Бесплатный фрагмент - The Critique of Pure Reason

PREFACE TO THE FIRST EDITION 1781

Human reason, in one sphere of its cognition, is called upon to consider questions, which it cannot decline, as they are presented by its own nature, but which it cannot answer, as they transcend every faculty of the mind. It falls into this difficulty without any fault of its own. It begins with principles, which cannot be dispensed with in the field of experience, and the truth and sufficiency of which are, at the same time, insured by experience. With these principles it rises, in obedience to the laws of its own nature, to ever higher and more remote conditions. But it quickly discovers that, in this way, its labours must remain ever incomplete, because new questions never cease to present themselves; and thus it finds itself compelled to have recourse to principles which transcend the region of experience, while they are regarded by common sense without distrust. It thus falls into confusion and contradictions, from which it conjectures the presence of latent errors, which, however, it is unable to discover, because the principles it employs, transcending the limits of experience, cannot be tested by that criterion. The arena of these endless contests is called Metaphysic. Time was, when she was the queen of all the sciences; and, if we take the will for the deed, she certainly deserves, so far as regards the high importance of her object-matter, this title of honour. Now, it is the fashion of the time to heap contempt and scorn upon her; and the matron mourns, forlorn and forsaken, like Hecuba: Modo maxima rerum, Tot generis, natisque potens…

Nunc trahor exul, inops. — Ovid, Metamorphoses. xiii

At first, her government, under the administration of the dogmatists, was an absolute despotism. But, as the legislative continued to show traces of the ancient barbaric rule, her empire gradually broke up, and intestine wars introduced the reign of anarchy; while the sceptics, like nomadic tribes, who hate a permanent habitation and settled mode of living, attacked from time to time those who had organized themselves into civil communities. But their number was, very happily, small; and thus they could not entirely put a stop to the exertions of those who persisted in raising new edifices, although on no settled or uniform plan. In recent times the hope dawned upon us of seeing those disputes settled, and the legitimacy of her claims established by a kind of physiology of the human understanding — that of the celebrated Locke. But it was found that — although it was affirmed that this so-called queen could not refer her descent to any higher source than that of common experience, a circumstance which necessarily brought suspicion on her claims — as this genealogy was incorrect, she persisted in the advancement of her claims to sovereignty.

Thus metaphysics necessarily fell back into the antiquated and rotten constitution of dogmatism, and again became obnoxious to the contempt from which efforts had been made to save it. At present, as all methods, according to the general persuasion, have been tried in vain, there reigns nought but weariness and complete indifferentism — the mother of chaos and night in the scientific world, but at the same time the source of, or at least the prelude to, the re-creation and reinstallation of a science, when it has fallen into confusion, obscurity, and disuse from ill directed effort. For it is in reality vain to profess indifference in regard to such inquiries, the object of which cannot be indifferent to humanity. Besides, these pretended indifferentists, however much they may try to disguise themselves by the assumption of a popular style and by changes on the language of the schools, unavoidably fall into metaphysical declarations and propositions, which they profess to regard with so much contempt. At the same time, this indifference, which has arisen in the world of science, and which relates to that kind of knowledge which we should wish to see destroyed the last, is a phenomenon that well deserves our attention and reflection. It is plainly not the effect of the levity, but of the matured judgement [1] of the age, which refuses to be any longer entertained with illusory knowledge, It is, in fact, a call to reason, again to undertake the most laborious of all tasks — that of self-examination, and to establish a tribunal, which may secure it in its well-grounded claims, while it pronounces against all baseless assumptions and pretensions, not in an arbitrary manner, but according to its own eternal and unchangeable laws. This tribunal is nothing less than the Critical Investigation of Pure Reason.

[1] We very often hear complaints of the shallowness of the present age, and of the decay of profound science. But I do not think that those which rest upon a secure foundation, such as mathematics, physical science, etc., in the least deserve this reproach, but that they rather maintain their ancient fame, and in the latter case, indeed, far surpass it. The same would be the case with the other kinds of cognition, if their principles were but firmly established. In the absence of this security, indifference, doubt, and finally, severe criticism are rather signs of a profound habit of thought. Our age is the age of criticism, to which everything must be subjected. The sacredness of religion, and the authority of legislation, are by many regarded as grounds of exemption from the examination of this tribunal. But, if they are exempted, they become the subjects of just suspicion, and cannot lay claim to sincere respect, which reason accords only to that which has stood the test of a free and public examination. I do not mean by this a criticism of books and systems, but a critical inquiry into the faculty of reason, with reference to the cognitions to which it strives to attain without the aid of experience; in other words, the solution of the question regarding the possibility or impossibility of metaphysics, and the determination of the origin, as well as of the extent and limits of this science. All this must be done on the basis of principles.

This path — the only one now remaining — has been entered upon by me; and I flatter myself that I have, in this way, discovered the cause of — and consequently the mode of removing — all the errors which have hitherto set reason at variance with itself, in the sphere of non-empirical thought. I have not returned an evasive answer to the questions of reason, by alleging the inability and limitation of the faculties of the mind; I have, on the contrary, examined them completely in the light of principles, and, after having discovered the cause of the doubts and contradictions into which reason fell, have solved them to its perfect satisfaction. It is true, these questions have not been solved as dogmatism, in its vain fancies and desires, had expected; for it can only be satisfied by the exercise of magical arts, and of these I have no knowledge. But neither do these come within the compass of our mental powers; and it was the duty of philosophy to destroy the illusions which had their origin in misconceptions, whatever darling hopes and valued expectations may be ruined by its explanations. My chief aim in this work has been thoroughness; and I make bold to say that there is not a single metaphysical problem that does not find its solution, or at least the key to its solution, here. Pure reason is a perfect unity; and therefore, if the principle presented by it prove to be insufficient for the solution of even a single one of those questions to which the very nature of reason gives birth, we must reject it, as we could not be perfectly certain of its sufficiency in the case of the others. While I say this, I think I see upon the countenance of the reader signs of dissatisfaction mingled with contempt, when he hears declarations which sound so boastful and extravagant; and yet they are beyond comparison more moderate than those advanced by the commonest author of the commonest philosophical programme, in which the dogmatist professes to demonstrate the simple nature of the soul, or the necessity of a primal being.

Such a dogmatist promises to extend human knowledge beyond the limits of possible experience; while I humbly confess that this is completely beyond my power. Instead of any such attempt, I confine myself to the examination of reason alone and its pure thought; and I do not need to seek far for the sum-total of its cognition, because it has its seat in my own mind. Besides, common logic presents me with a complete and systematic catalogue of all the simple operations of reason; and it is my task to answer the question how far reason can go, without the material presented and the aid furnished by experience. So much for the completeness and thoroughness necessary in the execution of the present task. The aims set before us are not arbitrarily proposed, but are imposed upon us by the nature of cognition itself. The above remarks relate to the matter of our critical inquiry. As regards the form, there are two indispensable conditions, which any one who undertakes so difficult a task as that of a critique of pure reason, is bound to fulfil. These conditions are certitude and clearness. As regards certitude, I have fully convinced myself that, in this sphere of thought, opinion is perfectly inadmissible, and that everything which bears the least semblance of an hypothesis must be excluded, as of no value in such discussions. For it is a necessary condition of every cognition that is to be established upon à priori grounds that it shall be held to be absolutely necessary; much more is this the case with an attempt to determine all pure à priori cognition, and to furnish the standard — and consequently an example — of all apodeictic (philosophical) certitude.

Whether I have succeeded in what I professed to do, it is for the reader to determine; it is the author’s business merely to adduce grounds and reasons, without determining what influence these ought to have on the mind of his judges. But, lest anything he may have said may become the innocent cause of doubt in their minds, or tend to weaken the effect which his arguments might otherwise produce — he may be allowed to point out those passages which may occasion mistrust or difficulty, although these do not concern the main purpose of the present work. He does this solely with the view of removing from the mind of the reader any doubts which might affect his judgement of the work as a whole, and in regard to its ultimate aim. I know no investigations more necessary for a full insight into the nature of the faculty which we call understanding, and at the same time for the determination of the rules and limits of its use, than those undertaken in the second chapter of the “Transcendental Analytic,” under the title of Deduction of the Pure Conceptions of the Understanding; and they have also cost me by far the greatest labour — labour which, I hope, will not remain uncompensated.

The view there taken, which goes somewhat deeply into the subject, has two sides. The one relates to the objects of the pure understanding, and is intended to demonstrate and to render comprehensible the objective validity of its à priori conceptions; and it forms for this reason an essential part of the Critique. The other considers the pure understanding itself, its possibility and its powers of cognition — that is, from a subjective point of view; and, although this exposition is of great importance, it does not belong essentially to the main purpose of the work, because the grand question is what and how much can reason and understanding, apart from experience, cognize, and not, how is the faculty of thought itself possible? As the latter is an inquiry into the cause of a given effect, and has thus in it some semblance of an hypothesis (although, as I shall show on another occasion, this is really not the fact), it would seem that, in the present instance, I had allowed myself to enounce a mere opinion, and that the reader must therefore be at liberty to hold a different opinion. But I beg to remind him that, if my subjective deduction does not produce in his mind the conviction of its certitude at which I aimed, the objective deduction, with which alone the present work is properly concerned, is in every respect satisfactory.

As regards clearness, the reader has a right to demand, in the first place, discursive or logical clearness, that is, on the basis of conceptions, and, secondly, intuitive or æsthetic clearness, by means of intuitions, that is, by examples or other modes of illustration in concreto. I have done what I could for the first kind of intelligibility. This was essential to my purpose; and it thus became the accidental cause of my inability to do complete justice to the second requirement. I have been almost always at a loss, during the progress of this work, how to settle this question. Examples and illustrations always appeared to me necessary, and, in the first sketch of the Critique, naturally fell into their proper places. But I very soon became aware of the magnitude of my task, and the numerous problems with which I should be engaged; and, as I perceived that this critical investigation would, even if delivered in the driest scholastic manner, be far from being brief, I found it unadvisable to enlarge it still more with examples and explanations, which are necessary only from a popular point of view. I was induced to take this course from the consideration also that the present work is not intended for popular use, that those devoted to science do not require such helps, although they are always acceptable, and that they would have materially interfered with my present purpose.

Abbé Terrasson remarks with great justice that, if we estimate the size of a work, not from the number of its pages, but from the time which we require to make ourselves master of it, it may be said of many a book — that it would be much shorter, if it were not so short. On the other hand, as regards the comprehensibility of a system of speculative cognition, connected under a single principle, we may say with equal justice: many a book would have been much clearer, if it had not been intended to be so very clear. For explanations and examples, and other helps to intelligibility, aid us in the comprehension of parts, but they distract the attention, dissipate the mental power of the reader, and stand in the way of his forming a clear conception of the whole; as he cannot attain soon enough to a survey of the system, and the colouring and embellishments bestowed upon it prevent his observing its articulation or organization — which is the most important consideration with him, when he comes to judge of its unity and stability.

The reader must naturally have a strong inducement to co-operate with the present author, if he has formed the intention of erecting a complete and solid edifice of metaphysical science, according to the plan now laid before him. Metaphysics, as here represented, is the only science which admits of completion — and with little labour, if it is united, in a short time; so that nothing will be left to future generations except the task of illustrating and applying it didactically. For this science is nothing more than the inventory of all that is given us by pure reason, systematically arranged. Nothing can escape our notice; for what reason produces from itself cannot lie concealed, but must be brought to the light by reason itself, so soon as we have discovered the common principle of the ideas we seek. The perfect unity of this kind of cognitions, which are based upon pure conceptions, and uninfluenced by any empirical element, or any peculiar intuition leading to determinate experience, renders this completeness not only practicable, but also necessary.

Tecum habita, et nôris quam sit tibi curta supellex. — Persius. Satirae iv. 52. Such a system of pure speculative reason I hope to be able to publish under the title of Metaphysic of Nature [2]. The content of this work (which will not be half so long) will be very much richer than that of the present Critique, which has to discover the sources of this cognition and expose the conditions of its possibility, and at the same time to clear and level a fit foundation for the scientific edifice. In the present work, I look for the patient hearing and the impartiality of a judge; in the other, for the good-will and assistance of a co-labourer. For, however complete the list of principles for this system may be in the Critique, the correctness of the system requires that no deduced conceptions should be absent. These cannot be presented à priori, but must be gradually discovered; and, while the synthesis of conceptions has been fully exhausted in the Critique, it is necessary that, in the proposed work, the same should be the case with their analysis. But this will be rather an amusement than a labour.

[2] In contradistinction to the Metaphysic of Ethics. This work was never published.

PREFACE TO THE SECOND EDITION 1787

Whether the treatment of that portion of our knowledge which lies within the province of pure reason advances with that undeviating certainty which characterizes the progress of science, we shall be at no loss to determine. If we find those who are engaged in metaphysical pursuits, unable to come to an understanding as to the method which they ought to follow; if we find them, after the most elaborate preparations, invariably brought to a stand before the goal is reached, and compelled to retrace their steps and strike into fresh paths, we may then feel quite sure that they are far from having attained to the certainty of scientific progress and may rather be said to be merely groping about in the dark. In these circumstances we shall render an important service to reason if we succeed in simply indicating the path along which it must travel, in order to arrive at any results — even if it should be found necessary to abandon many of those aims which, without reflection, have been proposed for its attainment. That Logic has advanced in this sure course, even from the earliest times, is apparent from the fact that, since Aristotle, it has been unable to advance a step and, thus, to all appearance has reached its completion. For, if some of the moderns have thought to enlarge its domain by introducing psychological discussions on the mental faculties, such as imagination and wit, metaphysical, discussions on the origin of knowledge and the different kinds of certitude, according to the difference of the objects (idealism, scepticism, and so on), or anthropological discussions on prejudices, their causes and remedies: this attempt, on the part of these authors, only shows their ignorance of the peculiar nature of logical science.

We do not enlarge but disfigure the sciences when we lose sight of their respective limits and allow them to run into one another. Now logic is enclosed within limits which admit of perfectly clear definition; it is a science which has for its object nothing but the exposition and proof of the formal laws of all thought, whether it be à priori or empirical, whatever be its origin or its object, and whatever the difficulties — natural or accidental — which it encounters in the human mind. The early success of logic must be attributed exclusively to the narrowness of its field, in which abstraction may, or rather must, be made of all the objects of cognition with their characteristic distinctions, and in which the understanding has only to deal with itself and with its own forms. It is, obviously, a much more difficult task for reason to strike into the sure path of science, where it has to deal not simply with itself, but with objects external to itself. Hence, logic is properly only a propædeutic — forms, as it were, the vestibule of the sciences; and while it is necessary to enable us to form a correct judgement with regard to the various branches of knowledge, still the acquisition of real, substantive knowledge is to be sought only in the sciences properly so called, that is, in the objective sciences. Now these sciences, if they can be termed rational at all, must contain elements of à priori cognition, and this cognition may stand in a twofold relation to its object. Either it may have to determine the conception of the object — which must be supplied extraneously, or it may have to establish its reality.

The former is theoretical, the latter practical, rational cognition. In both, the pure or à priori element must be treated first, and must be carefully distinguished from that which is supplied from other sources. Any other method can only lead to irremediable confusion. Mathematics and physics are the two theoretical sciences which have to determine their objects à priori. The former is purely à priori, the latter is partially so, but is also dependent on other sources of cognition. In the earliest times of which history affords us any record, mathematics had already entered on the sure course of science, among that wonderful nation, the Greeks. Still it is not to be supposed that it was as easy for this science to strike into, or rather to construct for itself, that royal road, as it was for logic, in which reason has only to deal with itself. On the contrary, I believe that it must have remained long — chiefly among the Egyptians — in the stage of blind groping after its true aims and destination, and that it was revolutionized by the happy idea of one man, who struck out and determined for all time the path which this science must follow, and which admits of an indefinite advancement.

The history of this intellectual revolution — much more important in its results than the discovery of the passage round the celebrated Cape of Good Hope — and of its author, has not been preserved. But Diogenes Laertius, in naming the supposed discoverer of some of the simplest elements of geometrical demonstration — elements which, according to the ordinary opinion, do not even require to be proved — makes it apparent that the change introduced by the first indication of this new path, must have seemed of the utmost importance to the mathematicians of that age, and it has thus been secured against the chance of oblivion. A new light must have flashed on the mind of the first man (Thales, or whatever may have been his name) who demonstrated the properties of the isosceles triangle. For he found that it was not sufficient to meditate on the figure, as it lay before his eyes, or the conception of it, as it existed in his mind, and thus endeavour to get at the knowledge of its properties, but that it was necessary to produce these properties, as it were, by a positive à priori construction; and that, in order to arrive with certainty at à priori cognition, he must not attribute to the object any other properties than those which necessarily followed from that which he had himself, in accordance with his conception, placed in the object.

A much longer period elapsed before Physics entered on the highway of science. For it is only about a century and a half since the wise BACON gave a new direction to physical studies, or rather — as others were already on the right track — imparted fresh vigour to the pursuit of this new direction. Here, too, as in the case of mathematics, we find evidence of a rapid intellectual revolution. In the remarks which follow I shall confine myself to the empirical side of natural science.

When GALILEI experimented with balls of a definite weight on the inclined plane, when TORRICELLI caused the air to sustain a weight which he had calculated beforehand to be equal to that of a definite column of water, or when STAHL, at a later period, converted metals into lime, and reconverted lime into metal, by the addition and subtraction of certain elements; [3] a light broke upon all natural philosophers. They learned that reason only perceives that which it produces after its own design; that it must not be content to follow, as it were, in the leading-strings of nature, but must proceed in advance with principles of judgement according to unvarying laws, and compel nature to reply its questions. For accidental observations, made according to no preconceived plan, cannot be united under a necessary law. But it is this that reason seeks for and requires. It is only the principles of reason which can give to concordant phenomena the validity of laws, and it is only when experiment is directed by these rational principles that it can have any real utility. Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose. To this single idea must the revolution be ascribed, by which, after groping in the dark for so many centuries, natural science was at length conducted into the path of certain progress.

[3] I do not here follow with exactness the history of the experimental method, of which, indeed, the first steps are involved in some obscurity. We come now to metaphysics, a purely speculative science, which occupies a completely isolated position and is entirely independent of the teachings of experience. It deals with mere conceptions — not, like mathematics, with conceptions applied to intuition — and in it, reason is the pupil of itself alone. It is the oldest of the sciences, and would still survive, even if all the rest were swallowed up in the abyss of an all-destroying barbarism. But it has not yet had the good fortune to attain to the sure scientific method. This will be apparent; if we apply the tests which we proposed at the outset. We find that reason perpetually comes to a stand, when it attempts to gain à priori the perception even of those laws which the most common experience confirms. We find it compelled to retrace its steps in innumerable instances, and to abandon the path on which it had entered, because this does not lead to the desired result.

We find, too, that those who are engaged in metaphysical pursuits are far from being able to agree among themselves, but that, on the contrary, this science appears to furnish an arena specially adapted for the display of skill or the exercise of strength in mock-contests — a field in which no combatant ever yet succeeded in gaining an inch of ground, in which, at least, no victory was ever yet crowned with permanent possession. This leads us to inquire why it is that, in metaphysics, the sure path of science has not hitherto been found. Shall we suppose that it is impossible to discover it? Why then should nature have visited our reason with restless aspirations after it, as if it were one of our weightiest concerns?

Nay, more, how little cause should we have to place confidence in our reason, if it abandons us in a matter about which, most of all, we desire to know the truth — and not only so, but even allures us to the pursuit of vain phantoms, only to betray us in the end? Or, if the path has only hitherto been missed, what indications do we possess to guide us in a renewed investigation, and to enable us to hope for greater success than has fallen to the lot of our predecessors?

It appears to me that the examples of mathematics and natural philosophy, which, as we have seen, were brought into their present condition by a sudden revolution, are sufficiently remarkable to fix our attention on the essential circumstances of the change which has proved so advantageous to them, and to induce us to make the experiment of imitating them, so far as the analogy which, as rational sciences, they bear to metaphysics may permit. It has hitherto been assumed that our cognition must conform to the objects; but all attempts to ascertain anything about these objects à priori, by means of conceptions, and thus to extend the range of our knowledge, have been rendered abortive by this assumption. Let us then make the experiment whether we may not be more successful in metaphysics, if we assume that the objects must conform to our cognition.

This appears, at all events, to accord better with the possibility of our gaining the end we have in view, that is to say, of arriving at the cognition of objects à priori, of determining something with respect to these objects, before they are given to us. We here propose to do just what COPERNICUS did in attempting to explain the celestial movements. When he found that he could make no progress by assuming that all the heavenly bodies revolved round the spectator, he reversed the process, and tried the experiment of assuming that the spectator revolved, while the stars remained at rest. We may make the same experiment with regard to the intuition of objects. If the intuition must conform to the nature of the objects, I do not see how we can know anything of them à priori. If, on the other hand, the object conforms to the nature of our faculty of intuition, I can then easily conceive the possibility of such an à priori knowledge. Now as I cannot rest in the mere intuitions, but — if they are to become cognitions — must refer them, as representations, to something, as object, and must determine the latter by means of the former, here again there are two courses open to me. Either, first, I may assume that the conceptions, by which I effect this determination, conform to the object — and in this case I am reduced to the same perplexity as before; or secondly, I may assume that the objects, or, which is the same thing, that experience, in which alone as given objects they are cognized, conform to my conceptions — and then I am at no loss how to proceed.

For experience itself is a mode of cognition which requires understanding. Before objects, are given to me, that is, à priori, I must presuppose in myself laws of the understanding which are expressed in conceptions à priori. To these conceptions, then, all the objects of experience must necessarily conform. Now there are objects which reason thinks, and that necessarily, but which cannot be given in experience, or, at least, cannot be given so as reason thinks them. The attempt to think these objects will hereafter furnish an excellent test of the new method of thought which we have adopted, and which is based on the principle that we only cognize in things à priori that which we ourselves place in them. [4]

[4] This method, accordingly, which we have borrowed from the natural philosopher, consists in seeking for the elements of pure reason in that which admits of confirmation or refutation by experiment. Now the propositions of pure reason, especially when they transcend the limits of possible experience, do not admit of our making any experiment with their objects, as in natural science. Hence, with regard to those conceptions and principles which we assume à priori, our only course will be to view them from two different sides. We must regard one and the same conception, on the one hand, in relation to experience as an object of the senses and of the understanding, on the other hand, in relation to reason, isolated and transcending the limits of experience, as an object of mere thought. Now if we find that, when we regard things from this double point of view, the result is in harmony with the principle of pure reason, but that, when we regard them from a single point of view, reason is involved in self-contradiction, then the experiment will establish the correctness of this distinction. This attempt succeeds as well as we could desire, and promises to metaphysics, in its first part — that is, where it is occupied with conceptions à priori, of which the corresponding objects may be given in experience — the certain course of science.

For by this new method we are enabled perfectly to explain the possibility of à priori cognition, and, what is more, to demonstrate satisfactorily the laws which lie à priori at the foundation of nature, as the sum of the objects of experience — neither of which was possible according to the procedure hitherto followed. But from this deduction of the faculty of à priori cognition in the first part of metaphysics, we derive a surprising result, and one which, to all appearance, militates against the great end of metaphysics, as treated in the second part. For we come to the conclusion that our faculty of cognition is unable to transcend the limits of possible experience; and yet this is precisely the most essential object of this science. The estimate of our rational cognition à priori at which we arrive is that it has only to do with phenomena, and that things in themselves, while possessing a real existence, lie beyond its sphere.

Here we are enabled to put the justice of this estimate to the test. For that which of necessity impels us to transcend the limits of experience and of all phenomena is the unconditioned, which reason absolutely requires in things as they are in themselves, in order to complete the series of conditions. Now, if it appears that when, on the one hand, we assume that our cognition conforms to its objects as things in themselves, the unconditioned cannot be thought without contradiction, and that when, on the other hand, we assume that our representation of things as they are given to us, does not conform to these things as they are in themselves, but that these objects, as phenomena, conform to our mode of representation, the contradiction disappears: we shall then be convinced of the truth of that which we began by assuming for the sake of experiment; we may look upon it as established that the unconditioned does not lie in things as we know them, or as they are given to us, but in things as they are in themselves, beyond the range of our cognition. [5]

[5] This experiment of pure reason has a great similarity to that of the Chemists, which they term the experiment of reduction, or, more usually, the synthetic process. The analysis of the metaphysician separates pure cognition à priori into two heterogeneous elements, viz., the cognition of things as phenomena, and of things in themselves. Dialectic combines these again into harmony with the necessary rational idea of the unconditioned, and finds that this harmony never results except through the above distinction, which is, therefore, concluded to be just. But, after we have thus denied the power of speculative reason to make any progress in the sphere of the supersensible, it still remains for our consideration whether data do not exist in practical cognition which may enable us to determine the transcendent conception of the unconditioned, to rise beyond the limits of all possible experience from a practical point of view, and thus to satisfy the great ends of metaphysics. Speculative reason has thus, at least, made room for such an extension of our knowledge: and, if it must leave this space vacant, still it does not rob us of the liberty to fill it up, if we can, by means of practical data — nay, it even challenges us to make the attempt. [6]

[6] So the central laws of the movements of the heavenly bodies established the truth of that which Copernicus, first, assumed only as a hypothesis, and, at the same time, brought to light that invisible force (Newtonian attraction) which holds the universe together. The latter would have remained forever undiscovered, if Copernicus had not ventured on the experiment — contrary to the senses but still just — of looking for the observed movements not in the heavenly bodies, but in the spectator. In this Preface I treat the new metaphysical method as a hypothesis with the view of rendering apparent the first attempts at such a change of method, which are always hypothetical. But in the Critique itself it will be demonstrated, not hypothetically, but apodeictically, from the nature of our representations of space and time, and from the elementary conceptions of the understanding. This attempt to introduce a complete revolution in the procedure of metaphysics, after the example of the geometricians and natural philosophers, constitutes the aim of the Critique of Pure Speculative Reason. It is a treatise on the method to be followed, not a system of the science itself. But, at the same time, it marks out and defines both the external boundaries and the internal structure of this science.

For pure speculative reason has this peculiarity, that, in choosing the various objects of thought, it is able to define the limits of its own faculties, and even to give a complete enumeration of the possible modes of proposing problems to itself, and thus to sketch out the entire system of metaphysics.

For, on the one hand, in cognition à priori, nothing must be attributed to the objects but what the thinking subject derives from itself; and, on the other hand, reason is, in regard to the principles of cognition, a perfectly distinct, independent unity, in which, as in an organized body, every member exists for the sake of the others, and all for the sake of each, so that no principle can be viewed, with safety, in one relationship, unless it is, at the same time, viewed in relation to the total use of pure reason. Hence, too, metaphysics has this singular advantage — an advantage which falls to the lot of no other science which has to do with objects — that, if once it is conducted into the sure path of science, by means of this criticism, it can then take in the whole sphere of its cognitions, and can thus complete its work, and leave it for the use of posterity, as a capital which can never receive fresh accessions. For metaphysics has to deal only with principles and with the limitations of its own employment as determined by these principles.

To this perfection it is, therefore, bound, as the fundamental science, to attain, and to it the maxim may justly be applied: Nil actum reputans, si quid superesset agendum. But, it will be asked, what kind of a treasure is this that we propose to bequeath to posterity? What is the real value of this system of metaphysics, purified by criticism, and thereby reduced to a permanent condition? A cursory view of the present work will lead to the supposition that its use is merely negative, that it only serves to warn us against venturing, with speculative reason, beyond the limits of experience. This is, in fact, its primary use. But this, at once, assumes a positive value, when we observe that the principles with which speculative reason endeavours to transcend its limits lead inevitably, not to the extension, but to the contraction of the use of reason, inasmuch as they threaten to extend the limits of sensibility, which is their proper sphere, over the entire realm of thought and, thus, to supplant the pure (practical) use of reason. So far, then, as this criticism is occupied in confining speculative reason within its proper bounds, it is only negative; but, inasmuch as it thereby, at the same time, removes an obstacle which impedes and even threatens to destroy the use of practical reason, it possesses a positive and very important value. In order to admit this, we have only to be convinced that there is an absolutely necessary use of pure reason — the moral use — in which it inevitably transcends the limits of sensibility, without the aid of speculation, requiring only to be insured against the effects of a speculation which would involve it in contradiction with itself. To deny the positive advantage of the service which this criticism renders us would be as absurd as to maintain that the system of police is productive of no positive benefit, since its main business is to prevent the violence which citizen has to apprehend from citizen, that so each may pursue his vocation in peace and security. That space and time are only forms of sensible intuition, and hence are only conditions of the existence of things as phenomena; that, moreover, we have no conceptions of the understanding, and, consequently, no elements for the cognition of things, except in so far as a corresponding intuition can be given to these conceptions; that, accordingly, we can have no cognition of an object, as a thing in itself, but only as an object of sensible intuition, that is, as phenomenon — all this is proved in the analytical part of the Critique; and from this the limitation of all possible speculative cognition to the mere objects of experience, follows as a necessary result. At the same time, it must be carefully borne in mind that, while we surrender the power of cognizing, we still reserve the power of thinking objects, as things in themselves. [7] For, otherwise, we should require to affirm the existence of an appearance, without something that appears — which would be absurd. Now let us suppose, for a moment, that we had not undertaken this criticism and, accordingly, had not drawn the necessary distinction between things as objects of experience and things as they are in themselves.

The principle of causality, and, by consequence, the mechanism of nature as determined by causality, would then have absolute validity in relation to all things as efficient causes. I should then be unable to assert, with regard to one and the same being, e.g., the human soul, that its will is free, and yet, at the same time, subject to natural necessity, that is, not free, without falling into a palpable contradiction, for in both propositions I should take the soul in the same signification, as a thing in general, as a thing in itself — as, without previous criticism, I could not but take it. Suppose now, on the other hand, that we have undertaken this criticism, and have learnt that an object may be taken in two senses, first, as a phenomenon, secondly, as a thing in itself; and that, according to the deduction of the conceptions of the understanding, the principle of causality has reference only to things in the first sense. We then see how it does not involve any contradiction to assert, on the one hand, that the will, in the phenomenal sphere — in visible action — is necessarily obedient to the law of nature, and, in so far, not free; and, on the other hand, that, as belonging to a thing in itself, it is not subject to that law, and, accordingly, is free.

Now, it is true that I cannot, by means of speculative reason, and still less by empirical observation, cognize my soul as a thing in itself and consequently, cannot cognize liberty as the property of a being to which I ascribe effects in the world of sense. For, to do so, I must cognize this being as existing, and yet not in time, which — since I cannot support my conception by any intuition — is impossible. At the same time, while I cannot cognize, I can quite well think freedom, that is to say, my representation of it involves at least no contradiction, if we bear in mind the critical distinction of the two modes of representation (the sensible and the intellectual) and the consequent limitation of the conceptions of the pure understanding and of the principles which flow from them.

Suppose now that morality necessarily presupposed liberty, in the strictest sense, as a property of our will; suppose that reason contained certain practical, original principles à priori, which were absolutely impossible without this presupposition; and suppose, at the same time, that speculative reason had proved that liberty was incapable of being thought at all. It would then follow that the moral presupposition must give way to the speculative affirmation, the opposite of which involves an obvious contradiction, and that liberty and, with it, morality must yield to the mechanism of nature; for the negation of morality involves no contradiction, except on the presupposition of liberty.

Now morality does not require the speculative cognition of liberty; it is enough that I can think it, that its conception involves no contradiction, that it does not interfere with the mechanism of nature. But even this requirement we could not satisfy, if we had not learnt the twofold sense in which things may be taken; and it is only in this way that the doctrine of morality and the doctrine of nature are confined within their proper limits. For this result, then, we are indebted to a criticism which warns us of our unavoidable ignorance with regard to things in themselves, and establishes the necessary limitation of our theoretical cognition to mere phenomena.

[7] In order to cognize an object, I must be able to prove its possibility, either from its reality as attested by experience, or à priori, by means of reason. But I can think what I please, provided only I do not contradict myself; that is, provided my conception is a possible thought, though I may be unable to answer for the existence of a corresponding object in the sum of possibilities. But something more is required before I can attribute to such a conception objective validity, that is real possibility — the other possibility being merely logical. We are not, however, confined to theoretical sources of cognition for the means of satisfying this additional requirement, but may derive them from practical sources.

The positive value of the critical principles of pure reason in relation to the conception of God and of the simple nature of the soul, admits of a similar exemplification; but on this point I shall not dwell. I cannot even make the assumption — as the practical interests of morality require — of God, freedom, and immortality, if I do not deprive speculative reason of its pretensions to transcendent insight. For to arrive at these, it must make use of principles which, in fact, extend only to the objects of possible experience, and which cannot be applied to objects beyond this sphere without converting them into phenomena, and thus rendering the practical extension of pure reason impossible. I must, therefore, abolish knowledge, to make room for belief.

The dogmatism of metaphysics, that is, the presumption that it is possible to advance in metaphysics without previous criticism, is the true source of the unbelief (always dogmatic) which militates against morality. Thus, while it may be no very difficult task to bequeath a legacy to posterity, in the shape of a system of metaphysics constructed in accordance with the Critique of Pure Reason, still the value of such a bequest is not to be depreciated. It will render an important service to reason, by substituting the certainty of scientific method for that random groping after results without the guidance of principles, which has hitherto characterized the pursuit of metaphysical studies. It will render an important service to the inquiring mind of youth, by leading the student to apply his powers to the cultivation of genuine science, instead of wasting them, as at present, on speculations which can never lead to any result, or on the idle attempt to invent new ideas and opinions.

But, above all, it will confer an inestimable benefit on morality and religion, by showing that all the objections urged against them may be silenced for ever by the Socratic method, that is to say, by proving the ignorance of the objector. For, as the world has never been, and, no doubt, never will be without a system of metaphysics of one kind or another, it is the highest and weightiest concern of philosophy to render it powerless for harm, by closing up the sources of error. This important change in the field of the sciences, this loss of its fancied possessions, to which speculative reason must submit, does not prove in any way detrimental to the general interests of humanity.

The advantages which the world has derived from the teachings of pure reason are not at all impaired. The loss falls, in its whole extent, on the monopoly of the schools, but does not in the slightest degree touch the interests of mankind. I appeal to the most obstinate dogmatist, whether the proof of the continued existence of the soul after death, derived from the simplicity of its substance; of the freedom of the will in opposition to the general mechanism of nature, drawn from the subtle but impotent distinction of subjective and objective practical necessity; or of the existence of God, deduced from the conception of an ens realissimum — the contingency of the changeable, and the necessity of a prime mover, has ever been able to pass beyond the limits of the schools, to penetrate the public mind, or to exercise the slightest influence on its convictions. It must be admitted that this has not been the case and that, owing to the unfitness of the common understanding for such subtle speculations, it can never be expected to take place. On the contrary, it is plain that the hope of a future life arises from the feeling, which exists in the breast of every man, that the temporal is inadequate to meet and satisfy the demands of his nature.

In like manner, it cannot be doubted that the clear exhibition of duties in opposition to all the claims of inclination, gives rise to the consciousness of freedom, and that the glorious order, beauty, and providential care, everywhere displayed in nature, give rise to the belief in a wise and great Author of the Universe. Such is the genesis of these general convictions of mankind, so far as they depend on rational grounds; and this public property not only remains undisturbed, but is even raised to greater importance, by the doctrine that the schools have no right to arrogate to themselves a more profound insight into a matter of general human concernment than that to which the great mass of men, ever held by us in the highest estimation, can without difficulty attain, and that the schools should, therefore, confine themselves to the elaboration of these universally comprehensible and, from a moral point of view, amply satisfactory proofs. The change, therefore, affects only the arrogant pretensions of the schools, which would gladly retain, in their own exclusive possession, the key to the truths which they impart to the public.

Quod mecum nescit, solus vult scire videri. At the same time it does not deprive the speculative philosopher of his just title to be the sole depositor of a science which benefits the public without its knowledge — I mean, the Critique of Pure Reason. This can never become popular and, indeed, has no occasion to be so; for finespun arguments in favour of useful truths make just as little impression on the public mind as the equally subtle objections brought against these truths. On the other hand, since both inevitably force themselves on every man who rises to the height of speculation, it becomes the manifest duty of the schools to enter upon a thorough investigation of the rights of speculative reason and, thus, to prevent the scandal which metaphysical controversies are sure, sooner or later, to cause even to the masses. It is only by criticism that metaphysicians (and, as such, theologians too) can be saved from these controversies and from the consequent perversion of their doctrines.

Criticism alone can strike a blow at the root of materialism, fatalism, atheism, free-thinking, fanaticism, and superstition, which are universally injurious — as well as of idealism and scepticism, which are dangerous to the schools, but can scarcely pass over to the public. If governments think proper to interfere with the affairs of the learned, it would be more consistent with a wise regard for the interests of science, as well as for those of society, to favour a criticism of this kind, by which alone the labours of reason can be established on a firm basis, than to support the ridiculous despotism of the schools, which raise a loud cry of danger to the public over the destruction of cobwebs, of which the public has never taken any notice, and the loss of which, therefore, it can never feel. This critical science is not opposed to the dogmatic procedure of reason in pure cognition; for pure cognition must always be dogmatic, that is, must rest on strict demonstration from sure principles à priori — but to dogmatism, that is, to the presumption that it is possible to make any progress with a pure cognition, derived from (philosophical) conceptions, according to the principles which reason has long been in the habit of employing — without first inquiring in what way and by what right reason has come into the possession of these principles.

Dogmatism is thus the dogmatic procedure of pure reason without previous criticism of its own powers, and in opposing this procedure, we must not be supposed to lend any countenance to that loquacious shallowness which arrogates to itself the name of popularity, nor yet to scepticism, which makes short work with the whole science of metaphysics. On the contrary, our criticism is the necessary preparation for a thoroughly scientific system of metaphysics which must perform its task entirely à priori, to the complete satisfaction of speculative reason, and must, therefore, be treated, not popularly, but scholastically. In carrying out the plan which the Critique prescribes, that is, in the future system of metaphysics, we must have recourse to the strict method of the celebrated WOLF, the greatest of all dogmatic philosophers.

He was the first to point out the necessity of establishing fixed principles, of clearly defining our conceptions, and of subjecting our demonstrations to the most severe scrutiny, instead of rashly jumping at conclusions. The example which he set served to awaken that spirit of profound and thorough investigation which is not yet extinct in Germany. He would have been peculiarly well fitted to give a truly scientific character to metaphysical studies, had it occurred to him to prepare the field by a criticism of the organum, that is, of pure reason itself. That he failed to perceive the necessity of such a procedure must be ascribed to the dogmatic mode of thought which characterized his age, and on this point the philosophers of his time, as well as of all previous times, have nothing to reproach each other with.

Those who reject at once the method of Wolf, and of the Critique of Pure Reason, can have no other aim but to shake off the fetters of science, to change labour into sport, certainty into opinion, and philosophy into philodoxy. In this second edition, I have endeavoured, as far as possible, to remove the difficulties and obscurity which, without fault of mine perhaps, have given rise to many misconceptions even among acute thinkers. In the propositions themselves, and in the demonstrations by which they are supported, as well as in the form and the entire plan of the work, I have found nothing to alter; which must be attributed partly to the long examination to which I had subjected the whole before offering it to the public and partly to the nature of the case. For pure speculative reason is an organic structure in which there is nothing isolated or independent, but every Single part is essential to all the rest; and hence, the slightest imperfection, whether defect or positive error, could not fail to betray itself in use.

I venture, further, to hope, that this system will maintain the same unalterable character for the future. I am led to entertain this confidence, not by vanity, but by the evidence which the equality of the result affords, when we proceed, first, from the simplest elements up to the complete whole of pure reason and, and then, backwards from the whole to each part. We find that the attempt to make the slightest alteration, in any part, leads inevitably to contradictions, not merely in this system, but in human reason itself. At the same time, there is still much room for improvement in the exposition of the doctrines contained in this work. In the present edition, I have endeavoured to remove misapprehensions of the æsthetical part, especially with regard to the conception of time; to clear away the obscurity which has been found in the deduction of the conceptions of the understanding; to supply the supposed want of sufficient evidence in the demonstration of the principles of the pure understanding; and, lastly, to obviate the misunderstanding of the paralogisms which immediately precede the Rational Psychology. Beyond this point — the end of the second main division of the “Transcendental Dialectic” — I have not extended my alterations, [8] partly from want of time, and partly because I am not aware that any portion of the remainder has given rise to misconceptions among intelligent and impartial critics, whom I do not here mention with that praise which is their due, but who will find that their suggestions have been attended to in the work itself.

[8] The only addition, properly so called — and that only in the method of proof — which I have made in the present edition, consists of a new refutation of psychological Idealism, and a strict demonstration — the only one possible, as I believe — of the objective reality of external intuition. However harmless idealism may be considered — although in reality it is not so — in regard to the essential ends of metaphysics, it must still remain a scandal to philosophy and to the general human reason to be obliged to assume, as an article of mere belief, the existence of things external to ourselves (from which, yet, we derive the whole material of cognition for the internal sense), and not to be able to oppose a satisfactory proof to any one who may call it in question. As there is some obscurity of expression in the demonstration as it stands in the text, I propose to alter the passage in question as follows: “But this permanent cannot be an intuition in me. For all the determining grounds of my existence which can be found in me are representations and, as such, do themselves require a permanent, distinct from them, which may determine my existence in relation to their changes, that is, my existence in time, wherein they change.” It may, probably, be urged in opposition to this proof that, after all, I am only conscious immediately of that which is in me, that is, of my representation of external things, and that, consequently, it must always remain uncertain whether anything corresponding to this representation does or does not exist externally to me. But I am conscious, through internal experience, of my existence in time (consequently, also, of the determinability of the former in the latter), and that is more than the simple consciousness of my representation. It is, in fact, the same as the empirical consciousness of my existence, which can only be determined in relation to something, which, while connected with my existence, is external to me.

This consciousness of my existence in time is, therefore, identical with the consciousness of a relation to something external to me, and it is, therefore, experience, not fiction, sense, not imagination, which inseparably connects the external with my internal sense. For the external sense is, in itself, the relation of intuition to something real, external to me; and the reality of this something, as opposed to the mere imagination of it, rests solely on its inseparable connection with internal experience as the condition of its possibility. If with the intellectual consciousness of my existence, in the representation: I am, which accompanies all my judgements, and all the operations of my understanding, I could, at the same time, connect a determination of my existence by intellectual intuition, then the consciousness of a relation to something external to me would not be necessary. But the internal intuition in which alone my existence can be determined, though preceded by that purely intellectual consciousness, is itself sensible and attached to the condition of time.

Hence this determination of my existence, and consequently my internal experience itself, must depend on something permanent which is not in me, which can be, therefore, only in something external to me, to which I must look upon myself as being related. Thus the reality of the external sense is necessarily connected with that of the internal, in order to the possibility of experience in general; that is, I am just as certainly conscious that there are things external to me related to my sense as I am that I myself exist as determined in time. But in order to ascertain to what given intuitions objects, external me, really correspond, in other words, what intuitions belong to the external sense and not to imagination, I must have recourse, in every particular case, to those rules according to which experience in general (even internal experience) is distinguished from imagination, and which are always based on the proposition that there really is an external experience. —

We may add the remark that the representation of something permanent in existence, is not the same thing as the permanent representation; for a representation may be very variable and changing — as all our representations, even that of matter, are — and yet refer to something permanent, which must, therefore, be distinct from all my representations and external to me, the existence of which is necessarily included in the determination of my own existence, and with it constitutes one experience — an experience which would not even be possible internally, if it were not also at the same time, in part, external.

To the question How? we are no more able to reply, than we are, in general, to think the stationary in time, the coexistence of which with the variable, produces the conception of change. In attempting to render the exposition of my views as intelligible as possible, I have been compelled to leave out or abridge various passages which were not essential to the completeness of the work, but which many readers might consider useful in other respects, and might be unwilling to miss. This trifling loss, which could not be avoided without swelling the book beyond due limits, may be supplied, at the pleasure of the reader, by a comparison with the first edition, and will, I hope, be more than compensated for by the greater clearness of the exposition as it now stands. I have observed, with pleasure and thankfulness, in the pages of various reviews and treatises, that the spirit of profound and thorough investigation is not extinct in Germany, though it may have been overborne and silenced for a time by the fashionable tone of a licence in thinking, which gives itself the airs of genius, and that the difficulties which beset the paths of criticism have not prevented energetic and acute thinkers from making themselves masters of the science of pure reason to which these paths conduct — a science which is not popular, but scholastic in its character, and which alone can hope for a lasting existence or possess an abiding value.

To these deserving men, who so happily combine profundity of view with a talent for lucid exposition — a talent which I myself am not conscious of possessing — I leave the task of removing any obscurity which may still adhere to the statement of my doctrines. For, in this case, the danger is not that of being refuted, but of being misunderstood. For my own part, I must henceforward abstain from controversy, although I shall carefully attend to all suggestions, whether from friends or adversaries, which may be of use in the future elaboration of the system of this Propædeutic. As, during these labours, I have advanced pretty far in years this month I reach my sixty-fourth year — it will be necessary for me to economize time, if I am to carry out my plan of elaborating the metaphysics of nature as well as of morals, in confirmation of the correctness of the principles established in this Critique of Pure Reason, both speculative and practical; and I must, therefore, leave the task of clearing up the obscurities of the present work — inevitable, perhaps, at the outset — as well as, the defence of the whole, to those deserving men, who have made my system their own.

A philosophical system cannot come forward armed at all points like a mathematical treatise, and hence it may be quite possible to take objection to particular passages, while the organic structure of the system, considered as a unity, has no danger to apprehend. But few possess the ability, and still fewer the inclination, to take a comprehensive view of a new system. By confining the view to particular passages, taking these out of their connection and comparing them with one another, it is easy to pick out apparent contradictions, especially in a work written with any freedom of style. These contradictions place the work in an unfavourable light in the eyes of those who rely on the judgement of others, but are easily reconciled by those who have mastered the idea of the whole. If a theory possesses stability in itself, the action and reaction which seemed at first to threaten its existence serve only, in the course of time, to smooth down any superficial roughness or inequality, and — if men of insight, impartiality, and truly popular gifts, turn their attention to it — to secure to it, in a short time, the requisite elegance also. KÖNIGSBERG, April 1787.

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 à priori, in contradistinction to empirical knowledge, which has its sources à posteriori, that is, in experience. But the expression, “à 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 à 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 à priori that it would have fallen;” that is, he needed not to have waited for the experience that it did actually fall. But still, à 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 à 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 à posteriori, that is, through experience. Knowledge à priori is either pure or impure.

Pure knowledge à priori is that with which no empirical element is mixed up. For example, the proposition, “Every change has a cause,” is a proposition à 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 “à 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 priori. 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 à 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 à 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 à 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 à 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 à 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 à 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 à 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 à priori. III. Philosophy stands in need of a Science which shall Determine the Possibility, Principles, and Extent of Human Knowledge “à 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 à 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 à 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 à 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, à 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 à 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 à 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 à priori and from pure conceptions. Upon such synthetical, that is augmentative propositions, depends the whole aim of our speculative knowledge à 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 “à 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 à 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 à 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 à 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 à 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 à priori, which I did not think in it. The proposition is therefore not analytical, but synthetical, and nevertheless conceived à 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 à priori. It is not merely the duty of metaphysics to dissect, and thereby analytically to illustrate the conceptions which we form à priori of things; but we seek to widen the range of our à 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 à 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 à 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 à 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 à 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 à 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 à 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 à 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. [9] 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. [9] As to the existence of pure natural science, or physics, perhaps many may still express doubts. But we have only to look at the different propositions which are commonly treated of at the commencement of proper (empirical) physical science — those, for example, relating to the permanence of the same quantity of matter, the vis inertiae, the equality of action and reaction, etc. — to be soon convinced that they form a science of pure physics (physica pura, or rationalis), which well deserves to be separately exposed as a special science, in its whole extent, whether that be great or confined. 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 à 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, à 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 à priori. Hence, pure reason is the faculty which contains the principles of cognizing anything absolutely à priori. An organon of pure reason would be a compendium of those principles according to which alone all pure cognitions à 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 propædeutic 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 à 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 à priori, but of our analytical à 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 à 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 à 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 à 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 à 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 à 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 à 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 à priori must be completely pure. Hence, although the highest principles and fundamental conceptions of morality are certainly cognitions à 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 à 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 ÆSTHETIC.

§ 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 à posteriori; the form must lie ready à 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 à 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 à 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 à priori, I call transcendental æsthetic. [10] 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. [10] The Germans are the only people who at present use this word to indicate what others call the critique of taste. At the foundation of this term lies the disappointed hope, which the eminent analyst, Baumgarten, conceived, of subjecting the criticism of the beautiful to principles of reason, and so of elevating its rules into a science. But his endeavours were vain. For the said rules or criteria are, in respect to their chief sources, merely empirical, consequently never can serve as determinate laws à priori, by which our judgement in matters of taste is to be directed. It is rather our judgement which forms the proper test as to the correctness of the principles. On this account it is advisable to give up the use of the term as designating the critique of taste, and to apply it solely to that doctrine, which is true science — the science of the laws of sensibility — and thus come nearer to the language and the sense of the ancients in their well-known division of the objects of cognition into aiotheta kai noeta, or to share it with speculative philosophy, and employ it partly in a transcendental, partly in a psychological signification. In the science of transcendental æsthetic 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 à priori. From this investigation it will be found that there are two pure forms of sensuous intuition, as principles of knowledge à priori, namely, space and time. To the consideration of these we shall now proceed.

SECTION I

[18] The tedious doctrine of the four syllogistic figures concerns only categorical syllogisms; and although it is nothing more than an artifice by surreptitiously introducing immediate conclusions (consequentiae immediatae) among the premises of a pure syllogism, to give ism give rise to an appearance of more modes of drawing a conclusion than that in the first figure, the artifice would not have had much success, had not its authors succeeded in bringing categorical judgements into exclusive respect, as those to which all others must be referred — a doctrine, however, which, according to §5, is utterly false. But if I investigate more closely the relation of given cognitions in every judgement, and distinguish it, as belonging to the understanding, from the relation which is produced according to laws of the reproductive imagination (which has only subjective validity), I find that judgement is nothing but the mode of bringing given cognitions under the objective unit of apperception. This is plain from our use of the term of relation is in judgements, in order to distinguish the objective unity of given representations from the subjective unity. For this term indicates the relation of these representations to the original apperception, and also their necessary unity, even although the judgement is empirical, therefore contingent, as in the judgement: “All bodies are heavy.” I do not mean by this, that these representations do necessarily belong to each other in empirical intuition, but that by means of the necessary unity of appreciation they belong to each other in the synthesis of intuitions, that is to say, they belong to each other according to principles of the objective determination of all our representations, in so far as cognition can arise from them, these principles being all deduced from the main principle of the transcendental unity of apperception. In this way alone can there arise from this relation a judgement, that is, a relation which has objective validity, and is perfectly distinct from that relation of the very same representations which has only subjective validity — a relation, to wit, which is produced according to laws of association. According to these laws, I could only say: “When I hold in my hand or carry a body, I feel an impression of weight”; but I could not say: “It, the body, is heavy”; for this is tantamount to saying both these representations are conjoined in the object, that is, without distinction as to the condition of the subject, and do not merely stand together in my perception, however frequently the perceptive act may be repeated. All Sensuous Intuitions are subject to the Categories, as Conditions under which alone the manifold Content of them can be united in one Consciousness §16

The manifold content given in a sensuous intuition comes necessarily under the original synthetical unity of apperception, because thereby alone is the unity of intuition possible (§13). But that act of the understanding, by which the manifold content of given representations (whether intuitions or conceptions) is brought under one apperception, is the logical function of judgements (§15). All the manifold, therefore, in so far as it is given in one empirical intuition, is determined in relation to one of the logical functions of judgement, by means of which it is brought into union in one consciousness. Now the categories are nothing else than these functions of judgement so far as the manifold in a given intuition is determined in relation to them (§9). Consequently, the manifold in a given intuition is necessarily subject to the categories of the understanding.

Observation §17

The manifold in an intuition, which I call mine, is represented by means of the synthesis of the understanding, as belonging to the necessary unity of self-consciousness, and this takes place by means of the category. [19] The category indicates accordingly that the empirical consciousness of a given manifold in an intuition is subject to a pure self-consciousness à priori, in the same manner as an empirical intuition is subject to a pure sensuous intuition, which is also à priori. In the above proposition, then, lies the beginning of a deduction of the pure conceptions of the understanding. Now, as the categories have their origin in the understanding alone, independently of sensibility, I must in my deduction make abstraction of the mode in which the manifold of an empirical intuition is given, in order to fix my attention exclusively on the unity which is brought by the understanding into the intuition by means of the category. In what follows (§22), it will be shown, from the mode in which the empirical intuition is given in the faculty of sensibility, that the unity which belongs to it is no other than that which the category (according to §16) imposes on the manifold in a given intuition, and thus, its à priori validity in regard to all objects of sense being established, the purpose of our deduction will be fully attained. [19] The proof of this rests on the represented unity of intuition, by means of which an object is given, and which always includes in itself a synthesis of the manifold to be intuited, and also the relation of this latter to unity of apperception. But there is one thing in the above demonstration of which I could not make abstraction, namely, that the manifold to be intuited must be given previously to the synthesis of the understanding, and independently of it. How this takes place remains here undetermined. For if I cogitate an understanding which was itself intuitive (as, for example, a divine understanding which should not represent given objects, but by whose representation the objects themselves should be given or produced), the categories would possess no significance in relation to such a faculty of cognition.

They are merely rules for an understanding, whose whole power consists in thought, that is, in the act of submitting the synthesis of the manifold which is presented to it in intuition from a very different quarter, to the unity of apperception; a faculty, therefore, which cognizes nothing per se, but only connects and arranges the material of cognition, the intuition, namely, which must be presented to it by means of the object. But to show reasons for this peculiar character of our understandings, that it produces unity of apperception à priori only by means of categories, and a certain kind and number thereof, is as impossible as to explain why we are endowed with precisely so many functions of judgement and no more, or why time and space are the only forms of our intuition.

In Cognition, its Application to Objects of Experience is the only legitimate use of the Category

§18

To think an object and to cognize an object are by no means the same thing. In cognition there are two elements: firstly, the conception, whereby an object is cogitated (the category); and, secondly, the intuition, whereby the object is given. For supposing that to the conception a corresponding intuition could not be given, it would still be a thought as regards its form, but without any object, and no cognition of anything would be possible by means of it, inasmuch as, so far as I knew, there existed and could exist nothing to which my thought could be applied. Now all intuition possible to us is sensuous; consequently, our thought of an object by means of a pure conception of the understanding, can become cognition for us only in so far as this conception is applied to objects of the senses. Sensuous intuition is either pure intuition (space and time) or empirical intuition — of that which is immediately represented in space and time by means of sensation as real. Through the determination of pure intuition we obtain à priori cognitions of objects, as in mathematics, but only as regards their form as phenomena; whether there can exist things which must be intuited in this form is not thereby established. All mathematical conceptions, therefore, are not per se cognition, except in so far as we presuppose that there exist things which can only be represented conformably to the form of our pure sensuous intuition. But things in space and time are given only in so far as they are perceptions (representations accompanied with sensation), therefore only by empirical representation.

Consequently the pure conceptions of the understanding, even when they are applied to intuitions à priori (as in mathematics), produce cognition only in so far as these (and therefore the conceptions of the understanding by means of them) can be applied to empirical intuitions. Consequently the categories do not, even by means of pure intuition afford us any cognition of things; they can only do so in so far as they can be applied to empirical intuition. That is to say, the categories serve only to render empirical cognition possible. But this is what we call experience. Consequently, in cognition, their application to objects of experience is the only legitimate use of the categories.

§19
The foregoing proposition is of the utmost importance, for it determines the limits of the exercise of the pure conceptions of the understanding in regard to objects, just as transcendental æsthetic determined the limits of the exercise of the pure form of our sensuous intuition. Space and time, as conditions of the possibility of the presentation of objects to us, are valid no further than for objects of sense, consequently, only for experience. Beyond these limits they represent to us nothing, for they belong only to sense, and have no reality apart from it. The pure conceptions of the understanding are free from this limitation, and extend to objects of intuition in general, be the intuition like or unlike to ours, provided only it be sensuous, and not intellectual. But this extension of conceptions beyond the range of our intuition is of no advantage; for they are then mere empty conceptions of objects, as to the possibility or impossibility of the existence of which they furnish us with no means of discovery. They are mere forms of thought, without objective reality, because we have no intuition to which the synthetical unity of apperception, which alone the categories contain, could be applied, for the purpose of determining an object. Our sensuous and empirical intuition can alone give them significance and meaning. If, then, we suppose an object of a non-sensuous intuition to be given we can in that case represent it by all those predicates which are implied in the presupposition that nothing appertaining to sensuous intuition belongs to it; for example, that it is not extended, or in space; that its duration is not time; that in it no change (the effect of the determinations in time) is to be met with, and so on. But it is no proper knowledge if I merely indicate what the intuition of the object is not, without being able to say what is contained in it, for I have not shown the possibility of an object to which my pure conception of understanding could be applicable, because I have not been able to furnish any intuition corresponding to it, but am only able to say that our intuition is not valid for it. But the most important point is this, that to a something of this kind not one category can be found applicable. Take, for example, the conception of substance, that is, something that can exist as subject, but never as mere predicate; in regard to this conception I am quite ignorant whether there can really be anything to correspond to such a determination of thought, if empirical intuition did not afford me the occasion for its application. But of this more in the sequel. Of the Application of the Categories to Objects of the Senses in general

§20

The pure conceptions of the understanding apply to objects of intuition in general, through the understanding alone, whether the intuition be our own or some other, provided only it be sensuous, but are, for this very reason, mere forms of thought, by means of which alone no determined object can be cognized. The synthesis or conjunction of the manifold in these conceptions relates, we have said, only to the unity of apperception, and is for this reason the ground of the possibility of à priori cognition, in so far as this cognition is dependent on the understanding. This synthesis is, therefore, not merely transcendental, but also purely intellectual. But because a certain form of sensuous intuition exists in the mind à priori which rests on the receptivity of the representative faculty (sensibility), the understanding, as a spontaneity, is able to determine the internal sense by means of the diversity of given representations, conformably to the synthetical unity of apperception, and thus to cogitate the synthetical unity of the apperception of the manifold of sensuous intuition à priori, as the condition to which must necessarily be submitted all objects of human intuition. And in this manner the categories as mere forms of thought receive objective reality, that is, application to objects which are given to us in intuition, but that only as phenomena, for it is only of phenomena that we are capable of à priori intuition. This synthesis of the manifold of sensuous intuition, which is possible and necessary à priori, may be called figurative (synthesis speciosa), in contradistinction to that which is cogitated in the mere category in regard to the manifold of an intuition in general, and is called connection or conjunction of the understanding (synthesis intellectualis). Both are transcendental, not merely because they themselves precede à priori all experience, but also because they form the basis for the possibility of other cognition à priori. But the figurative synthesis, when it has relation only to the originally synthetical unity of apperception, that is to the transcendental unity cogitated in the categories, must, to be distinguished from the purely intellectual conjunction, be entitled the transcendental synthesis of imagination. Imagination is the faculty of representing an object even without its presence in intuition. Now, as all our intuition is sensuous, imagination, by reason of the subjective condition under which alone it can give a corresponding intuition to the conceptions of the understanding, belongs to sensibility.

But in so far as the synthesis of the imagination is an act of spontaneity, which is determinative, and not, like sense, merely determinable, and which is consequently able to determine sense à priori, according to its form, conformably to the unity of apperception, in so far is the imagination a faculty of determining sensibility à priori, and its synthesis of intuitions according to the categories must be the transcendental synthesis of the imagination. It is an operation of the understanding on sensibility, and the first application of the understanding to objects of possible intuition, and at the same time the basis for the exercise of the other functions of that faculty. As figurative, it is distinguished from the merely intellectual synthesis, which is produced by the understanding alone, without the aid of imagination. Now, in so far as imagination is spontaneity, I sometimes call it also the productive imagination, and distinguish it from the reproductive, the synthesis of which is subject entirely to empirical laws, those of association, namely, and which, therefore, contributes nothing to the explanation of the possibility of à priori cognition, and for this reason belongs not to transcendental philosophy, but to psychology. We have now arrived at the proper place for explaining the paradox which must have struck every one in our exposition of the internal sense (§6), namely — how this sense represents us to our own consciousness, only as we appear to ourselves, not as we are in ourselves, because, to wit, we intuite ourselves only as we are inwardly affected. Now this appears to be contradictory, inasmuch as we thus stand in a passive relation to ourselves; and therefore in the systems of psychology, the internal sense is commonly held to be one with the faculty of apperception, while we, on the contrary, carefully distinguish them.

That which determines the internal sense is the understanding, and its original power of conjoining the manifold of intuition, that is, of bringing this under an apperception (upon which rests the possibility of the understanding itself). Now, as the human understanding is not in itself a faculty of intuition, and is unable to exercise such a power, in order to conjoin, as it were, the manifold of its own intuition, the synthesis of understanding is, considered per se, nothing but the unity of action, of which, as such, it is self-conscious, even apart from sensibility, by which, moreover, it is able to determine our internal sense in respect of the manifold which may be presented to it according to the form of sensuous intuition. Thus, under the name of a transcendental synthesis of imagination, the understanding exercises an activity upon the passive subject, whose faculty it is; and so we are right in saying that the internal sense is affected thereby. Apperception and its synthetical unity are by no means one and the same with the internal sense. The former, as the source of all our synthetical conjunction, applies, under the name of the categories, to the manifold of intuition in general, prior to all sensuous intuition of objects.

The internal sense, on the contrary, contains merely the form of intuition, but without any synthetical conjunction of the manifold therein, and consequently does not contain any determined intuition, which is possible only through consciousness of the determination of the manifold by the transcendental act of the imagination (synthetical influence of the understanding on the internal sense), which I have named figurative synthesis. This we can indeed always perceive in ourselves. We cannot cogitate a geometrical line without drawing it in thought, nor a circle without describing it, nor represent the three dimensions of space without drawing three lines from the same point perpendicular to one another. We cannot even cogitate time, unless, in drawing a straight line (which is to serve as the external figurative representation of time), we fix our attention on the act of the synthesis of the manifold, whereby we determine successively the internal sense, and thus attend also to the succession of this determination. Motion as an act of the subject (not as a determination of an object), [20] consequently the synthesis of the manifold in space, if we make abstraction of space and attend merely to the act by which we determine the internal sense according to its form, is that which produces the conception of succession. The understanding, therefore, does by no means find in the internal sense any such synthesis of the manifold, but produces it, in that it affects this sense. At the same time, how “I who think” is distinct from the “i” which intuites itself (other modes of intuition being cogitable as at least possible), and yet one and the same with this latter as the same subject; how, therefore, I am able to say: “I, as an intelligence and thinking subject, cognize myself as an object thought, so far as I am, moreover, given to myself in intuition — only, like other phenomena, not as I am in myself, and as considered by the understanding, but merely as I appear” — is a question that has in it neither more nor less difficulty than the question — “How can I be an object to myself?” or this —

“How I can be an object of my own intuition and internal perceptions?” But that such must be the fact, if we admit that space is merely a pure form of the phenomena of external sense, can be clearly proved by the consideration that we cannot represent time, which is not an object of external intuition, in any other way than under the image of a line, which we draw in thought, a mode of representation without which we could not cognize the unity of its dimension, and also that we are necessitated to take our determination of periods of time, or of points of time, for all our internal perceptions from the changes which we perceive in outward things. It follows that we must arrange the determinations of the internal sense, as phenomena in time, exactly in the same manner as we arrange those of the external senses in space. And consequently, if we grant, respecting this latter, that by means of them we know objects only in so far as we are affected externally, we must also confess, with regard to the internal sense, that by means of it we intuite ourselves only as we are internally affected by ourselves; in other words, as regards internal intuition, we cognize our own subject only as phenomenon, and not as it is in itself. [21]

[20] Motion of an object in space does not belong to a pure science, consequently not to geometry; because, that a thing is movable cannot be known à priori, but only from experience. But motion, considered as the description of a space, is a pure act of the successive synthesis of the manifold in external intuition by means of productive imagination, and belongs not only to geometry, but even to transcendental philosophy.

[21] I do not see why so much difficulty should be found in admitting that our internal sense is affected by ourselves. Every act of attention exemplifies it. In such an act the understanding determines the internal sense by the synthetical conjunction which it cogitates, conformably to the internal intuition which corresponds to the manifold in the synthesis of the understanding. How much the mind is usually affected thereby every one will be able to perceive in himself.

§21
On the other hand, in the transcendental synthesis of the manifold content of representations, consequently in the synthetical unity of apperception, I am conscious of myself, not as I appear to myself, nor as I am in myself, but only that “I am.” This representation is a thought, not an intuition. Now, as in order to cognize ourselves, in addition to the act of thinking, which subjects the manifold of every possible intuition to the unity of apperception, there is necessary a determinate mode of intuition, whereby this manifold is given; although my own existence is certainly not mere phenomenon (much less mere illusion), the determination of my existence [22] Can only take place conformably to the form of the internal sense, according to the particular mode in which the manifold which I conjoin is given in internal intuition, and I have therefore no knowledge of myself as I am, but merely as I appear to myself. The consciousness of self is thus very far from a knowledge of self, in which I do not use the categories, whereby I cogitate an object, by means of the conjunction of the manifold in one apperception. In the same way as I require, for the sake of the cognition of an object distinct from myself, not only the thought of an object in general (in the category), but also an intuition by which to determine that general conception, in the same way do I require, in order to the cognition of myself, not only the consciousness of myself or the thought that I think myself, but in addition an intuition of the manifold in myself, by which to determine this thought. It is true that I exist as an intelligence which is conscious only of its faculty of conjunction or synthesis, but subjected in relation to the manifold which this intelligence has to conjoin to a limitative conjunction called the internal sense.

My intelligence (that is, I) can render that conjunction or synthesis perceptible only according to the relations of time, which are quite beyond the proper sphere of the conceptions of the understanding and consequently cognize itself in respect to an intuition (which cannot possibly be intellectual, nor given by the understanding), only as it appears to itself, and not as it would cognize itself, if its intuition were intellectual.

[22] The “I think” expresses the act of determining my own existence. My existence is thus already given by the act of consciousness; but the mode in which I must determine my existence, that is, the mode in which I must place the manifold belonging to my existence, is not thereby given. For this purpose intuition of self is required, and this intuition possesses a form given à priori, namely, time, which is sensuous, and belongs to our receptivity of the determinable. Now, as I do not possess another intuition of self which gives the determining in me (of the spontaneity of which I am conscious), prior to the act of determination, in the same manner as time gives the determinable, it is clear that I am unable to determine my own existence as that of a spontaneous being, but I am only able to represent to myself the spontaneity of my thought, that is, of my determination, and my existence remains ever determinable in a purely sensuous manner, that is to say, like the existence of a phenomenon. But it is because of this spontaneity that I call myself an intelligence. Transcendental Deduction of the universally possible employment in experience of the Pure Conceptions of the Understanding

§22
In the metaphysical deduction, the à priori origin of categories was proved by their complete accordance with the general logical of thought; in the transcendental deduction was exhibited the possibility of the categories as à priori cognitions of objects of an intuition in general (§16 and 17). At present we are about to explain the possibility of cognizing, à priori, by means of the categories, all objects which can possibly be presented to our senses, not, indeed, according to the form of their intuition, but according to the laws of their conjunction or synthesis, and thus, as it were, of prescribing laws to nature and even of rendering nature possible. For if the categories were inadequate to this task, it would not be evident to us why everything that is presented to our senses must be subject to those laws which have an à priori origin in the understanding itself. I premise that by the term synthesis of apprehension I understand the combination of the manifold in an empirical intuition, whereby perception, that is, empirical consciousness of the intuition (as phenomenon), is possible. We have à priori forms of the external and internal sensuous intuition in the representations of space and time, and to these must the synthesis of apprehension of the manifold in a phenomenon be always comformable, because the synthesis itself can only take place according to these forms. But space and time are not merely forms of sensuous intuition, but intuitions themselves (which contain a manifold), and therefore contain à priori the determination of the unity of this manifold. [23] (See the Transcendent Æsthetic.) Therefore is unity of the synthesis of the manifold without or within us, consequently also a conjunction to which all that is to be represented as determined in space or time must correspond, given à priori along with (not in) these intuitions, as the condition of the synthesis of all apprehension of them. But this synthetical unity can be no other than that of the conjunction of the manifold of a given intuition in general, in a primitive act of consciousness, according to the categories, but applied to our sensuous intuition. Consequently all synthesis, whereby alone is even perception possible, is subject to the categories. And, as experience is cognition by means of conjoined perceptions, the categories are conditions of the possibility of experience and are therefore valid à priori for all objects of experience.

[23] Space represented as an object (as geometry really requires it to be) contains more than the mere form of the intuition; namely, a combination of the manifold given according to the form of sensibility into a representation that can be intuited; so that the form of the intuition gives us merely the manifold, but the formal intuition gives unity of representation. In the æsthetic, I regarded this unity as belonging entirely to sensibility, for the purpose of indicating that it antecedes all conceptions, although it presupposes a synthesis which does not belong to sense, through which alone, however, all our conceptions of space and time are possible. For as by means of this unity alone (the understanding determining the sensibility) space and time are given as intuitions, it follows that the unity of this intuition à priori belongs to space and time, and not to the conception of the understanding (§20). When, then, for example, I make the empirical intuition of a house by apprehension of the manifold contained therein into a perception, the necessary unity of space and of my external sensuous intuition lies at the foundation of this act, and I, as it were, draw the form of the house conformably to this synthetical unity of the manifold in space. But this very synthetical unity remains, even when I abstract the form of space, and has its seat in the understanding, and is in fact the category of the synthesis of the homogeneous in an intuition; that is to say, the category of quantity, to which the aforesaid synthesis of apprehension, that is, the perception, must be completely conformable. [24]
[24] In this manner it is proved, that the synthesis of apprehension, which is empirical, must necessarily be conformable to the synthesis of apperception, which is intellectual, and contained à priori in the category. It is one and the same spontaneity which at one time, under the name of imagination, at another under that of understanding, produces conjunction in the manifold of intuition. To take another example, when I perceive the freezing of water, I apprehend two states (fluidity and solidity), which, as such, stand toward each other mutually in a relation of time. But in the time, which I place as an internal intuition, at the foundation of this phenomenon, I represent to myself synthetical unity of the manifold, without which the aforesaid relation could not be given in an intuition as determined (in regard to the succession of time). Now this synthetical unity, as the à priori condition under which I conjoin the manifold of an intuition, is, if I make abstraction of the permanent form of my internal intuition (that is to say, of time), the category of cause, by means of which, when applied to my sensibility, I determine everything that occurs according to relations of time.

Consequently apprehension in such an event, and the event itself, as far as regards the possibility of its perception, stands under the conception of the relation of cause and effect: and so in all other cases. Categories are conceptions which prescribe laws à priori to phenomena, consequently to nature as the complex of all phenomena (natura materialiter spectata). And now the question arises — inasmuch as these categories are not derived from nature, and do not regulate themselves according to her as their model (for in that case they would be empirical) — how it is conceivable that nature must regulate herself according to them, in other words, how the categories can determine à priori the synthesis of the manifold of nature, and yet not derive their origin from her. The following is the solution of this enigma. It is not in the least more difficult to conceive how the laws of the phenomena of nature must harmonize with the understanding and with its à priori form — that is, its faculty of conjoining the manifold — than it is to understand how the phenomena themselves must correspond with the à priori form of our sensuous intuition. For laws do not exist in the phenomena any more than the phenomena exist as things in themselves. Laws do not exist except by relation to the subject in which the phenomena inhere, in so far as it possesses understanding, just as phenomena have no existence except by relation to the same existing subject in so far as it has senses. To things as things in themselves, conformability to law must necessarily belong independently of an understanding to cognize them.

But phenomena are only representations of things which are utterly unknown in respect to what they are in themselves. But as mere representations, they stand under no law of conjunction except that which the conjoining faculty prescribes. Now that which conjoins the manifold of sensuous intuition is imagination, a mental act to which understanding contributes unity of intellectual synthesis, and sensibility, manifoldness of apprehension. Now as all possible perception depends on the synthesis of apprehension, and this empirical synthesis itself on the transcendental, consequently on the categories, it is evident that all possible perceptions, and therefore everything that can attain to empirical consciousness, that is, all phenomena of nature, must, as regards their conjunction, be subject to the categories. And nature (considered merely as nature in general) is dependent on them, as the original ground of her necessary conformability to law (as natura formaliter spectata).

But the pure faculty (of the understanding) of prescribing laws à priori to phenomena by means of mere categories, is not competent to enounce other or more laws than those on which a nature in general, as a conformability to law of phenomena of space and time, depends. Particular laws, inasmuch as they concern empirically determined phenomena, cannot be entirely deduced from pure laws, although they all stand under them. Experience must be superadded in order to know these particular laws; but in regard to experience in general, and everything that can be cognized as an object thereof, these à priori laws are our only rule and guide. Result of this Deduction of the Conceptions of the Understanding

§23

We cannot think any object except by means of the categories; we cannot cognize any thought except by means of intuitions corresponding to these conceptions. Now all our intuitions are sensuous, and our cognition, in so far as the object of it is given, is empirical. But empirical cognition is experience; consequently no à priori cognition is possible for us, except of objects of possible experience. [25]

Lest my readers should stumble at this assertion, and the conclusions that may be too rashly drawn from it, I must remind them that the categories in the act of thought are by no means limited by the conditions of our sensuous intuition, but have an unbounded sphere of action. It is only the cognition of the object of thought, the determining of the object, which requires intuition. In the absence of intuition, our thought of an object may still have true and useful consequences in regard to the exercise of reason by the subject. But as this exercise of reason is not always directed on the determination of the object, in other words, on cognition thereof, but also on the determination of the subject and its volition, I do not intend to treat of it in this place. But this cognition, which is limited to objects of experience, is not for that reason derived entirely, from, experience, but — and this is asserted of the pure intuitions and the pure conceptions of the understanding — there are, unquestionably, elements of cognition, which exist in the mind à priori. Now there are only two ways in which a necessary harmony of experience with the conceptions of its objects can be cogitated.

Either experience makes these conceptions possible, or the conceptions make experience possible. The former of these statements will not hold good with respect to the categories (nor in regard to pure sensuous intuition), for they are à priori conceptions, and therefore independent of experience. The assertion of an empirical origin would attribute to them a sort of generatio aequivoca. Consequently, nothing remains but to adopt the second alternative (which presents us with a system, as it were, of the epigenesis of pure reason), namely, that on the part of the understanding the categories do contain the grounds of the possibility of all experience. But with respect to the questions how they make experience possible, and what are the principles of the possibility thereof with which they present us in their application to phenomena, the following section on the transcendental exercise of the faculty of judgement will inform the reader. It is quite possible that someone may propose a species of preformation-system of pure reason — a middle way between the two — to wit, that the categories are neither innate and first à priori principles of cognition, nor derived from experience, but are merely subjective aptitudes for thought implanted in us contemporaneously with our existence, which were so ordered and disposed by our Creator, that their exercise perfectly harmonizes with the laws of nature which regulate experience.

Now, not to mention that with such an hypothesis it is impossible to say at what point we must stop in the employment of predetermined aptitudes, the fact that the categories would in this case entirely lose that character of necessity which is essentially involved in the very conception of them, is a conclusive objection to it. The conception of cause, for example, which expresses the necessity of an effect under a presupposed condition, would be false, if it rested only upon such an arbitrary subjective necessity of uniting certain empirical representations according to such a rule of relation. I could not then say — “The effect is connected with its cause in the object (that is, necessarily),” but only, “I am so constituted that I can think this representation as so connected, and not otherwise.” Now this is just what the sceptic wants. For in this case, all our knowledge, depending on the supposed objective validity of our judgement, is nothing but mere illusion; nor would there be wanting people who would deny any such subjective necessity in respect to themselves, though they must feel it. At all events, we could not dispute with any one on that which merely depends on the manner in which his subject is organized.

Short view of the above Deduction. The foregoing deduction is an exposition of the pure conceptions of the understanding (and with them of all theoretical à priori cognition), as principles of the possibility of experience, but of experience as the determination of all phenomena in space and time in general — of experience, finally, from the principle of the original synthetical unity of apperception, as the form of the understanding in relation to time and space as original forms of sensibility. I consider the division by paragraphs to be necessary only up to this point, because we had to treat of the elementary conceptions. As we now proceed to the exposition of the employment of these, I shall not designate the chapters in this manner any further. BOOK II. Analytic of Principles

General logic is constructed upon a plan which coincides exactly with the division of the higher faculties of cognition. These are, understanding, judgement, and reason. This science, accordingly, treats in its analytic of conceptions, judgements, and conclusions in exact correspondence with the functions and order of those mental powers which we include generally under the generic denomination of understanding. As this merely formal logic makes abstraction of all content of cognition, whether pure or empirical, and occupies itself with the mere form of thought (discursive cognition), it must contain in its analytic a canon for reason. For the form of reason has its law, which, without taking into consideration the particular nature of the cognition about which it is employed, can be discovered à priori, by the simple analysis of the action of reason into its momenta. Transcendental logic, limited as it is to a determinate content, that of pure à priori cognitions, to wit, cannot imitate general logic in this division. For it is evident that the transcendental employment of reason is not objectively valid, and therefore does not belong to the logic of truth (that is, to analytic), but as a logic of illusion, occupies a particular department in the scholastic system under the name of transcendental dialectic. Understanding and judgement accordingly possess in transcendental logic a canon of objectively valid, and therefore true exercise, and are comprehended in the analytical department of that logic. But reason, in her endeavours to arrive by à priori means at some true statement concerning objects and to extend cognition beyond the bounds of possible experience, is altogether dialectic, and her illusory assertions cannot be constructed into a canon such as an analytic ought to contain. Accordingly, the analytic of principles will be merely a canon for the faculty of judgement, for the instruction of this faculty in its application to phenomena of the pure conceptions of the understanding, which contain the necessary condition for the establishment of à priori laws. On this account, although the subject of the following chapters is the especial principles of understanding, I shall make use of the term Doctrine of the faculty of judgement, in order to define more particularly my present purpose.

INTRODUCTION

Of the Transcendental Faculty of judgement in General
If understanding in general be defined as the faculty of laws or rules, the faculty of judgement may be termed the faculty of subsumption under these rules; that is, of distinguishing whether this or that does or does not stand under a given rule (casus datae legis). General logic contains no directions or precepts for the faculty of judgement, nor can it contain any such. For as it makes abstraction of all content of cognition, no duty is left for it, except that of exposing analytically the mere form of cognition in conceptions, judgements, and conclusions, and of thereby establishing formal rules for all exercise of the understanding. Now if this logic wished to give some general direction how we should subsume under these rules, that is, how we should distinguish whether this or that did or did not stand under them, this again could not be done otherwise than by means of a rule. But this rule, precisely because it is a rule, requires for itself direction from the faculty of judgement. Thus, it is evident that the understanding is capable of being instructed by rules, but that the judgement is a peculiar talent, which does not, and cannot require tuition, but only exercise. This faculty is therefore the specific quality of the so-called mother wit, the want of which no scholastic discipline can compensate. For although education may furnish, and, as it were, engraft upon a limited understanding rules borrowed from other minds, yet the power of employing these rules correctly must belong to the pupil himself; and no rule which we can prescribe to him with this purpose is, in the absence or deficiency of this gift of nature, secure from misuse. [26] A physician therefore, a judge or a statesman, may have in his head many admirable pathological, juridical, or political rules, in a degree that may enable him to be a profound teacher in his particular science, and yet in the application of these rules he may very possibly blunder — either because he is wanting in natural judgement (though not in understanding) and, whilst he can comprehend the general in abstracto, cannot distinguish whether a particular case in concreto ought to rank under the former; or because his faculty of judgement has not been sufficiently exercised by examples and real practice. Indeed, the grand and only use of examples, is to sharpen the judgement. For as regards the correctness and precision of the insight of the understanding, examples are commonly injurious rather than otherwise, because, as casus in terminis they seldom adequately fulfil the conditions of the rule. Besides, they often weaken the power of our understanding to apprehend rules or laws in their universality, independently of particular circumstances of experience; and hence, accustom us to employ them more as formulae than as principles. Examples are thus the go-cart of the judgement, which he who is naturally deficient in that faculty cannot afford to dispense with.

Deficiency in judgement is properly that which is called stupidity; and for such a failing we know no remedy. A dull or narrow-minded person, to whom nothing is wanting but a proper degree of understanding, may be improved by tuition, even so far as to deserve the epithet of learned. But as such persons frequently labour under a deficiency in the faculty of judgement, it is not uncommon to find men extremely learned who in the application of their science betray a lamentable degree this irremediable want. But although general logic cannot give directions to the faculty of judgement, the case is very different as regards transcendental logic, insomuch that it appears to be the especial duty of the latter to secure and direct, by means of determinate rules, the faculty of judgement in the employment of the pure understanding. For, as a doctrine, that is, as an endeavour to enlarge the sphere of the understanding in regard to pure à priori cognitions, philosophy is worse than useless, since from all the attempts hitherto made, little or no ground has been gained. But, as a critique, in order to guard against the mistakes of the faculty of judgement (lapsus judicii) in the employment of the few pure conceptions of the understanding which we possess, although its use is in this case purely negative, philosophy is called upon to apply all its acuteness and penetration. But transcendental philosophy has this peculiarity, that besides indicating the rule, or rather the general condition for rules, which is given in the pure conception of the understanding, it can, at the same time, indicate à priori the case to which the rule must be applied.

The cause of the superiority which, in this respect, transcendental philosophy possesses above all other sciences except mathematics, lies in this: it treats of conceptions which must relate à priori to their objects, whose objective validity consequently cannot be demonstrated à posteriori, and is, at the same time, under the obligation of presenting in general but sufficient tests, the conditions under which objects can be given in harmony with those conceptions; otherwise they would be mere logical forms, without content, and not pure conceptions of the understanding. Our transcendental doctrine of the faculty of judgement will contain two chapters. The first will treat of the sensuous condition under which alone pure conceptions of the understanding can be employed — that is, of the schematism of the pure understanding. The second will treat of those synthetical judgements which are derived à priori from pure conceptions of the understanding under those conditions, and which lie à priori at the foundation of all other cognitions, that is to say, it will treat of the principles of the pure understanding.

TRANSCENDENTAL DOCTRINE OF THE FACULTY OF JUDGEMENT OR, ANALYTIC OF PRINCIPLES

Chapter I

Of the Schematism at of the Pure Conceptions of the Understanding
In all subsumptions of an object under a conception, the representation of the object must be homogeneous with the conception; in other words, the conception must contain that which is represented in the object to be subsumed under it. For this is the meaning of the expression: “An object is contained under a conception.” Thus the empirical conception of a plate is homogeneous with the pure geometrical conception of a circle, inasmuch as the roundness which is cogitated in the former is intuited in the latter. But pure conceptions of the understanding, when compared with empirical intuitions, or even with sensuous intuitions in general, are quite heterogeneous, and never can be discovered in any intuition. How then is the subsumption of the latter under the former, and consequently the application of the categories to phenomena, possible? — For it is impossible to say, for example: “Causality can be intuited through the senses and is contained in the phenomenon.” — This natural and important question forms the real cause of the necessity of a transcendental doctrine of the faculty of judgement, with the purpose, to wit, of showing how pure conceptions of the understanding can be applied to phenomena. In all other sciences, where the conceptions by which the object is thought in the general are not so different and heterogeneous from those which represent the object in concreto — as it is given, it is quite unnecessary to institute any special inquiries concerning the application of the former to the latter. Now it is quite clear that there must be some third thing, which on the one side is homogeneous with the category, and with the phenomenon on the other, and so makes the application of the former to the latter possible. This mediating representation must be pure (without any empirical content), and yet must on the one side be intellectual, on the other sensuous. Such a representation is the transcendental schema.

The conception of the understanding contains pure synthetical unity of the manifold in general. Time, as the formal condition of the manifold of the internal sense, consequently of the conjunction of all representations, contains à priori a manifold in the pure intuition. Now a transcendental determination of time is so far homogeneous with the category, which constitutes the unity thereof, that it is universal and rests upon a rule à priori. On the other hand, it is so far homogeneous with the phenomenon, inasmuch as time is contained in every empirical representation of the manifold. Thus an application of the category to phenomena becomes possible, by means of the transcendental determination of time, which, as the schema of the conceptions of the understanding, mediates the subsumption of the latter under the former. After what has been proved in our deduction of the categories, no one, it is to be hoped, can hesitate as to the proper decision of the question, whether the employment of these pure conceptions of the understanding ought to be merely empirical or also transcendental; in other words, whether the categories, as conditions of a possible experience, relate à priori solely to phenomena, or whether, as conditions of the possibility of things in general, their application can be extended to objects as things in themselves.

For we have there seen that conceptions are quite impossible, and utterly without signification, unless either to them, or at least to the elements of which they consist, an object be given; and that, consequently, they cannot possibly apply to objects as things in themselves without regard to the question whether and how these may be given to us; and, further, that the only manner in which objects can be given to us is by means of the modification of our sensibility; and, finally, that pure à priori conceptions, in addition to the function of the understanding in the category, must contain à priori formal conditions of sensibility (of the internal sense, namely), which again contain the general condition under which alone the category can be applied to any object. This formal and pure condition of sensibility, to which the conception of the understanding is restricted in its employment, we shall name the schema of the conception of the understanding, and the procedure of the understanding with these schemata we shall call the schematism of the pure understanding.

The schema is, in itself, always a mere product of the imagination. But, as the synthesis of imagination has for its aim no single intuition, but merely unity in the determination of sensibility, the schema is clearly distinguishable from the image. Thus, if I place five points one after another… this is an image of the number five. On the other hand, if I only think a number in general, which may be either five or a hundred, this thought is rather the representation of a method of representing in an image a sum (e.g., a thousand) in conformity with a conception, than the image itself, an image which I should find some little difficulty in reviewing, and comparing with the conception. Now this representation of a general procedure of the imagination to present its image to a conception, I call the schema of this conception. In truth, it is not images of objects, but schemata, which lie at the foundation of our pure sensuous conceptions. No image could ever be adequate to our conception of a triangle in general. For the generalness of the conception it never could attain to, as this includes under itself all triangles, whether right-angled, acute-angled, etc., whilst the image would always be limited to a single part of this sphere.

The schema of the triangle can exist nowhere else than in thought, and it indicates a rule of the synthesis of the imagination in regard to pure figures in space. Still less is an object of experience, or an image of the object, ever to the empirical conception. On the contrary, the conception always relates immediately to the schema of the imagination, as a rule for the determination of our intuition, in conformity with a certain general conception. The conception of a dog indicates a rule, according to which my imagination can delineate the figure of a four-footed animal in general, without being limited to any particular individual form which experience presents to me, or indeed to any possible image that I can represent to myself in concreto. This schematism of our understanding in regard to phenomena and their mere form, is an art, hidden in the depths of the human soul, whose true modes of action we shall only with difficulty discover and unveil. Thus much only can we say: “The image is a product of the empirical faculty of the productive imagination — the schema of sensuous conceptions (of figures in space, for example) is a product, and, as it were, a monogram of the pure imagination à priori, whereby and according to which images first become possible, which, however, can be connected with the conception only mediately by means of the schema which they indicate, and are in themselves never fully adequate to it.”

On the other hand, the schema of a pure conception of the understanding is something that cannot be reduced into any image — it is nothing else than the pure synthesis expressed by the category, conformably, to a rule of unity according to conceptions. It is a transcendental product of the imagination, a product which concerns the determination of the internal sense, according to conditions of its form (time) in respect to all representations, in so far as these representations must be conjoined à priori in one conception, conformably to the unity of apperception. Without entering upon a dry and tedious analysis of the essential requisites of transcendental schemata of the pure conceptions of the understanding, we shall rather proceed at once to give an explanation of them according to the order of the categories, and in connection therewith. For the external sense the pure image of all quantities (quantorum) is space; the pure image of all objects of sense in general, is time. But the pure schema of quantity (quantitatis) as a conception of the understanding, is number, a representation which comprehends the successive addition of one to one (homogeneous quantities). Thus, number is nothing else than the unity of the synthesis of the manifold in a homogeneous intuition, by means of my generating time itself in my apprehension of the intuition. Reality, in the pure conception of the understanding, is that which corresponds to a sensation in general; that, consequently, the conception of which indicates a being (in time). Negation is that the conception of which represents a not-being (in time). The opposition of these two consists therefore in the difference of one and the same time, as a time filled or a time empty.

Now as time is only the form of intuition, consequently of objects as phenomena, that which in objects corresponds to sensation is the transcendental matter of all objects as things in themselves (Sachheit, reality). Now every sensation has a degree or quantity by which it can fill time, that is to say, the internal sense in respect of the representation of an object, more or less, until it vanishes into nothing (= 0 = negatio). Thus there is a relation and connection between reality and negation, or rather a transition from the former to the latter, which makes every reality representable to us as a quantum; and the schema of a reality as the quantity of something in so far as it fills time, is exactly this continuous and uniform generation of the reality in time, as we descend in time from the sensation which has a certain degree, down to the vanishing thereof, or gradually ascend from negation to the quantity thereof. The schema of substance is the permanence of the real in time; that is, the representation of it as a substratum of the empirical determination of time; a substratum which therefore remains, whilst all else changes. (Time passes not, but in it passes the existence of the changeable. To time, therefore, which is itself unchangeable and permanent, corresponds that which in the phenomenon is unchangeable in existence, that is, substance, and it is only by it that the succession and coexistence of phenomena can be determined in regard to time.)

The schema of cause and of the causality of a thing is the real which, when posited, is always followed by something else. It consists, therefore, in the succession of the manifold, in so far as that succession is subjected to a rule. The schema of community (reciprocity of action and reaction), or the reciprocal causality of substances in respect of their accidents, is the coexistence of the determinations of the one with those of the other, according to a general rule. The schema of possibility is the accordance of the synthesis of different representations with the conditions of time in general (as, for example, opposites cannot exist together at the same time in the same thing, but only after each other), and is therefore the determination of the representation of a thing at any time. The schema of reality is existence in a determined time.

The schema of necessity is the existence of an object in all time. It is clear, from all this, that the schema of the category of quantity contains and represents the generation (synthesis) of time itself, in the successive apprehension of an object; the schema of quality the synthesis of sensation with the representation of time, or the filling up of time; the schema of relation the relation of perceptions to each other in all time (that is, according to a rule of the determination of time): and finally, the schema of modality and its categories, time itself, as the correlative of the determination of an object — whether it does belong to time, and how. The schemata, therefore, are nothing but à priori determinations of time according to rules, and these, in regard to all possible objects, following the arrangement of the categories, relate to the series in time, the content in time, the order in time, and finally, to the complex or totality in time. Hence it is apparent that the schematism of the understanding, by means of the transcendental synthesis of the imagination, amounts to nothing else than the unity of the manifold of intuition in the internal sense, and thus indirectly to the unity of apperception, as a function corresponding to the internal sense (a receptivity). Thus, the schemata of the pure conceptions of the understanding are the true and only conditions whereby our understanding receives an application to objects, and consequently significance.

Finally, therefore, the categories are only capable of empirical use, inasmuch as they serve merely to subject phenomena to the universal rules of synthesis, by means of an à priori necessary unity (on account of the necessary union of all consciousness in one original apperception); and so to render them susceptible of a complete connection in one experience. But within this whole of possible experience lie all our cognitions, and in the universal relation to this experience consists transcendental truth, which antecedes all empirical truth, and renders the latter possible. It is, however, evident at first sight, that although the schemata of sensibility are the sole agents in realizing the categories, they do, nevertheless, also restrict them, that is, they limit the categories by conditions which lie beyond the sphere of understanding — namely, in sensibility. Hence the schema is properly only the phenomenon, or the sensuous conception of an object in harmony with the category. (Numerus est quantitas phaenomenon — sensatio realitas phaenomenon; constans et perdurabile rerum substantia phaenomenon — aeternitas, necessitas, phaenomena, etc.)

Now, if we remove a restrictive condition, we thereby amplify, it appears, the formerly limited conception. In this way, the categories in their pure signification, free from all conditions of sensibility, ought to be valid of things as they are, and not, as the schemata represent them, merely as they appear; and consequently the categories must have a significance far more extended, and wholly independent of all schemata. In truth, there does always remain to the pure conceptions of the understanding, after abstracting every sensuous condition, a value and significance, which is, however, merely logical. But in this case, no object is given them, and therefore they have no meaning sufficient to afford us a conception of an object. The notion of substance, for example, if we leave out the sensuous determination of permanence, would mean nothing more than a something which can be cogitated as subject, without the possibility of becoming a predicate to anything else. Of this representation I can make nothing, inasmuch as it does not indicate to me what determinations the thing possesses which must thus be valid as premier subject. Consequently, the categories, without schemata are merely functions of the understanding for the production of conceptions, but do not represent any object. This significance they derive from sensibility, which at the same time realizes the understanding and restricts it. Chapter II. System of all Principles of the Pure Understanding

In the foregoing chapter we have merely considered the general conditions under which alone the transcendental faculty of judgement is justified in using the pure conceptions of the understanding for synthetical judgements. Our duty at present is to exhibit in systematic connection those judgements which the understanding really produces à priori. For this purpose, our table of the categories will certainly afford us the natural and safe guidance. For it is precisely the categories whose application to possible experience must constitute all pure à priori cognition of the understanding; and the relation of which to sensibility will, on that very account, present us with a complete and systematic catalogue of all the transcendental principles of the use of the understanding. Principles à priori are so called, not merely because they contain in themselves the grounds of other judgements, but also because they themselves are not grounded in higher and more general cognitions.

This peculiarity, however, does not raise them altogether above the need of a proof. For although there could be found no higher cognition, and therefore no objective proof, and although such a principle rather serves as the foundation for all cognition of the object, this by no means hinders us from drawing a proof from the subjective sources of the possibility of the cognition of an object. Such a proof is necessary, moreover, because without it the principle might be liable to the imputation of being a mere gratuitous assertion. In the second place, we shall limit our investigations to those principles which relate to the categories. For as to the principles of transcendental æsthetic, according to which space and time are the conditions of the possibility of things as phenomena, as also the restriction of these principles, namely, that they cannot be applied to objects as things in themselves — these, of course, do not fall within the scope of our present inquiry. In like manner, the principles of mathematical science form no part of this system, because they are all drawn from intuition, and not from the pure conception of the understanding. The possibility of these principles, however, will necessarily be considered here, inasmuch as they are synthetical judgements à priori, not indeed for the purpose of proving their accuracy and apodeictic certainty, which is unnecessary, but merely to render conceivable and deduce the possibility of such evident à priori cognitions. But we shall have also to speak of the principle of analytical judgements, in opposition to synthetical judgements, which is the proper subject of our inquiries, because this very opposition will free the theory of the latter from all ambiguity, and place it clearly before our eyes in its true nature.

SYSTEM OF THE PRINCIPLES OF THE PURE UNDERSTANDING

Section I

Of the Supreme Principle of all Analytical Judgements

Whatever may be the content of our cognition, and in whatever manner our cognition may be related to its object, the universal, although only negative conditions of all our judgements is that they do not contradict themselves; otherwise these judgements are in themselves (even without respect to the object) nothing. But although there may exist no contradiction in our judgement, it may nevertheless connect conceptions in such a manner that they do not correspond to the object, or without any grounds either à priori or à posteriori for arriving at such a judgement, and thus, without being self-contradictory, a judgement may nevertheless be either false or groundless. Now, the proposition: “No subject can have a predicate that contradicts it,” is called the principle of contradiction, and is a universal but purely negative criterion of all truth. But it belongs to logic alone, because it is valid of cognitions, merely as cognitions and without respect to their content, and declares that the contradiction entirely nullifies them. We can also, however, make a positive use of this principle, that is, not merely to banish falsehood and error (in so far as it rests upon contradiction), but also for the cognition of truth. For if the judgement is analytical, be it affirmative or negative, its truth must always be recognizable by means of the principle of contradiction. For the contrary of that which lies and is cogitated as conception in the cognition of the object will be always properly negatived, but the conception itself must always be affirmed of the object, inasmuch as the contrary thereof would be in contradiction to the object.

We must therefore hold the principle of contradiction to be the universal and fully sufficient Principle of all analytical cognition. But as a sufficient criterion of truth, it has no further utility or authority. For the fact that no cognition can be at variance with this principle without nullifying itself, constitutes this principle the sine qua non, but not the determining ground of the truth of our cognition. As our business at present is properly with the synthetical part of our knowledge only, we shall always be on our guard not to transgress this inviolable principle; but at the same time not to expect from it any direct assistance in the establishment of the truth of any synthetical proposition. There exists, however, a formula of this celebrated principle — a principle merely formal and entirely without content — which contains a synthesis that has been inadvertently and quite unnecessarily mixed up with it. It is this: “It is impossible for a thing to be and not to be at the same time.” Not to mention the superfluousness of the addition of the word impossible to indicate the apodeictic certainty, which ought to be self-evident from the proposition itself, the proposition is affected by the condition of time, and as it were says: “A thing = A, which is something = B, cannot at the same time be non-B.” But both, B as well as non-B, may quite well exist in succession. For example, a man who is young cannot at the same time be old; but the same man can very well be at one time young, and at another not young, that is, old. Now the principle of contradiction as a merely logical proposition must not by any means limit its application merely to relations of time, and consequently a formula like the preceding is quite foreign to its true purpose.

The misunderstanding arises in this way. We first of all separate a predicate of a thing from the conception of the thing, and afterwards connect with this predicate its opposite, and hence do not establish any contradiction with the subject, but only with its predicate, which has been conjoined with the subject synthetically — a contradiction, moreover, which obtains only when the first and second predicate are affirmed in the same time. If I say: “A man who is ignorant is not learned,” the condition “at the same time” must be added, for he who is at one time ignorant, may at another be learned. But if I say: “No ignorant man is a learned man,” the proposition is analytical, because the characteristic ignorance is now a constituent part of the conception of the subject; and in this case the negative proposition is evident immediately from the proposition of contradiction, without the necessity of adding the condition “the same time.” This is the reason why I have altered the formula of this principle — an alteration which shows very clearly the nature of an analytical proposition.

Section II

Of the Supreme Principle of all Synthetical Judgements

The explanation of the possibility of synthetical judgements is a task with which general logic has nothing to do; indeed she needs not even be acquainted with its name. But in transcendental logic it is the most important matter to be dealt with — indeed the only one, if the question is of the possibility of synthetical judgements à priori, the conditions and extent of their validity. For when this question is fully decided, it can reach its aim with perfect ease, the determination, to wit, of the extent and limits of the pure understanding. In an analytical judgement I do not go beyond the given conception, in order to arrive at some decision respecting it. If the judgement is affirmative, I predicate of the conception only that which was already cogitated in it; if negative, I merely exclude from the conception its contrary. But in synthetical judgements, I must go beyond the given conception, in order to cogitate, in relation with it, something quite different from that which was cogitated in it, a relation which is consequently never one either of identity or contradiction, and by means of which the truth or error of the judgement cannot be discerned merely from the judgement itself. Granted, then, that we must go out beyond a given conception, in order to compare it synthetically with another, a third thing is necessary, in which alone the synthesis of two conceptions can originate. Now what is this tertium quid that is to be the medium of all synthetical judgements?

It is only a complex in which all our representations are contained, the internal sense to wit, and its form à priori, time. The synthesis of our representations rests upon the imagination; their synthetical unity (which is requisite to a judgement), upon the unity of apperception. In this, therefore, is to be sought the possibility of synthetical judgements, and as all three contain the sources of à priori representations, the possibility of pure synthetical judgements also; nay, they are necessary upon these grounds, if we are to possess a knowledge of objects, which rests solely upon the synthesis of representations. If a cognition is to have objective reality, that is, to relate to an object, and possess sense and meaning in respect to it, it is necessary that the object be given in some way or another. Without this, our conceptions are empty, and we may indeed have thought by means of them, but by such thinking we have not, in fact, cognized anything, we have merely played with representation. To give an object, if this expression be understood in the sense of “to present” the object, not mediately but immediately in intuition, means nothing else than to apply the representation of it to experience, be that experience real or only possible. Space and time themselves, pure as these conceptions are from all that is empirical, and certain as it is that they are represented fully à priori in the mind, would be completely without objective validity, and without sense and significance, if their necessary use in the objects of experience were not shown.

Nay, the representation of them is a mere schema, that always relates to the reproductive imagination, which calls up the objects of experience, without which they have no meaning. And so it is with all conceptions without distinction. The possibility of experience is, then, that which gives objective reality to all our à priori cognitions. Now experience depends upon the synthetical unity of phenomena, that is, upon a synthesis according to conceptions of the object of phenomena in general, a synthesis without which experience never could become knowledge, but would be merely a rhapsody of perceptions, never fitting together into any connected text, according to rules of a thoroughly united (possible) consciousness, and therefore never subjected to the transcendental and necessary unity of apperception. Experience has therefore for a foundation, à priori principles of its form, that is to say, general rules of unity in the synthesis of phenomena, the objective reality of which rules, as necessary conditions even of the possibility of experience can which rules, as necessary conditions — even of the possibility of experience — can always be shown in experience. But apart from this relation, à priori synthetical propositions are absolutely impossible, because they have no third term, that is, no pure object, in which the synthetical unity can exhibit the objective reality of its conceptions. Although, then, respecting space, or the forms which productive imagination describes therein, we do cognize much à priori in synthetical judgements, and are really in no need of experience for this purpose, such knowledge would nevertheless amount to nothing but a busy trifling with a mere chimera, were not space to be considered as the condition of the phenomena which constitute the material of external experience.

Hence those pure synthetical judgements do relate, though but mediately, to possible experience, or rather to the possibility of experience, and upon that alone is founded the objective validity of their synthesis. While then, on the one hand, experience, as empirical synthesis, is the only possible mode of cognition which gives reality to all other synthesis; on the other hand, this latter synthesis, as cognition à priori, possesses truth, that is, accordance with its object, only in so far as it contains nothing more than what is necessary to the synthetical unity of experience. Accordingly, the supreme principle of all synthetical judgements is: “Every object is subject to the necessary conditions of the synthetical unity of the manifold of intuition in a possible experience.”

À priori synthetical judgements are possible when we apply the formal conditions of the à priori intuition, the synthesis of the imagination, and the necessary unity of that synthesis in a transcendental apperception, to a possible cognition of experience, and say: “The conditions of the possibility of experience in general are at the same time conditions of the possibility of the objects of experience, and have, for that reason, objective validity in an à priori synthetical judgement.”

Section III

Systematic Representation of all Synthetical Principles of the Pure Understanding

That principles exist at all is to be ascribed solely to the pure understanding, which is not only the faculty of rules in regard to that which happens, but is even the source of principles according to which everything that can be presented to us as an object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. Even the laws of nature, if they are contemplated as principles of the empirical use of the understanding, possess also a characteristic of necessity, and we may therefore at least expect them to be determined upon grounds which are valid à priori and antecedent to all experience. But all laws of nature, without distinction, are subject to higher principles of the understanding, inasmuch as the former are merely applications of the latter to particular cases of experience. These higher principles alone therefore give the conception, which contains the necessary condition, and, as it were, the exponent of a rule; experience, on the other hand, gives the case which comes under the rule. There is no danger of our mistaking merely empirical principles for principles of the pure understanding, or conversely; for the character of necessity, according to conceptions which distinguish the latter, and the absence of this in every empirical proposition, how extensively valid soever it may be, is a perfect safeguard against confounding them. There are, however, pure principles à priori, which nevertheless I should not ascribe to the pure understanding — for this reason, that they are not derived from pure conceptions, but (although by the mediation of the understanding) from pure intuitions. But understanding is the faculty of conceptions. Such principles mathematical science possesses, but their application to experience, consequently their objective validity, nay the possibility of such à priori synthetical cognitions (the deduction thereof) rests entirely upon the pure understanding.

On this account, I shall not reckon among my principles those of mathematics; though I shall include those upon the possibility and objective validity à priori, of principles of the mathematical science, which, consequently, are to be looked upon as the principle of these, and which proceed from conceptions to intuition, and not from intuition to conceptions. In the application of the pure conceptions of the understanding to possible experience, the employment of their synthesis is either mathematical or dynamical, for it is directed partly on the intuition alone, partly on the existence of a phenomenon. But the à priori conditions of intuition are in relation to a possible experience absolutely necessary, those of the existence of objects of a possible empirical intuition are in themselves contingent. Hence the principles of the mathematical use of the categories will possess a character of absolute necessity, that is, will be apodeictic; those, on the other hand, of the dynamical use, the character of an à priori necessity indeed, but only under the condition of empirical thought in an experience, therefore only mediately and indirectly. Consequently they will not possess that immediate evidence which is peculiar to the former, although their application to experience does not, for that reason, lose its truth and certitude. But of this point we shall be better able to judge at the conclusion of this system of principles. The table of the categories is naturally our guide to the table of principles, because these are nothing else than rules for the objective employment of the former. Accordingly, all principles of the pure understanding are: 1 Axioms of Intuition 2 3 Anticipations Analogies of Perception of Experience 4 Postulates of Empirical Thought in general

These appellations I have chosen advisedly, in order that we might not lose sight of the distinctions in respect of the evidence and the employment of these principles. It will, however, soon appear that — a fact which concerns both the evidence of these principles, and the à priori determination of phenomena — according to the categories of quantity and quality (if we attend merely to the form of these), the principles of these categories are distinguishable from those of the two others, in as much as the former are possessed of an intuitive, but the latter of a merely discursive, though in both instances a complete, certitude. I shall therefore call the former mathematical, and the latter dynamical principles. It must be observed, however, that by these terms I mean just as little in the one case the principles of mathematics as those of general (physical) dynamics in the other. I have here in view merely the principles of the pure understanding, in their application to the internal sense (without distinction of the representations given therein), by means of which the sciences of mathematics and dynamics become possible. Accordingly, I have named these principles rather with reference to their application than their content; and I shall now proceed to consider them in the order in which they stand in the table.

All combination (conjunctio) is either composition (compositio) or connection (nexus). The former is the synthesis of a manifold, the parts of which do not necessarily belong to each other. For example, the two triangles into which a square is divided by a diagonal, do not necessarily belong to each other, and of this kind is the synthesis of the homogeneous in everything that can be mathematically considered. This synthesis can be divided into those of aggregation and coalition, the former of which is applied to extensive, the latter to intensive quantities. The second sort of combination (nexus) is the synthesis of a manifold, in so far as its parts do belong necessarily to each other; for example, the accident to a substance, or the effect to the cause. Consequently it is a synthesis of that which though heterogeneous, is represented as connected à priori. This combination — not an arbitrary one — I entitle dynamical because it concerns the connection of the existence of the manifold. This, again, may be divided into the physical synthesis, of the phenomena divided among each other, and the metaphysical synthesis, or the connection of phenomena à priori in the faculty of cognition.

1. AXIOMS OF INTUITION

The principle of these is: All Intuitions are Extensive Quantities

PROOF. All phenomena contain, as regards their form, an intuition in space and time, which lies à priori at the foundation of all without exception. Phenomena, therefore, cannot be apprehended, that is, received into empirical consciousness otherwise than through the synthesis of a manifold, through which the representations of a determinate space or time are generated; that is to say, through the composition of the homogeneous and the consciousness of the synthetical unity of this manifold (homogeneous). Now the consciousness of a homogeneous manifold in intuition, in so far as thereby the representation of an object is rendered possible, is the conception of a quantity (quanti). Consequently, even the perception of an object as phenomenon is possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous manifold in the conception of a quantity is cogitated; that is to say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time they must be represented by means of the same synthesis through which space and time themselves are determined. An extensive quantity I call that wherein the representation of the parts renders possible (and therefore necessarily antecedes) the representation of the whole.

I cannot represent to myself any line, however small, without drawing it in thought, that is, without generating from a point all its parts one after another, and in this way alone producing this intuition. Precisely the same is the case with every, even the smallest, portion of time. I cogitate therein only the successive progress from one moment to another, and hence, by means of the different portions of time and the addition of them, a determinate quantity of time is produced. As the pure intuition in all phenomena is either time or space, so is every phenomenon in its character of intuition an extensive quantity, inasmuch as it can only be cognized in our apprehension by successive synthesis (from part to part). All phenomena are, accordingly, to be considered as aggregates, that is, as a collection of previously given parts; which is not the case with every sort of quantities, but only with those which are represented and apprehended by us as extensive. On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition à priori, under which alone the schema of a pure conception of external intuition can exist; for example, “be tween two points only one straight line is possible,” “two straight lines cannot enclose a space,” etc. These are the axioms which properly relate only to quantities (quanta) as such. But, as regards the quantity of a thing (quantitas), that is to say, the answer to the question: “How large is this or that object?” although, in respect to this question, we have various propositions synthetical and immediately certain (indemonstrabilia); we have, in the proper sense of the term, no axioms. For example, the propositions: “If equals be added to equals, the wholes are equal”; “If equals be taken from equals, the remainders are equal”; are analytical, because I am immediately conscious of the identity of the production of the one quantity with the production of the other; whereas axioms must be à priori synthetical propositions. On the other hand, the self-evident propositions as to the relation of numbers, are certainly synthetical but not universal, like those of geometry, and for this reason cannot be called axioms, but numerical formulae. That 7 +5 = 12 is not an analytical proposition. For neither in the representation of seven, nor of five, nor of the composition of the two numbers, do I cogitate the number twelve. (Whether I cogitate the number in the addition of both, is not at present the question; for in the case of an analytical proposition, the only point is whether I really cogitate the predicate in the representation of the subject.)

But although the proposition is synthetical, it is nevertheless only a singular proposition. In so far as regard is here had merely to the synthesis of the homogeneous (the units), it cannot take place except in one manner, although our use of these numbers is afterwards general. If I say: “A triangle can be constructed with three lines, any two of which taken together are greater than the third,” I exercise merely the pure function of the productive imagination, which may draw the lines longer or shorter and construct the angles at its pleasure. On the contrary, the number seven is possible only in one manner, and so is likewise the number twelve, which results from the synthesis of seven and five. Such propositions, then, cannot be termed axioms (for in that case we should have an infinity of these), but numerical formulae. This transcendental principle of the mathematics of phenomena greatly enlarges our à priori cognition. For it is by this principle alone that pure mathematics is rendered applicable in all its precision to objects of experience, and without it the validity of this application would not be so self-evident; on the contrary, contradictions and confusions have often arisen on this very point. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition (of space and time); consequently, what geometry affirms of the latter, is indisputably valid of the former. All evasions, such as the statement that objects of sense do not conform to the rules of construction in space (for example, to the rule of the infinite divisibility of lines or angles), must fall to the ground. For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics can be applied to phenomena. The synthesis of spaces and times as the essential form of all intuition, is that which renders possible the apprehension of a phenomenon, and therefore every external experience, consequently all cognition of the objects of experience; and whatever mathematics in its pure use proves of the former, must necessarily hold good of the latter.

All objections are but the chicaneries of an ill-instructed reason, which erroneously thinks to liberate the objects of sense from the formal conditions of our sensibility, and represents these, although mere phenomena, as things in themselves, presented as such to our understanding. But in this case, no à priori synthetical cognition of them could be possible, consequently not through pure conceptions of space and the science which determines these conceptions, that is to say, geometry, would itself be impossible.

2. ANTICIPATIONS OF PERCEPTION

The principle of these is: In all phenomena the Real, that which is an object of sensation, has Intensive Quantity, that is, has a Degree. PROOF. Perception is empirical consciousness, that is to say, a consciousness which contains an element of sensation. Phenomena as objects of perception are not pure, that is, merely formal intuitions, like space and time, for they cannot be perceived in themselves. [28] They contain, then, over and above the intuition, the materials for an object (through which is represented something existing in space or time), that is to say, they contain the real of sensation, as a representation merely subjective, which gives us merely the consciousness that the subject is affected, and which we refer to some external object. Now, a gradual transition from empirical consciousness to pure consciousness is possible, inasmuch as the real in this consciousness entirely vanishes, and there remains a merely formal consciousness (à priori) of the manifold in time and space; consequently there is possible a synthesis also of the production of the quantity of a sensation from its commencement, that is, from the pure intuition = 0 onwards up to a certain quantity of the sensation. Now as sensation in itself is not an objective representation, and in it is to be found neither the intuition of space nor of time, it cannot possess any extensive quantity, and yet there does belong to it a quantity (and that by means of its apprehension, in which empirical consciousness can within a certain time rise from nothing = 0 up to its given amount), consequently an intensive quantity. And thus we must ascribe intensive quantity, that is, a degree of influence on sense to all objects of perception, in so far as this perception contains sensation.

[28] They can be perceived only as phenomena, and some part of them must always belong to the non-ego; whereas pure intuitions are entirely the products of the mind itself, and as such are cognized in themselves. — Tr
All cognition, by means of which I am enabled to cognize and determine à priori what belongs to empirical cognition, may be called an anticipation; and without doubt this is the sense in which Epicurus employed his expression prholepsis. But as there is in phenomena something which is never cognized à priori, which on this account constitutes the proper difference between pure and empirical cognition, that is to say, sensation (as the matter of perception), it follows, that sensation is just that element in cognition which cannot be at all anticipated. On the other hand, we might very well term the pure determinations in space and time, as well in regard to figure as to quantity, anticipations of phenomena, because they represent à priori that which may always be given à posteriori in experience. But suppose that in every sensation, as sensation in general, without any particular sensation being thought of, there existed something which could be cognized à priori, this would deserve to be called anticipation in a special sense — special, because it may seem surprising to forestall experience, in that which concerns the matter of experience, and which we can only derive from itself. Yet such really is the case here. Apprehension [29], by means of sensation alone, fills only one moment, that is, if I do not take into consideration a succession of many sensations. As that in the phenomenon, the apprehension of which is not a successive synthesis advancing from parts to an entire representation, sensation has therefore no extensive quantity; the want of sensation in a moment of time would represent it as empty, consequently = 0. That which in the empirical intuition corresponds to sensation is reality (realitas phaenomenon); that which corresponds to the absence of it, negation = 0. Now every sensation is capable of a diminution, so that it can decrease, and thus gradually disappear. Therefore, between reality in a phenomenon and negation, there exists a continuous concatenation of many possible intermediate sensations, the difference of which from each other is always smaller than that between the given sensation and zero, or complete negation. That is to say, the real in a phenomenon has always a quantity, which however is not discoverable in apprehension, inasmuch as apprehension take place by means of mere sensation in one instant, and not by the successive synthesis of many sensations, and therefore does not progress from parts to the whole. Consequently, it has a quantity, but not an extensive quantity

[29] Apprehension is the Kantian word for preception, in the largest sense in which we employ that term. It is the genus which includes under i, as species, perception proper and sensation proper — Tr
Now that quantity which is apprehended only as unity, and in which plurality can be represented only by approximation to negation = O, I term intensive quantity. Consequently, reality in a phenomenon has intensive quantity, that is, a degree. If we consider this reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change), we call the degree of reality in its character of cause a momentum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the apprehension of which is not successive, but instantaneous. This, however, I touch upon only in passing, for with causality I have at present nothing to do. Accordingly, every sensation, consequently every reality in phenomena, however small it may be, has a degree, that is, an intensive quantity, which may always be lessened, and between reality and negation there exists a continuous connection of possible realities, and possible smaller perceptions. Every colour — for example, red — has a degree, which, be it ever so small, is never the smallest, and so is it always with heat, the momentum of weight, etc.

This property of quantities, according to which no part of them is the smallest possible (no part simple), is called their continuity. Space and time are quanta continua, because no part of them can be given, without enclosing it within boundaries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only boundaries, that is, the mere places or positions of their limitation. But places always presuppose intuitions which are to limit or determine them; and we cannot conceive either space or time composed of constituent parts which are given before space or time. Such quantities may also be called flowing, because synthesis (of the productive imagination) in the production of these quantities is a progression in time, the continuity of which we are accustomed to indicate by the expression flowing. All phenomena, then, are continuous quantities, in respect both to intuition and mere perception (sensation, and with it reality). In the former case they are extensive quantities; in the latter, intensive. When the synthesis of the manifold of a phenomenon is interrupted, there results merely an aggregate of several phenomena, and not properly a phenomenon as a quantity, which is not produced by the mere continuation of the productive synthesis of a certain kind, but by the repetition of a synthesis always ceasing. For example, if I call thirteen dollars a sum or quantity of money, I employ the term quite correctly, inasmuch as I understand by thirteen dollars the value of a mark in standard silver, which is, to be sure, a continuous quantity, in which no part is the smallest, but every part might constitute a piece of money, which would contain material for still smaller pieces. If, however, by the words thirteen dollars I understand so many coins (be their value in silver what it may), it would be quite erroneous to use the expression a quantity of dollars; on the contrary, I must call them aggregate, that is, a number of coins. And as in every number we must have unity as the foundation, so a phenomenon taken as unity is a quantity, and as such always a continuous quantity (quantum continuum).

Now, seeing all phenomena, whether considered as extensive or intensive, are continuous quantities, the proposition: “All change (transition of a thing from one state into another) is continuous,” might be proved here easily, and with mathematical evidence, were it not that the causality of a change lies, entirely beyond the bounds of a transcendental philosophy, and presupposes empirical principles. For of the possibility of a cause which changes the condition of things, that is, which determines them to the contrary to a certain given state, the understanding gives us à priori no knowledge; not merely because it has no insight into the possibility of it (for such insight is absent in several à priori cognitions), but because the notion of change concerns only certain determinations of phenomena, which experience alone can acquaint us with, while their cause lies in the unchangeable. But seeing that we have nothing which we could here employ but the pure fundamental conceptions of all possible experience, among which of course nothing empirical can be admitted, we dare not, without injuring the unity of our system, anticipate general physical science, which is built upon certain fundamental experiences.