necessarily dependent on one another. At the same time, I am far from regarding these conceptions as merely borrowed from experience, and the necessity, that is presented in them, as fictitious and mere illusion, induced in us by long custom. I have, rather, sufficiently shown that both they and the axioms deduced from them, subsist à priori before all experience, and possess indubitable objective correctness, though unquestionably only in respect of experiences.
Although I cannot have the slightest notion of such a connection of things in themselves as of their existing as substances, working as causes, or being able to stand in community with other [substances] as parts of a real whole, I can still less conceive such properties in phenomena as phenomena, because these conceptions contain nothing that lies in the phenomena, but something the understanding alone can conceive. We have, then, from such a connection of presentations in our understanding, and, indeed, in judgments generally, a similar conception, namely, that presentations cohere in one kind of judgments, as subject with reference to predicate, in another as cause with reference to effect, in a third as parts together making up a complete possible cognition. Further, we cognise à priori, that without the presentation of an object, in respect of one or the other of these momenta, to be considered as something definite, we could have no cognition that could be valid of objects, and if we occupied ourselves with the object in itself, there would be no single mark possible, by which I could cognise whether it was determined in respect of one or of another cogitated moment, i.e., whether it cohered under the conception of substance, or of cause, or (in relation to other substances) of reciprocity, for of the possibility of such a connection of existence I should have no conception. But it is not the question, how things in themselves, but how cognition of experience of things in respect of cogitated momenta of judgments generally, is defined, that is, how things as objects of experience can and should be subsumed under the above conceptions of the understanding. And hence it is clear, that I fully recognise not only the possibility, but also the necessity, of subsuming all phenomena under these conceptions, namely, of using them as axioms of the possibility of experience.
Let us now attempt a solution of Hume’s problematical conception (his crux metaphysicorum ), namely, the conception of Cause. Firstly, there is given me, à priori, by means of Logic, the form of a conditioned judgment generally, one cognition as antecedent and another as consequent. But it is possible that in the perception, a rule of the relation may be met with, which will say, that on [the occurrence of a] given phenomenon another always follows (though not conversely), and this would be a case in which to make use of the hypothetical judgment, and to say, for instance, if a body be illumined long enough by the sun, it will become warm. There is certainly no necessity of connection here, in other words, no conception of cause. But I continue: if the above proposition, which is a mere subjective connection of perception, is to be a proposition of experience, it must be regarded as necessary and universally valid; but such a proposition would run: Sun is through its light the cause of heat. The above empirical rule is now looked upon as law, and indeed, not alone as valid of phenomena, but valid of them in relation to a possible experience, which requires thoroughly, and therefore necessarily, valid rules. I perfectly understand, then, the conception of Cause, as a conception necessarily belonging to the mere form of experience, and its possibility as a synthetic union of perceptions, in a consciousness in general; but the possibility of a thing in general as a cause I do not understand, because the conception of cause does not refer at all to things, but only indicates the condition attaching to experience, namely, that this can be only an objectively valid knowledge of phenomena, and their sequence in time, in so far as the antecedent can be united to the consequent according to the rule of hypothetical judgments.
Hence the pure conceptions of the understanding have no meaning whatever, when they quit the objects of experience and refer to things in themselves ( noumena ). They serve, as it were, to spell out phenomena, that these may be able to be read as experience. The axioms arising from their relation to the world of sense, only serve our understanding for use in experience. Beyond this, are only arbitrary combinations, destitute of objective reality, and the possibility of which can neither be known à priori, nor their reference to objects be confirmed, or even made intelligible by an example, because all examples are borrowed from some possible experience, and consequently the objects of those conceptions are nothing but what may be met with in a possible experience.
This complete solution of Hume’s problem, although it turns out to be contrary to the opinion of its originator, preserves for the pure conceptions of the understanding their origin à priori, and for the universal laws of Nature their validity as laws of the understanding, but in such a manner that their use is limited to experience, because their possibility has its basis, solely, in the reference of the understanding to experience; not because they are derived from experience, but because experience is derived from them, which completely reversed mode of connection never occurred to Hume.
The following result of all previous researches follows from the above investigations: “All synthetic axioms à priori are nothing more than principles of possible experience,” and can never be referred to things in themselves, but only to phenomena as objects of experience. Hence pure mathematics no less than pure natural science can never refer to anything more than mere phenomena, and only present that which either makes experience in general possible, or which, inasmuch as it is derived from these principles, must always be able to be presented in some possible experience.
And thus we have at last something definite to hold by in all metaphysical undertakings, which hitherto, bold enough, but always blind, have pursued all things without distinction. Dogmatic thinkers have never let it occur to them, that the goal of their endeavours should be extended such a short way from them, and even those most confident in their imagined common sense have started with conceptions and principles of the mere Reason, legitimate and natural, it is true, but intended merely for use in experience, [in search of] spheres of knowledge, for which they neither knew nor could know of any definite boundaries, because they had neither reflected nor could reflect on the nature or even the possibility of any such pure understanding.
Many a naturalist of the pure Reason (by which I understand he who ventures to decide in questions of metaphysics, without any science) might well profess that what has been here put forward with so much preparation, or if he will have it so, with tediously pedantic pomp, he has long ago not merely conjectured but known and penetrated, by the prophetic spirit of his common sense, namely, “that with all our Reason, we can never pass beyond the field of experiences.” But he must confess, notwithstanding, when questioned seriatim as to his principles of Reason, that amongst these there are many to be found not drawn from experience, and therefore valid, independently thereof, and à priori. How then, and on what grounds, will he hold the dogmatist and himself in limits, who use these conceptions and principles outside all possible experience, simply because they are recognised as independent of it? And even this adept of common sense, in spite of all his pretended, cheaply acquired, wisdom, is not proof against wandering, unobserved, beyond the objects of experience into the field of chimeras. He is, indeed, in the ordinary way, deeply enough involved therein, although by the use of popular language, by putting everything forward as probability, reasonable supposition or analogy, he gives some colour to his groundless assumptions.
From the earliest ages of philosophy, investigators of the pure Reason have postulated, beyond the sensible essences ( phenomena ) which constitute the world of sense, special essences of the understanding ( noumena ) which are supposed to constitute a world of understanding; and since they held appearance and illusion [ Erscheinung und Schein ] for the same thing, which in an undeveloped epoch is to be excused, ascribed reality to the intelligible essence alone.
In fact, when we regard the objects of sense, as is correct, as mere appearances, we thereby at the same time confess that a thing in itself lies at their foundation, although we do not know it, as it is constituted in itself, but only its appearance, that is, the manner in which our senses are affected by this unknown something. The understanding then, by accepting appearances, admits also the existence of things in themselves, and we may even say that the presentation of such essences as lie at the basis of appearances, in short, mere essences of the understanding, is not only admissible, but unavoidable.
Our critical deduction does not by any means exclude such things ( noumena ), but rather limits the principles of æsthetic, in so far that these should not be extended to all things, whereby everything would be changed into mere appearance, but that they should only be valid of objects of a possible experience. Essences of the understanding are hereby admitted only by the emphasising of this rule, which admits of no exception, that we know nothing definite whatever of these pure essences of the understanding, neither can we know anything of them, because our pure conceptions of the understanding no less than our pure intuitions, concern nothing but objects of a possible experience, in short, mere essences of sense, and as soon as we leave these, the above conceptions have not the least significance remaining.
There is indeed something seductive about our pure conceptions of the understanding, as regards temptation to a transcendent use; for so I name that which transcends all possible experience. Not only do our conceptions of substance, force, action, reality, c., which are entirely independent of experience containing no phenomenon of sense, really seem to concern things in themselves ( noumena ); but what strengthens this supposition is, that they contain a necessity of determination in themselves, to which experience can never approach. The conception of cause contains a rule, according to which from one state another follows in a necessary manner; but experience only teaches us that often, or at most usually, one state of a thing follows upon another, and can therefore acquire neither strict universality nor necessity.
Hence these conceptions of the understanding seem to have far too much significance and content for mere use in experience to exhaust their entire determination, and the understanding builds in consequence, unobserved, by the side of the house of experience, a much more imposing wing, which it fills with sheer essences of thought, without even noticing that it has overstepped the legitimate bounds of its otherwise correct conceptions.
There were two important, and indeed altogether indispensable, although exceedingly dry investigations necessary, that have been undertaken in the Critique (p. 107), in the first of which it was shown that the senses do not furnish the pure conceptions of the understanding in concreto, but only the schema for their use, and that the object which conforms to it is only to be met with in experience as the [common] product of the understanding, and the materials of sense. In the second investigation (Critique, p. 178) it is shown, that—notwithstanding the independence of our pure conceptions of the understanding and principles of experience, even to the apparently greater range of their use—nothing whatever could be conceived through them outside the field of experience, because they can do nothing but determine the merely logical form of judgment in respect of given intuitions. But since, beyond the field of sensibility, no intuition is given, these pure conceptions become totally void of meaning, masmuch as they can in no way be presented in concreto. Consequently, all these noumena together with their sum-total, an intelligible world, 1 are nothing but presentations of a problem, the subject of which in itself is indeed possible, but the solution of which is, by the nature of our understanding, utterly impossible, since our understanding is no faculty of intuition, but is merely the connection of given intuitions in an experience, and must comprise therefore all objects for our conceptions; but apart from these, all conceptions which cannot be supported by an intuition, must be without meaning.
The imagination may perhaps be forgiven, if it sometimes dreams, and fails to keep itself carefully within the limits of experience; for certainly it is invigorated and strengthened by a free flight like this, and it is always easier to moderate its boldness than to stimulate its languor. But for the understanding, which ought to think, to dream instead, can never be forgiven, as it is our only support in setting bounds to the fantasies of the imagination, where this is necessary.
It begins, however, very innocently and modestly. First of all, it reduces the elementary cognitions inhering in it before all experience, but having their application, notwithstanding, in experience, to their pure state. Gradually it lets fall these limits; and what is there then to hinder it, seeing that the understanding has taken its principles quite freely from itself? First of all, it is led to newly invented powers in Nature, soon after to essences outside Nature, in a word, to a world for whose fitting-up we can never fail in material, because by a fruitful imagination this will always be richly procured, and although not substantiated by experience, will yet never be confuted by it. This is the reason why young thinkers are so fond of metaphysics, treated in a genuinely dogmatic manner, and sacrifice to it their time and talents which might be otherwise useful.
But it is of no avail attempting to moderate these fruitless attempts of the pure Reason, by all manner of cautions as to the difficulty of the solution of such deeply-hidden questions, lamentations over the limits of our Reason, and by lowering assertions to mere conjectures. For if their impossibility be not clearly shown, and the self-knowledge of the Reason be not [raised to] a true science, in which the field of its right use is separated from that of its nugatory and fruitless use, so to speak, with geometrical certainty, these vain endeavours will never be completely laid aside.
This question, which is the highest point the transcendental philosophy can ever touch, and to which it must also, as its boundary and completion, be directed, properly comprises two questions.
Firstly: How is Nature, in its material signification, namely, as intuition, as the sum-total of phenomena—how is space, time, and that which fills them both, namely, the object of feeling in general—possible? The answer is, by means of the construction of our sensibility, in accordance with which, it is affected in a special manner by objects, in themselves unknown and entirely distinct from these appearances. This answer has been given in the book itself in the Transcendental Æsthetic, but in these Prolegomena in the solution of the first general question.
Secondly: How is Nature in its formal signification—as the sum-total of the rules to which all phenomena must be subordinated, if they are to be thought of as connected in an experience—possible? The answer cannot but be: It is only possible by means of the construction of our understanding, in accordance with which all the above presentations of sensibility are necessarily referred to a consciousness, and whereby the special manner of our thought (namely, by rules), and by means of these, experience (which is to be wholly distinguished from a knowledge of things in themselves) is possible. This answer has been given in the book itself in the Transcendental Logic, but in these Prolegomena in the course of the solution of the second general question.
But how this special property of our sensibility itself, or of our understanding together with the necessary apperception lying at its basis, and at that of all thought, is possible, will not admit of any further solution or answer, because we invariably require it for all answers and for all thought of objects.
There are many laws of Nature that we can only know by means of experience, but regularity in the connection of phenomena, i.e., Nature in general, we can never learn through experience, because experience itself requires such laws, and these lie at the foundation of its possibility à priori. The possibility of experience in general is at once the universal law of Nature, and the axioms of the one are at the same time the laws of the other. For we know nothing of Nature otherwise than as the sum-total of phenomena, namely, of presentations in us, and hence can derive the law of their connection in no other way than from the principles of the same connection in ourselves; in other words, from the conditions of necessary union in a consciousness, which constitutes the possibility of experience.
Even the main proposition, worked out through the whole of this section, that universal natural laws are to be known à priori, of itself leads to the further proposition, that the highest legislation of Nature must lie in ourselves, namely, in our understanding, and that we must seek its universal laws, not in Nature, by means of experience; but conversely, must seek Nature, as to its universal regularity, solely in the conditions of the possibility of experience lying in our sensibility and understanding. For how would it otherwise be possible to know these laws à priori if they be not rules of analytic knowledge, but actually synthetic extensions of the same? Such a necessary agreement of the principles of possible experience with the laws of the possibility of Nature can only occur from one of two causes; either the laws are borrowed from Nature by means of experience, or conversely, Nature is derived from the laws of the possibility of experience generally, and is entirely the same thing as the purely formal regularity of the latter. The first supposition contradicts itself, for the universal laws of Nature can and must be known à priori (i.e., independently of all experience), and be posited as the basis of the empirical use of the understanding; so that only the second [hypothesis] remains to us. 1
But we must distinguish the empirical laws of Nature, which always presuppose particular perceptions, from the pure or universal natural laws, which without any particular perceptions at their foundation, merely contain the conditions of their necessary union in an experience; and in respect of the last, Nature and possible experience are the same thing. Hence, as in this, the legitimacy rests on the necessary connection of phenomena in an experience, in other words, on the original laws of the understanding (without which we could cognise no object of the sensuous world whatever), it sounds at first singular, but is none the less certain, when I say in respect of the latter: The understanding draws its laws ( à priori ) not from Nature, but prescribes them to it.
We will illustrate this apparently daring proposition by an instance, showing that laws, which we discover in objects of sensuous intuition, especially when they are cognised as necessary, are held by ourselves to be such as the understanding has placed them, although in all other respects they may resemble the natural laws we attribute to experience.
If we consider the properties of the circle, by which the figure unites in itself so many arbitrary determinations of space, in a universal rule, one cannot do otherwise than attribute a nature to this geometrical thing. Two lines, for instance, which intersect one another and the circle, it matters not how they may be drawn, are yet always so regular that the rectangle under the segments of the one line is equal to that under the segments of the other. Now I ask, “Does this law lie in the circle or in the understanding?” in other words, does this figure contain independently of the understanding the ground of this law in itself, or does the understanding impose the law that chords cut one another in geometrical proportion, upon it, inasmuch as it has itself constructed the figure according to its own conceptions, namely, the equality of radii? We soon perceive when we follow the proofs of this law, that it can only be derived from the condition the understanding places at the foundation of the construction of this figure, namely, the equality of radii. If we extend the conception, in order to pursue still farther the unity of the manifold properties of geometrical figure under common laws, and consider the circle as a conic section, subordinated to the same fundamental conditions of construction as other conic sections, we find that all chords that intersect within the ellipse (parabola and hyperbola) always intersect, so that the rectangles under their segments, though not indeed equal, yet stand in the same ratio to one another. If we proceed still farther, namely, to the fundamental doctrines of physical astronomy, a physical law of mutual attraction is seen extended over the whole of material nature, whose rule is, that it decreases inversely as the square of the distance from each attracting point, that is, as the spherical surfaces, in which this power diffuses itself, increase; and this seems to lie necessarily in the nature of things themselves, and therefore is usually enunciated as cognisable à priori. However simple the sources of this law may be, as they rest merely on the relations of spherical surfaces of different radii, the consequences are so valuable, as regards the manifold nature of its agreement and regularity, that not only all possible orbits of the heavenly bodies [are described] in conic sections, but such a relation of them among one another follows, that no law of attraction could be conceived as suitable for a world-system, other than that of the inverse square of the distance.
Here then is Nature resting on laws which the understanding cognises à priori, and indeed mainly on universal principles of the determination of space. Now I ask: Do these natural laws lie in space, and does the understanding learn them by merely seeking to investigate the abundant meaning contained therein, or do they lie in the understanding and in the manner in which this determines space according to the conditions of synthetic unity, on which all these conceptions hinge? Space is something so uniform, and as regards all particular properties so indefinite, that certainly no one will seek for any wealth of natural laws in it. On the other hand that which determines space to the circular form, to the figure of the cone or of the sphere, is the understanding in so far as it contains the ground of the unity of its construction. The mere universal form of intuition called space, is the substratum of all particular objects of definable intuitions, and in this certainly lies the condition of its possibility and variety. But the unity of objects is determined simply by the understanding, according to conditions that lie in its own nature, and the understanding is thus the source of the universal order of Nature, since it comprehends all phenomena under its own laws; and thereby it first constructs experience (according to its form) à priori, by means of which all that is to be known through experience becomes necessarily subordinated to its laws. For we have nothing to do with the nature of things in themselves, which is as independent of the conditions of our sensibility as of those of the understanding, but with Nature as the object of a possible experience; and the understanding, while making this possible, [insists] that the world of sense be either no object of experience at all, or else, a Nature.
There can be nothing more desired by a philosopher than that the variety of conceptions or principles he had previously had presented to him in a scattered manner through the use he had made of them in concreto, should be deduced from one principle à priori, and should be all united in this manner in one cognition. Formerly he only believed that those things which remained over, after a certain abstraction, and which by comparison with one another seemed to constitute a particular kind of cognitions, were completely collected; but this was only an aggregate. Now he knows that exactly so many, neither more nor less, can constitute the mode of cognition, and sees the necessity of their division, which is a comprehension; and thus, for the first time, he has a system.
To search out conceptions from common cognitions, having no particular experience at their bases, and at the same time occurring in all cognition of experience, of which they constitute, as it were, the mere form of connection, presupposes no greater reflection or more insight than to search out in a language rules for the real use of words in general, and thus to get together the elements of a grammar. Indeed, both investigations are very nearly related, even if we are unable to give a reason why each language has precisely this and no other formal construction, and still less why exactly so many, neither more nor less, of such formal determinations of the same, generally, are to be found.
Aristotle collected ten such pure elementary cognitions under the name of categories. 1 To these, which were also called predicaments, he saw himself, subsequently, obliged to add five post-predicaments, 2 which yet lay partly in the former (as prius, simul, motus ); but this rhapsody could but serve, and be admired, as a hint for future investigators, rather than be valid as a regularly developed idea; hence in more advanced [stages] of philosophy it has been rejected as altogether useless. On investigation of the pure elements (containing nothing empirical) of the human cognition, I first succeeded, after long reflection, in distinguishing and separating with confidence the elementary conceptions of sensibility (space and time) from those of the understanding, Under these circumstances, the 7th, 8th, and 9th categories were excluded from the list. The remainder could be of no use to me, because there was no principle at hand by which the understanding could be fully gauged, and all its functions, from which its pure conceptions arise, be defined completely and with precision.
In order to find out such a principle, I looked about me for an act of the understanding containing all the rest, and distinguishing itself, only through different modifications or momenta, in bringing the manifold of presentation under the unity of thought generally, and I then found this act of the understanding to consist in judgment. There lay already before me the entire, although not altogether faultless, work of the logicians, whereby I was placed in a position to present a complete table of the pure functions of the understanding that were indefinite as regards the whole object-world. I finally referred these functions of judgment to objects generally, or rather to the conditions determining judgments as objectively valid, and there arose pure conceptions of the understanding, respecting which I could be without doubt that they alone, and only so many of them, neither more nor less, could constitute our whole cognition of things from mere understanding. I called them, as was suitable, by their old name of categories; in doing which, however, I reserved to myself the right to add in their entirety, under the name of predicables, all conceptions to be derived from these—whether by connection with one another, or with the pure form of the phenomenon (space and time), or with their matter so far as it is not empirically determined (object of feeling, generally), as soon as a system of transcendental philosophy, in furtherance of which I was now occupied with a Critique of the Reason itself, should be constructed.
But that which is essential in this system of categories, and distinguishes it from the old rhapsody which proceeded without any principle, and that which alone entitles it to be counted as philosophy, consists in that by its means the true significance of the pure conceptions of the understanding and the conditions of their use can be clearly defined. For it is evident that they are only logical functions in themselves, and as such do not constitute the least conception of an object in themselves, but require sensuous intuition at their foundation. And hence they serve only to determine in respect of the same empirical judgments that are otherwise undetermined and indifferent as regards all functions of judgment; to procure for them thereby universality, and by means of them to make judgments of experience generally, possible.
Such an insight into the nature of the categories, at the same time limiting them to use in experience, never occurred either to their first originator or to any one after him. But without this insight (which exactly depends on their derivation or deduction) they are quite purposeless, and a miserable list of names without explanation or rule of use. Had anything of the kind ever entered into the minds of the ancients, without doubt the whole study of the cognition of the pure Reason, which under the name of metaphysics has through long centuries ruined many a good head, would have come down to us in quite a different form, and would have enlightened the human understanding instead of, as has actually happened, [causing it] to exhaust itself in obscure and vain subtleties, and making it unfruitful for true science.
This system of categories makes all treatment of any object of the pure Reason itself systematic, and affords an indubitable direction or clue how and to what point in the investigation every metaphysical consideration, if it is to be complete, must be reduced; for it exhausts all the momenta of the understanding, under which every other principle must be brought. It is thus that the table of conceptions has arisen, of whose completeness we can only be assured by means of the system of categories. 1 And even in the division of these conceptions destined to transcend the physiological use of the understanding (Critique, pp. 207 and 257), it is always the same clue, which, because it must be always carried through the same fixed points, determined à priori in the human understanding, invariably forms a closed circle, leaving no doubt remaining that the object of a pure conception of the understanding or of the Reason, in so far as it is to be weighed philosophically and according to principles à priori, can be completely known in such a manner. I have not been able even to omit from this derivation, to make use of the most abstract of ontological divisions, namely, the manifold distinction of conceptions of something and nothing, and accordingly to construct a regular and necessary table (Critique, p. 207).
This system, like every true system based on a universal principle, shows its inestimable utility, in that all foreign conceptions, which might otherwise creep in between the above pure conceptions of the understanding, are excluded, and its place given to every cognition. Those conceptions which under the name of conceptions of reflection, I had reduced to a table, on the clue of the categories, mingle themselves, in an ontology without favour or just claim, under the pure conceptions of the understanding, although the latter are conceptions of the connection [of the object] and thereby of the object itself; but the former are the mere comparison of previously given conceptions, and have therefore an altogether different nature and use: by my legitimate division 1 they are saved from this confusion. But the utility of the above separate table of the categories will be seen much more clearly, when, as we are now about to do, we separate the table of the transcendental conceptions of the Reason which are of quite a different nature and origin from the former conceptions of the understanding, and must consequently have a form other than the latter. This necessary separation has never yet taken place in any system of metaphysics, where ideas of the Reason and conceptions of the understanding intermingle, without distinction, as though they were members of one family—a state of confusion which in the absence of a special system of categories could never be avoided.
Pure mathematics and pure natural science would not require for their own security and certainty a deduction such as we have just concluded with respect to them both; for the former rests upon its own evidence, while the latter, although arising from the pure sources of the understanding, is dependent upon the complete substantiation of experience, a witness it is unable altogether to repudiate and do without, seeing that with all its certainty, as philosophy, it can never compete with mathematics. Both these sciences required the foregoing investigation, not for their own sake, but for the sake of another science, namely, metaphysics.
Metaphysics is concerned not merely with natural conceptions, having invariably an application in experience, but, in addition to these, with pure conceptions of the Reason, which can never be given in any possible experience; that is, with conceptions whose objective reality (as distinguished from simple cobwebs of the brain), and with assumptions whose truth or falsity can be confirmed or discovered by no experience. This part of metaphysics is precisely that which constitutes its essential purpose, all else being merely a means thereto, and hence this science requires such a deduction for its own sake. The third problem, now before us, concerns, as it were, the essence and speciality of metaphysics, namely, the occupation of the Reason with itself alone, inasmuch as it broods over its own conceptions and the knowledge of objects supposed to arise immediately from them, without having need of the mediation of experience, or indeed without the possibility of being able to attain thereto by its means. 1 Without a satisfactory solution of this problem, Reason can never be just to itself. The empirical use to which the Reason limits the understanding, does not exhaust its own function. Each special experience is but a portion of the whole sphere of its domain. But the absolute totality of all possible experience, though in itself no experience, constitutes nevertheless for the Reason a necessary problem, to the mere presentation of which it demands quite different conceptions from the pure conceptions of the understanding, the use of which is only immanent, i.e., referable to experience, so far as it can be given; whereas the conceptions of the Reason extend to the completeness, i.e., the collective unity of all possible experience, thereby passing beyond any given experience and becoming transcendent.
As, then, the understanding required the Categories for experience, so the Reason contains in itself the ground of Ideas, by which I understand necessary conceptions the subject of which cannot be given in any experience. The latter are as inherent in the nature of the Reason as the former in the nature of the Understanding, and if they carry with them an illusion that may easily mislead, this illusion is unavoidable, although we may very well guard ourselves from being misled by it.
As all illusion consists in the subjective ground of judgment being taken for objective, the self-knowledge of the pure Reason, in its transcendent (exaggerated) use, is the only preservative against the aberrations into which the Reason falls when it misapplies its function, and refers its transcendent character, concerning only its own subject and its direction in all immanent uses, to the object itself.
The distinction between the ideas, or pure conceptions of the Reason, and the categories or pure conceptions of the understanding as being cognitions of quite another order, origin, and use, is so important a point in the foundation of a science, destined to contain the system of all these cognitions à priori, that without a division of this kind metaphysics would be simply impossible, or at best an incoherent, clumsy attempt at building a house of cards, without a knowledge of the materials handled, and of their capacity for this or that purpose. If the Critique of the Pure Reason had only accomplished the direction of attention to the distinction for the first time, it would have thereby contributed more to the explanation of our conceptions and to the guidance of investigation in the field of metaphysics, than all the fruitless endeavours at solving the transcendental problems of the pure Reason that have ever been undertaken, in which the suspicion has never occurred that the field was quite other than that of the pure understanding, and where consequently the conceptions of the understanding and the Reason have been classed together as though they were of the same kind.
All pure cognitions of the understanding have the peculiarity that their conceptions are given in experience, and their axioms can be confirmed by experience; whereas the transcendent cognitions of the Reason are neither given as concerns their ideas in experience, nor can their axioms be confirmed or refuted by experience. Hence the error possibly arising can be detected by nothing else but pure Reason itself, and this is very difficult, because the Reason by means of its ideas is naturally dialectic, and this unavoidable illusion can be held in check by no objective and dogmatic investigations of the matter, but solely by the subjectivity of the Reason itself as a source of ideas.
It has always been my greatest aim in the Critique, not alone to distinguish carefully the modes of cognition, but also to derive from their common source all the conceptions pertaining to them severally, so that I should not only be informed whence they come and hence be able to determine their use with certainty, but also that I should have the altogether unexpected, but priceless, advantage of knowing the numeration, classification, and specification of the conceptions à priori, and, therefore, according to principles. Without this, everything in metaphysics is mere rhapsody, in which one never knows whether what one possesses is sufficient, or whether there may not be something wanting in it; and if so, where. We can certainly only have this advantage in pure philosophy, but of this latter it constitutes the essence.
As I had found the origin of the categories in the four logical functions of all judgments of the understanding, it was only natural to seek the origin of the ideas in the three functions of the conclusions of the Reason. For if such pure conceptions of the Reason (transcendental ideas) be once given, they could not, unless they were regarded as innate, be found elsewhere than in the same act of Reason, which, as far as form is concerned, constitutes the logical element of the conclusions of the Reason, but so far as it presents the judgments of the understanding as determined with respect, either to one or the other form à priori, [constitutes] the transcendental conceptions of the pure Reason.
The formal distinction of the conclusions of the Reason, renders their division into categorical, hypothetical and disjunctive, necessary. The conceptions of the Reason based thereon, contain, firstly, the idea of the complete subject (substantial); secondly, the idea of the complete series of conditions; thirdly, the determination of all conceptions in the idea of a complete content ( Inbegriff ) of the possible. 1 The first idea is psychological, the second cosmological, and the third theological; and as all three give occasion to a dialectic, each of its own kind, the division of the whole dialectic of the pure Reason founded thereupon, is into the Paralogism, the Antinomy, and finally the Ideal of the same. By this division we are fully assured that all demands of the pure Reason are here presented, in their completeness; that no single one can fail, because the capacity of the Reason itself, as that from which they all take their origin, is thereby completely surveyed.
In this general consideration it is noteworthy, that the ideas of the Reason, unlike the categories, are not of any service whatever in the use of the understanding in experience, but can be wholly dispensed with in this connection; indeed, they are impediments to the maxims of the understanding’s knowledge of nature, notwithstanding their necessity for another purpose, yet to be determined. Whether the soul be, or be not, a simple substance, can be quite indifferent to us, so far as the explanation of its phenomena is concerned, for we cannot render the conception of a simple essence comprehensible, sensuously or in concreto, by any possible experience; and hence it is quite barren as to the hoped-for insight into the cause of the phenomena; and cannot serve as any principle of explanation for what is afforded, either by internal or external experience. Just as little can the cosmological ideas of the beginning of the world or of the eternity of the world ( a parte ante ) avail us to explain an occurrence in the world itself. Finally, we must, in accordance with a just maxim of the philosophy of Nature, refrain from all explanation of the order of Nature, which is derived from the will of a Supreme Being, because this is no longer a philosophy of Nature, but a confession that we have finished with the latter. Hence these ideas have quite a different determination of their use from the categories, by means of which, and of the principles based upon them, experience itself is first possible. But our laborious analytic of the understanding would be quite superfluous, if our aim were nothing else but mere knowledge of Nature, such as can be given in experience; for Reason accomplishes its work both in mathematics and natural science, certainly and well, without any of this subtle deduction. Thus our Critique of the understanding combines with the ideas of the pure Reason, in an aim placed beyond the empirical use of the understanding, of which we have above said that, in this respect, it is quite impossible, and destitute alike of object and meaning. But there must, nevertheless, be an agreement between that which belongs to the nature of the Reason and of the understanding, and the former must contribute to the completion of the latter, and cannot possibly confuse it.
The solution of this problem is as follows: the pure Reason has no particular objects denoted by its ideas which lie outside the field of experience in view, but merely requires completeness of the use of the understanding within the system of experience. This completeness, however, can only be a completeness of principles, but not of intuitions and objects. But in order to represent the former definitely, it regards them as the cognition of an object, a cognition completely determined as regards these rules, but the object of which is only an idea, designed to bring the cognition of the understanding as near as possible to the completeness indicated by that idea.
We have above (§§ 33, 34) shown, that the purity of the categories, from all admixture of sensuous determinations, may mislead the Reason into extending its use entirely beyond the range of all experience, to things in themselves; for although they can find no intuition that could lend them meaning and sense in concreto, yet as mere logical functions they may represent a thing in general, notwithstanding that, independently, they are unable to give a definite conception of anything whatever. Such hyperbolical objects are what are termed noumena, or pure essences of the Understanding (better essences of thought), as, for instance, substance, when considered as without permanence in time, or a cause, which does not operate in time, c., inasmuch as predicates are then attached to them, which serve merely to make the conformability of experience to law possible, and at the same time all the conditions of intuition—under which experience is alone possible—are taken away from them, whereby these conceptions lose all significance. There is, however, no danger of the understanding of itself, unimpressed by laws foreign to it, branching out so rashly into the field of mere essences of thought. But when the Reason, which cannot be completely satisfied with an empirical use of the rules of the understanding, requires the completion of this chain of conditions, the understanding is driven out of its own sphere, partly to present objects of experience in a series extended so far that no experience can grasp it, and partly (in order to complete this series) to search for noumena, wholly outside the same, to which it may attach the above chain, and thereby, being at last independent of experience, render its attitude once for all complete. These are the transcendental ideas, which, in accordance with the true but hidden ends of the natural determination of our Reason, are designed not for extravagant conceptions, but merely for the unlimited extension of empirical use; but which, however, by an unavoidable illusion seduce the understanding into a transcendent use, that although deceitful, cannot be kept within the bounds of experience by any resolution, but can only be restrained within [due] limits with pains, and by means of scientific instruction.
It has long been observed that the subject proper, in all substances, namely, that which remains over after all accidents (as predicates) have been abstracted, that is, the substantial itself, is unknown, and oft-repeated complaints have been made of these limitations of our insight. But it is to be observed as regards this, that the human understanding is not to be taken to task for not knowing the substantial of things, that is, for not being able to determine it by itself, but rather for expecting to know it definitely, like a given object, when it is a mere idea. The pure Reason requires of every predicate of a thing the subject belonging to it, but to this, which is again necessarily only predicate, it requires a further subject, and so on ad infinitum (or as far as we can reach). But it follows from the above, that nothing to which we can attain is to be taken for an ultimate subject, and that the substantial itself can never be thought by our understanding, however deeply penetrating it may be, not even if the whole of Nature were unveiled before it; because the specific nature of our understanding consists in that it thinks all things discursively, i.e., through conceptions, and hence solely by means of predicates, to which the absolute subject must always be wanting. For this reason all real qualities whereby we cognise bodies, even to impenetrability, which must always present itself as the effect of a force, are simply accidents, the subject of which eludes us.
Now it seems as though in our own consciousness (the thinking subject) we have this substantial, and indeed in an immediate intuition; for all predicates of the internal sense refer to the ego, the subject, and this cannot be thought of as predicate of any other subject whatever. Here, then, the completeness in the connection of the given conceptions as predicates of a subject, not merely an idea, but an existence, namely, the absolute subject itself, seem to be given in experience. But this experience is vain, for the ego is no conception at all, 1 but merely a designation of the object of the internal sense, so far as we can cognise it by no further predicate, and hence in itself it can indeed be no predicate of another thing, and just as little a definite conception of an absolute subject, but only, as in all other cases, the reference of the internal phenomena to their unknown subject. At the same time, this idea (which serves well enough, as regulative principle, completely to annihilate all materialistic explanations of the internal phenomena of our soul) occasions, owing to a perfectly natural misunderstanding, a very plausible argument, by inferring from this supposed cognition of the substantial in our thinking entity, its nature, in so far as the knowledge of the same falls entirely outside the content of experience.
This thinking self (the soul) may however, as the ultimate subject of thought, which cannot be conceived as the predicate of another thing, be called substance; but this conception remains wholly barren, and void of all results, if permanence, which makes the conception of substances in experience fruitful, cannot be proved of it.
But permanence can never be proved from the conception of a substance, as a thing in itself, but only for the purposes of experience. The above has been fully explained in the first analogy of experience (Critique, p. 136), and, if this demonstration be not accepted, the attempt need only be made as to whether it is possible to prove, from the conception of a subject, not existing as the predicate of some other thing, that its existence is thoroughly permanent, and that neither in itself, nor through any natural cause, can it arise or pass away. Such synthetic propositions à priori can never be proved in themselves, but only with reference to things as objects of possible experience.
When from the conception of the soul as substance we infer its permanence, this can be only valid of it as an object of possible experience, and not as a thing in itself, outside all possible experience. Now the subjective condition of all our possible experience is life; consequently, the permanence of the soul can only be inferred in life, for the death of man is the end of all experience, of which the soul is an object, unless the contrary be proved, and this is precisely the question. Hence, the permanence of the soul can only be proved in the life of man (the proof of which will not be required of us), but not after death, which is the real point at issue, for the general reason that the conception of substance, viewed as necessarily conjoined with the conception of permanence, is only [based on] an axiom of possible experience, and therefore only serviceable for the purposes of the latter. 1
That something real not merely corresponds but must correspond to our external perceptions, can be proved as concerns experience, but not as a connection of things in themselves. This is as much as to say, that something of an empirical kind, as phenomenon in space, exists outside us, can be proved; for with objects, other than those belonging to a possible experience, we have nothing to do, because, inasmuch as they can be given in no experience, they are to us nothing. That is empirically outside me which can be intuited in space, and as the latter, together with all the phenomena it contains, belongs to the presentations, whose connection according to the laws of experience proves their objective reality, just as much as the connection of the phenomena of the internal sense proves the reality of my soul, as an object of the internal sense; so, by means of external experience, I am just as conscious of the reality of bodies as external phenomena in space, as I am of the existence of my soul in time by means of the internal experience, which I also cognise only through phenomena, as an object of the internal sense, [that is, as] constituting an internal condition, of which the essence in itself, lying at the foundation of these phenomena, is unknown to me. The Cartesian idealism only distinguishes external experience from dream; its regularity being the criterion of the truth of the one as against the irregularity and false illusion of the other. It presupposes, in both of them, space and time as conditions of the reality of the objects, and only asks whether the objects of our external sense, which when awake we meet with in space, are really to be found therein, and in the same way whether the object of the internal sense, the soul, really exists in time; in other words, whether experience can afford certain criteria for the distinction between truth and imagination. Now this doubt may be easily decided, and we always do decide it in common life, in that we investigate the connection of the phenomena in both according to universal laws of experience, and we cannot doubt, when the presentation of external things thoroughly agrees with these, that they constitute reliable experience. Material idealism may accordingly be refuted very easily, inasmuch as phenomena quâ phenomena are only considered as to their connection in experience; and it is just as certain an experience that bodies exist outside ourselves (in space), as that I myself according to the presentation of the internal sense exist (in time); for the conception of outside ourselves, denotes simply existence in space. But as the I in the proposition I am, signifies not merely the object of internal intuition (in time) but the subject of consciousness, so in the same way body signifies not merely the external intuition (in space), but also the thing in itself at the basis of this phenomenon, and hence the question as to whether bodies (as phenomena of the external sense) exist apart from my thoughts as bodies, may, in the nature of things, be denied without hesitation. But there is no difference as to the question, whether I myself as phenomenon of the internal sense (soul, according to the empirical psychology) exist in time, apart from my power of presentation, for this must be just as much denied. In the same way, everything when reduced to its true meaning is decided and certain. Formal idealism (otherwise called transcendental by me) really refutes the material or Cartesian [idealism]. For if space be nothing but a form of my sensibility, it is just as real as a presentation in me as I am myself, and the question only turns on the empirical truth of phenomena in the same. If this, however, be not the case, but space and the phenomena [contained] therein are something existing outside ourselves, all criteria of experience, apart from our perception, can never prove the reality of the objects external to us.
This product of the pure Reason in its transcendent use is its most remarkable phenomenon, and is moreover the one most powerful in awakening philosophy out of its dogmatic slumber, and in urging it on, to the heavy tasks of the Critique of the Reason.
I term this idea cosmological, because it always takes its object from the world of sense, and only requires those [conceptions] whose object is an object of sense, being therefore native [immanent] and not transcendent, and consequently, thus far, no idea; while, on the other hand, to conceive the soul as a simple substance, is equivalent to conceiving an object (the simple) which cannot be presented to the senses. But notwithstanding this, the cosmological idea extends the connection of the conditioned with its condition (whether mathematical or dynamical) so far, that experience can never reach it, and hence remains, as regards this point, always an idea, the object of which can never be adequately given in any experience whatever.
It is here that the usefulness of a system of categories shows itself so plainly and unmistakably, that, even were there not several other proofs of it, this alone would quite sufficiently demonstrate its indispensableness in the system of the pure Reason. There are not more than four of these transcendent ideas, as many as there are classes of categories; but each of them is only concerned with the absolute completion of a series of conditions to a given conditioned. In accordance with these cosmological ideas there are four dialectical assertions of the pure Reason, which, inasmuch as they are dialectical, show that to each one is opposed a contradictory assumption, on equally plausible principles of the pure Reason; and this is a conflict no metaphysical art of the subtlest distinction can avoid, but which compels philosophers to go back to the primary sources of the pure Reason. The above antinomy, which is not arbitrarily invented, but has its basis in the nature of the human Reason, and is hence unavoidable and never-ending, contains the following four theses together with their antitheses:—
| 1. | ||
| Thesis. | Antithesis. | |
| The world has a beginning (boundary) in time and space. | The world is infinite in time and space. | |
| 2. | ||
| Thesis. | Antithesis. | |
| Everything in the world consists of simple [parts]. | There is nothing simple, but everything is composite. | |
| 3. | ||
| Thesis. | Antithesis. | |
| There are in the world causes through freedom. | There is no freedom, but all is Nature. |