Introduction

I. Of the difference between Pure and Empirical Knowledge

        That all our knowledge begins with experience there can be no doubt. For how is it possible that the faculty of cognition should be awakened into exercise otherwise than by means of objects which affect our senses, and partly of themselves produce representations, partly rouse our powers of understanding into activity, to compare to connect, or to separate these, and so to convert the raw material of our sensuous impressions into a knowledge of objects, which is called experience? In respect of time, therefore, no knowledge of ours is antecedent to experience, but begins with it.

        But, though all our knowledge begins with experience, it by no means follows that all arises out of experience. For, on the contrary, it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion), an addition which we cannot distinguish from the original element given by sense, till long practice has made us attentive to, and skilful in separating it. It is, therefore, a question which requires close investigation, and not to be answered at first sight, whether there exists a knowledge altogether independent of experience, and even of all sensuous impressions? Knowledge of this kind is called a priori, in contradistinction to empirical knowledge, which has its sources a posteriori, that is, in experience.

        But the expression, "a priori," is not as yet definite enough adequately to indicate the whole meaning of the question above started. For, in speaking of knowledge which has its sources in experience, we are wont to say, that this or that may be known a priori, because we do not derive this knowledge immediately from experience, but from a general rule, which, however, we have itself borrowed from experience. Thus, if a man undermined his house, we say, "he might know a priori that it would have fallen;" that is, he needed not to have waited for the experience that it did actually fall. But still, a priori, he could not know even this much. For, that bodies are heavy, and, consequently, that they fall when their supports are taken away, must have been known to him previously, by means of experience.

        By the term "knowledge a priori," therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience. Knowledge a priori is either pure or impure. Pure knowledge a priori is that with which no empirical element is mixed up. For example, the proposition, "Every change has a cause," is a proposition a priori, but impure, because change is a conception which can only be derived from experience.

II. The Human Intellect, even in an Unphilosophical State, is in Possession of Certain Cognitions "a priori."

        The question now is as to a criterion, by which we may securely distinguish a pure from an empirical cognition. Experience no doubt teaches us that this or that object is constituted in such and such a manner, but not that it could not possibly exist otherwise.         Now, in the first place, if we have a proposition which contains the idea of necessity in its very conception, it is a if, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely priori. Secondly, an empirical judgement never exhibits strict and absolute, but only assumed and comparative universality (by induction); therefore, the most we can say is—so far as we have hitherto observed, there is no exception to this or that rule. If, on the other hand, a judgement carries with it strict and absolute universality, that is, admits of no possible exception, it is not derived from experience, but is valid absolutely a priori.

        Empirical universality is, therefore, only an arbitrary extension of validity, from that which may be predicated of a proposition valid in most cases, to that which is asserted of a proposition which holds good in all; as, for example, in the affirmation, "All bodies are heavy." When, on the contrary, strict universality characterizes a judgement, it necessarily indicates another peculiar source of knowledge, namely, a faculty of cognition a priori. Necessity and strict universality, therefore, are infallible tests for distinguishing pure from empirical knowledge, and are inseparably connected with each other. But as in the use of these criteria the empirical limitation is sometimes more easily detected than the contingency of the judgement, or the unlimited universality which we attach to a judgement is often a more convincing proof than its necessity, it may be advisable to use the criteria separately, each being by itself infallible.

        Now, that in the sphere of human cognition we have judgements which are necessary, and in the strictest sense universal, consequently pure a priori, it will be an easy matter to show. If we desire an example from the sciences, we need only take any proposition in mathematics. If we cast our eyes upon the commonest operations of the understanding, the proposition, "Every change must have a cause," will amply serve our purpose. In the latter case, indeed, the conception of a cause so plainly involves the conception of a necessity of connection with an effect, and of a strict universality of the law, that the very notion of a cause would entirely disappear, were we to derive it, like Hume, from a frequent association of what happens with that which precedes; and the habit thence originating of connecting representations—the necessity inherent in the judgement being therefore merely subjective. Besides, without seeking for such examples of principles existing a priori in cognition, we might easily show that such principles are the indispensable basis of the possibility of experience itself, and consequently prove their existence a priori. For whence could our experience itself acquire certainty, if all the rules on which it depends were themselves empirical, and consequently fortuitous? No one, therefore, can admit the validity of the use of such rules as first principles. But, for the present, we may content ourselves with having established the fact, that we do possess and exercise a faculty of pure a priori cognition; and, secondly, with having pointed out the proper tests of such cognition, namely, universality and necessity.

        Not only in judgements, however, but even in conceptions, is an a priori origin manifest. For example, if we take away by degrees from our conceptions of a body all that can be referred to mere sensuous experience—colour, hardness or softness, weight, even impenetrability—the body will then vanish; but the space which it occupied still remains, and this it is utterly impossible to annihilate in thought. Again, if we take away, in like manner, from our empirical conception of any object, corporeal or incorporeal, all properties which mere experience has taught us to connect with it, still we cannot think away those through which we cogitate it as substance, or adhering to substance, although our conception of substance is more determined than that of an object. Compelled, therefore, by that necessity with which the conception of substance forces itself upon us, we must confess that it has its seat in our faculty of cognition a priori.

III. Philosophy stands in need of a Science which shall Determine the Possibility, Principles, and Extent of Human Knowledge "a priori."

        Of far more importance than all that has been above said, is the consideration that certain of our cognitions rise completely above the sphere of all possible experience, and by means of conceptions, to which there exists in the whole extent of experience no corresponding object, seem to extend the range of our judgements beyond its bounds. And just in this transcendental or supersensible sphere, where experience affords us neither instruction nor guidance, lie the investigations of reason, which, on account of their importance, we consider far preferable to, and as having a far more elevated aim than, all that the understanding can achieve within the sphere of sensuous phenomena. So high a value do we set upon these investigations, that even at the risk of error, we persist in following them out, and permit neither doubt nor disregard nor indifference to restrain us from the pursuit. These unavoidable problems of mere pure reason are God, freedom (of will), and immortality. The science which, with all its preliminaries, has for its especial object the solution of these problems is named metaphysics—a science which is at the very outset dogmatical, that is, it confidently takes upon itself the execution of this task without any previous investigation of the ability or inability of reason for such an undertaking.

        Now the safe ground of experience being thus abandoned, it seems nevertheless natural that we should hesitate to erect a building with the cognitions we possess, without knowing whence they come, and on the strength of principles, the origin of which is undiscovered. Instead of thus trying to build without a foundation, it is rather to be expected that we should long ago have put the question, how the understanding can arrive at these a priori cognitions, and what is the extent, validity, and worth which they may possess? We say, "This is natural enough," meaning by the word natural, that which is consistent with a just and reasonable way of thinking; but if we understand by the term, that which usually happens, nothing indeed could be more natural and more comprehensible than that this investigation should be left long unattempted. For one part of our pure knowledge, the science of mathematics, has been long firmly established, and thus leads us to form flattering expectations with regard to others, though these may be of quite a different nature. Besides, when we get beyond the bounds of experience, we are of course safe from opposition in that quarter; and the charm of widening the range of our knowledge is so great that, unless we are brought to a standstill by some evident contradiction, we hurry on undoubtingly in our course. This, however, may be avoided, if we are sufficiently cautious in the construction of our fictions, which are not the less fictions on that account.

        Mathematical science affords us a brilliant example, how far, independently of all experience, we may carry our a priori knowledge. It is true that the mathematician occupies himself with objects and cognitions only in so far as they can be represented by means of intuition. But this circumstance is easily overlooked, because the said intuition can itself be given a priori, and therefore is hardly to be distinguished from a mere pure conception. Deceived by such a proof of the power of reason, we can perceive no limits to the extension of our knowledge. The light dove cleaving in free flight the thin air, whose resistance it feels, might imagine that her movements would be far more free and rapid in airless space. Just in the same way did Plato, abandoning the world of sense because of the narrow limits it sets to the understanding, venture upon the wings of ideas beyond it, into the void space of pure intellect. He did not reflect that he made no real progress by all his efforts; for he met with no resistance which might serve him for a support, as it were, whereon to rest, and on which he might apply his powers, in order to let the intellect acquire momentum for its progress. It is, indeed, the common fate of human reason in speculation, to finish the imposing edifice of thought as rapidly as possible, and then for the first time to begin to examine whether the foundation is a solid one or no. Arrived at this point, all sorts of excuses are sought after, in order to console us for its want of stability, or rather, indeed, to enable Us to dispense altogether with so late and dangerous an investigation. But what frees us during the process of building from all apprehension or suspicion, and flatters us into the belief of its solidity, is this. A great part, perhaps the greatest part, of the business of our reason consists in the analysation of the conceptions which we already possess of objects. By this means we gain a multitude of cognitions, which although really nothing more than elucidations or explanations of that which (though in a confused manner) was already thought in our conceptions, are, at least in respect of their form, prized as new introspections; whilst, so far as regards their matter or content, we have really made no addition to our conceptions, but only disinvolved them.         But as this process does furnish a real priori knowledge, which has a sure progress and useful results, reason, deceived by this, slips in, without being itself aware of it, assertions of a quite different kind; in which, to given conceptions it adds others, a priori indeed, but entirely foreign to them, without our knowing how it arrives at these, and, indeed, without such a question ever suggesting itself. I shall therefore at once proceed to examine the difference between these two modes of knowledge.

IV. Of the Difference Between Analytical and Synthetical Judgements.

        In all judgements wherein the relation of a subject to the predicate is cogitated (I mention affirmative judgements only here; the application to negative will be very easy), this relation is possible in two different ways. Either the predicate B belongs to the subject A, as somewhat which is contained (though covertly) in the conception A; or the predicate B lies completely out of the conception A, although it stands in connection with it. In the first instance, I term the judgement analytical, in the second, synthetical. Analytical judgements (affirmative) are therefore those in which the connection of the predicate with the subject is cogitated through identity; those in which this connection is cogitated without identity, are called synthetical judgements. The former may be called explicative, the latter augmentative judgements; because the former add in the predicate nothing to the conception of the subject, but only analyse it into its constituent conceptions, which were thought already in the subject, although in a confused manner; the latter add to our conceptions of the subject a predicate which was not contained in it, and which no analysis could ever have discovered therein. For example, when I say, "All bodies are extended," this is an analytical judgement. For I need not go beyond the conception of body in order to find extension connected with it, but merely analyse the conception, that is, become conscious of the manifold properties which I think in that conception, in order to discover this predicate in it: it is therefore an analytical judgement. On the other hand, when I say, "All bodies are heavy," the predicate is something totally different from that which I think in the mere conception of a body. By the addition of such a predicate, therefore, it becomes a synthetical judgement.

        Judgements of experience, as such, are always synthetical. For it would be absurd to think of grounding an analytical judgement on experience, because in forming such a judgement I need not go out of the sphere of my conceptions, and therefore recourse to the testimony of experience is quite unnecessary. That "bodies are extended" is not an empirical judgement, but a proposition which stands firm a priori. For before addressing myself to experience, I already have in my conception all the requisite conditions for the judgement, and I have only to extract the predicate from the conception, according to the principle of contradiction, and thereby at the same time become conscious of the necessity of the judgement, a necessity which I could never learn from experience. On the other hand, though at first I do not at all include the predicate of weight in my conception of body in general, that conception still indicates an object of experience, a part of the totality of experience, to which I can still add other parts; and this I do when I recognize by observation that bodies are heavy. I can cognize beforehand by analysis the conception of body through the characteristics of extension, impenetrability, shape, etc., all which are cogitated in this conception. But now I extend my knowledge, and looking back on experience from which I had derived this conception of body, I find weight at all times connected with the above characteristics, and therefore I synthetically add to my conceptions this as a predicate, and say, "All bodies are heavy." Thus it is experience upon which rests the possibility of the synthesis of the predicate of weight with the conception of body, because both conceptions, although the one is not contained in the other, still belong to one another (only contingently, however), as parts of a whole, namely, of experience, which is itself a synthesis of intuitions.

        But to synthetical judgements a priori, such aid is entirely wanting. If I go out of and beyond the conception A, in order to recognize another B as connected with it, what foundation have I to rest on, whereby to render the synthesis possible? I have here no longer the advantage of looking out in the sphere of experience for what I want. Let us take, for example, the proposition, "Everything that happens has a cause." In the conception of "something that happens," I indeed think an existence which a certain time antecedes, and from this I can derive analytical judgements. But the conception of a cause lies quite out of the above conception, and indicates something entirely different from "that which happens," and is consequently not contained in that conception. How then am I able to assert concerning the general conception—"that which happens"—something entirely different from that conception, and to recognize the conception of cause although not contained in it, yet as belonging to it, and even necessarily? what is here the unknown = X, upon which the understanding rests when it believes it has found, out of the conception A a foreign predicate B, which it nevertheless considers to be connected with it? It cannot be experience, because the principle adduced annexes the two representations, cause and effect, to the representation existence, not only with universality, which experience cannot give, but also with the expression of necessity, therefore completely a priori and from pure conceptions. Upon such synthetical, that is augmentative propositions, depends the whole aim of our speculative knowledge a priori; for although analytical judgements are indeed highly important and necessary, they are so, only to arrive at that clearness of conceptions which is requisite for a sure and extended synthesis, and this alone is a real acquisition.

V. In all Theoretical Sciences of Reason, Synthetical Judgements "a priori" are contained as Principles.

        1. Mathematical judgements are always synthetical. Hitherto this fact, though incontestably true and very important in its consequences, seems to have escaped the analysts of the human mind, nay, to be in complete opposition to all their conjectures. For as it was found that mathematical conclusions all proceed according to the principle of contradiction (which the nature of every apodeictic certainty requires), people became persuaded that the fundamental principles of the science also were recognized and admitted in the same way. But the notion is fallacious; for although a synthetical proposition can certainly be discerned by means of the principle of contradiction, this is possible only when another synthetical proposition precedes, from which the latter is deduced, but never of itself.

        Before all, be it observed, that proper mathematical propositions are always judgements a priori, and not empirical, because they carry along with them the conception of necessity, which cannot be given by experience. If this be demurred to, it matters not; I will then limit my assertion to pure mathematics, the very conception of which implies that it consists of knowledge altogether non-empirical and a priori.

        We might, indeed at first suppose that the proposition 7 + 5 = 12 is a merely analytical proposition, following (according to the principle of contradiction) from the conception of a sum of seven and five. But if we regard it more narrowly, we find that our conception of the sum of seven and five contains nothing more than the uniting of both sums into one, whereby it cannot at all be cogitated what this single number is which embraces both. The conception of twelve is by no means obtained by merely cogitating the union of seven and five; and we may analyse our conception of such a possible sum as long as we will, still we shall never discover in it the notion of twelve. We must go beyond these conceptions, and have recourse to an intuition which corresponds to one of the two—our five fingers, for example, or like Segner in his Arithmetic five points, and so by degrees, add the units contained in the five given in the intuition, to the conception of seven. For I first take the number 7, and, for the conception of 5 calling in the aid of the fingers of my hand as objects of intuition, I add the units, which I before took together to make up the number 5, gradually now by means of the material image my hand, to the number 7, and by this process, I at length see the number 12 arise. That 7 should be added to 5, I have certainly cogitated in my conception of a sum = 7 + 5, but not that this sum was equal to 12. Arithmetical propositions are therefore always synthetical, of which we may become more clearly convinced by trying large numbers. For it will thus become quite evident that, turn and twist our conceptions as we may, it is impossible, without having recourse to intuition, to arrive at the sum total or product by means of the mere analysis of our conceptions. Just as little is any principle of pure geometry analytical. "A straight line between two points is the shortest," is a synthetical proposition. For my conception of straight contains no notion of quantity, but is merely qualitative. The conception of the shortest is therefore fore wholly an addition, and by no analysis can it be extracted from our conception of a straight line. Intuition must therefore here lend its aid, by means of which, and thus only, our synthesis is possible.

        Some few principles preposited by geometricians are, indeed, really analytical, and depend on the principle of contradiction. They serve, however, like identical propositions, as links in the chain of method, not as principles—for example, a = a, the whole is equal to itself, or (a+b) —> a, the whole is greater than its part. And yet even these principles themselves, though they derive their validity from pure conceptions, are only admitted in mathematics because they can be presented in intuition. What causes us here commonly to believe that the predicate of such apodeictic judgements is already contained in our conception, and that the judgement is therefore analytical, is merely the equivocal nature of the expression. We must join in thought a certain predicate to a given conception, and this necessity cleaves already to the conception. But the question is, not what we must join in thought to the given conception, but what we really think therein, though only obscurely, and then it becomes manifest that the predicate pertains to these conceptions, necessarily indeed, yet not as thought in the conception itself, but by virtue of an intuition, which must be added to the conception.

        2. The science of natural philosophy (physics) contains in itself synthetical judgements a priori, as principles. I shall adduce two propositions. For instance, the proposition, "In all changes of the material world, the quantity of matter remains unchanged"; or, that, "In all communication of motion, action and reaction must always be equal." In both of these, not only is the necessity, and therefore their origin a priori clear, but also that they are synthetical propositions. For in the conception of matter, I do not cogitate its permanency, but merely its presence in space, which it fills. I therefore really go out of and beyond the conception of matter, in order to think on to it something a priori, which I did not think in it. The proposition is therefore not analytical, but synthetical, and nevertheless conceived a priori; and so it is with regard to the other propositions of the pure part of natural philosophy.

        3. As to metaphysics, even if we look upon it merely as an attempted science, yet, from the nature of human reason, an indispensable one, we find that it must contain synthetical propositions a priori. It is not merely the duty of metaphysics to dissect, and thereby analytically to illustrate the conceptions which we form a priori of things; but we seek to widen the range of our a priori knowledge. For this purpose, we must avail ourselves of such principles as add something to the original conception—something not identical with, nor contained in it, and by means of synthetical judgements a priori, leave far behind us the limits of experience; for example, in the proposition, "the world must have a beginning," and such like. Thus metaphysics, according to the proper aim of the science, consists merely of synthetical propositions a priori.

VI. The Universal Problem of Pure Reason.

        It is extremely advantageous to be able to bring a number of investigations under the formula of a single problem. For in this manner, we not only facilitate our own labour, inasmuch as we define it clearly to ourselves, but also render it more easy for others to decide whether we have done justice to our undertaking. The proper problem of pure reason, then, is contained in the question: "How are synthetical judgements a priori possible?"

        That metaphysical science has hitherto remained in so vacillating a state of uncertainty and contradiction, is only to be attributed to the fact that this great problem, and perhaps even the difference between analytical and synthetical judgements, did not sooner suggest itself to philosophers. Upon the solution of this problem, or upon sufficient proof of the impossibility of synthetical knowledge a priori, depends the existence or downfall of the science of metaphysics. Among philosophers, David Hume came the nearest of all to this problem; yet it never acquired in his mind sufficient precision, nor did he regard the question in its universality. On the contrary, he stopped short at the synthetical proposition of the connection of an effect with its cause (principium causalitatis), insisting that such proposition a priori was impossible. According to his conclusions, then, all that we term metaphysical science is a mere delusion, arising from the fancied insight of reason into that which is in truth borrowed from experience, and to which habit has given the appearance of necessity. Against this assertion, destructive to all pure philosophy, he would have been guarded, had he had our problem before his eyes in its universality. For he would then have perceived that, according to his own argument, there likewise could not be any pure mathematical science, which assuredly cannot exist without synthetical propositions a priori—an absurdity from which his good understanding must have saved him.

        In the solution of the above problem is at the same time comprehended the possibility of the use of pure reason in the foundation and construction of all sciences which contain theoretical knowledge a priori of objects, that is to say, the answer to the following questions:

        How is pure mathematical science possible?

        How is pure natural science possible?

        Respecting these sciences, as they do certainly exist, it may with propriety be asked, how they are possible?—for that they must be possible is shown by the fact of their really existing.* But as to metaphysics, the miserable progress it has hitherto made, and the fact that of no one system yet brought forward, far as regards its true aim, can it be said that this science really exists, leaves any one at liberty to doubt with reason the very possibility of its existence.

        Yet, in a certain sense, this kind of knowledge must unquestionably be looked upon as given; in other words, metaphysics must be considered as really existing, if not as a science, nevertheless as a natural disposition of the human mind (metaphysica naturalis). For human reason, without any instigations imputable to the mere vanity of great knowledge, unceasingly progresses, urged on by its own feeling of need, towards such questions as cannot be answered by any empirical application of reason, or principles derived therefrom; and so there has ever really existed in every man some system of metaphysics. It will always exist, so soon as reason awakes to the exercise of its power of speculation. And now the question arises: "How is metaphysics, as a natural disposition, possible?" In other words, how, from the nature of universal human reason, do those questions arise which pure reason proposes to itself, and which it is impelled by its own feeling of need to answer as well as it can?

        But as in all the attempts hitherto made to answer the questions which reason is prompted by its very nature to propose to itself, for example, whether the world had a beginning, or has existed from eternity, it has always met with unavoidable contradictions, we must not rest satisfied with the mere natural disposition of the mind to metaphysics, that is, with the existence of the faculty of pure reason, whence, indeed, some sort of metaphysical system always arises; but it must be possible to arrive at certainty in regard to the question whether we know or do not know the things of which metaphysics treats. We must be able to arrive at a decision on the subjects of its questions, or on the ability or inability of reason to form any judgement respecting them; and therefore either to extend with confidence the bounds of our pure reason, or to set strictly defined and safe limits to its action. This last question, which arises out of the above universal problem, would properly run thus: "How is metaphysics possible as a science?"

        Thus, the critique of reason leads at last, naturally and necessarily, to science; and, on the other hand, the dogmatical use of reason without criticism leads to groundless assertions, against which others equally specious can always be set, thus ending unavoidably in scepticism.

        Besides, this science cannot be of great and formidable prolixity, because it has not to do with objects of reason, the variety of which is inexhaustible, but merely with Reason herself and her problems; problems which arise out of her own bosom, and are not proposed to her by the nature of outward things, but by her own nature. And when once Reason has previously become able completely to understand her own power in regard to objects which she meets with in experience, it will be easy to determine securely the extent and limits of her attempted application to objects beyond the confines of experience.

        We may and must, therefore, regard the attempts hitherto made to establish metaphysical science dogmatically as non-existent. For what of analysis, that is, mere dissection of conceptions, is contained in one or other, is not the aim of, but only a preparation for metaphysics proper, which has for its object the extension, by means of synthesis, of our a priori knowledge. And for this purpose, mere analysis is of course useless, because it only shows what is contained in these conceptions, but not how we arrive, a priori, at them; and this it is her duty to show, in order to be able afterwards to determine their valid use in regard to all objects of experience, to all knowledge in general. But little self-denial, indeed, is needed to give up these pretensions, seeing the undeniable, and in the dogmatic mode of procedure, inevitable contradictions of Reason with herself, have long since ruined the reputation of every system of metaphysics that has appeared up to this time. It will require more firmness to remain undeterred by difficulty from within, and opposition from without, from endeavouring, by a method quite opposed to all those hitherto followed, to further the growth and fruitfulness of a science indispensable to human reason—a science from which every branch it has borne may be cut away, but whose roots remain indestructible.

VII. Idea and Division of a Particular Science, under the Name of a Critique of Pure Reason.

        From all that has been said, there results the idea of a particular science, which may be called the Critique of Pure Reason. For reason is the faculty which furnishes us with the principles of knowledge a priori. Hence, pure reason is the faculty which contains the principles of cognizing anything absolutely a priori. An organon of pure reason would be a compendium of those principles according to which alone all pure cognitions a priori can be obtained. The completely extended application of such an organon would afford us a system of pure reason. As this, however, is demanding a great deal, and it is yet doubtful whether any extension of our knowledge be here possible, or, if so, in what cases; we can regard a science of the mere criticism of pure reason, its sources and limits, as the propaedeutic to a system of pure reason. Such a science must not be called a doctrine, but only a critique of pure reason; and its use, in regard to speculation, would be only negative, not to enlarge the bounds of, but to purify, our reason, and to shield it against error—which alone is no little gain. I apply the term transcendental to all knowledge which is not so much occupied with objects as with the mode of our cognition of these objects, so far as this mode of cognition is possible a priori. A system of such conceptions would be called transcendental philosophy. But this, again, is still beyond the bounds of our present essay. For as such a science must contain a complete exposition not only of our synthetical a priori, but of our analytical a priori knowledge, it is of too wide a range for our present purpose, because we do not require to carry our analysis any farther than is necessary to understand, in their full extent, the principles of synthesis a priori, with which alone we have to do. This investigation, which we cannot properly call a doctrine, but only a transcendental critique, because it aims not at the enlargement, but at the correction and guidance, of our knowledge, and is to serve as a touchstone of the worth or worthlessness of all knowledge a priori, is the sole object of our present essay. Such a critique is consequently, as far as possible, a preparation for an organon; and if this new organon should be found to fail, at least for a canon of pure reason, according to which the complete system of the philosophy of pure reason, whether it extend or limit the bounds of that reason, might one day be set forth both analytically and synthetically. For that this is possible, nay, that such a system is not of so great extent as to preclude the hope of its ever being completed, is evident. For we have not here to do with the nature of outward objects, which is infinite, but solely with the mind, which judges of the nature of objects, and, again, with the mind only in respect of its cognition a priori. And the object of our investigations, as it is not to be sought without, but, altogether within, ourselves, cannot remain concealed, and in all probability is limited enough to be completely surveyed and fairly estimated, according to its worth or worthlessness. Still less let the reader here expect a critique of books and systems of pure reason; our present object is exclusively a critique of the faculty of pure reason itself. Only when we make this critique our foundation, do we possess a pure touchstone for estimating the philosophical value of ancient and modern writings on this subject; and without this criterion, the incompetent historian or judge decides upon and corrects the groundless assertions of others with his own, which have themselves just as little foundation.

        Transcendental philosophy is the idea of a science, for which the Critique of Pure Reason must sketch the whole plan architectonically, that is, from principles, with a full guarantee for the validity and stability of all the parts which enter into the building. It is the system of all the principles of pure reason. If this Critique itself does not assume the title of transcendental philosophy, it is only because, to be a complete system, it ought to contain a full analysis of all human knowledge a priori. Our critique must, indeed, lay before us a complete enumeration of all the radical conceptions which constitute the said pure knowledge. But from the complete analysis of these conceptions themselves, as also from a complete investigation of those derived from them, it abstains with reason; partly because it would be deviating from the end in view to occupy itself with this analysis, since this process is not attended with the difficulty and insecurity to be found in the synthesis, to which our critique is entirely devoted, and partly because it would be inconsistent with the unity of our plan to burden this essay with the vindication of the completeness of such an analysis and deduction, with which, after all, we have at present nothing to do. This completeness of the analysis of these radical conceptions, as well as of the deduction from the conceptions a priori which may be given by the analysis, we can, however, easily attain, provided only that we are in possession of all these radical conceptions, which are to serve as principles of the synthesis, and that in respect of this main purpose nothing is wanting.

        To the Critique of Pure Reason, therefore, belongs all that constitutes transcendental philosophy; and it is the complete idea of transcendental philosophy, but still not the science itself; because it only proceeds so far with the analysis as is necessary to the power of judging completely of our synthetical knowledge a priori.

        The principal thing we must attend to, in the division of the parts of a science like this, is that no conceptions must enter it which contain aught empirical; in other words, that the knowledge a priori must be completely pure. Hence, although the highest principles and fundamental conceptions of morality are certainly cognitions a priori, yet they do not belong to transcendental philosophy; because, though they certainly do not lay the conceptions of pain, pleasure, desires, inclinations, etc. (which are all of empirical origin), at the foundation of its precepts, yet still into the conception of duty—as an obstacle to be overcome, or as an incitement which should not be made into a motive—these empirical conceptions must necessarily enter, in the construction of a system of pure morality. Transcendental philosophy is consequently a philosophy of the pure and merely speculative reason. For all that is practical, so far as it contains motives, relates to feelings, and these belong to empirical sources of cognition.

        If we wish to divide this science from the universal point of view of a science in general, it ought to comprehend, first, a Doctrine of the Elements, and, secondly, a Doctrine of the Method of pure reason. Each of these main divisions will have its subdivisions, the separate reasons for which we cannot here particularize. Only so much seems necessary, by way of introduction of premonition, that there are two sources of human knowledge (which probably spring from a common, but to us unknown root), namely, sense and understanding. By the former, objects are given to us; by the latter, thought. So far as the faculty of sense may contain representations a priori, which form the conditions under which objects are given, in so far it belongs to transcendental philosophy. The transcendental doctrine of sense must form the first part of our science of elements, because the conditions under which alone the objects of human knowledge are given must precede those under which they are thought.

I. TRANSCENDENTAL DOCTRINE OF ELEMENTS. FIRST PART. TRANSCENDENTAL AESTHETIC.

SS I. Introductory.

        In whatsoever mode, or by whatsoever means, our knowledge may relate to objects, it is at least quite clear that the only manner in which it immediately relates to them is by means of an intuition. To this as the indispensable groundwork, all thought points. But an intuition can take place only in so far as the object is given to us. This, again, is only possible, to man at least, on condition that the object affect the mind in a certain manner.         The capacity for receiving representations (receptivity) through the mode in which we are affected by objects, objects, is called sensibility. By means of sensibility, therefore, objects are given to us, and it alone furnishes us with intuitions; by the understanding they are thought, and from it arise conceptions. But an thought must directly, or indirectly, by means of certain signs, relate ultimately to intuitions; consequently, with us, to sensibility, because in no other way can an object be given to us.

        The effect of an object upon the faculty of representation, so far as we are affected by the said object, is sensation. That sort of intuition which relates to an object by means of sensation is called an empirical intuition. The undetermined object of an empirical intuition is called phenomenon. That which in the phenomenon corresponds to the sensation, I term its matter; but that which effects that the content of the phenomenon can be arranged under certain relations, I call its form. But that in which our sensations are merely arranged, and by which they are susceptible of assuming a certain form, cannot be itself sensation. It is, then, the matter of all phenomena that is given to us a posteriori; the form must lie ready a priori for them in the mind, and consequently can be regarded separately from all sensation.

        I call all representations pure, in the transcendental meaning of the word, wherein nothing is met with that belongs to sensation. And accordingly we find existing in the mind a priori, the pure form of sensuous intuitions in general, in which all the manifold content of the phenomenal world is arranged and viewed under certain relations. This pure form of sensibility I shall call pure intuition. Thus, if I take away from our representation of a body all that the understanding thinks as belonging to it, as substance, force, divisibility, etc., and also whatever belongs to sensation, as impenetrability, hardness, colour, etc.; yet there is still something left us from this empirical intuition, namely, extension and shape. These belong to pure intuition, which exists a priori in the mind, as a mere form of sensibility, and without any real object of the senses or any sensation.

        The science of all the principles of sensibility a priori, I call transcendental aesthetic. There must, then, be such a science forming the first part of the transcendental doctrine of elements, in contradistinction to that part which contains the principles of pure thought, and which is called transcendental logic.

        In the science of transcendental aesthetic accordingly, we shall first isolate sensibility or the sensuous faculty, by separating from it all that is annexed to its perceptions by the conceptions of understanding, so that nothing be left but empirical intuition. In the next place we shall take away from this intuition all that belongs to sensation, so that nothing may remain but pure intuition, and the mere form of phenomena, which is all that the sensibility can afford a priori. From this investigation it will be found that there are two pure forms of sensuous intuition, as principles of knowledge a priori, namely, space and time. To the consideration of these we shall now proceed.

SECTION I. Of Space.

SS 2. Metaphysical Exposition of this Conception.

        By means of the external sense (a property of the mind), we represent to ourselves objects as without us, and these all in space. Herein alone are their shape, dimensions, and relations to each other determined or determinable. The internal sense, by means of which the mind contemplates itself or its internal state, gives, indeed, no intuition of the soul as an object; yet there is nevertheless a determinate form, under which alone the contemplation of our internal state is possible, so that all which relates to the inward determinations of the mind is represented in relations of time. Of time we cannot have any external intuition, any more than we can have an internal intuition of space. What then are time and space? Are they real existences? Or, are they merely relations or determinations of things, such, however, as would equally belong to these things in themselves, though they should never become objects of intuition; or, are they such as belong only to the form of intuition, and consequently to the subjective constitution of the mind, without which these predicates of time and space could not be attached to any object? In order to become informed on these points, we shall first give an exposition of the conception of space. By exposition, I mean the clear, though not detailed, representation of that which belongs to a conception; and an exposition is metaphysical when it contains that which represents the conception as given a priori.

        1. Space is not a conception which has been derived from outward experiences. For, in order that certain sensations may relate to something without me (that is, to something which occupies a different part of space from that in which I am); in like manner, in order that I may represent them not merely as without, of, and near to each other, but also in separate places, the representation of space must already exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phenomena through experience; but, on the contrary, this external experience is itself only possible through the said antecedent representation.

        2. Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. We never can imagine or make a representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and by no means as a determination dependent on them, and is a representation a priori, which necessarily supplies the basis for external phenomena.

        3. Space is no discursive, or as we say, general conception of the relations of things, but a pure intuition. For, in the first place, we can only represent to ourselves one space, and, when we talk of divers spaces, we mean only parts of one and the same space. Moreover, these parts cannot antecede this one all-embracing space, as the component parts from which the aggregate can be made up, but can be cogitated only as existing in it. Space is essentially one, and multiplicity in it, consequently the general notion of spaces, of this or that space, depends solely upon limitations. Hence it follows that an a priori intuition (which is not empirical) lies at the root of all our conceptions of space. Thus, moreover, the principles of geometry—for example, that "in a triangle, two sides together are greater than the third," are never deduced from general conceptions of line and triangle, but from intuition, and this a priori, with apodeictic certainty.

        4. Space is represented as an infinite given quantity. Now every conception must indeed be considered as a representation which is contained in an infinite multitude of different possible representations, which, therefore, comprises these under itself; but no conception, as such, can be so conceived, as if it contained within itself an infinite multitude of representations. Nevertheless, space is so conceived of, for all parts of space are equally capable of being produced to infinity. Consequently, the original representation of space is an intuition a priori, and not a conception.

SS 3. Transcendental Exposition of the Conception of Space.

        By a transcendental exposition, I mean the explanation of a conception, as a principle, whence can be discerned the possibility of other synthetical a priori cognitions. For this purpose, it is requisite, firstly, that such cognitions do really flow from the given conception; and, secondly, that the said cognitions are only possible under the presupposition of a given mode of explaining this conception.

        Geometry is a science which determines the properties of space synthetically, and yet a priori. What, then, must be our representation of space, in order that such a cognition of it may be possible? It must be originally intuition, for from a mere conception, no propositions can be deduced which go out beyond the conception, and yet this happens in geometry. (Introd. V.) But this intuition must be found in the mind a priori, that is, before any perception of objects, consequently must be pure, not empirical, intuition. For geometrical principles are always apodeictic, that is, united with the consciousness of their necessity, as: "Space has only three dimensions." But propositions of this kind cannot be empirical judgements, nor conclusions from them. (Introd. II.) Now, how can an external intuition anterior to objects themselves, and in which our conception of objects can be determined a priori, exist in the human mind? Obviously not otherwise than in so far as it has its seat in the subject only, as the formal capacity of the subject's being affected by objects, and thereby of obtaining immediate representation, that is, intuition; consequently, only as the form of the external sense in general.

        Thus it is only by means of our explanation that the possibility of geometry, as a synthetical science a priori, becomes comprehensible. Every mode of explanation which does not show us this possibility, although in appearance it may be similar to ours, can with the utmost certainty be distinguished from it by these marks.

SS 4. Conclusions from the foregoing Conceptions.

        (a) Space does not represent any property of objects as things in themselves, nor does it represent them in their relations to each other; in other words, space does not represent to us any determination of objects such as attaches to the objects themselves, and would remain, even though all subjective conditions of the intuition were abstracted. For neither absolute nor relative determinations of objects can be intuited prior to the existence of the things to which they belong, and therefore not a priori.

        (b) Space is nothing else than the form of all phenomena of the external sense, that is, the subjective condition of the sensibility, under which alone external intuition is possible. Now, because the receptivity or capacity of the subject to be affected by objects necessarily antecedes all intuitions of these objects, it is easily understood how the form of all phenomena can be given in the mind previous to all actual perceptions, therefore a priori, and how it, as a pure intuition, in which all objects must be determined, can contain principles of the relations of these objects prior to all experience.

        It is therefore from the human point of view only that we can speak of space, extended objects, etc. If we depart from the subjective condition, under which alone we can obtain external intuition, or, in other words, by means of which we are affected by objects, the representation of space has no meaning whatsoever. This predicate is only applicable to things in so far as they appear to us, that is, are objects of sensibility. The constant form of this receptivity, which we call sensibility, is a necessary condition of all relations in which objects can be intuited as existing without us, and when abstraction of these objects is made, is a pure intuition, to which we give the name of space. It is clear that we cannot make the special conditions of sensibility into conditions of the possibility of things, but only of the possibility of their existence as far as they are phenomena. And so we may correctly say that space contains all which can appear to us externally, but not all things considered as things in themselves, be they intuited or not, or by whatsoever subject one will. As to the intuitions of other thinking beings, we cannot judge whether they are or are not bound by the same conditions which limit our own intuition, and which for us are universally valid. If we join the limitation of a judgement to the conception of the subject, then the judgement will possess unconditioned validity. For example, the proposition, "All objects are beside each other in space," is valid only under the limitation that these things are taken as objects of our sensuous intuition. But if I join the condition to the conception and say, "All things, as external phenomena, are beside each other in space," then the rule is valid universally, and without any limitation. Our expositions, consequently, teach the reality (i.e., the objective validity) of space in regard of all which can be presented to us externally as object, and at the same time also the ideality of space in regard to objects when they are considered by means of reason as things in themselves, that is, without reference to the constitution of our sensibility. We maintain, therefore, the empirical reality of space in regard to all possible external experience, although we must admit its transcendental ideality; in other words, that it is nothing, so soon as we withdraw the condition upon which the possibility of all experience depends and look upon space as something that belongs to things in themselves.

        But, with the exception of space, there is no representation, subjective and referring to something external to us, which could be called objective a priori. For there are no other subjective representations from which we can deduce synthetical propositions a priori, as we can from the intuition of space. (See SS 3.) Therefore, to speak accurately, no ideality whatever belongs to these, although they agree in this respect with the representation of space, that they belong merely to the subjective nature of the mode of sensuous perception; such a mode, for example, as that of sight, of hearing, and of feeling, by means of the sensations of colour, sound, and heat, but which, because they are only sensations and not intuitions, do not of themselves give us the cognition of any object, least of all, an a priori cognition. My purpose, in the above remark, is merely this: to guard any one against illustrating the asserted ideality of space by examples quite insufficient, for example, by colour, taste, etc.; for these must be contemplated not as properties of things, but only as changes in the subject, changes which may be different in different men. For, in such a case, that which is originally a mere phenomenon, a rose, for example, is taken by the empirical understanding for a thing in itself, though to every different eye, in respect of its colour, it may appear different. On the contrary, the transcendental conception of phenomena in space is a critical admonition, that, in general, nothing which is intuited in space is a thing in itself, and that space is not a form which belongs as a property to things; but that objects are quite unknown to us in themselves, and what we call outward objects, are nothing else but mere representations of our sensibility, whose form is space, but whose real correlate, the thing in itself, is not known by means of these representations, nor ever can be, but respecting which, in experience, no inquiry is ever made.

SECTION II. Of Time.

SS 5. Metaphysical Exposition of this Conception.

        1. Time is not an empirical conception. For neither coexistence nor succession would be perceived by us, if the representation of time did not exist as a foundation a priori. Without this presupposition we could not represent to ourselves that things exist together at one and the same time, or at different times, that is, contemporaneously, or in succession.

        2. Time is a necessary representation, lying at the foundation of all our intuitions. With regard to phenomena in general, we cannot think away time from them, and represent them to ourselves as out of and unconnected with time, but we can quite well represent to ourselves time void of phenomena. Time is therefore given a priori. In it alone is all reality of phenomena possible. These may all be annihilated in thought, but time itself, as the universal condition of their possibility, cannot be so annulled.

        3. On this necessity a priori is also founded the possibility of apodeictic principles of the relations of time, or axioms of time in general, such as: "Time has only one dimension," "Different times are not coexistent but successive" (as different spaces are not successive but coexistent). These principles cannot be derived from experience, for it would give neither strict universality, nor apodeictic certainty. We should only be able to say, "so common experience teaches us," but not "it must be so." They are valid as rules, through which, in general, experience is possible; and they instruct us respecting experience, and not by means of it.

        4. Time is not a discursive, or as it is called, general conception, but a pure form of the sensuous intuition. Different times are merely parts of one and the same time. But the representation which can only be given by a single object is an intuition. Besides, the proposition that different times cannot be coexistent could not be derived from a general conception. For this proposition is synthetical, and therefore cannot spring out of conceptions alone. It is therefore contained immediately in the intuition and representation of time.

        5. The infinity of time signifies nothing more than that every determined quantity of time is possible only through limitations of one time lying at the foundation. Consequently, the original representation, time, must be given as unlimited. But as the determinate representation of the parts of time and of every quantity of an object can only be obtained by limitation, the complete representation of time must not be furnished by means of conceptions, for these contain only partial representations. Conceptions, on the contrary, must have immediate intuition for their basis.

SS 6 Transcendental Exposition of the Conception of Time.

        I may here refer to what is said above (SS 5, 3), where, for or sake of brevity, I have placed under the head of metaphysical exposition, that which is properly transcendental. Here I shall add that the conception of change, and with it the conception of motion, as change of place, is possible only through and in the representation of time; that if this representation were not an intuition (internal) a priori, no conception, of whatever kind, could render comprehensible the possibility of change, in other words, of a conjunction of contradictorily opposed predicates in one and the same object, for example, the presence of a thing in a place and the non-presence of the same thing in the same place. It is only in time that it is possible to meet with two contradictorily opposed determinations in one thing, that is, after each other. Thus our conception of time explains the possibility of so much synthetical knowledge a priori, as is exhibited in the general doctrine of motion, which is not a little fruitful.

SS 7. Conclusions from the above Conceptions.

        (a) Time is not something which subsists of itself, or which inheres in things as an objective determination, and therefore remains, when abstraction is made of the subjective conditions of the intuition of things. For in the former case, it would be something real, yet without presenting to any power of perception any real object. In the latter case, as an order or determination inherent in things themselves, it could not be antecedent to things, as their condition, nor discerned or intuited by means of synthetical propositions a priori. But all this is quite possible when we regard time as merely the subjective condition under which all our intuitions take place. For in that case, this form of the inward intuition can be represented prior to the objects, and consequently a priori.

        (b) Time is nothing else than the form of the internal sense, that is, of the intuitions of self and of our internal state. For time cannot be any determination of outward phenomena. It has to do neither with shape nor position; on the contrary, it determines the relation of representations in our internal state. And precisely because this internal intuition presents to us no shape or form, we endeavour to supply this want by analogies, and represent the course of time by a line progressing to infinity, the content of which constitutes a series which is only of one dimension; and we conclude from the properties of this line as to all the properties of time, with this single exception, that the parts of the line are coexistent, whilst those of time are successive. From this it is clear also that the representation of time is itself an intuition, because all its relations can be expressed in an external intuition.

        (c) Time is the formal condition a priori of all phenomena whatsoever. Space, as the pure form of external intuition, is limited as a condition a priori to external phenomena alone. On the other hand, because all representations, whether they have or have not external things for their objects, still in themselves, as determinations of the mind, belong to our internal state; and because this internal state is subject to the formal condition of the internal intuition, that is, to time—time is a condition a priori of all phenomena whatsoever—the immediate condition of all internal, and thereby the mediate condition of all external phenomena. If I can say a priori, "All outward phenomena are in space, and determined a priori according to the relations of space," I can also, from the principle of the internal sense, affirm universally, "All phenomena in general, that is, all objects of the senses, are in time and stand necessarily in relations of time."

        If we abstract our internal intuition of ourselves and all external intuitions, possible only by virtue of this internal intuition and presented to us by our faculty of representation, and consequently take objects as they are in themselves, then time is nothing. It is only of objective validity in regard to phenomena, because these are things which we regard as objects of our senses. It no longer objective we, make abstraction of the sensuousness of our intuition, in other words, of that mode of representation which is peculiar to us, and speak of things in general. Time is therefore merely a subjective condition of our (human) intuition (which is always sensuous, that is, so far as we are affected by objects), and in itself, independently of the mind or subject, is nothing. Nevertheless, in respect of all phenomena, consequently of all things which come within the sphere of our experience, it is necessarily objective. We cannot say, "All things are in time," because in this conception of things in general, we abstract and make no mention of any sort of intuition of things. But this is the proper condition under which time belongs to our representation of objects. If we add the condition to the conception, and say, "All things, as phenomena, that is, objects of sensuous intuition, are in time," then the proposition has its sound objective validity and universality a priori.

        What we have now set forth teaches, therefore, the empirical reality of time; that is, its objective validity in reference to all objects which can ever be presented to our senses. And as our intuition is always sensuous, no object ever can be presented to us in experience, which does not come under the conditions of time. On the other hand, we deny to time all claim to absolute reality; that is, we deny that it, without having regard to the form of our sensuous intuition, absolutely inheres in things as a condition or property. Such properties as belong to objects as things in themselves never can be presented to us through the medium of the senses. Herein consists, therefore, the transcendental ideality of time, according to which, if we abstract the subjective conditions of sensuous intuition, it is nothing, and cannot be reckoned as subsisting or inhering in objects as things in themselves, independently of its relation to our intuition. This ideality, like that of space, is not to be proved or illustrated by fallacious analogies with sensations, for this reason—that in such arguments or illustrations, we make the presupposition that the phenomenon, in which such and such predicates inhere, has objective reality, while in this case we can only find such an objective reality as is itself empirical, that is, regards the object as a mere phenomenon. In reference to this subject, see the remark in Section I (SS 4)

SS 8. Elucidation.

        Against this theory, which grants empirical reality to time, but denies to it absolute and transcendental reality, I have heard from intelligent men an objection so unanimously urged that I conclude that it must naturally present itself to every reader to whom these considerations are novel. It runs thus: "Changes are real" (this the continual change in our own representations demonstrates, even though the existence of all external phenomena, together with their changes, is denied). Now, changes are only possible in time, and therefore time must be something real. But there is no difficulty in answering this. I grant the whole argument. Time, no doubt, is something real, that is, it is the real form of our internal intuition. It therefore has subjective reality, in reference to our internal experience, that is, I have really the representation of time and of my determinations therein. Time, therefore, is not to be regarded as an object, but as the mode of representation of myself as an object. But if I could intuite myself, or be intuited by another being, without this condition of sensibility, then those very determinations which we now represent to ourselves as changes, would present to us a knowledge in which the representation of time, and consequently of change, would not appear. The empirical reality of time, therefore, remains, as the condition of all our experience. But absolute reality, according to what has been said above, cannot be granted it. Time is nothing but the form of our internal intuition. If we take away from it the special condition of our sensibility, the conception of time also vanishes; and it inheres not in the objects themselves, but solely in the subject (or mind) which intuites them.

        But the reason why this objection is so unanimously brought against our doctrine of time, and that too by disputants who cannot start any intelligible arguments against the doctrine of the ideality of space, is this—they have no hope of demonstrating apodeictically the absolute reality of space, because the doctrine of idealism is against them, according to which the reality of external objects is not capable of any strict proof. On the other hand, the reality of the object of our internal sense (that is, myself and my internal state) is clear immediately through consciousness. The former—external objects in space—might be a mere delusion, but the latter—the object of my internal perception—is undeniably real. They do not, however, reflect that both, without question of their reality as representations, belong only to the genus phenomenon, which has always two aspects, the one, the object considered as a thing in itself, without regard to the mode of intuiting it, and the nature of which remains for this very reason problematical, the other, the form of our intuition of the object, which must be sought not in the object as a thing in itself, but in the subject to which it appears—which form of intuition nevertheless belongs really and necessarily to the phenomenal object.

        Time and space are, therefore, two sources of knowledge, from which, a priori, various synthetical cognitions can be drawn. Of this we find a striking example in the cognitions of space and its relations, which form the foundation of pure mathematics. They are the two pure forms of all intuitions, and thereby make synthetical propositions a priori possible. But these sources of knowledge being merely conditions of our sensibility, do therefore, and as such, strictly determine their own range and purpose, in that they do not and cannot present objects as things in themselves, but are applicable to them solely in so far as they are considered as sensuous phenomena. The sphere of phenomena is the only sphere of their validity, and if we venture out of this, no further objective use can be made of them. For the rest, this formal reality of time and space leaves the validity of our empirical knowledge unshaken; for our certainty in that respect is equally firm, whether these forms necessarily inhere in the things themselves, or only in our intuitions of them.         On the other hand, those who maintain the absolute reality of time and space, whether as essentially subsisting, or only inhering, as modifications, in things, must find themselves at utter variance with the principles of experience itself. For, if they decide for the first view, and make space and time into substances, this being the side taken by mathematical natural philosophers, they must admit two self-subsisting nonentities, infinite and eternal, which exist (yet without there being anything real) for the purpose of containing in themselves everything that is real. If they adopt the second view of inherence, which is preferred by some metaphysical natural philosophers, and regard space and time as relations (contiguity in space or succession in time), abstracted from experience, though represented confusedly in this state of separation, they find themselves in that case necessitated to deny the validity of mathematical doctrines a priori in reference to real things (for example, in space)—at all events their apodeictic certainty. For such certainty cannot be found in an a posteriori proposition; and the conceptions a priori of space and time are, according to this opinion, mere creations of the imagination, having their source really in experience, inasmuch as, out of relations abstracted from experience, imagination has made up something which contains, indeed, general statements of these relations, yet of which no application can be made without the restrictions attached thereto by nature. The former of these parties gains this advantage, that they keep the sphere of phenomena free for mathematical science. On the other hand, these very conditions (space and time) embarrass them greatly, when the understanding endeavours to pass the limits of that sphere. The latter has, indeed, this advantage, that the representations of space and time do not come in their way when they wish to judge of objects, not as phenomena, but merely in their relation to the understanding. Devoid, however, of a true and objectively valid a priori intuition, they can neither furnish any basis for the possibility of mathematical cognitions a priori, nor bring the propositions of experience into necessary accordance with those of mathematics.         In our theory of the true nature of these two original forms of the sensibility, both difficulties are surmounted.

        In conclusion, that transcendental aesthetic cannot contain any more than these two elements—space and time, is sufficiently obvious from the fact that all other conceptions appertaining to sensibility, even that of motion, which unites in itself both elements, presuppose something empirical. Motion, for example, presupposes the perception of something movable. But space considered in itself contains nothing movable, consequently motion must be something which is found in space only through experience—in other words, an empirical datum. In like manner, transcendental aesthetic cannot number the conception of change among its data a priori; for time itself does not change, but only something which is in time. To acquire the conception of change, therefore, the perception of some existing object and of the succession of its determinations, in one word, experience, is necessary.

SS 9. General Remarks on Transcendental Aesthetic.

        I. In order to prevent any misunderstanding, it will be requisite, in the first place, to recapitulate, as clearly as possible, what our opinion is with respect to the fundamental nature of our sensuous cognition in general. We have intended, then, to say that all our intuition is nothing but the representation of phenomena; that the things which we intuite, are not in themselves the same as our representations of them in intuition, nor are their relations in themselves so constituted as they appear to us; and that if we take away the subject, or even only the subjective constitution of our senses in general, then not only the nature and relations of objects in space and time, but even space and time themselves disappear; and that these, as phenomena, cannot exist in themselves, but only in us. What may be the nature of objects considered as things in themselves and without reference to the receptivity of our sensibility is quite unknown to us. We know nothing more than our mode of perceiving them, which is peculiar to us, and which, though not of necessity pertaining to every animated being, is so to the whole human race. With this alone we have to do. Space and time are the pure forms thereof; sensation the matter. The former alone can we cognize a priori, that is, antecedent to all actual perception; and for this reason such cognition is called pure intuition. The latter is that in our cognition which is called cognition a posteriori, that is, empirical intuition. The former appertain absolutely and necessarily to our sensibility, of whatsoever kind our sensations may be; the latter may be of very diversified character. Supposing that we should carry our empirical intuition even to the very highest degree of clearness, we should not thereby advance one step nearer to a knowledge of the constitution of objects as things in themselves. For we could only, at best, arrive at a complete cognition of our own mode of intuition, that is of our sensibility, and this always under the conditions originally attaching to the subject, namely, the conditions of space and time; while the question: "What are objects considered as things in themselves?" remains unanswerable even after the most thorough examination of the phenomenal world.

        To say, then, that all our sensibility is nothing but the confused representation of things containing exclusively that which belongs to them as things in themselves, and this under an accumulation of characteristic marks and partial representations which we cannot distinguish in consciousness, is a falsification of the conception of sensibility and phenomenization, which renders our whole doctrine thereof empty and useless. The difference between a confused and a clear representation is merely logical and has nothing to do with content. No doubt the conception of right, as employed by a sound understanding, contains all that the most subtle investigation could unfold from it, although, in the ordinary practical use of the word, we are not conscious of the manifold representations comprised in the conception. But we cannot for this reason assert that the ordinary conception is a sensuous one, containing a mere phenomenon, for right cannot appear as a phenomenon; but the conception of it lies in the understanding, and represents a property (the moral property) of actions, which belongs to them in themselves. On the other hand, the representation in intuition of a body contains nothing which could belong to an object considered as a thing in itself, but merely the phenomenon or appearance of something, and the mode in which we are affected by that appearance; and this receptivity of our faculty of cognition is called sensibility, and remains toto caelo different from the cognition of an object in itself, even though we should examine the content of the phenomenon to the very bottom.

        It must be admitted that the Leibnitz-Wolfian philosophy has assigned an entirely erroneous point of view to all investigations into the nature and origin of our cognitions, inasmuch as it regards the distinction between the sensuous and the intellectual as merely logical, whereas it is plainly transcendental, and concerns not merely the clearness or obscurity, but the content and origin of both. For the faculty of sensibility not only does not present us with an indistinct and confused cognition of objects as things in themselves, but, in fact, gives us no knowledge of these at all. On the contrary, so soon as we abstract in thought our own subjective nature, the object represented, with the properties ascribed to it by sensuous intuition, entirely disappears, because it was only this subjective nature that determined the form of the object as a phenomenon.

        In phenomena, we commonly, indeed, distinguish that which essentially belongs to the intuition of them, and is valid for the sensuous faculty of every human being, from that which belongs to the same intuition accidentally, as valid not for the sensuous faculty in general, but for a particular state or organization of this or that sense. Accordingly, we are accustomed to say that the former is a cognition which represents the object itself, whilst the latter presents only a particular appearance or phenomenon thereof. This distinction, however, is only empirical. If we stop here (as is usual), and do not regard the empirical intuition as itself a mere phenomenon (as we ought to do), in which nothing that can appertain to a thing in itself is to be found, our transcendental distinction is lost, and we believe that we cognize objects as things in themselves, although in the whole range of the sensuous world, investigate the nature of its objects as profoundly as we may, we have to do with nothing but phenomena. Thus, we call the rainbow a mere appearance of phenomenon in a sunny shower, and the rain, the reality or thing in itself; and this is right enough, if we understand the latter conception in a merely physical sense, that is, as that which in universal experience, and under whatever conditions of sensuous perception, is known in intuition to be so and so determined, and not otherwise. But if we consider this empirical datum generally, and inquire, without reference to its accordance with all our senses, whether there can be discovered in it aught which represents an object as a thing in itself (the raindrops of course are not such, for they are, as phenomena, empirical objects), the question of the relation of the representation to the object is transcendental; and not only are the raindrops mere phenomena, but even their circular form, nay, the space itself through which they fall, is nothing in itself, but both are mere modifications or fundamental dispositions of our sensuous intuition, whilst the transcendental object remains for us utterly unknown.

        The second important concern of our aesthetic is that it does not obtain favour merely as a plausible hypothesis, but possess as undoubted a character of certainty as can be demanded of any theory which is to serve for an organon. In order fully to convince the reader of this certainty, we shall select a case which will serve to make its validity apparent, and also to illustrate what has been said in SS 3.

        Suppose, then, that space and time are in themselves objective, and conditions of the—possibility of objects as things in themselves. In the first place, it is evident that both present us, with very many apodeictic and synthetic propositions a priori, but especially space—and for this reason we shall prefer it for investigation at present. As the propositions of geometry are cognized synthetically a priori, and with apodeictic certainty, I inquire: Whence do you obtain propositions of this kind, and on what basis does the understanding rest, in order to arrive at such absolutely necessary and universally valid truths?

        There is no other way than through intuitions or conceptions, as such; and these are given either a priori or a posteriori. The latter, namely, empirical conceptions, together with the empirical intuition on which they are founded, cannot afford any synthetical proposition, except such as is itself also empirical, that is, a proposition of experience. But an empirical proposition cannot possess the qualities of necessity and absolute universality, which, nevertheless, are the characteristics of all geometrical propositions. As to the first and only means to arrive at such cognitions, namely, through mere conceptions or intuitions a priori, it is quite clear that from mere conceptions no synthetical cognitions, but only analytical ones, can be obtained. Take, for example, the proposition: "Two straight lines cannot enclose a space, and with these alone no figure is possible," and try to deduce it from the conception of a straight line and the number two; or take the proposition: "It is possible to construct a figure with three straight lines," and endeavour, in like manner, to deduce it from the mere conception of a straight line and the number three. All your endeavours are in vain, and you find yourself forced to have recourse to intuition, as, in fact, geometry always does. You therefore give yourself an object in intuition. But of what kind is this intuition? Is it a pure a priori, or is it an empirical intuition? If the latter, then neither an universally valid, much less an apodeictic proposition can arise from it, for experience never can give us any such proposition. You must, therefore, give yourself an object a priori in intuition, and upon that ground your synthetical proposition. Now if there did not exist within you a faculty of intuition a priori; if this subjective condition were not in respect to its form also the universal condition a priori under which alone the object of this external intuition is itself possible; if the object (that is, the triangle) were something in itself, without relation to you the subject; how could you affirm that that which lies necessarily in your subjective conditions in order to construct a triangle, must also necessarily belong to the triangle in itself? For to your conceptions of three lines, you could not add anything new (that is, the figure); which, therefore, must necessarily be found in the object, because the object is given before your cognition, and not by means of it. If, therefore, space (and time also) were not a mere form of your intuition, which contains conditions a priori, under which alone things can become external objects for you, and without which subjective conditions the objects are in themselves nothing, you could not construct any synthetical proposition whatsoever regarding external objects. It is therefore not merely possible or probable, but indubitably certain, that space and time, as the necessary conditions of all our external and internal experience, are merely subjective conditions of all our intuitions, in relation to which all objects are therefore mere phenomena, and not things in themselves, presented to us in this particular manner. And for this reason, in respect to the form of phenomena, much may be said a priori, whilst of the thing in itself, which may lie at the foundation of these phenomena, it is impossible to say anything.

        II. In confirmation of this theory of the ideality of the external as well as internal sense, consequently of all objects of sense, as mere phenomena, we may especially remark that all in our cognition that belongs to intuition contains nothing more than mere relations. (The feelings of pain and pleasure, and the will, which are not cognitions, are excepted.) The relations, to wit, of place in an intuition (extension), change of place (motion), and laws according to which this change is determined (moving forces). That, however, which is present in this or that place, or any operation going on, or result taking place in the things themselves, with the exception of change of place, is not given to us by intuition. Now by means of mere relations, a thing cannot be known in itself; and it may therefore be fairly concluded, that, as through the external sense nothing but mere representations of relations are given us, the said external sense in its representation can contain only the relation of the object to the subject, but not the essential nature of the object as a thing in itself.

        The same is the case with the internal intuition, not only because, in the internal intuition, the representation of the external senses constitutes the material with which the mind is occupied; but because time, in which we place, and which itself antecedes the consciousness of, these representations in experience, and which, as the formal condition of the mode according to which objects are placed in the mind, lies at the foundation of them, contains relations of the successive, the coexistent, and of that which always must be coexistent with succession, the permanent. Now that which, as representation, can antecede every exercise of thought (of an object), is intuition; and when it contains nothing but relations, it is the form of the intuition, which, as it presents us with no representation, except in so far as something is placed in the mind, can be nothing else than the mode in which the mind is affected by its own activity, to wit—its presenting to itself representations, consequently the mode in which the mind is affected by itself; that is, it can be nothing but an internal sense in respect to its form. Everything that is represented through the medium of sense is so far phenomenal; consequently, we must either refuse altogether to admit an internal sense, or the subject, which is the object of that sense, could only be represented by it as phenomenon, and not as it would judge of itself, if its intuition were pure spontaneous activity, that is, were intellectual. The difficulty here lies wholly in the question: How can the subject have an internal intuition of itself? But this difficulty is common to every theory. The consciousness of self (apperception) is the simple representation of the "ego"; and if by means of that representation alone, all the manifold representations in the subject were spontaneously given, then our internal intuition would be intellectual. This consciousness in man requires an internal perception of the manifold representations which are previously given in the subject; and the manner in which these representations are given in the mind without spontaneity, must, on account of this difference (the want of spontaneity), be called sensibility. If the faculty of self-consciousness is to apprehend what lies in the mind, it must all act that and can in this way alone produce an intuition of self. But the form of this intuition, which lies in the original constitution of the mind, determines, in the representation of time, the manner in which the manifold representations are to combine themselves in the mind; since the subject intuites itself, not as it would represent itself immediately and spontaneously, but according to the manner in which the mind is internally affected, consequently, as it appears, and not as it is.

        III. When we say that the intuition of external objects, and also the self-intuition of the subject, represent both, objects and subject, in space and time, as they affect our senses, that is, as they appear—this is by no means equivalent to asserting that these objects are mere illusory appearances. For when we speak of things as phenomena, the objects, nay, even the properties which we ascribe to them, are looked upon as really given; only that, in so far as this or that property depends upon the mode of intuition of the subject, in the relation of the given object to the subject, the object as phenomenon is to be distinguished from the object as a thing in itself. Thus I do not say that bodies seem or appear to be external to me, or that my soul seems merely to be given in my self-consciousness, although I maintain that the properties of space and time, in conformity to which I set both, as the condition of their existence, abide in my mode of intuition, and not in the objects in themselves. It would be my own fault, if out of that which I should reckon as phenomenon, I made mere illusory appearance. But this will not happen, because of our principle of the ideality of all sensuous intuitions. On the contrary, if we ascribe objective reality to these forms of representation, it becomes impossible to avoid changing everything into mere appearance. For if we regard space and time as properties, which must be found in objects as things in themselves, as sine quibus non of the possibility of their existence, and reflect on the absurdities in which we then find ourselves involved, inasmuch as we are compelled to admit the existence of two infinite things, which are nevertheless not substances, nor anything really inhering in substances, nay, to admit that they are the necessary conditions of the existence of all things, and moreover, that they must continue to exist, although all existing things were annihilated—we cannot blame the good Berkeley for degrading bodies to mere illusory appearances. Nay, even our own existence, which would in this case depend upon the self-existent reality of such a mere nonentity as time, would necessarily be changed with it into mere appearance—an absurdity which no one has as yet been guilty of.

        IV. In natural theology, where we think of an object—God—which never can be an object of intuition to us, and even to himself can never be an object of sensuous intuition, we carefully avoid attributing to his intuition the conditions of space and time—and intuition all his cognition must be, and not thought, which always includes limitation. But with what right can we do this if we make them forms of objects as things in themselves, and such, moreover, as would continue to exist as a priori conditions of the existence of things, even though the things themselves were annihilated? For as conditions of all existence in general, space and time must be conditions of the existence of the Supreme Being also. But if we do not thus make them objective forms of all things, there is no other way left than to make them subjective forms of our mode of intuition—external and internal; which is called sensuous, because it is not primitive, that is, is not such as gives in itself the existence of the object of the intuition (a mode of intuition which, so far as we can judge, can belong only to the Creator), but is dependent on the existence of the object, is possible, therefore, only on condition that the representative faculty of the subject is affected by the object.

        It is, moreover, not necessary that we should limit the mode of intuition in space and time to the sensuous faculty of man. It may well be that all finite thinking beings must necessarily in this respect agree with man (though as to this we cannot decide), but sensibility does not on account of this universality cease to be sensibility, for this very reason, that it is a deduced (intuitus derivativus), and not an original (intuitus originarius), consequently not an intellectual intuition, and this intuition, as such, for reasons above mentioned, seems to belong solely to the Supreme Being, but never to a being dependent, quoad its existence, as well as its intuition (which its existence determines and limits relatively to given objects). This latter remark, however, must be taken only as an illustration, and not as any proof of the truth of our aesthetical theory.

SS 10. Conclusion of the Transcendental Aesthetic.

        We have now completely before us one part of the solution of the grand general problem of transcendental philosophy, namely, the question: "How are synthetical propositions a priori possible?" That is to say, we have shown that we are in possession of pure a priori intuitions, namely, space and time, in which we find, when in a judgement a priori we pass out beyond the given conception, something which is not discoverable in that conception, but is certainly found a priori in the intuition which corresponds to the conception, and can be united synthetically with it. But the judgements which these pure intuitions enable us to make, never reach farther than to objects of the senses, and are valid only for objects of possible experience.