(First Half)
P 004 BACO DE VERULAMIO INSTAURATIO MAGNA. PRAEFATIO. De nobis ipsis silemus: De re autem, quae agitur, petimus: ut homines eam non Opinionem, sed Opus esse cogitent; ac pro certo habeant, non Sectae nos alicujus, aut Placiti, sed utilitatis et amplitudinis humanae fundamenta moliri. Deinde ut suis commodis aequi ... in commune consulant, ... et ipsi in partem veniant. Praeterea ut bene sperent, neque Instaurationem nostram ut quiddam infini- tum et ultra mortale fingant, et animo concipiant; quum revera sit infiniti erroris finis et terminus legitimus. P 005 To his Excellency The Royal Minister of State Baron von Zedlitz HONOURED SIR, To further, so far as in us lies, the growth of the sciences is to work along the lines of your Excellency's own interests, which are closely bound up with the sciences, not only in virtue of your exalted position as a patron, but through your more intimate relation to them as lover and enlightened judge. I therefore avail myself of the only means that is in any degree in my power, of expressing my gratitude for the gracious confidence with which your Excellency honours me, if that I could perhaps be of assistance in this respect. To the same gracious attention with which your Excellency has honoured the first edition of this work I now dedicate this second edition, and therewith I crave the protection of all the other con- cerns of my literary mission, and remain with the most profound reverence, Your Excellency's Humble, most obedient servant, IMMANUEL KANT. Whoever limiting his worldly ambitions finds satisfaction in the speculative life has in the approval of an enlightened and competent judge a powerful incentive to labours, the benefits of which are great but remote, and therefore such as the vulgar altogether fail to recognise. To such a judge and to his gracious attention I now dedicate this work, and to his PREFACE TO FIRST EDITION PREFACE TO FIRST EDITION HUMAN reason has this peculiar fate that in one species of its knowledge it is burdened by questions which, as pre- scribed by the very nature of reason itself, it is not able to ignore, but which, as transcending all its powers, it is also not able to answer. The perplexity into which it thus falls is not due to any fault of its own. It begins with principles which it has no option save to employ in the course of experience, and which this experience at the same time abundantly justifies it in using. Rising with their aid (since it is determined to this also by its own nature) to ever higher, ever more remote, conditions, it soon becomes aware that in this way -- the questions never ceasing -- its work must always remain incomplete; and it therefore finds itself compelled to resort to principles which overstep all possible empirical employ- ment, and which yet seem so unobjectionable that even ordinary consciousness readily accepts them. But by this procedure human reason precipitates itself into darkness and contradictions; and while it may indeed conjecture that these must be in some way due to concealed errors, it is not in a position to be able to detect them. For since the principles of which it is making use transcend the limits of experience, they are no longer subject to any empirical test. The battle-field of these endless controversies is called metaphysics. Time was when metaphysics was entitled the Queen of all the sciences; and if the will be taken for the deed, the pre- eminent importance of her accepted tasks gives her every right to this title of honour. Now, however, the changed fashion of the time brings her only scorn; a matron outcast P 008 and forsaken, she mourns like Hecuba: Modo maxima rerum, tot generis natisque potens -- nunc trahor exul, inops. Her government, under the administration of the dogmat- ists, was at first despotic. But inasmuch as the legislation still bore traces of the ancient barbarism, her empire gradu- ally through intestine wars gave way to complete anarchy; and the sceptics, a species of nomads, despising all settled modes of life, broke up from time to time all civil society. Happily they were few in number, and were unable to prevent its being established ever anew, although on no uniform and self-consistent plan. In more recent times, it has seemed as if an end might be put to all these controversies and the claims of metaphysics receive final judgment, through a certain physiology of the human understanding -- that of the celebrated Locke. But it has turned out quite otherwise. For however the attempt be made to cast doubt upon the pre- tensions of the supposed Queen by tracing her lineage to vulgar origins in common experience, this genealogy has, as a matter of fact, been fictitiously invented, and she has still continued to uphold her claims. Metaphysics has accord- ingly lapsed back into the ancient time-worn dogmatism, and so again suffers that depreciation from which it was to have been rescued. And now, after all methods, so it is believed, have been tried and found wanting, the prevailing mood is that of weariness and complete indifferentism -- the mother, in all sciences, of chaos and night, but happily in this case the source, or at least the prelude, of their approaching reform and restoration. For it at least puts an end to that ill- applied industry which has rendered them thus dark, confused, and unserviceable. But it is idle to feign indifference to such enquiries, the object of which can never be indifferent to our human nature. Indeed these pretended indifferentists, however they may try to disguise themselves by substituting a popular tone for the language of the Schools, inevitably fall back, in so far as they think at all, into those very metaphysical assertions which they profess so greatly to despise. Ovid, Metam. P 009 None the less this indifference, showing itself in the midst of flourishing sciences, and affecting precisely those P 009 sciences, the knowledge of which, if attainable, we should least of all care to dispense with, is a phenomenon that calls for attention and reflection. It is obviously the effect not of levity but of the matured judgment of the age, which refuses to be any longer put off with illusory knowledge. It is a call to reason to undertake anew the most difficult of all its tasks, namely, that of self-knowledge, and to institute a tribunal which will assure to reason its lawful claims, and dismiss all groundless pretensions, not by despotic decrees, but in accordance with its own eternal and unalterable laws. This tribunal is no other than the critique of pure reason. I do not mean by this a critique of books and systems, but of the faculty of reason in general, in respect of all know- ledge after which it may strive independently of all experi- ence. It will therefore decide as to the possibility or impossi- bility of metaphysics in general, and determine its sources, its extent, and its limits -- all in accordance with principles. I have entered upon this path -- the only one that has re- mained unexplored -- and flatter myself that in following it I have found a way of guarding against all those errors which have hitherto set reason, in its non-empirical employment, at P 010 variance with itself. P 009n We often hear complaints of shallowness of thought in our age and of the consequent decline of sound science. But I do not see that the sciences which rest upon a secure foundation, such as mathe- matics, physics, etc. , in the least deserve this reproach. On the con- trary, they merit their old reputation for solidity, and, in the case of physics, even surpass it. The same spirit would have become active in other kinds of knowledge, if only attention had first been directed to the determination of their principles. Till this is done, in- difference, doubt, and, in the final issue, severe criticism, are them- selves proofs of a profound habit of thought. Our age is, in especial degree, the age of criticism, and to criticism everything must sub- mit. Religion through its sanctity, and law-giving through its majesty, may seek to exempt themselves from it. But they then awaken just suspicion, and cannot claim the sincere respect which reason accords only to that which has been able to sustain the test of free and open examination. P 010 I have not evaded its questions by plead- ing the insufficiency of human reason. On the contrary, I have specified these questions exhaustively, according to prin- ciples; and after locating the point at which, through mis- understanding, reason comes into conflict with itself, I have solved them to its complete satisfaction. The answer to these questions has not, indeed, been such as a dogmatic and vision- ary insistence upon knowledge might lead us to expect -- that can be catered for only through magical devices, in which I am no adept. Such ways of answering them are, indeed, not within the intention of the natural constitution of our reason; and inasmuch as they have their source in misunderstanding, it is the duty of philosophy to counteract their deceptive in- fluence, no matter what prized and cherished dreams may have to be disowned. In this enquiry I have made completeness my chief aim, and I venture to assert that there is not a single metaphysical problem which has not been solved, or for the solution of which the key at least has not been supplied. Pure reason is, indeed, so perfect a unity that if its principle were insufficient for the solution of even a single one of all the questions to which it itself gives birth we should have no alternative but to reject the principle, since we should then no longer be able to place implicit reliance upon it in dealing with any one of the other questions. While I am saying this I can fancy that I detect in the face of the reader an expression of indignation, mingled with con- tempt, at pretensions seemingly so arrogant and vain-glorious. Yet they are incomparably more moderate than the claims of all those writers who on the lines of the usual programme profess to prove the simple nature of the soul or the necessity of a first beginning of the world. For while such writers pledge themselves to extend human knowledge beyond all limits of possible experience, I humbly confess that this is entirely be- yond my power. I have to deal with nothing save reason itself and its pure thinking; and to obtain complete knowledge of these, there is no need to go far afield, since I come upon them in my own self. Common logic itself supplies an example, how all the simple acts of reason can be enumerated completely and systematically. The subject of the present enquiry is the [kindred] question, how much we can hope to achieve by P 011 reason, when all the material and assistance of experience are taken away. So much as regards completeness in our determination of each question, and exhaustiveness in our determination of all the questions with which we have to deal. These questions are not arbitrarily selected; they are prescribed to us, by the very nature of knowledge itself, as being the subject-matter of our critical enquiry. As regards the form of our enquiry, certainty and clearness are two essential requirements, rightly to be exacted from any- one who ventures upon so delicate an undertaking. As to certainty, I have prescribed to myself the maxim, that in this kind of investigation it is in no wise permissible to hold opinions. Everything, therefore, which bears any manner of resemblance to an hypothesis is to be treated as contra- band; it is not to be put up for sale even at the lowest price, but forthwith confiscated, immediately upon detection. Any knowledge that professes to hold a priori lays claim to be regarded as absolutely necessary. This applies still more to any determination of all pure a priori knowledge, since such deter- mination has to serve as the measure, and therefore as the [supreme] example, of all apodeictic (philosophical) certainty. Whether I have succeeded in what I have undertaken must be left altogether to the reader's judgment; the author's task is solely to adduce grounds, not to speak as to the effect which they should have upon those who are sitting in judgment. But the author, in order that he may not himself, innocently, be the cause of any weakening of his arguments, may be permitted to draw attention to certain passages, which, although merely incidental, may yet occasion some mistrust. Such timely inter- vention may serve to counteract the influence which even quite undefined doubts as to these minor matters might otherwise exercise upon the reader's attitude in regard to the main issue. I know no enquiries which are more important for ex- ploring the faculty which we entitle understanding, and for determining the rules and limits of its employment, than those which I have instituted in the second chapter of the Trans- cendental Analytic under the title Deduction of the Pure Concepts of Understanding. They are also those which have P 012 cost me the greatest labour -- labour, as I hope, not unre- warded. This enquiry, which is somewhat deeply grounded, has two sides. The one refers to the objects of pure under- standing, and is intended to expound and render intelligible the objective validity of its a priori concepts. It is therefore essential to my purposes. The other seeks to investigate the pure understanding itself, its possibility and the cognitive faculties upon which it rests; and so deals with it in its sub- jective aspect. Although this latter exposition is of great importance for my chief purpose, it does not form an essential part of it. For the chief question is always simply this: -- what and how much can the understanding and reason know apart from all experience? not: -- how is the faculty of thought itself possible? The latter is, as it were, the search for the cause of a given effect, and to that extent is somewhat hypothetical in character (though, as I shall show elsewhere, it is not really so); and I would appear to be taking the liberty simply of expressing an opinion, in which case the reader would be free to express a different opinion. For this reason I must forestall the reader's criticism by pointing out that the objective de- duction with which I am here chiefly concerned retains its full force even if my subjective deduction should fail to produce that complete conviction for which I hope. On this matter, what has been said on pp. 92-93 should in any case suffice by itself. As regards clearness, the reader has a right to demand, in the first place, a discursive (logical) clearness, through con- cepts, and secondly, an intuitive (aesthetic) clearness, through intuitions, that is, through examples and other concrete illustrations. For the first I have sufficiently provided. That was essential to my purpose; but it has also been the incidental cause of my not being in a position to do justice to the second demand, which, if not so pressing, is yet still quite reasonable. I have been almost continuously at a loss, during the progress of my work, how I should proceed in this matter. Examples and illustrations seemed always to be necessary, and so took their place, as required, in my first draft. But I very soon became aware of the magnitude of my task and of the multi- plicity of matters with which I should have to deal; and as P 013 I perceived that even if treated in dry, purely scholastic fashion, the outcome would by itself be already quite suffi- ciently large in bulk, I found it inadvisable to enlarge it yet further through examples and illustrations. These are neces- sary only from a popular point of view; and this work can never be made suitable for popular consumption. Such assistance is not required by genuine students of the science, and, though always pleasing, might very well in this case have been self-defeating in its effects. Abbot Terrasson has remarked that if the size of a volume be measured not by the number of its pages but by the time required for mastering it, it can be said of many a book, that it would be much shorter if it were not so short. On the other hand, if we have in view the comprehensibility of a whole of speculative knowledge, which, though wide-ranging, has the coherence that follows from unity of principle, we can say with equal justice that many a book would have been much clearer if it had not made such an effort to be clear. For the aids to clearness, though they may be of assistance in regard to details, often interfere with our grasp of the whole. The reader is not allowed to arrive sufficiently quickly at a conspectus of the whole; the bright colouring of the illustrative material intervenes to cover over and conceal the articulation and organisation of the system, which, if we are to be able to judge of its unity and solidity, are what chiefly concern us. The reader, I should judge, will feel it to be no small inducement to yield his willing co-operation, when the author is thus endeavouring, according to the plan here proposed, to carry through a large and important work in a complete and lasting manner. Metaphysics, on the view which we are adopt- ing, is the only one of all the sciences which dare promise that through a small but concentrated effort it will attain, and this in a short time, such completion as will leave no task to our successors save that of adapting it in a didactic manner according to their own preferences, without their P 014 being able to add anything whatsoever to its content. For it is nothing but the inventory of all our possessions through pure reason, systematically arranged. In this field nothing can escape us. What reason produces entirely out of itself cannot be concealed, but is brought to light by reason itself immediately the common principle has been discovered. The complete unity of this kind of knowledge, and the fact that it is derived solely from pure concepts, entirely unin- fluenced by any experience or by special intuition, such as might lead to any determinate experience that would enlarge and increase it, make this unconditioned completeness not only practicable but also necessary. Tecum habita, et noris quam sit tibi curta supellex. Such a system of pure (speculative) reason I hope myself to produce under the title Metaphysics of Nature. It will be not half as large, yet incomparably richer in content than this present Critique, which has as its first task to discover the sources and conditions of the possibility of such criticism, clearing, as it were, and levelling what has hitherto been waste- ground. In this present enterprise I look to my reader for the patience and impartiality of a judge; whereas in the other I shall look for the benevolent assistance of a fellow-worker. For however completely all the principles of the system are presented in this Critique, the completeness of the system itself likewise requires that none of the derivative concepts be lacking. These cannot be enumerated by any a priori com- putation, but must be discovered gradually. Whereas, there- fore, in this Critique the entire synthesis of the concepts has been exhausted, there will still remain the further work of making their analysis similarly complete, a task which is rather an amusement than a labour. I have only a few remarks to add of a typographical character. As the beginning of the printing was delayed, I was not able to see more than about half of the proof-sheets, and I now find some misprints, which do not, however, affect the sense except on p. 379, line 4 from the bottom, where specific has to be read in place of sceptical. Persius. P 014 The antinomy P 015 of pure reason, from p. 425 to p. 461, has been so arranged, in tabular form, that all that belongs to the thesis stands on the left and what belongs to the antithesis on the right. This I have done in order that proposition and counter- proposition may be the more easily compared with one another. P 017 PREFACE TO THE SECOND EDITION WHETHER the treatment of such knowledge as lies within the province of reason does or does not follow the secure path of a science, is easily to be determined from the outcome. For if after elaborate preparations, frequently renewed, it is brought to a stop immediately it nears its goal; if often it is com- pelled to retrace its steps and strike into some new line of approach; or again, if the various participants are unable to agree in any common plan of procedure, then we may rest assured that it is very far from having entered upon the secure path of a science, and is indeed a merely random groping. In these circumstances, we shall be rendering a service to reason should we succeed in discovering the path upon which it can securely travel, even if, as a result of so doing, much that is comprised in our original aims, adopted without reflection, may have to be abandoned as fruitless. That logic has already, from the earliest times, proceeded upon this sure path is evidenced by the fact that since Aris- totle it has not required to retrace a single step, unless, indeed, we care to count as improvements the removal of certain need- less subtleties or the clearer exposition of its recognised teach- ing, features which concern the elegance rather than the cer- tainty of the science. It is remarkable also that to the present day this logic has not been able to advance a single step, and is thus to all appearance a closed and completed body of doc- trine. If some of the moderns have thought to enlarge it by introducing psychological chapters on the different faculties of knowledge (imagination, wit, etc. ), metaphysical chapters on the origin of knowledge or on the different kinds of certainty according to difference in the objects (idealism, scepticism, etc. ), or anthropological chapters on prejudices, their causes and remedies, this could only arise from their ignorance of the P 018 peculiar nature of logical science. We do not enlarge but disfigure sciences, if we allow them to trespass upon one another's territory. The sphere of logic is quite precisely de- limited; its sole concern is to give an exhaustive exposition and a strict proof of the formal rules of all thought, whether it be a priori or empirical, whatever be its origin or its object, and whatever hindrances, accidental or natural, it may encounter in our minds. That logic should have been thus successful is an advan- tage which it owes entirely to its limitations, whereby it is justified in abstracting -- indeed, it is under obligation to do so -- from all objects of knowledge and their differences, leav- ing the understanding nothing to deal with save itself and its form. But for reason to enter on the sure path of science is, of course, much more difficult, since it has to deal not with itself alone but also with objects. Logic, therefore, as a pro- paedeutic, forms, as it were, only the vestibule of the sciences; and when we are concerned with specific modes of know- ledge, while logic is indeed presupposed in any critical estimate of them, yet for the actual acquiring of them we have to look to the sciences properly and objectively so called. Now if reason is to be a factor in these sciences, something in them must be known a priori, and this knowledge may be related to its object in one or other of two ways, either as merely determining it and its concept (which must be supplied from elsewhere) or as also making it actual. The former is theoretical, the latter practical knowledge of reason. In both, that part in which reason determines its object completely a priori, namely, the pure part -- however much or little this part may contain -- must be first and separately dealt with, in case it be confounded with what comes from other sources. For it is bad management if we blindly pay out what comes in, and are not able, when the income falls into arrears, to distinguish which part of it can justify expenditure, and in which line we must make reductions. Mathematics and physics, the two sciences in which reason yields theoretical knowledge, have to determine their objects a priori, the former doing so quite purely, the latter having P 019 to reckon, at least partially, with sources of knowledge other than reason. In the earliest times to which the history of human reason extends, mathematics, among that wonderful people, the Greeks, had already entered upon the sure path of science. But it must not be supposed that it was as easy for mathematics as it was for logic -- in which reason has to deal with itself alone -- to light upon, or rather to construct for itself, that royal road. On the contrary, I believe that it long remained, especially among the Egyptians, in the groping stage, and that the trans- formation must have been due to a revolution brought about by the happy thought of a single man, the experiment which he devised marking out the path upon which the science must enter, and by following which, secure progress throughout all time and in endless expansion is infallibly secured. The his- tory of this intellectual revolution -- far more important than the discovery of the passage round the celebrated Cape of Good Hope -- and of its fortunate author, has not been pre- served. But the fact that Diogenes Laertius, in handing down an account of these matters, names the reputed author of even the least important among the geometrical demonstrations, even of those which, for ordinary consciousness, stand in need of no such proof, does at least show that the memory of the revolution, brought about by the first glimpse of this new path, must have seemed to mathematicians of such outstanding im- portance as to cause it to survive the tide of oblivion. A new light flashed upon the mind of the first man (be he Thales or some other) who demonstrated the properties of the isosceles triangle. The true method, so he found, was not to inspect what he dis- cerned either in the figure, or in the bare concept of it, and from this, as it were, to read off its properties; but to bring out what was necessarily implied in the concepts that he had himself formed a priori, and had put into the figure in the construction by which he presented it to himself. If he is to know anything with a priori certainty he must not ascribe to the figure any- thing save what necessarily follows from what he has himself set into it in accordance with his concept. Natural science was very much longer in entering upon the highway of science. It is, indeed, only about a century and a P 020 half since Bacon, by his ingenious proposals, partly initiated this discovery, partly inspired fresh vigour in those who were already on the way to it. In this case also the discovery can be explained as being the sudden outcome of an intellectual revolution. In my present remarks I am referring to natural science only in so far as it is founded on empirical principles. When Galileo caused balls, the weights of which he had himself previously determined, to roll down an inclined plane; when Torricelli made the air carry a weight which he had cal- culated beforehand to be equal to that of a definite column of water; or in more recent times, when Stahl changed metal into lime, and lime back into metal, by withdrawing some- thing and then restoring it, a light broke upon all students of nature. They learned that reason has insight only into that which it produces after a plan of its own, and that it must not allow itself to be kept, as it were, in nature's leading-strings, but must itself show the way with principles of judgment based upon fixed laws, constraining nature to give answer to ques- tions of reason's own determining. Accidental observations, made in obedience to no previously thought-out plan, can never be made to yield a necessary law, which alone reason is concerned to discover. Reason, holding in one hand its prin- ciples, according to which alone concordant appearances can be admitted as equivalent to laws, and in the other hand the experiment which it has devised in conformity with these prin- ciples, must approach nature in order to be taught by it. It must not, however, do so in the character of a pupil who listens to everything that the teacher chooses to say, but of an appointed judge who compels the witnesses to answer questions which he has himself formulated. Even physics, therefore, owes the beneficent revolution in its point of view entirely to the happy thought, that while reason must seek in nature, not fictitiously ascribe to it, whatever as not being knowable through reason's own resources has to be learnt, if learnt at all, only from nature, it must adopt as its guide, in so seeking, that which it has itself put into nature. It is thus that the study of nature has entered on the secure path of a P 021 science, after having for so many centuries been nothing but a process of merely random groping. P 020n I am not, in my choice of examples, tracing the exact course of the history of the experimental method; we have indeed no very pre- cise knowledge of its first beginnings. P 021 Metaphysics is a completely isolated speculative science of reason, which soars far above the teachings of experience, and in which reason is indeed meant to be its own pupil. Meta- physics rests on concepts alone -- not, like mathematics, on their application to intuition. But though it is older than all other sciences, and would survive even if all the rest were swallowed up in the abyss of an all-destroying barbarism, it has not yet had the good fortune to enter upon the secure path of a science. For in it reason is perpetually being brought to a stand, even when the laws into which it is seeking to have, as it professes, an a priori insight are those that are confirmed by our most com- mon experiences. Ever and again we have to retrace our steps, as not leading us in the direction in which we desire to go. So far, too, are the students of metaphysics from exhibiting any kind of unanimity in their contentions, that metaphysics has rather to be regarded as a battle-ground quite peculiarly suited for those who desire to exercise themselves in mock combats, and in which no participant has ever yet succeeded in gaining even so much as an inch of territory, not at least in such manner as to secure him in its permanent possession. This shows, beyond all questioning, that the procedure of meta- physics has hitherto been a merely random groping, and, what is worst of all, a groping among mere concepts. What, then, is the reason why, in this field, the sure road to science has not hitherto been found? Is it, perhaps, im- possible of discovery? Why, in that case, should nature have visited our reason with the restless endeavour whereby it is ever searching for such a path, as if this were one of its most important concerns. Nay, more, how little cause have we to place trust in our reason, if, in one of the most important domains of which we would fain have knowledge, it does not merely fail us, but lures us on by deceitful promises, and in the end betrays us! Or if it be only that we have thus far failed to find the true path, are there any indications to justify the hope that by renewed efforts we may have better fortune than has fallen to our predecessors? The examples of mathematics and natural science, which by a single and sudden revolution have become what they P 022 now are, seem to me sufficiently remarkable to suggest our considering what may have been the essential features in the changed point of view by which they have so greatly bene- fited. Their success should incline us, at least by way of experi- ment, to imitate their procedure, so far as the analogy which, as species of rational knowledge, they bear to metaphysics may permit. Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our know- ledge of objects by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge. This would agree better with what is desired, namely, that it should be possible to have knowledge of objects a priori, determining something in regard to them prior to their being given. We should then be proceeding precisely on the lines of Copernicus' primary hypothesis. Failing of satisfactory progress in ex- plaining the movements of the heavenly bodies on the supposi- tion that they all revolved round the spectator, he tried whether he might not have better success if he made the spectator to revolve and the stars to remain at rest. A similar experi- ment can be tried in metaphysics, as regards the intuition of objects. If intuition must conform to the constitution of the objects, I do not see how we could know anything of the latter a priori; but if the object (as object of the senses) must conform to the constitution of our faculty of intuition, I have no difficulty in conceiving such a possibility. Since I cannot rest in these intuitions if they are to become known, but must relate them as representations to something as their object, and determine this latter through them, either I must assume that the concepts, by means of which I obtain this determination, conform to the object, or else I assume that the objects, or what is the same thing, that the experience in which alone, as given objects, they can be known, conform to the concepts. In the former case, I am again in the same per- plexity as to how I can know anything a priori in regard to the objects. In the latter case the outlook is more hopeful. For experience is itself a species of knowledge which involves P 023 understanding; and understanding has rules which I must pre- suppose as being in me prior to objects being given to me, and therefore as being a priori. They find expression in a priori concepts to which all objects of experience necessarily con- form, and with which they must agree. As regards objects which are thought solely through reason, and indeed as necessary, but which can never -- at least not in the manner in which reason thinks them -- be given in experience, the attempts at thinking them (for they must admit of being thought) will furnish an excellent touchstone of what we are adopting as our new method of thought, namely, that we can know a priori of things only what we ourselves put into them. This experiment succeeds as well as could be desired, and promises to metaphysics, in its first part -- the part that is occupied with those concepts a priori to which the correspond- ing objects, commensurate with them, can be given in ex- perience -- the secure path of a science. For the new point of view enables us to explain how there can be knowledge a priori; and, in addition, to furnish satisfactory proofs of the laws which form the a priori basis of nature, regarded as the sum of the objects of experience -- neither achievement being possible on the procedure hitherto followed. This method, modelled on that of the student of nature, con- sists in looking for the elements of pure reason in what admits of con- firmation or refutation by experiment. Now the propositions of pure reason, especially if they venture out beyond all limits of possible experience, cannot be brought to the test through any experiment with their objects, as in natural science. In dealing with those con- cepts and principles which we adopt a priori, all that we can do is to contrive that they be used for viewing objects from two different points of view -- on the one hand, in connection with experience, as objects of the senses and of the understanding, and on the other hand, for the isolated reason that strives to transcend all limits of experience, as objects which are thought merely. If, when things are viewed from this twofold standpoint, we find that there is agreement with the principle of pure reason, but that when we regard them only from a single point of view reason is involved in unavoidable self-conflict, the experiment decides in favour of the correctness of this distinction. P 023 But this deduction of our power of knowing a priori, in the first part of metaphysics, has a consequence which is startling, and which has the appearance P 024 of being highly prejudicial to the whole purpose of meta- physics, as dealt with in the second part. For we are brought to the conclusion that we can never transcend the limits of possible experience, though that is precisely what this science is concerned, above all else, to achieve. This situation yields, however, just the very experiment by which, indirectly, we are enabled to prove the truth of this first estimate of our a priori knowledge of reason, namely, that such knowledge has to do only with appearances, and must leave the thing in itself as indeed real per se, but as not known by us. For what necessarily forces us to transcend the limits of experience and of all appearances is the unconditioned, which reason, by necessity and by right, demands in things in themselves, as required to complete the series of con- ditions. If, then, on the supposition that our empirical know- ledge conforms to objects as things in themselves, we find that the unconditioned cannot be thought without contradiction, and that when, on the other hand, we suppose that our repre- sentation of things, as they are given to us, does not conform to these things as they are in themselves, but that these objects, as appearances, conform to our mode of representation, the contradiction vanishes; and if, therefore, we thus find that the unconditioned is not to be met with in things, so far as we know them, that is, so far as they are given to us, but only so far as we do not know them, that is, so far as they are things in themselves, we are justified in concluding that what we at first assumed for the purposes of experiment is now definitely confirmed. This experiment of pure reason bears a great similarity to what in chemistry is sometimes entitled the experiment of reduction, or more usually the synthetic process. The analysis of the metaphysician separates pure a priori knowledge into two very heterogeneous elements, namely, the knowledge of things as appearances, and the knowledge of things in themselves; his dialectic combines these two again, in harmony with the necessary idea of the unconditioned demanded by reason, and finds that this harmony can never be ob- tained except through the above distinction, which must therefore be accepted. P 024 But when all progress in the field of the supersensible has thus been denied to speculative reason, it is still open to us to enquire whether, in the practical P 025 knowledge of reason, data may not be found sufficient to de- termine reason's transcendent concept of the unconditioned, and so to enable us, in accordance with the wish of meta- physics, and by means of knowledge that is possible a priori, though only from a practical point of view, to pass beyond the limits of all possible experience. Speculative reason has thus at least made room for such an extension; and if it must at the same time leave it empty, yet none the less we are at liberty, indeed we are summoned, to take occupation of it, if we can, by practical data of reason. This attempt to alter the procedure which has hitherto prevailed in metaphysics, by completely revolutionising it in accordance with the example set by the geometers and physicists, forms indeed the main purpose of this critique of pure speculative reason. It is a treatise on the method, not a system of the science itself. But at the same time it marks out the whole plan of the science, both as regards its limits and as regards its entire internal structure. For pure speculative reason has this peculiarity, that it can measure its powers according to the different ways in which it chooses the objects of its thinking, and can also give an exhaustive enumeration of the various ways in which it propounds its problems, and so is able, nay bound, to trace the complete outline of a system of metaphysics. As regards the first point, nothing in a priori knowledge can be ascribed to objects save what the thinking subject derives from itself; Similarly, the fundamental laws of the motions of the heavenly bodies gave established certainty to what Copernicus had at first assumed only as an hypothesis, and at the same time yielded proof of the invisible force (the Newtonian attraction) which holds the universe together. The latter would have remained for ever un- discovered if Copernicus had not dared, in a manner contradictory of the senses, but yet true, to seek the observed movements, not in the heavenly bodies, but in the spectator. The change in point of view, analogous to this hypothesis, which is expounded in the Critique, I put forward in this preface as an hypothesis only, in order to draw attention to the character of these first attempts at such a change, which are always hypothetical. But in the Critique itself it will be proved, apodeictically not hypothetically, from the nature of our representations of space and time and from the elementary concepts of the understanding. P 025 as regards the second point, pure reason, so far as the principles of its knowledge are concerned, P 026 is a quite separate self-subsistent unity, in which, as in an organised body, every member exists for every other, and all for the sake of each, so that no principle can safely be taken in any one relation, unless it has been investigated in the entirety of its relations to the whole employment of pure reason. Consequently, metaphysics has also this singular advantage, such as falls to the lot of no other science which deals with objects (for logic is concerned only with the form of thought in general), that should it, through this critique, be set upon the secure path of a science, it is capable of ac- quiring exhaustive knowledge of its entire field. Metaphysics has to deal only with principles, and with the limits of their employment as determined by these principles themselves, and it can therefore finish its work and bequeath it to posterity as a capital to which no addition can be made. Since it is a fundamental science, it is under obligation to achieve this completeness. We must be able to say of it: nil actum re- putans, si quid superesset agendum. But, it will be asked, what sort of a treasure is this that we propose to bequeath to posterity? What is the value of the metaphysics that is alleged to be thus purified by criti- cism and established once for all? On a cursory view of the present work it may seem that its results are merely negative, warning us that we must never venture with speculative reason beyond the limits of experience. Such is in fact its primary use. But such teaching at once acquires a positive value when we recognise that the principles with which speculative reason ventures out beyond its proper limits do not in effect extend the employment of reason, but, as we find on closer scrutiny, inevitably narrow it. These principles properly belong [not to reason but] to sensibility, and when thus employed they threaten to make the bounds of sensibility coextensive with the real, and so to supplant reason in its pure (practical) em- ployment. So far, therefore, as our Critique limits speculative reason, it is indeed negative; but since it thereby removes an obstacle which stands in the way of the employment of practi- cal reason, nay threatens to destroy it, it has in reality a posi- tive and very important use. At least this is so, immediately we are convinced that there is an absolutely necessary prac- tical employment of pure reason -- the moral -- in which it P 027 inevitably goes beyond the limits of sensibility. Though [practical] reason, in thus proceeding, requires no assistance from speculative reason, it must yet be assured against its opposition, that reason may not be brought into conflict with itself. To deny that the service which the Critique renders is Positive in character, would thus be like saying that the police are of no positive benefit, inasmuch as their main busi- ness is merely to prevent the violence of which citizens stand in mutual fear, in order that each may pursue his vocation in peace and security. That space and time are only forms of sens- ible intuition, and so only conditions of the existence of things as appearances; that, moreover, we have no concepts of under- standing, and consequently no elements for the knowledge of things, save in so far as intuition can be given corresponding to these concepts; and that we can therefore have no knowledge of any object as thing in itself, but only in so far as it is an object of sensible intuition, that is, an appearance -- all this is proved in the analytical part of the Critique. Thus it does in- deed follow that all possible speculative knowledge of reason is limited to mere objects of experience. But our further con- tention must also be duly borne in mind, namely, that though We cannot know these objects as things in themselves, we must yet be in position at least to think them as things in them- selves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears. Now let us suppose that the distinction, which our Critique has shown to be necessary, between things as objects of experience and those same things as things in themselves, had not been made. To know an object I must be able to prove its possibility, either from its actuality as attested by experience, or a priori by means of reason. But I can think whatever I please, provided only that I do not contradict myself, that is, provided my concept is a possible thought. This suffices for the possibility of the concept, even though I may not be able to answer for there being, in the sum of all possi- bilities, an object corresponding to it. But something more is re- quired before I can ascribe to such a concept objective validity, that is, real possibility; the former possibility is merely logical. This some- thing more need not, however, be sought in the theoretical sources of knowledge; it may lie in those that are practical. P 027 In that case all things in general, as far as they are P 028 efficient causes, would be determined by the principle of caus- ality and consequently by the mechanism of nature. I could not, therefore, without palpable contradiction, say of one and the same being, for instance the human soul, that its will is free and yet is subject to natural necessity, that is, is not free. For I have taken the soul in both propositions in one and the same sense, namely as a thing in general, that is, as a thing in itself; and save by means of a preceding critique, could not have done otherwise. But if our Critique is not in error in teaching that the object is to be taken in a twofold sense, namely as appear- ance and as thing in itself; if the deduction of the concepts of understanding is valid, and the principle of causality there- fore applies only to things taken in the former sense, namely, in so far as they are objects of experience -- these same objects, taken in the other sense, not being subject to the principle -- then there is no contradiction in supposing that one and the same will is, in the appearance, that is, in its visible acts, necessarily subject to the law of nature, and so far not free, while yet, as belonging to a thing in itself, it is not subject to that law, and is therefore free. My soul, viewed from the latter standpoint, cannot indeed be known by means of specu- lative reason (and still less through empirical observation); and freedom as a property of a being to which I attribute effects in the sensible world, is therefore also not knowable in any such fashion. For I should then have to know such a being as determined in its existence, and yet as not determined in time -- which is impossible, since I cannot support my concept by any intuition. But though I cannot know, I can yet think freedom; that is to say, the representation of it is at least not self-con- tradictory, provided due account be taken of our critical dis- tinction between the two modes of representation, the sensible and the intellectual, and of the resulting limitation of the pure concepts of understanding and of the principles which flow from them. If we grant that morality necessarily presupposes freedom (in the strictest sense) as a property of our will; if, that is to say, we grant that it yields practical principles -- original prin- ciples, proper to our reason -- as a priori data of reason, and that this would be absolutely impossible save on the assump- P 029 tion of freedom; and if at the same time we grant that speculative reason has proved that such freedom does not allow of being thought, then the former supposition -- that made on behalf of morality -- would have to give way to this other contention, the opposite of which involves a palpable contradiction. For since it is only on the assumption of free- dom that the negation of morality contains any contradiction, freedom, and with it morality, would have to yield to the mechanism of nature. Morality does not, indeed, require that freedom should be understood, but only that it should not contradict itself, and so should at least allow of being thought, and that as thus thought it should place no obstacle in the way of a free act (viewed in another relation) likewise conforming to the mechan- ism of nature. The doctrine of morality and the doctrine of nature may each, therefore, make good its position. This, however, is only possible in so far as criticism has previously established our unavoidable ignorance of things in themselves, and has limited all that we can theoretically know to mere appearances. This discussion as to the positive advantage of critical principles of pure reason can be similarly developed in regard to the concept of God and of the simple nature of our soul; but for the sake of brevity such further discussion may be omitted. [From what has already been said, it is evident that] even the assumption--as made on behalf of the necessary practical em- ployment of my reason -- of God, freedom, and immortality is not permissible unless at the same time speculative reason be deprived of its pretensions to transcendent insight. For in order to arrive at such insight it must make use of principles which, in fact, extend only to objects of possible experience, and which, if also applied to what cannot be an object of experience, always really change this into an appearance, thus rendering all practical extension of pure reason impossible. I have therefore found it necessary to deny knowledge, in order to make room for faith. The dogmatism of metaphysics, that is, the precon- ception that it is possible to make headway in metaphysics with- out a previous criticism of pure reason, is the source of all that unbelief, always very dogmatic, which wars against morality. P 030 Though it may not, then, be very difficult to leave to pos- terity the bequest of a systematic metaphysic, constructed in conformity with a critique of pure reason, yet such a gift is not to be valued lightly. For not only will reason be enabled to follow the secure path of a science, instead of, as hitherto, groping at random, without circumspection or self-criticism; our enquiring youth will also be in a position to spend their time more profitably than in the ordinary dogmatism by which they are so early and so greatly encouraged to indulge in easy speculation about things of which they understand nothing, and into which neither they nor any- one else will ever have any insight -- encouraged, indeed, to invent new ideas and opinions, while neglecting the study of the better-established sciences. But, above all, there is the inestimable benefit, that all objections to morality and religion will be for ever silenced, and this in Socratic fashion, namely, by the clearest proof of the ignorance of the objectors. There has always existed in the world, and there will always continue to exist, some kind of metaphysics, and with it the dialectic that is natural to pure reason. It is therefore the first and most important task of philosophy to deprive meta- physics, once and for all, of its injurious influence, by attack- ing its errors at their very source. Notwithstanding this important change in the field of the sciences, and the loss of its fancied possessions which specula- tive reason must suffer, general human interests remain in the same privileged position as hitherto, and the advantages which the world has hitherto derived from the teachings of pure reason are in no way diminished. The loss affects only the monopoly of the schools, in no respect the interests of humanity. I appeal to the most rigid dogmatist, whether the proof of the continued existence of our soul after death, derived from the simplicity of substance, or of the freedom of the will as opposed to a universal mechanism, arrived at through the subtle but ineffectual distinctions between subjective and objective prac- tical necessity, or of the existence of God as deduced from the concept of an ens realissimum (of the contingency of the changeable and of the necessity of a prime mover), have ever, upon passing out from the schools, succeeded in reaching the public mind or in exercising the slightest influence on its con- P 031 victions? That has never been found to occur, and in view of the unfitness of the common human understanding for such subtle speculation, ought never to have been expected. Such widely held convictions, so far as they rest on rational grounds, are due to quite other considerations. The hope of a future life has its source in that notable characteristic of our nature, never to be capable of being satisfied by what is temporal (as insufficient for the capacities of its whole destination); the consciousness of freedom rests exclusively on the clear ex- hibition of duties, in opposition to all claims of the inclina- tions; the belief in a wise and great Author of the world is generated solely by the glorious order, beauty, and providen- tial care everywhere displayed in nature. When the schools have been brought to recognise that they can lay no claim to higher and fuller insight in a matter of universal human concern than that which is equally within the reach of the great mass of men (ever to be held by us in the highest esteem), and that, as Schools of philosophy, they should limit themselves to the study of those universally comprehensible, and, for moral purposes, sufficient grounds of proof, then not only do these latter possessions remain undisturbed, but through this very fact they acquire yet greater authority. The change affects only the arrogant pretensions of the Schools, which would fain be counted the sole authors and possessors of such truths (as, indeed, they can justly claim to be in many other branches of knowledge), reserving the key to themselves, and communicating to the public their use only -- quod mecum nescit, solus vult scire videri. At the same time due regard is paid to the more moderate claims of the speculative philosopher. He still remains the sole authority in regard to a science which benefits the public without their knowing it, namely, the critique of reason. That critique can never become popular, and indeed there is no need that it should. For just as fine-spun arguments in favour of useful truths make no appeal to the general mind, so neither do the subtle objections that can be raised against them. On the other hand, both inevitably present themselves to everyone who rises to the height of speculation; and it is therefore the duty of the Schools, by means of a thorough investigation of the rights of speculative reason, once for all to prevent the scandal which, sooner or later, is sure to P 032 break out even among the masses, as the result of the disputes in which metaphysicians (and, as such, finally also the clergy) inevitably become involved to the consequent perversion of their teaching. Criticism alone can sever the root of materialism, fatalism, atheism, free-thinking, fanati- cism, and superstition, which can be injurious universally; as well as of idealism and scepticism, which are dangerous chiefly to the Schools, and hardly allow of being handed on 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 science as well as for mankind, to favour the free- dom of such criticism, 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 public danger over the destruction of cobwebs to which the public has never paid any attention, and the loss of which it can therefore never feel. This critique is not opposed to the dogmatic procedure of reason in its pure knowledge, as science, for that must always be dogmatic, that is, yield strict proof from sure principles a priori. It is opposed only to dogmatism, that is, to the pre- sumption that it is possible to make progress with pure know- ledge, according to principles, from concepts alone (those that are philosophical), as reason has long been in the habit of doing; and that it is possible to do this without having first in- vestigated in what way and by what right reason has come into possession of these concepts. Dogmatism is thus the dogmatic procedure of pure reason, without previous criticism of its own powers. In withstanding dogmatism we must not allow ourselves to give free rein to that loquacious shallowness, which assumes for itself the name of popularity, nor yet to scepticism, which makes short work with all metaphysics. On the contrary, such criticism is the necessary preparation for a thoroughly grounded metaphysics, which, as science, must necessarily be developed dogmatically, according to the strictest demands of system, in such manner as to satisfy not the general public but the re- quirements of the Schools. For that is a demand to which it stands pledged, and which it may not neglect, namely, that it carry out its work entirely a priori, to the complete satisfaction of speculative reason. In the execution of the plan prescribed P 033 by the critique, that is, in the future system of metaphysics we have therefore to follow the strict method of the celebrated Wolff, the greatest of all the dogmatic philosophers. He was the first to show by example (and by his example he awakened that spirit of thoroughness which is not extinct in Germany) how the secure progress of a science is to be attained only through orderly establishment of principles, clear determina- tion of concepts, insistence upon strictness of proof, and avoid- ance of venturesome, non-consecutive steps in our inferences. He was thus peculiarly well fitted to raise metaphysics to the dignity of a science, if only it had occurred to him to prepare the ground beforehand by a critique of the organ, that is, of pure reason itself. The blame for his having failed to do so lies not so much with himself as with the dogmatic way of thinking prevalent in his day, and with which the philo- sophers of his time, and of all previous times, have no right to reproach one another. Those who reject both the method of Wolff and the procedure of a critique of pure reason can have no other aim than to shake off the fetters of science altogether, and thus to change work into play, certainty into opinion, philosophy into philodoxy. Now, as regards this second edition, I have, as is fitting, endeavoured to profit by the opportunity, in order to remove, wherever possible, difficulties and obscurity which, not per- haps without my fault, may have given rise to the many misunderstandings into which even acute thinkers have fallen in passing judgment upon my book. In the propositions them- selves and their proofs, and also in the form and completeness of the [architectonic] plan, I have found nothing to alter. This is due partly to the long examination to which I have sub- jected them, before offering them to the public, partly to the nature of the subject-matter with which we are dealing. For pure speculative reason has a structure wherein everything is an organ, the whole being for the sake of every part, and every part for the sake of all the others, so that even the smallest imperfection, be it a fault (error) or a deficiency, must inevitably betray itself in use. This system will, as I hope, maintain, throughout the future, this unchangeableness. It is not self-conceit which justifies me in this confidence, but P 034 the evidence experimentally obtained through the parity of the result, whether we proceed from the smallest elements to the whole of pure reason or reverse-wise from the whole (for this also is presented to reason through its final end in the sphere of the practical) to each part. Any attempt to change even the smallest part at once gives rise to contradic- tions, not merely in the system, but in human reason in general. As to the mode of exposition, on the other hand, much still remains to be done; and in this edition I have sought to make improvements which should help in removing, first, the misunderstanding in regard to the Aesthetic, especi- ally concerning the concept of time; secondly, the obscurity of the deduction of the concepts of understanding; thirdly, a supposed want of sufficient evidence in the proofs of the prin- ciples of pure understanding; and finally, the false interpreta- tion placed upon the paralogisms charged against rational psychology. Beyond this point, that is, beyond the end of the first chapter of the Transcendental Dialectic, I have made no changes in the mode of exposition. Time was too short to P 035 allow of further changes; P 034n The only addition, strictly so called, though one affecting the method of proof only, is the new refutation of psychological idealism (cf. below, p. 244), and a strict (also, as I believe, the only possible) proof of the objective reality of outer intuition. However harmless idealism may be considered in respect of the essential aims of meta- physics (though, in fact, it is not thus harmless), it still remains a scandal to philosophy and to human reason in general that the existence of things outside us (from which we derive the whole material of knowledge, even for our inner sense) must be accepted merely on faith, and that if anyone thinks good to doubt their exist- ence, we are unable to counter his doubts by any satisfactory proof. Since there is some obscurity in the expressions used in the proof, from the third line to the sixth line, I beg to alter the passage as follows: "But this permanent cannot be an intuition in me. For all grounds of determination of my existence which are to be met with in me are representations; and as representations themselves require a permanent distinct from them, in relation to which their change, and so my existence in the time wherein they change, may be deter- mined. To this proof it will probably be objected, that I am im- mediately conscious only of that which is in me, that is, of my repre- sentation of outer things; and consequently that it must still remain uncertain whether outside me there is anything corresponding to it, or not. P 035 and besides, I have not found among competent and impartial critics any misapprehension in regard to the remaining sections. Though I shall not venture to name these critics with the praise that is their due, the attention which I have paid to their comments will easily be recognised in the [new] passages [above mentioned]. These improvements involve, however, a small loss, not to be prevented save by making the book too voluminous, namely, that I have had to omit or abridge certain passages, which, though not indeed essential to the completeness of the whole, may yet be missed by many readers as otherwise helpful. Only so could I obtain space for what, as I hope, is now a more intelligible exposition, which, though altering absolutely nothing in the fundamentals of the propositions put for- ward or even in their proofs, yet here and there departs so far from the previous method of treatment, that mere in- terpolations could not be made to suffice. This loss, which is small and can be remedied by consulting the first edition, will, I hope, be compensated by the greater clearness of the new P 036 text. P 034n But through inner experience I am conscious of my existence P 035n in time (consequently also of its determinability in time), and this is more than to be conscious merely of my representation. It is identical with the empirical consciousness of my existence, which is determin- able only through relation to something which, while bound up with my existence, is outside me. This consciousness of my existence in time is bound up in the way of identity with the consciousness of a relation to something outside me, and it is therefore experience not invention, sense not imagination, which inseparably connects this outside something with my inner sense. For outer sense is already in itself a relation of intuition to something actual outside me, and the reality of outer sense, in its distinction from imagination, rests simply on that which is here found to take place, namely, its being inseparably bound up with inner experience, as the condition of its possibility. If, with the intellectual consciousness of my existence, in the representation 'I am', which accompanies all my judgments and acts of understanding, I could at the same time connect a determina- tion of my existence through intellectual intuition, the conscious- ness of a relation to something outside me would not be required. But though that intellectual consciousness does indeed come first, the inner intuition, in which my existence can alone be determined, is sensible and is bound up with the condition of time. This deter- mination, however, and therefore the inner experience itself, depends P 036n upon something permanent which is not in me, and consequently can be only in something outside me, to which I must regard my- self as standing in relation. P 036 I have observed, with pleasure and thankfulness, in various published works -- alike in critical reviews and in in- dependent treatises -- that the spirit of thoroughness is not extinct in Germany, but has only been temporarily over- shadowed by the prevalence of a pretentiously free manner of thinking; and that the thorny paths of the Critique have not discouraged courageous and clear heads from setting them- selves to master my book -- a work which leads to a method- ical, and as such alone enduring, and therefore most necessary, science of pure reason. To these worthy men, who so happily combine thoroughness of insight with a talent for lucid ex- position -- which I cannot regard myself as possessing -- I leave the task of perfecting what, here and there, in its exposition, is still somewhat defective; for in this regard the danger is not that of being refuted, but of not being P 037 understood. P 036n The reality of outer sense is thus neces- sarily bound up with inner sense, if experience in general is to be possible at all; that is, I am just as certainly conscious that there are things outside me, which are in relation to my sense, as I am con- scious that I myself exist as determined in time. In order to deter- mine to which given intuitions objects outside me actually corre- spond, and which therefore belong to outer sense (to which, and not to the faculty of imagination, they are to be ascribed), we must in each single case appeal to the rules according to which experience in general, even inner experience, is distinguished from imagination -- the proposition that there is such a thing as outer experience being always presupposed. This further remark may be added. The repre- sentation of something permanent in existence is not the same as permanent representation. For though the representation of [some- thing permanent] may be very transitory and variable like all our other representations, not excepting those of matter, it yet refers to something permanent. This latter must therefore be an external thing distinct from all my representations, and its existence must be included in the determination of my own existence, constituting with it but a single experience such as would not take place even inwardly if it were not also at the same time, in part, outer. How this should be possible we are as little capable of explaining further as we are of accounting for our being able to think the abiding in time, the co- existence of which with the changing generates the concept of altera- tion. P 037 From now on, though I cannot allow myself to enter into controversy, I shall take careful note of all sugges- tions, be they from friends or from opponents, for use, in accordance with this propaedeutic, in the further elaboration of the system. In the course of these labours I have advanced somewhat far in years (this month I reach my sixty-fourth year), and I must be careful with my time if I am to succeed in my proposed scheme of providing a metaphysic of nature and of morals which will confirm the truth of my Critique in the two fields, of speculative and of practical reason. The clearing up of the obscurities in the present work -- they are hardly to be avoided in a new enterprise -- and the defence of it as a whole, I must therefore leave to those worthy men who have made my teaching their own. A philosophical work cannot be armed at all points, like a mathematical treatise, and may therefore be open to objection in this or that respect, while yet the structure of the system, taken in its unity, is not in the least endangered. Few have the versatility of mind to familiarise themselves with a new system; and owing to the general distaste for all innovation, still fewer have the inclina- tion to do so. If we take single passages, torn from their contexts, and compare them with one another, apparent con- tradictions are not likely to be lacking, especially in a work that is written with any freedom of expression. In the eyes of those who rely on the judgment of others, such contradic- tions have the effect of placing the work in an unfavourable light; but they are easily resolved by those who have mastered the idea of the whole. If a theory has in itself stability, the stresses and strains which may at first have seemed very threatening to it serve only, in the course of time, to smooth away its inequalities; and if men of impartiality, insight, and true popularity devote themselves to its exposition, it may also, in a short time, secure for itself the necessary elegance of statement. Konigsberg, April 1787. P 041 INTRODUCTION 1. THE DISTINCTION BETWEEN PURE AND EMPIRICAL KNOWLEDGE THERE can be no doubt that all our knowledge begins with experience. For how should our faculty of knowledge be awakened into action did not objects affecting our senses partly of themselves produce representations, partly arouse the activity of our understanding to compare these repre- sentations, and, by combining or separating them, work up the raw material of the sensible impressions into that knowledge of objects which is entitled experience? In the order of time, therefore, we have no knowledge antecedent to experience, and with experience all our knowledge begins. But though all our knowledge begins with experience, it does not follow that it all arises out of experience. I. THE IDEA OF TRANSCENDENTAL PHILOSOPHY Experience is, beyond all doubt, the first product to which our understanding gives rise, in working up the raw material of sensible impressions. Experience is therefore our first instruction, and in its progress is so inexhaustible in new information, that in the interconnected lives of all future generations there will never be any lack of new knowledge that can be thus ingathered. Nevertheless, it is by no means P 042a the sole field to which our understanding is confined. P 041 For it P 042 may well be that even our empirical knowledge is made up of what we receive through impressions and of what our own faculty of knowledge (sensible impressions serving merely as the occasion) supplies from itself. If our faculty of knowledge makes any such addition, it may be that we are not in a posi- tion to distinguish it from the raw material, until with long practice of attention we have become skilled in separating it. This, then, is a question which at least calls for closer examination, and does not allow of any off-hand answer: -- whether there is any knowledge that is thus independent of experience and even of all impressions of the senses. Such knowledge is entitled a priori, and distinguished from the P 043 empirical, which has its sources a posteriori, that is, in experi- ence. P 042a Experi- ence tells us, indeed, what is, but not that it must necessarily be so, and not otherwise. It therefore gives us no true universality; and reason, which is so insistent upon this kind of knowledge, is therefore more stimulated by it than satisfied. Such universal modes of knowledge, which at the same time possess the character of inner necessity, must in themselves, independently of experience, be clear and certain. They are therefore entitled knowledge a priori; whereas, on the other hand, that which is borrowed solely from experience is, as we say, known only a posteriori, or empirically. Now we find, what is especially noteworthy, that even into our experiences there enter modes of knowledge which must have their origin a priori, and which perhaps serve only to give coherence to our sense-representations. For if we elimin- ate from our experiences everything which belongs to the senses, there still remain certain original concepts and certain judgments derived from them, which must have arisen com- pletely a priori, independently of experience, inasmuch as they enable us to say, or at least lead us to believe that we can say, in regard to the objects which appear to the senses, more than mere experience would teach -- giving to assertions true universality and strict necessity, such as mere empirical know- ledge cannot supply. P 043 The expression 'a priori' does not, however, indicate with sufficient precision the full meaning of our question. For it has been customary to say, even of much knowledge that is derived from empirical sources, that we have it or are capable of having it a priori, meaning thereby that we do not derive it immediately from experience, but from a universal rule -- a rule which is itself, however, borrowed by us from experience. Thus we would say of a man who undermined the foundations of his house, that he might have known a priori that it would fall, that is, that he need not have waited for the experience of its actual falling. But still he could not know this completely a priori. For he had first to learn through experience that bodies are heavy, and therefore fall when their supports are withdrawn. In what follows, therefore, we shall understand by a priori knowledge, not knowledge independent of this or that experi- ence, but knowledge absolutely independent of all experience. Opposed to it is empirical knowledge, which is knowledge possible only a posteriori, that is, through experience. A - priori modes of knowledge are entitled pure when there is no admixture of anything empirical. Thus, for instance, the proposition, 'every alteration has its cause', while an a priori proposition, is not a pure proposition, because alteration is a concept which can be derived only from experience. II. WE ARE IN POSSESSION OF CERTAIN MODES OF A PRIORI KNOWLEDGE, AND EVEN THE COMMON UNDERSTAND- ING IS NEVER WITHOUT THEM What we here require is a criterion by which to distinguish with certainty between pure and empirical knowledge. Ex- perience teaches us that a thing is so and so, but not that it cannot be otherwise. First, then, if we have a proposition which in being thought is thought as necessary, it is an a priori judgment; and if, besides, it is not derived from any proposi- tion except one which also has the validity of a necessary judgment, it is an absolutely a priori judgment. Secondly, P 044 experience never confers on its judgments true or strict but only assumed and comparative universality, through induc- tion. We can properly only say, therefore, that so far as we have hitherto observed, there is no exception to this or that rule. If, then, a judgment is thought with strict univer- sality, that is, in such manner that no exception is allowed as possible, it is not derived from experience, but is valid abso- lutely a priori. Empirical universality is only an arbitrary ex- tension of a validity holding in most cases to one which holds in all, for instance, in the proposition, 'all bodies are heavy'. When, on the other hand, strict universality is essential to a a judgment, this indicates a special source of knowledge, namely, a faculty of a priori knowledge. Necessity and strict universality are thus sure criteria of a priori knowledge, and are inseparable from one another. But since in the employ- ment of these criteria the contingency of judgments is some- times more easily shown than their empirical limitation, or, as sometimes also happens, their unlimited universality can be more convincingly proved than their necessity, it is advis- able to use the two criteria separately, each by itself being infallible. Now it is easy to show that there actually are in human knowledge judgments which are necessary and in the strictest sense universal, and which are therefore pure a priori judg- ments. If an example from the sciences be desired, we have only to look to any of the propositions of mathematics; if we seek an example from the understanding in its quite ordinary employment, the proposition, 'every alteration must have a cause', will serve our purpose. In the latter case, indeed, the very concept of a cause so manifestly contains the concept of a necessity of connection with an effect and of the strict uni- versality of the rule, that the concept would be altogether lost if we attempted to derive it, as Hume has done, from a repeated association of that which happens with that which precedes, and from a custom of connecting representations, a custom originating in this repeated association, and constituting therefore a merely subjective necessity. Even without appeal- P 045 ing to such examples, it is possible to show that pure a priori principles are indispensable for the possibility of experience, and so to prove their existence a priori. For whence could experience derive its certainty, if all the rules, according to which it proceeds, were always themselves empirical, and therefore contingent? Such rules could hardly be regarded as first principles. At present, however, we may be content to have established the fact that our faculty of knowledge does have a pure employment, and to have shown what are the criteria of such an employment. Such a priori origin is manifest in certain concepts, no less than in judgments. If we remove from our empirical concept of a body, one by one, every feature in it which is [merely] empirical, the colour, the hardness or softness, the weight, even the impenetrability, there still remains the space which the body (now entirely vanished) occupied, and this cannot be removed. Again, if we remove from our em- pirical concept of any object, corporeal or incorporeal, all properties which experience has taught us, we yet cannot take away that property through which the object is thought as substance or as inhering in a substance (although this concept of substance is more determinate than that of an object in general). Owing, therefore, to the necessity with which this concept of substance forces itself upon us, we have no option save to admit that it has its seat in our faculty of a priori knowledge. III. PHILOSOPHY STANDS IN NEED OF A SCIENCE WHICH SHALL DETERMINE THE POSSIBILITY, THE PRINCIPLES, AND THE EXTENT OF ALL A PRIORI KNOWLEDGE But what is still more extraordinary than all the preceding is this, that certain modes of knowledge leave the field of all possible experiences and have the appearance of extending the scope of our judgments beyond all limits of experience, and this by means of concepts to which no corresponding object can ever be given in experience. It is precisely by means of the latter modes of knowledge, in a realm beyond the world of the senses, where experience P 046 can yield neither guidance nor correction, that our reason carries on those enquiries which owing to their importance we consider to be far more excellent, and in their purpose far more lofty, than all that the understanding can learn in the field of appearances. Indeed we prefer to run every risk of error rather than desist from such urgent enquiries, on the ground of their dubious character, or from disdain and in- difference. These unavoidable problems set by pure reason itself are God, freedom, and immortality. The science which, with all its preparations, is in its final intention directed solely to their solution is metaphysics; and its procedure is at first dogmatic, that is, it confidently sets itself to this task without any previous examination of the capacity or incapacity of reason for so great an undertaking. Now it does indeed seem natural that, as soon as we have left the ground of experience, we should, through careful en- quiries, assure ourselves as to the foundations of any building that we propose to erect, not making use of any knowledge that we possess without first determining whence it has come, and not trusting to principles without knowing their origin. It is natural, that is to say, that the question should first be considered, how the understanding can arrive at all this know- ledge a priori, and what extent, validity, and worth it may have. Nothing, indeed, could be more natural, if by the term 'natural' we signify what fittingly and reasonably ought to happen. But if we mean by 'natural' what ordinarily happens, then on the contrary nothing is more natural and more in- telligible than the fact that this enquiry has been so long neg- lected. For one part of this knowledge, the mathematical, has long been of established reliability, and so gives rise to a favour- able presumption as regards the other part, which may yet be of quite different nature. Besides, once we are outside the circle of experience, we can be sure of not being contradicted by experience. The charm of extending our knowledge is so great that nothing short of encountering a direct contra- diction can suffice to arrest us in our course; and this can be avoided, if we are careful in our fabrications -- which none the less will still remain fabrications. Mathematics gives us a shin- P 047 ing example of how far, independently of experience, we can progress in a priori knowledge. It does, indeed, occupy itself with objects and with knowledge solely in so far as they allow of being exhibited in intuition. But this circumstance is easily overlooked, since the intuition, in being thought, can itself be given a priori, and is therefore hardly to be distinguished from a bare and pure concept. Misled by such a proof of the power of reason, the demand for the extension of knowledge recog- nises no limits. The light dove, cleaving the air in her free flight, and feeling its resistance, might imagine that its flight would be still easier in empty space. It was thus that Plato left the world of the senses, as setting too narrow limits to the understanding, and ventured out beyond it on the wings of the ideas, in the empty space of the pure understanding. He did not observe that with all his efforts he made no ad- vance -- meeting no resistance that might, as it were, serve as a support upon which he could take a stand, to which he could apply his powers, and so set his understanding in motion. It is, indeed, the common fate of human reason to complete its speculative structures as speedily as may be, and only afterwards to enquire whether the foundations are reliable. All sorts of excuses will then be appealed to, in order to reassure us of their solidity, or rather indeed to enable us to dispense altogether with so late and so dangerous an enquiry. But what keeps us, during the actual building, free from all apprehension and suspicion, and flatters us with a seeming thoroughness, is this other circumstance, namely, that a great, perhaps the greatest, part of the business of our reason consists in analysis of the concepts which we already have of objects. This analysis supplies us with a consider- able body of knowledge, which, while nothing but explanation or elucidation of what has already been thought in our con- cepts, though in a confused manner, is yet prized as being, at least as regards its form, new insight. But so far as the matter or content is concerned, there has been no extension of our previously possessed concepts, but only an analysis of them. Since this procedure yields real knowledge a priori, which P 048 progresses in an assured and useful fashion, reason is so far misled as surreptitiously to introduce, without itself being aware of so doing, assertions of an entirely different order, in which it attaches to given concepts others completely foreign to them, and moreover attaches them a priori. And yet it is not known how reason can be in position to do this. Such a question is never so much as thought of. I shall therefore at once proceed to deal with the difference between these two kinds of knowledge. IV. THE DISTINCTION BETWEEN ANALYTIC AND SYNTHETIC JUDGMENTS In all judgments in which the relation of a subject to the predicate is thought (I take into consideration affirmative judgments only, the subsequent application to negative judg- ments being easily made), this relation is possible in two different ways. Either the predicate to the subject A, as something which is (covertly) contained in this concept A; or outside the concept A, although it does indeed stand in connection with it. In the one case I entitle the judg- ment analytic, in the other synthetic. Analytic judgments (affirmative) are therefore those in which the connection of the predicate with the subject is thought through identity; those in which this connection is thought without identity should be entitled synthetic. The former, as adding nothing through the predicate to the concept of the subject, but merely break- ing it up into those constituent concepts that have all along been thought in it, although confusedly, can also be entitled explicative. The latter, on the other hand, add to the concept of the subject a predicate which has not been in any wise thought in it, and which no analysis could possibly extract from it; and they may therefore be entitled ampliative. If I say, for instance, 'All bodies are extended', this is an analytic judgment. For I do not require to go beyond the concept which I connect with 'body' in order to find extension as bound up with it. To P 049 meet with this predicate, I have merely to analyse the concept, that is, to become conscious to myself of the manifold which I always think in that concept. The judgment is therefore analytic. But when I say, 'All bodies are heavy', the predi- cate is something quite different from anything that I think in the mere concept of body in general; and the addition of such a predicate therefore yields a synthetic judgment. * Judgments of experience, as such, are one and all synthetic. For it would be absurd to found an analytic judgment on ex- perience. Since, in framing the judgment, I must not go out- side my concept, there is no need to appeal to the testimony of experience in its support. That a body is extended is a pro- position that holds a priori and is not empirical. For, before appealing to experience, I have already in the concept of body all the conditions required for my judgment. I have only to ex- tract from it, in accordance with the principle of contradiction, the required predicate, and in so doing can at the same time become conscious of the necessity of the judgment -- and that is what experience could never have taught me. On the other hand, though I do not include in the concept of a body in general the predicate 'weight', none the less this concept indi- cates an object of experience through one of its parts, and I can add to that part other parts of this same experience, as in this way belonging together with the concept. *Thus it is evident: 1. that through analytic judgments our knowledge is not in any way extended, and that the concept which I already have is merely set forth and made intelligible to me; 2. that in synthetic judgments I must have besides the concept of the subject something else (X), upon which the un- derstanding may rely, if it is to know that a predicate, not contained in this concept, nevertheless belongs to it. In the case of empirical judgments, judgments of experi- ence, there is no difficulty whatsoever in meeting this demand. This X is the complete experience of the object which I think through the concept A -- a concept which forms only one part of this experience. P 049 From the start P 050 I can apprehend the concept of body analytically through the characters of extension, impenetrability, figure, etc. , all of which are thought in the concept. Now, however, looking back on the experience from which I have derived this con- cept of body, and finding weight to be invariably connected with the above characters, I attach it as a predicate to the concept; and in doing so I attach it synthetically, and am therefore extending my knowledge. The possibility of the syn- thesis of the predicate 'weight' with the concept of 'body' thus rests upon experience. While the one concept is not contained in the other, they yet belong to one another, though only con- tingently, as parts of a whole, namely, of an experience which is itself a synthetic combination of intuitions. But in a priori synthetic judgments this help is entirely lacking. [I do not here have the advantage of looking around in the field of experience. ] Upon what, then, am I to rely, when I seek to go beyond the concept A, and to know that another concept B is connected with it? Through what is the syn- thesis made possible? Let us take the proposition, 'Every- thing which happens has its cause'. In the concept of 'some- thing which happens', I do indeed think an existence which is preceded by a time, etc. , and from this concept analytic judg- ments may be obtained. P 049a For though I do not include in the concept P 050a of a body in general the predicate 'weight', the concept none the less indicates the complete experience through one of its parts; and to this part, as belonging to it, I can therefore add other parts of the same experience. By prior analysis I can ap- prehend the concept of body through the characters of exten- sion, impenetrability, figure, etc. , all of which are thought in this concept. To extend my knowledge, I then look back to the experience from which I have derived this concept of body, and find that weight is always connected with the above characters. Experience is thus the X which lies outside the concept A, and on which rests the possibility of the synthesis of the predicate 'weight' (B) with the concept (A). P 050 But the concept of a 'cause' lies entirely outside the other concept, and signifies something different P 051 from 'that which happens', and is not therefore in any way contained in this latter representation. How come I then to predicate of that which happens something quite different, and to apprehend that the concept of cause, though not con- tained in it, yet belongs, and indeed necessarily belongs to it? What is here the unknown = X which gives support to the understanding when it believes that it can discover outside the concept A a predicate B foreign to this concept, which it yet at the same time considers to be connected with it? It cannot be experience, because the suggested principle has connected the second representation with the first, not only with greater universality, but also with the character of necessity, and therefore completely a priori and on the basis of mere concepts. Upon such synthetic, that is, ampliative principles, all our a priori speculative knowledge must ulti- mately rest; analytic judgments are very important, and indeed necessary, but only for obtaining that clearness in the con- cepts which is requisite for such a sure and wide synthesis as will lead to a genuinely new addition to all previous know- ledge. * A certain mystery lies here concealed; and only upon its solution can the advance into the limitless field of the knowledge yielded by pure understanding be made sure and trustworthy. What we must do is to discover, in all its proper universality, the ground of the possibility of a priori synthetic judgments, to obtain insight into the conditions which make P 052a each kind of such judgments possible, and to mark out all this knowledge, which forms a genus by itself, not in any cursory outline, but in a system, with completeness and in a manner sufficient for any use, according to its original sources, divi- sions, extent, and limits. So much, meantime, as regards what is peculiar in synthetic judgments. P 051n * If it had occurred to any of the ancients even to raise this question, this by itself would, up to our own time, have been a power- ful influence against all systems of pure reason, and would have saved us so many of those vain attempts, which have been blindly undertaken without knowledge of what it is that requires to be done. P 052 V. IN ALL THEORETICAL SCIENCES OF REASON SYNTHETIC A PRIORI JUDGMENTS ARE CONTAINED AS PRINCIPLES 1. All mathematical judgments, without exception, are synthetic. This fact, though incontestably certain and in its consequences very important, has hitherto escaped the notice of those who are engaged in the analysis of human reason, and is, indeed, directly opposed to all their conjectures. For as it was found that all mathematical inferences proceed in accordance with the principle of contradiction (which the nature of all apodeictic certainty requires), it was supposed that the fundamental propositions of the science can themselves be known to be true through that principle. This is an erroneous view. For though a synthetic proposition can indeed be dis- cerned in accordance with the principle of contradiction, this can only be if another synthetic proposition is presupposed, and if it can then be apprehended as following from this other proposition; it can never be so discerned in and by itself. First of all, it has to be noted that mathematical proposi- tions, strictly so called, are always judgments a priori, not empirical; because they carry with them necessity, which cannot be derived from experience. If this be demurred to, I am willing to limit my statement to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure a priori knowledge. We might, indeed, at first suppose that the proposition 7 & 5 = 12 is a merely analytic proposition, and follows by the principle of contradiction from the concept of a sum of 7 and 5. But if we look more closely we find that the concept of the sum of 7 and 5 contains nothing save the union of the two numbers into one, and in this no thought is being taken P 053 as to what that single number may be which combines both. The concept of 12 is by no means already thought in merely thinking this union of 7 and 5; and I may analyse my concept of such a possible sum as long as I please, still I shall never find the 12 in it. We have to go outside these concepts, and call in the aid of the intuition which corresponds to one of them, our five fingers, for instance, or, as Segner does in his Arithmetic, five points, adding to the concept of 7, unit by unit, the five given in intuition. For starting with the number 7, and for the concept of 5 calling in the aid of the fingers of my hand as intuition, I now add one by one to the number 7 the units which I previously took together to form the number 5, and with the aid of that figure [the hand] see the number 12 come into being. That 5 should be added to 7, I have indeed already thought in the concept of a sum = 7 & 5, but not that this sum is equivalent to the number 12. Arithmetical pro- positions are therefore always synthetic. This is still more evident if we take larger numbers. For it is then obvious that, however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what [the number is that] is the sum. Just as little is any fundamental proposition of pure geometry analytic. That the straight line between two points is the shortest, is a synthetic proposition. For my concept of straight contains nothing of quantity, but only of quality. The concept of the shortest is wholly an addition, and cannot be derived, through any process of analysis, from the concept of the straight line. Intuition, therefore, must here be called in; only by its aid is the synthesis possible. What here causes us commonly to believe that the predicate of such apodeictic judgments is already contained in our concept, and that the judgment is therefore analytic, is merely the ambiguous character of the terms used. We are required to join in thought a certain predicate to a given concept, and this neces- P 054 sity is inherent in the concepts themselves. But the question is not what we ought to join in thought to the given concept, but what we actually think in it, even if only obscurely; and it is then manifest that, while the predicate is indeed attached necessarily to the concept, it is so in virtue of an intuition which must be added to the concept, not as thought in the concept itself. Some few fundamental propositions, presupposed by the geometrician, are, indeed, really analytic, and rest on the principle of contradiction. But, as identical propositions, they serve only as links in the chain of method and not as prin- ciples; for instance, a = a; the whole is equal to itself; or (a & b) a, that is, the whole is greater than its part. And even these propositions, though they are valid according to pure concepts, are only admitted in mathematics because they can be exhibited in intuition. 2. Natural science (physics) contains a priori synthetic judgments as principles. I need cite only two such judgments: that in all changes of the material world the quantity of matter remains unchanged; and that in all communication of motion, action and reaction must always be equal. Both propositions, it is evident, are not only necessary, and therefore in their origin a priori, but also synthetic. For in the concept of matter I do not think its permanence, but only its presence in the space which it occupies. I go outside and beyond the concept of matter, joining to it a priori in thought something which I have not thought in it. The proposition is not, therefore, ana- lytic, but synthetic, and yet is thought a priori; and so likewise are the other propositions of the pure part of natural science. 3. Metaphysics, even if we look upon it as having hitherto failed in all its endeavours, is yet, owing to the nature of human reason, a quite indispensable science, and ought to contain a priori synthetic knowledge. For its business is not merely to analyse concepts which we make for ourselves a - priori of things, and thereby to clarify them analytically, but to extend our a priori knowledge. And for this purpose we must employ principles which add to the given concept some- thing that was not contained in it, and through a priori syn- thetic judgments venture out so far that experience is quite P 055 unable to follow us, as, for instance, in the proposition, that the world must have a first beginning, and such like. Thus metaphysics consists, at least in intention, entirely of a priori synthetic propositions. VI. THE GENERAL PROBLEM OF PURE REASON Much is already gained if we can bring a number of in- vestigations under the formula of a single problem. For we not only lighten our own task, by defining it accurately, but make it easier for others, who would test our results, to judge whether or not we have succeeded in what we set out to do. Now the proper problem of pure reason is contained in the question: How are a priori synthetic judgments possible? That metaphysics has hitherto remained in so vacillating a state of uncertainty and contradiction, is entirely due to the fact that this problem, and perhaps even the distinction be- tween analytic and synthetic judgments, has never previously been considered. Upon the solution of this problem, or upon a sufficient proof that the possibility which it desires to have explained does in fact not exist at all, depends the success or failure of metaphysics. Among philosophers, David Hume came nearest to envisaging this problem, but still was very far from conceiving it with sufficient definiteness and universality. He occupied himself exclusively with the synthetic proposi- tion regarding the connection of an effect with its cause (principium causalitatis), and he believed himself to have shown that such an a priori proposition is entirely impos- sible. If we accept his conclusions, then all that we call metaphysics is a mere delusion whereby we fancy ourselves to have rational insight into what, in actual fact, is borrowed solely from experience, and under the influence of custom has taken the illusory semblance of necessity. If he had envisaged our problem in all its universality, he would never have been guilty of this statement, so destructive of all pure philosophy. For he would then have recognised that, according to his own argument, pure mathematics, as certainly containing a priori synthetic propositions, would also not be possible; and from such an assertion his good sense would have saved him. In the solution of the above problem, we are at the same P 056 time deciding as to the possibility of the employment of pure reason in establishing and developing all those sciences which contain a theoretical a priori knowledge of objects, and have therefore to answer the questions: How is pure mathematics possible? How is pure science of nature possible? Since these sciences actually exist, it is quite proper to ask how they are possible; for that they must be possible is proved by the fact that they exist. But the poor progress which has hitherto been made in metaphysics, and the fact that no system yet propounded can, in view of the essential purpose of metaphysics, be said really to exist, leaves everyone suffi- cient ground for doubting as to its possibility. Yet, in a certain sense, this kind of knowledge is to be looked upon as given; that is to say, metaphysics actually exists, if not as a science, yet still as natural disposition (meta- physica naturalis). For human reason, without being moved merely by the idle desire for extent and variety of knowledge, proceeds impetuously, driven on by an inward need, to ques- tions such as cannot be answered by any empirical employ- ment of reason, or by principles thence derived. Thus in all men, as soon as their reason has become ripe for speculation, there has always existed and will always continue to exist some kind of metaphysics. And so we have the question: How is metaphysics, as natural disposition, possible? that is, how from the nature of universal human reason do those questions arise which pure reason propounds to itself, and which it is impelled by its own need to answer as best it can? * Many may still have doubts as regards pure natural science. We have only, however, to consider the various propositions that are to be found at the beginning of (empirical) physics, properly so called, those, for instance, relating to the permanence in the quantity of matter, to inertia, to the equality of action and reaction, etc. , in order to be soon convinced that they constitute a physica pura, or rationalis, which well deserves, as an independent science, to be separately dealt with in its whole extent, be that narrow or wide. P 056 But since all attempts which have hitherto been made to answer these natural questions -- for instance, whether the P 057 world has a beginning or is from eternity -- have always met with unavoidable contradictions, we cannot rest satisfied with the mere natural disposition to metaphysics, that is, with the pure faculty of reason itself, from which, indeed, some sort of metaphysics (be it what it may) always arises. It must be possible for reason to attain to certainty whether we know or do not know the objects of metaphysics, that is, to come to a decision either in regard to the objects of its enquiries or in regard to the capacity or incapacity of reason to pass any judgment upon them, so that we may either with confidence extend our pure reason or set to it sure and determinate limits. This last question, which arises out of the previous general problem, may, rightly stated, take the form: How is metaphysics, as science, possible? Thus the critique of reason, in the end, necessarily leads to scientific knowledge; while its dogmatic employment, on the other hand, lands us in dogmatic assertions to which other assertions, equally specious, can always be opposed -- that is, in scepticism. This science cannot be of any very formidable prolixity, since it has to deal not with the objects of reason, the variety of which is inexhaustible, but only with itself and the prob- lems which arise entirely from within itself, and which are imposed upon it by its own nature, not by the nature of things which are distinct from it. When once reason has learnt com- pletely to understand its own power in respect of objects which can be presented to it in experience, it should easily be able to determine, with completeness and certainty, the extent and the limits of its attempted employment beyond the bounds of all experience. We may, then, and indeed we must, regard as abortive all attempts, hitherto made, to establish a metaphysic dogmatic- ally. For the analytic part in any such attempted system, namely, the mere analysis of the concepts that inhere in our reason a priori, is by no means the aim of, but only a prepara- tion for, metaphysics proper, that is, the extension of its a - priori synthetic knowledge. For such a purpose, the analysis of concepts is useless, since it merely shows what is contained in these concepts, not how we arrive at them a priori. A solution P 058 of this latter problem is required, that we may be able to de- termine the valid employment of such concepts in regard to the objects of all knowledge in general. Nor is much self-denial needed to give up these claims, seeing that the undeniable, and in the dogmatic procedure of reason also unavoidable, contradictions of reason with itself have long since undermined the authority of every metaphysical system yet propounded. Greater firmness will be required if we are not to be deterred by inward difficulties and outward opposition from endeavour- ing, through application of a method entirely different from any hitherto employed, at last to bring to a prosperous and fruitful growth a science indispensable to human reason -- a science whose every branch may be cut away but whose root cannot be destroyed. VII. THE IDEA AND DIVISION OF A SPECIAL SCIENCE, UNDER THE TITLE "CRITIQUE OF PURE REASON" In view of all these considerations, we arrive at the idea of a special science which can be entitled the Critique of Pure Reason. * For reason is the faculty which supplies the principles of a priori knowledge. Pure reason is, therefore, that which contains the principles whereby we know anything absolutely a priori. An organon of pure reason would be the sum-total of those principles according to which all modes of pure a priori knowledge can be acquired and actually brought into being. The exhaustive application of such an organon would give rise to a system of pure reason. But as this would be asking rather much, and as it is still doubtful whether, and in what cases, any extension of our knowledge be here possible, we P 059 can regard a science of the mere examination of pure reason, of its sources and limits, as the propaedeutic to the system of pure reason. P 058a *Any knowledge is entitled pure, if it be not mixed with any- thing extraneous. But knowledge is more particularly to be called absolutely pure, if no experience or sensation whatso- ever be mingled with it, and if it be therefore possible com- pletely a priori. P 059 As such, it should be called a critique, not a doctrine, of pure reason. Its utility, in speculation, ought properly to be only negative, not to extend, but only to clarify our reason, and keep it free from errors -- which is already a very great gain. I entitle transcendental all knowledge which is occupied not so much with objects as with the mode of our knowledge of objects in so far as this mode of knowledge is to be possible a priori. A system of such con- cepts might be entitled transcendental philosophy. But that is still, at this stage, too large an undertaking. For since such a science must contain, with completeness, both kinds of a priori knowledge, the analytic no less than the synthetic, it is, so far as our present purpose is concerned, much too comprehensive. We have to carry the analysis so far only as is indispensably necessary in order to comprehend, in their whole extent, the principles of a priori synthesis, with which alone we are called upon to deal. It is upon this enquiry, which should be entitled not a doctrine, but only a transcendental critique, that we are now engaged. Its pur- pose is not to extend knowledge, but only to correct it, and to supply a touchstone of the value, or lack of value, of all a priori knowledge. Such a critique is therefore a preparation, so far as may be possible, for an organon; and should this turn out not to be possible, then at least for a canon, according to which, in due course, the complete system of the philosophy of pure reason -- be it in extension or merely in limitation of its know- ledge -- may be carried into execution, analytically as well as synthetically. That such a system is possible, and indeed that it may not be of such great extent as to cut us off from the hope of entirely completing it, may already be gathered from the fact that what here constitutes our subject-matter is not the nature of things, which is inexhaustible, but the understand- ing which passes judgment upon the nature of things; and this understanding, again, only in respect of its a priori knowledge. These a priori possessions of the understanding, since they P 060 have not to be sought for without, cannot remain hidden from of our apprehending them in their completeness of judging them. Still less may the reader here expect a critique of books and systems of pure reason; we are concerned only with the critique of the faculty of pure reason itself. Only in so far as we build upon this foundation do we have a reliable touch- stone for estimating the philosophical value of old and new works in this field. Otherwise the unqualified historian or critic is passing judgments upon the groundless assertions of others by means of his own, which are equally groundless. Transcendental philosophy is only the idea of a science, for which the critique of pure reason has to lay down the complete architectonic plan. That is to say, it has to guaran- tee, as following from principles, the completeness and cer- tainty of the structure in all its parts. It is the system of all principles of pure reason. And if this critique is not itself to be entitled a transcendental philosophy, it is solely be- cause, to be a complete system, it would also have to contain an exhaustive analysis of the whole of a priori human know- ledge. Our critique must, indeed, supply a complete enumera- tion of all the fundamental concepts that go to constitute such pure knowledge. But it is not required to give an exhaustive analysis of these concepts, nor a complete review of those that can be derived from them. Such a demand would be unreasonable, partly because this analysis would not be appropriate to our main purpose, inasmuch as there is no such uncertainty in regard to analysis as we encounter in the case of synthesis, for the sake of which alone our whole critique is undertaken; and partly because it would be inconsistent with the unity of our plan to assume responsibility for the com- pleteness of such an analysis and derivation, when in view of our purpose we can be excused from doing so. The analysis of these a priori concepts, which later we shall have to enumerate, and the derivation of other concepts from them, can easily, how- P 061 ever, be made complete when once they have been established as exhausting the principles of synthesis, and if in this essen- tial respect nothing be lacking in them. The critique of pure reason therefore will contain all that is essential in transcendental philosophy. While it is the com- plete idea of transcendental philosophy, it is not equivalent to that latter science; for it carries the analysis only so far as is requisite for the complete examination of knowledge which is a priori and synthetic. What has chiefly to be kept in view in the division of such a science, is that no concepts be allowed to enter which con- tain in themselves anything empirical, or, in other words, that it consist in knowledge wholly a priori. Accordingly, although the highest principles and fundamental concepts of morality are a priori knowledge, they have no place in tran- scendental philosophy, because, although they do not lay at the foundation of their precepts the concepts of pleasure and pain, of the desires and inclinations, etc. , all of which are of empirical origin, yet in the construction of a system of pure morality these empirical concepts must necessarily be brought into the concept of duty, as representing either a hindrance, which we have to overcome, or an allurement, which must not be made into a motive. Transcendental philosophy is therefore a philosophy of pure and merely speculative reason. All that is practical, so far as it contains motives, relates to feelings, and these belong to the empirical sources of know- ledge. If we are to make a systematic division of the science which we are engaged in presenting, it must have first a doctrine of the elements, and secondly, a doctrine of the method of pure reason. Each of these chief divisions will have its subdivisions, but the grounds of these we are not yet in a position to explain. By way of introduction or anticipation we need only say that there are two stems of human know- ledge, namely, sensibility and understanding, which perhaps spring from a common, but to us unknown, root. Through the former, objects are given to us; through the latter, they are P 062 thought. Now in so far as sensibility may be found to contain a priori representations constituting the condition under which objects are given to us, it will belong to transcendental philosophy. And since the conditions under which alone the objects of human knowledge are given must precede those under which they are thought, the transcendental doctrine of sensibility will constitute the first part of the science of the elements. P 063 CRITIQUE OF PURE REASON I TRANSCENDENTAL DOCTRINE OF ELEMENTS P 065 TRANSCENDENTAL DOCTRINE OF ELEMENTS FIRST PART TRANSCENDENTAL AESTHETIC $1 IN whatever manner and by whatever means a mode of know- ledge may relate to objects, intuition is that through which it is in immediate relation to them, and to which all thought as a means is directed. But intuition takes place only in so far as the object is given to us. This again is only possible, to man at least, in so far as the mind is affected in a certain way. The capacity (receptivity) for receiving representations through the mode in which we are affected by objects, is entitled sensibility. Objects are given to us by means of sensibility, and it alone yields us intuitions; they are thought through the understand- ing, and from the understanding arise concepts. But all thought must, directly or indirectly, by way of certain characters relate ultimately to intuitions, and therefore, with us, to sensi- bility, 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 it, is sensation. That intuition which is in relation to the object through sensation, is entitled empirical. The undetermined object of an empirical intuition is entitled appearance. That in the appearance which corresponds to sensation P 066 I term its matter; but that which so determines the manifold of appearance that it allows of being ordered in certain re- lations, I term the form of appearance. That in which alone the sensations can be posited and ordered in a certain form, cannot itself be sensation; and therefore, while the matter of all appearance is given to us a posteriori only, its form must lie ready for the sensations a priori in the mind, and so must allow of being considered apart from all sensation. I term all representations pure (in the transcendental sense) in which there is nothing that belongs to sensation. The pure form of sensible intuitions in general, in which all the manifold of intuition is intuited in certain relations, must be found in the mind a priori. This pure form of sensibility may also itself be called pure intuition. Thus, if I take away from the representation of a body that which the understanding thinks in regard to it, substance, force, divisibility, etc. , and likewise what belongs to sensation, impenetrability, hardness, colour, etc. , something still remains over from this empirical intuition, namely, extension and figure. These belong to pure intuition, which, even without any actual object of the senses or of sensation, exists in the mind a priori as a mere form of sensibility. The science of all principles of a priori sensibility I call transcendental aesthetic. The Germans are the only people who currently make use of the word 'aesthetic' in order to signify what others call the critique of taste. This usage originated in the abortive attempt made by Baumgarten, that admirable analytical thinker, to bring the critical treatment of the beautiful under rational principles, and so to raise its rules to the rank of a science. But such endeavours are fruitless. The said rules or criteria are, as regards their chief sources, merely empirical, and consequently can never serve as determinate a - priori laws by which our judgment of taste must be directed. On the contrary, our judgment is the proper test of the correctness of the rules. For this reason it is advisable either to give up using the name in this sense of critique of taste, and to reserve it for that doctrine of sensibility which is true science -- thus P 067n approximating to the language and sense of the ancients, in their far-famed division of knowledge into aisthyta kai noyta -- or else to share the name with speculative philosophy, employing it partly in the transcendental and partly in the psychological sense. P 066 There must be such a science, forming P 067 the first part of the transcendental doctrine of elements, in distinction from that part which deals with the principles of pure thought, and which is called transcendental logic. In the transcendental aesthetic we shall, therefore, first isolate sensibility, by taking away from it everything which the understanding thinks through its concepts, so that nothing may be left save empirical intuition. Secondly, we shall also separate off from it everything which belongs to sensation, so that nothing may remain save pure intuition and the mere form of appearances, which is all that sensibility can supply a priori. In the course of this investigation it will be found that there are two pure forms of sensible intuition, serving as principles of a priori knowledge, namely, space and time. To the consideration of these we shall now proceed. THE TRANSCENDENTAL AESTHETIC SECTION I SPACE $2 Metaphysical Exposition of this Concept By means of outer sense, a property of our mind, we repre- sent to ourselves objects as outside us, and all without excep- tion in space. In space their shape, magnitude, and relation to one another are determined or determinable. Inner sense, by means of which the mind intuits itself or its inner state, yields indeed no intuition of the soul itself as an object; but there is nevertheless a determinate form [namely, time] in which alone the intuition of inner states is possible, and every- thing which belongs to inner determinations is therefore P 068 represented in relations of time. Time cannot be outwardly intuited, any more than space can be intuited as something in us. What, then, are space and time? Are they real exist- ences? Are they only determinations or relations of things, yet such as would belong to things even if they were not intuited? Or are space and time such that they belong only to the form of intuition, and therefore to the subjective constitution of our mind, apart from which they could not be ascribed to anything whatsoever? In order to obtain light upon these questions, let us first give an exposition of the concept of space. By exposition (expositio) I mean the clear, though not necessarily exhaustive, representation of that which belongs to a concept: the exposition is metaphysical when it contains that which exhibits the concept as given a priori. 1. Space is not an empirical concept which has been de- rived from outer experiences. For in order that certain sensa- tions be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must be presupposed. The representation of space can- not, therefore, be empirically obtained from the relations of outer appearance. On the contrary, this outer experience is itself possible at all only through that representation. 2. Space is a necessary a priori representation, which underlies all outer intuitions. We can never represent to our- selves the absence of space, though we can quite well think it as empty of objects. It must therefore be regarded as the con- dition of the possibility of appearances, and not as a determina- tion dependent upon them. It is an a priori representation, which necessarily underlies outer appearances. * 3. The apodeictic certainty of all geometrical propositions and the possibility of their a priori construction is grounded in this a priori necessity of space. P 069 3. Space is not a discursive or, as we say, general concept of relations of things in general, but a pure intuition. For, in the first place, we can represent to ourselves only one space; and if we speak of diverse spaces, we mean thereby only parts of one and the same unique space. Secondly, these parts cannot precede the one all-embracing space, as being, as it were, constituents out of which it can be composed; on the contrary, they can be thought only as in it. Space is essentially one; the manifold in it, and therefore the general concept of spaces, depends solely on [the introduction of] limitations. Hence it follows that an a priori, and not an empirical, intuition under- lies all concepts of space. For kindred reasons, geometrical propositions, that, for instance, in a triangle two sides together are greater than the third, can never be derived from the general concepts of line and triangle, but only from intuition, and this indeed a priori, with apodeictic certainty. 4. Space is represented as an infinite given magnitude. P 068a Were this representation of P 069a space a concept acquired a posteriori, and derived from outer experience in general, the first principles of mathematical determination would be nothing but perceptions. They would therefore all share in the contingent character of perception; that there should be only one straight line between two points would not be necessary, but only what experience always teaches. What is derived from experience has only compara- tive universality, namely, that which is obtained through in- duction. We should therefore only be able to say that, so far as hitherto observed, no space has been found which has more than three dimensions. * 5. Space is represented as an infinite given magnitude. A general concept of space, which is found alike in a foot and in an ell, cannot determine anything in regard to magnitude. If there were no limitlessness in the progression of intuition, no concept of relations could yield a principle of their infini- tude. P 069 Now every concept must be thought as a representation which is contained in an infinite number of different possible P 070 representations (as their common character), and which therefore contains these under itself; but no concept, as such, can be thought as containing an infinite number of representa- tions within itself. It is in this latter way, however, that space is thought; for all the parts of space coexist ad infinitum. Consequently, the original representation of space is an a - priori intuition, not a concept. $3 The Transcendental Exposition of the Concept of Space I understand by a transcendental exposition the explana- tion of a concept, as a principle from which the possibility of other a priori synthetic knowledge can be understood. For this purpose it is required (1) that such knowledge does really flow from the given concept, (2) that this knowledge is possible only on the assumption of a given mode of explaining the concept. Geometry is a science which determines the properties of space synthetically, and yet a priori. What, then, must be our representation of space, in order that such knowledge of it may be possible? It must in its origin be intuition; for from a mere concept no propositions can be obtained which go beyond the concept -- as happens in geometry (Introduc- tion, V). Further, this intuition must be a priori, that is, it must be found in us prior to any perception of an object, and must therefore be pure, not empirical, intuition. For geometrical propositions are one and all apodeictic, that is, are bound up with the consciousness of their necessity; for instance, that space has only three dimensions. Such pro- positions cannot be empirical or, in other words, judgments of experience, nor can they be derived from any such judg- ments (Introduction, II). How, then, can there exist in the mind an outer intui- tion which precedes the objects themselves, and in which the concept of these objects can be determined a priori? Manifestly, not otherwise than in so far as the intuition has its seat in the subject only, as the formal character of the P 071 subject, in virtue of which, in being affected by objects, it obtains immediate representation, that is, intuition, of them; and only in so far, therefore, as it is merely the form of outer sense in general. Our explanation is thus the only explanation that makes intelligible the possibility of geometry, as a body of a priori synthetic knowledge. Any mode of explanation which fails to do this, although it may otherwise seem to be somewhat similar, can by this criterion be distinguished from it with the greatest certainty. Conclusions from the above Concepts (a) Space does not represent any property of things in themselves, nor does it represent them in their relation to one another. That is to say, space does not represent any determination that attaches to the objects themselves, and which remains even when abstraction has been made of all the subjective conditions of intuition. For no determina- tions, whether absolute or relative, can be intuited prior to the existence of the things to which they belong, and none, therefore, can be intuited a priori. (b) Space is nothing but the form of all appearances of outer sense. It is the subjective condition of sensibility, under which alone outer intuition is possible for us. Since, then, the receptivity of the subject, its capacity to be affected by objects, must necessarily precede all intuitions of these objects, it can readily be understood how the form of all appearances can be given prior to all actual perceptions, and so exist in the mind a priori, and how, as a pure intuition, in which all objects must be determined, it can contain, prior to all experience, principles which determine the relations of these objects. It is, therefore, solely from the human standpoint that we can speak of space, of extended things, etc. If we depart from the subjective condition under which alone we can have outer intuition, namely, liability to be affected by objects, the representation of space stands for nothing whatsoever. P 072 This predicate can be ascribed to things only in so far as they appear to us, that is, only to objects of sensibility. The con- stant form of this receptivity, which we term sensibility, is a necessary condition of all the relations in which objects can be intuited as outside us; and if we abstract from these objects, it is a pure intuition, and bears the name of space. Since we cannot treat the special conditions of sensibility as conditions of the possibility of things, but only of their appear- ances, we can indeed say that space comprehends all things that appear to us as external, but not all things in themselves, by whatever subject they are intuited, or whether they be intuited or not. For we cannot judge in regard to the intui- tions of other thinking beings, whether they are bound by the same conditions as those which limit our intuition and which for us are universally valid. If we add to the concept of the subject of a judgment the limitation under which the judg- ment is made, the judgment is then unconditionally valid. The proposition, that all things are side by side in space, is valid under the limitation that these things are viewed as objects of our sensible intuition. If, now, I add the condition to the concept, and say that all things, as outer appearances, are side by side in space, the rule is valid universally and without limitation. Our exposition therefore establishes the reality, that is, the objective validity, of space in respect of whatever can be presented to us outwardly as object, but also at the same time the ideality of space in respect of things when they are considered in themselves through reason, that is, without regard to the constitution of our sensibility. We assert, then, the empirical reality of space, as regards all possible outer experience; and yet at the same time we assert its transcendental ideality -- in other words, that it is nothing at all, immediately we withdraw the above con- dition, namely, its limitation to possible experience, and so look upon it as something that underlies things in them- selves. With the sole exception of space there is no subjective representation, referring to something outer, which could be P 073 entitled [at once] objective [and] a priori. For there is no other subjective representation from which we can derive a priori synthetic propositions, as we can from intuition in space ($3). Strictly speaking, therefore, these other representations have no ideality, although they agree with the representation of space in this respect, that they belong merely to the subjective constitu- tion of our manner of sensibility, for instance, of sight, hearing, touch, as in the case of the sensations of colours, sounds, and heat, which, since they are mere sensations and not intuitions, do not of themselves yield knowledge of any object, least of all any a priori knowledge. The above remark is intended only to guard anyone from supposing that the ideality of space as here asserted can be illustrated by examples so altogether insufficient as colours, taste, etc. For these cannot rightly be regarded as properties of things, but only as changes in the subject, changes which may, indeed, be different for different men. In such examples as these, that which originally is itself only appearance, for instance, a rose, is being treated by the empirical understand- ing as a thing in itself, which, nevertheless, in respect of its colour, can appear differently to every observer. * This subjective condition of all outer appearances cannot, therefore, be compared to any other. The taste of a wine does not belong to the objective determinations of the wine, not even if by the wine as an object we mean the wine as appear- ance, but to the special constitution of sense in the subject that tastes it. Colours are not properties of the bodies to the in- tuition of which they are attached, but only modifications of the sense of sight, which is affected in a certain manner by light. Space, on the other hand, as condition of outer objects, necessarily belongs to their appearance or intuition. Taste and colours are not necessary conditions under which alone objects can be for us objects of the senses. P 073 The tran- scendental concept of appearances in space, on the other hand, is a critical reminder that nothing intuited in space is a thing in itself, that space is not a form inhering in things in themselves P 074 as their intrinsic property, that objects in themselves are quite unknown to us, and that what we call outer objects are nothing but mere representations of our sensibility, the form of which is space. The true correlate of sensibility, the thing in itself, is not known, and cannot be known, through these representations; and in experience no question is ever asked in regard to it. TRANSCENDENTAL AESTHETIC SECTION II TIME $4 Metaphysical exposition of the Concept of Time 1. Time is not an empirical concept that has been derived from any experience. For neither coexistence nor succession would ever come within our perception, if the repre- sentation of time were not presupposed as underlying them a priori. Only on the presupposition of time can we represent to ourselves a number of things as existing at one and the same time (simultaneously) or at different times (successively). P 073a They are connected with P 074a the appearances only as effects accidentally added by the par- ticular constitution of the sense organs. Accordingly, they are not a priori representations, but are grounded in sensation, and, indeed, in the case of taste, even upon feeling (pleasure and pain), as an effect of sensation. Further, no one can have a priori a representation of a colour or of any taste; whereas, since space concerns only the pure form of intuition, and therefore involves no sensation whatsoever, and nothing em- pirical, all kinds and determinations of space can and must be represented a priori, if concepts of figures and of their rela- tions are to arise. Through space alone is it possible that things should be outer objects to us. P 074 2. Time is a necessary representation that underlies all P 075 intuitions. We cannot, in respect of appearances in general, remove time itself, though we can quite well think time as void of appearances. Time is, therefore, given a priori. In it alone is actuality of appearances possible at all. Appearances may, one and all, vanish; but time (as the universal condition of their possibility) cannot itself be removed. 3. The possibility of apodeictic principles concerning the relations of time, or of axioms of time in general, is also grounded upon this a priori necessity. Time has only one dimension; different times are not simultaneous but successive (just as different spaces are not successive but simultaneous). These principles cannot be derived from experience, for ex- perience would give neither strict universality nor apodeictic certainty. We should only be able to say that common experi- ence teaches us that it is so; not that it must be so. These principles are valid as rules under which alone experiences are possible; and they instruct us in regard to the experiences, not by means of them. 4. Time is not a discursive, or what is called a general con- cept, but a pure form of sensible intuition. Different times are but parts of one and the same time; and the representation which can be given only through a single object is intuition. Moreover, the proposition that different times cannot be simultaneous is not to be derived from a general concept. The proposition is synthetic, and cannot have its origin in concepts alone. It is immediately contained in the intuition and representation of time. 5. The infinitude of time signifies nothing more than that every determinate magnitude of time is possible only through limitations of one single time that underlies it. The original representation, time, must therefore be given as unlimited. But when an object is so given that its parts, and every quan- tity of it, can be determinately represented only through limitation, the whole representation cannot be given through concepts, since they contain only partial representations; on the contrary, such concepts must themselves rest on immediate intuition. P 076 $5 The Transcendental exposition of the Concept of Time I may here refer to No. 3, where, for the sake of brevity, I have placed under the title of metaphysical exposition what is properly transcendental. Here I may add that the concept of alteration, and with it the concept of motion, as alteration of place, is possible only through and in the representation of time; and that if this representation were not an a priori (inner) intuition, no concept, no matter what it might be, could render comprehensible the possibility of an alteration, that is, of a combination of contradictorily opposed predicates in one and the same object, for instance, the being and the not-being of one and the same thing in one and the same place. Only in time can two contradictorily opposed predicates meet in one and the same object, namely, one after the other. Thus our concept of time explains the possibility of that body of a priori synthetic knowledge which is exhibited in the general doc- trine of motion, and which is by no means unfruitful. $6 Conclusions from these Concepts (a) Time is not something which exists of itself, or which inheres in things as an objective determination, and it does not, therefore, remain when abstraction is made of all sub- jective conditions of its intuition. Were it self-subsistent, it would be something which would be actual and yet not an actual object. Were it a determination or order inhering in things themselves, it could not precede the objects as their condition, and be known and intuited a priori by means of synthetic propositions. But this last is quite possible if time is nothing but the subjective condition under which alone intuition can take place in us. For that being so, this form of inner intuition can be represented prior to the objects, and therefore a priori. P 077 (b) Time is nothing but the form of inner sense, that is, of the intuition of ourselves and of our inner state. It cannot be a determination of outer appearances; it has to do neither with shape nor position, but with the relation of representations in our inner state. And just because this inner intuition yields no shape, we endeavour to make up for this want by analogies. We represent the time-sequence by a line progressing to in- finity, in which the manifold constitutes a series of one dimen- sion only; and we reason from the properties of this line to all the properties of time, with this one exception, that while the parts of the line are simultaneous the parts of time are always successive. From this fact also, that all the relations of time allow of being expressed in an outer intuition, it is evident that the representation is itself an intuition. (c) Time is the formal a priori condition of all appearances whatsoever. Space, as the pure form of all outer intuition, is so far limited; it serves as the a priori condition only of outer appearances. But since all representations, whether they have for their objects outer things or not, belong, in themselves, as determinations of the mind, to our inner state; and since this inner state stands under the formal condition of inner intui- tion, and so belongs to time, time is an a priori condition of all appearance whatsoever. It is the immediate condition of inner appearances (of our souls), and thereby the mediate con- dition of outer appearances. Just as I can say a priori that all outer appearances are in space, and are determined a priori in conformity with the relations of space, I can also say, from the principle of inner sense, that all appearances whatsoever, that is, all objects of the senses, are in time, and necessarily stand in time-relations. If we abstract from our mode of inwardly intuiting our- selves -- the mode of intuition in terms of which we likewise take up into our faculty of representation all outer intuitions -- and so take objects as they may be in themselves, then time is nothing. It has objective validity only in respect of appear- ances, these being things which we take as objects of our senses. It is no longer objective, if we abstract from the sensi- bility of our intuition, that is, from that mode of representation which is peculiar to us, and speak of things in general. Time is P 078 therefore a purely subjective condition of our (human) intuition (which is always sensible, that is, so far as we are affected by objects), and in itself, apart from the subject, is nothing. Nevertheless, in respect of all appearances, and therefore of all the things which can enter into our experience, it is neces- sarily objective. We cannot say that all things are in time, be- cause in this concept of things in general we are abstracting from every mode of their intuition and therefore from that condition under which alone objects can be represented as being in time. If, however, the condition be added to the concept, and we say that all things as appearances, that is, as objects of sensible intuition, are in time, then the proposition has legitimate objective validity and universality a priori. What we are maintaining is, therefore, the empirical reality of time, that is, its objective validity in respect of all objects which allow of ever being given to our senses. And since our intuition is always sensible, no object can ever be given to us in experience which does not conform to the condition of time. On the other hand, we deny to time all claim to absolute reality; that is to say, we deny that it belongs to things absolutely, as their condition or property, independ- ently of any reference to the form of our sensible intuition; properties that belong to things in themselves can never be given to us through the senses. This, then, is what constitutes the transcendental ideality of time. What we mean by this phrase is that if we abstract from the subjective conditions of sensible intuition, time is nothing, and cannot be ascribed to the objects in themselves (apart from their relation to our in- tuition) in the way either of subsistence or of inherence. This ideality, like that of space, must not, however, be illustrated by false analogies with sensation, because it is then assumed that the appearance, in which the sensible predicates inhere, itself has objective reality. In the case of time, such objective reality falls entirely away, save in so far as it is merely empir- ical, that is, save in so far as we regard the object itself merely as appearance. On this subject, the reader may refer to what has been said at the close of the preceding section. P 079 $7 Elucidation Against this theory, which admits the empirical reality of time, but denies its absolute and transcendental reality, I have heard men of intelligence so unanimously voicing an objection, that I must suppose it to occur spontaneously to every reader to whom this way of thinking is unfamiliar. The objection is this. Alterations are real, this being proved by change of our own representations -- even if all outer appearances, together with their alterations, be denied. Now alterations are possible only in time, and time is therefore something real. There is no difficulty in meeting this objection. I grant the whole argument. Certainly time is something real, namely, the real form of inner intuition. It has therefore subjective reality in respect of inner experience; that is, I really have the representation of time and of my determinations in it. Time is therefore to be regarded as real, not indeed as object but as the mode of representation of myself as object. If without this condition of sensibility I could intuit myself, or be intuited by another being, the very same determinations which we now represent to ourselves as alterations would yield knowledge into which the representa- tion of time, and therefore also of alteration, would in no way enter. Thus empirical reality has to be allowed to time, as the condition of all our experiences; on our theory, it is only its absolute reality that has to be denied. It is nothing but the form of our inner intuition. If we take away from our inner intuition the peculiar condition of our sensibility, the concept of time likewise vanishes; it does not inhere in the objects, but merely in the subject which intuits them. I can indeed say that my representations follow one another; but this is only to say that we are conscious of them as in a time- sequence, that is, in conformity with the form of inner sense. Time is not, therefore, something in itself, nor is it an objective determina- tion inherent in things. P 079 But the reason why this objection is so unanimously urged, P 080 and that too by those who have nothing very convincing to say against the doctrine of the ideality of space, is this. They have no expectation of being able to prove apodeictically the abso- lute reality of space; for they are confronted by idealism, which teaches that the reality of outer objects does not allow of strict proof. On the other hand, the reality of the object of our inner sense (the reality of myself and my state) is, [they argue,] immediately evident through consciousness. The former may be merely an illusion; the latter is, on their view, undeniably something real. What they have failed, how- ever, to recognise is that both are in the same position; in neither case can their reality as representations be questioned, and in both cases they belong only to appearance, which always has two sides, the one by which the object is viewed in and by itself (without regard to the mode of intuiting it -- its nature therefore remaining always problematic), the other by which the form of the intuition of this object is taken into account. This form is not to be looked for in the object in it- self, but in the subject to which the object appears; neverthe- less, it belongs really and necessarily to the appearance of this object. Time and space are, therefore, two sources of knowledge, from which bodies of a priori synthetic knowledge can be derived. (Pure mathematics is a brilliant example of such knowledge, especially as regards space and its relations. ) Time and space, taken together, are the pure forms of all sensible intuition, and so are what make a priori synthetic propositions possible. But these a priori sources of know- ledge, being merely conditions of our sensibility, just by this very fact determine their own limits, namely, that they apply to objects only in so far as objects are viewed as appear- ances, and do not present things as they are in themselves. This is the sole field of their validity; should we pass beyond it, no objective use can be made of them. This ideality of space and time leaves, however, the certainty of empirical know- ledge unaffected, for we are equally sure of it, whether these forms necessarily inhere in things in themselves or only in our intuition of them. Those, on the other hand, who maintain the absolute reality of space and time, whether as P 081 subsistent or only as inherent, must come into conflict with the principles of experience itself. For if they decide for the former alternative (which is generally the view taken by mathematical students of nature), they have to admit two eternal and infinite self-subsistent non-entities (space and time), which are there (yet without there being anything real) only in order to contain in themselves all that is real. If they adopt the latter alternative (as advocated by certain meta- physical students of nature), and regard space and time as relations of appearances, alongside or in succession to one another -- relations abstracted from experience, and in this isolation confusedly represented -- they are obliged to deny that a priori mathematical doctrines have any validity in respect of real things (for instance, in space), or at least to deny their apodeictic certainty. For such certainty is not to be found in the a posteriori. On this view, indeed, the a priori concepts of space and time are merely creatures of the im- agination, whose source must really be sought in experience, the imagination framing out of the relations abstracted from experience something that does indeed contain what is general in these relations, but which cannot exist without the restrictions which nature has attached to them. The former thinkers obtain at least this advantage, that they keep the field of appearances open for mathematical propositions. On the other hand, they have greatly embarrassed them- selves by those very conditions [space and time, eternal, infinite, and self-subsistent], when with the understanding they endeavour to go out beyond this field. The latter have indeed an advantage, in that the representations of space and time do not stand in their way if they seek to judge of objects, not as appearances but merely in their relation to the understanding. But since they are unable to appeal to a true and objectively valid a priori intuition, they can neither account for the possibility of a priori mathematical know- ledge, nor bring the propositions of experience into necessary agreement with it. On our theory of the true character of these two original forms of sensibility, both difficulties are removed. Lastly, transcendental aesthetic cannot contain more than P 082 these two elements, space and time. This is evident from the fact that all other concepts belonging to sensibility, even that of motion, in which both elements are united, presuppose something empirical. Motion presupposes the perception of something movable. But in space, considered in itself, there is nothing movable; consequently the movable must be something that is found in space only through experience, and must therefore be an empirical datum. For the same reason, transcendental aesthetic cannot count the concept of alteration among its a priori data. Time itself does not alter, but only something which is in time. The concept of time thus presupposes the perception of something existing and of the succession of its determinations; that is to say, it presupposes experience. $8 General Observations on Transcendental Aesthetic I. To avoid all misapprehension, it is necessary to ex- plain, as clearly as possible, what our view is regarding the fundamental constitution of sensible knowledge in general. What we have meant to say is that all our intuition is nothing but the representation of appearance; that the things which we intuit are not in themselves what we intuit them as being, nor their relations so constituted in themselves as they appear to us, and that if the subject, or even only the subjective constitution of the senses in general, be removed, the whole constitution and all the relations of objects in space and time, nay space and time themselves, would vanish. As appearances, they cannot exist in themselves, but only in us. What objects may be in themselves, and apart from all this receptivity of our sensibility, remains completely unknown to us. We know nothing but our mode of perceiving them -- a mode which is peculiar to us, and not necessarily shared in by every being, though, certainly, by every human being. With this alone have we any concern. Space and time are its pure forms, and sensation in general its matter. The former alone can we know a priori, that is, prior to all actual perception; and such knowledge is therefore called pure P 083 intuition. The latter is that in our knowledge which leads to its being called a posteriori knowledge, that is, empirical intuition. The former inhere in our sensibility with absolute necessity, no matter of what kind our sensations may be; the latter can exist in varying modes. Even if we could bring our intuition to the highest degree of clearness, we should not thereby come any nearer to the constitution of objects in themselves. We should still know only our mode of intuition, that is, our sensibility. We should, indeed, know it completely, but always only under the conditions of space and time -- conditions which are originally inherent in the subject. What the objects may be in themselves would never be- come known to us even through the most enlightened knowledge of that which is alone given us, namely, their appearance. The concept of sensibility and of appearance would be falsified, and our whole teaching in regard to them would be rendered empty and useless, if we were to accept the view that our entire sensibility is nothing but a confused representation of things, containing only what belongs to them in themselves, but doing so under an aggregation of characters and partial representations that we do not consciously distinguish. For the difference between a confused and a clear representation is merely logical, and does not concern the content. No doubt the concept of 'right', in its common-sense usage, contains all that the subtlest speculation can develop out of it, though in its ordinary and practical use we are not conscious of the manifold representations comprised in this thought But we cannot say that the common concept is therefore sensible, con- taining a mere appearance. For 'right' can never be an appear- ance; it is a concept in the understanding, and represents a property (the moral property) of actions, which belongs to them in themselves. The representation of a body in intuition, on the other hand, contains nothing that can belong to an object in itself, but merely the appearance of something, and the mode in which we are affected by that something; and this receptivity of our faculty of knowledge is termed sensibility. Even if that appearance could become completely transparent P 084 to us, such knowledge would remain toto coelo different from knowledge of the object in itself. The philosophy of Leibniz and Wolff, in thus treating the difference between the sensible and the intelligible as merely logical, has given a completely wrong direction to all in- vestigations into the nature and origin of our knowledge. This difference is quite evidently transcendental. It does not merely concern their [logical] form, as being either clear or confused. It concerns their origin and content. It is not that by our sensibility we cannot know the nature of things in themselves in any save a confused fashion; we do not apprehend them in any fashion whatsoever. If our subjective constitution be re- moved, the represented object, with the qualities which sen- sible intuition bestows upon it, is nowhere to be found, and cannot possibly be found. For it is this subjective constitution which determines its form as appearance. We commonly distinguish in appearances that which is essentially inherent in their intuition and holds for sense in all human beings, from that which belongs to their intuition accidentally only, and is valid not in relation to sensibility in general but only in relation to a particular standpoint or to a peculiarity of structure in this or that sense. The former kind of knowledge is then declared to represent the object in itself, the latter its appearance only. But this distinction is merely empirical. If, as generally happens, we stop short at this point, and do not proceed, as we ought, to treat the empirical in- tuition as itself mere appearance, in which nothing that belongs to a thing in itself can be found, our transcendental distinction is lost. We then believe that we know things in themselves, and this in spite of the fact that in the world of sense, how- ever deeply we enquire into its objects, we have to do with nothing but appearances. The rainbow in a sunny shower may be called a mere appearance, and the rain the thing in itself. This is correct, if the latter concept be taken in a merely physical sense. Rain will then be viewed only as that which, in all experience and in all its various positions relative to the senses, is determined thus, and not otherwise, in our intuition. But if we take this empirical object in its general character, and ask, without considering whether or not it is the same for all human sense, whether it represents an object in P 085 itself (and by that we cannot mean the drops of rain, for these are already, as appearances, empirical objects), the question as to the relation of the representation to the object at once becomes transcendental. We then realise that not only are the drops of rain mere appearances, but that even their round shape, nay even the space in which they fall, are nothing in themselves, but merely modifications or fundamental forms of our sensible intuition, and that the transcendental object remains unknown to us. The second important concern of our Transcendental Aes- thetic is that it should not obtain favour merely as a plausible hypothesis, but should have that certainty and freedom from doubt which is required of any theory that is to serve as an organon. To make this certainty completely convincing, we shall select a case by which the validity of the position adopted will be rendered obvious, and which will serve to set what has been said in $3 in a clearer light. Let us suppose that space and time are in themselves objective, and are conditions of the possibility of things in themselves. In the first place, it is evident that in regard to both there is a large number of a priori apodeictic and syn- thetic propositions. This is especially true of space, to which our chief attention will therefore be directed in this enquiry. Since the propositions of geometry are synthetic a priori, and are known with apodeictic certainty, I raise the question, whence do you obtain such propositions, and upon what does the understanding rely in its endeavour to achieve such abso- lutely necessary and universally valid truths? There is no other way than through concepts or through intuitions; and these are given either a priori or a posteriori. In their latter form, namely, as empirical concepts, and also as that upon which these are grounded, the empirical intuition, neither the concepts nor the intuitions can yield any synthetic proposition except such as is itself also merely empirical (that is, a pro- position of experience), and which for that very reason can never possess the necessity and absolute universality which are characteristic of all geometrical propositions. As regards the first and sole means of arriving at such knowledge, namely, in a priori fashion through mere concepts or through in- tuitions, it is evident that from mere concepts only analytic P 086 knowledge, not synthetic knowledge, is to be obtained. Take, for instance, the proposition, "Two straight lines cannot en- close a space, and with them alone no figure is possible", and try to derive it from the concept of straight lines and of the number two. Or take the proposition, "Given three straight lines, a figure is possible", and try, in like manner, to derive it from the concepts involved. All your labour is vain; and you find that you are constrained to have recourse to intuition, as is always done in geometry. You therefore give yourself an object in intuition. But of what kind is this intuition? Is it a pure a - priori intuition or an empirical intuition? Were it the latter, no universally valid proposition could ever arise out of it -- still less an apodeictic proposition -- for experience can never yield such. You must therefore give yourself an object a priori in intuition, and ground upon this your synthetic proposition. If there did not exist in you a power of a priori intuition; and if that subjective condition were not also at the same time, as regards its form, the universal a priori condition under which alone the object of this outer intuition is itself possible; if the object (the triangle) were something in itself, apart from any relation to you, the subject, how could you say that what necessarily exist in you as subjective conditions for the con- struction of a triangle, must of necessity belong to the triangle itself? You could not then add anything new (the figure) to your concepts (of three lines) as something which must neces- sarily be met with in the object, since this object is [on that view] given antecedently to your knowledge, and not by means of it. If, therefore, space (and the same is true of time) were not merely a form of your intuition, containing conditions a - priori, under which alone things can be outer objects to you, and without which subjective conditions outer objects are in themselves nothing, you could not in regard to outer objects determine anything whatsoever in an a priori and synthetic manner. It is, therefore, not merely possible or probable, but indubitably certain, that space and time, as the necessary conditions of all outer and inner experience, are merely sub- jective conditions of all our intuition, and that in relation to these conditions all objects are therefore mere appearances, and not given us as things in themselves which exist in this P 087 manner. For this reason also, while much can be said a priori as regards the form of appearances, nothing whatsoever can be asserted of the thing in itself, which may underlie these appearances. II. In confirmation of this theory of the ideality of both outer and inner sense, and therefore of all objects of the senses, as mere appearances, it is especially relevant to observe that everything in our knowledge which belongs to intuition -- feeling of pleasure and pain, and the will, not being know- ledge, are excluded -- contains nothing but mere relations; namely, of locations in an intuition (extension), of change of location (motion), and of laws according to which this change is determined (moving forces). What it is that is present in this or that location, or what it is that is operative in the things themselves apart from change of location, is not given through intuition. Now a thing in itself cannot be known through mere relations; and we may therefore conclude that since outer sense gives us nothing but mere relations, this sense can contain in its representation only the relation of an object to the subject, and not the inner properties of the object in itself. This also holds true of inner sense, not only because the representations of the outer senses constitute the proper material with which we occupy our mind, but because the time in which we set these representations, which is itself ante- cedent to the consciousness of them in experience, and which underlies them as the formal condition of the mode in which we posit them in the mind, itself contains [only] relations of succession, coexistence, and of that which is coexistent with succession, the enduring. Now that which, as representation, can be antecedent to any and every act of thinking any- thing, is intuition; and if it contains nothing but relations, it is the form of intuition. Since this form does not represent anything save in so far as something is posited in the mind, it can be nothing but the mode in which the mind is affected through its own activity (namely, through this positing of its representation), and so is affected by itself; in other words, it is P 088 nothing but an inner sense in respect of the form of that sense. Everything that is represented through a sense is so far always appearance, and consequently we must either refuse to admit that there is an inner sense, or we must recognise that the sub- ject, which is the object of the sense, can be represented through it only as appearance, not as that subject would judge of itself if its intuition were self-activity only, that is, were intellectual. The whole difficulty is as to how a subject can inwardly intuit itself; and this is a difficulty common to every theory. The con- sciousness of self (apperception) is the simple representation of the 'I', and if all that is manifold in the subject were given by the activity of the self, the inner intuition would be intel- lectual. In man this consciousness demands inner perception of the manifold which is antecedently given in the subject, and the mode in which this manifold is given in the mind must, as non-spontaneous, be entitled sensibility. If the faculty of coming to consciousness of oneself is to seek out (to apprehend) that which lies in the mind, it must affect the mind, and only in this way can it give rise to an intuition of itself. But the form of this intuition, which exists antecedently in the mind, determines, in the representation of time, the mode in which the manifold is together in the mind, since it then in- tuits itself not as it would represent itself if immediately self- active, but as it is affected by itself, and therefore as it appears to itself, not as it is. III. When I say that the intuition of outer objects and the self-intuition of the mind alike represent the objects and the mind, in space and in time, as they affect our senses, that is, as they appear, I do not mean to say that these objects are a mere illusion. For in an appearance the objects, nay even the pro- perties that we ascribe to them, are always regarded as some- thing actually given. Since, however, in the relation of the given object to the subject, such properties depend upon the mode of intuition of the subject, this object as appearance is to be distinguished from itself as object in itself. Thus when I maintain that the quality of space and of time, in conformity with which, as a condition of their existence, I posit both bodies and my own soul, lies in my mode of intuition and not in those objects in themselves, I am not saying that bodies merely seem P 089 to be outside me, or that my soul only seems to be given in my self- consciousness. It would be my own fault, if out of that which I ought to reckon as appearance, I made mere illusion. That does not follow as a consequence of our principle of the ideality of all our sensible intuitions -- quite the contrary. It is only if we ascribe objective reality to these forms of representation, that it becomes impossible for us to prevent everything being thereby transformed into mere illusion. For if we regard space and time as properties which, if they are to be possible at all, must be found in things in themselves, and if we reflect on the absurdities in which we are then involved, in that two infinite things, which are not substances, nor anything actually in- hering in substances, must yet have existence, nay, must be the necessary condition of the existence of all things, and moreover must continue to exist, even although all existing things be removed, -- we cannot blame the good Berkeley for degrading bodies to mere illusion. Nay, even our own existence, in being made thus dependent upon the self-sub- sistent reality of a non-entity, such as time, would necessarily be changed with it into sheer illusion -- an absurdity of which no one has yet been guilty. The predicates of the appearance can be ascribed to the object itself, in relation to our sense, for instance, the red colour or the scent to the rose. But what is illusory can never be ascribed as predicate to an object (for the sufficient reason that we then attribute to the object, taken by itself, what belongs to it only in relation to the senses, or in general to the subject), for instance, the two handles which were formerly ascribed to Saturn. That which, while in- separable from the representation of the object, is not to be met with in the object in itself, but always in its relation to the subject, is appearance. Accordingly the predicates of space and time are rightly ascribed to the objects of the senses, as such; and in this there is no illusion. On the other hand, if I describe redness to the rose in itself [handles to Satum], or extension to all outer objects in them- selves, without paying regard to the determinate relation of these objects to the subject, and without limiting my judgment to that relation, illusion then first arises. P 089 IV. In natural theology, in thinking an object [God], who not only can never be an object of intuition to us but P 090 cannot be an object of sensible intuition even to himself, we are careful to remove the conditions of time and space from his intuition -- for all his knowledge must be intuition, and not thought, which always involves limitations. But with what right can we do this if we have previously made time and space forms of things in themselves, and such as would remain, as a priori conditions of the existence of things, even though the things themselves were removed? As conditions of all existence in general, they must also be conditions of the existence of God. If we do not thus treat them as objective forms of all things, the only alternative is to view them as subjective forms of our inner and outer intuition, which is termed sensible, for the very reason that it is not original, that is, is not such as can itself give us the existence of its object -- a mode of intuition which, so far as we can judge, can belong only to the prim- ordial being. Our mode of intuition is dependent upon the existence of the object, and is therefore possible only if the subject's faculty of representation is affected by that object. This mode of intuiting in space and time need not be limited to human sensibility. It may be that all finite, thinking beings necessarily agree with man in this respect, although we are not in a position to judge whether this is actually so. But however universal this mode of sensibility may be, it does not therefore cease to be sensibility. It is derivative (intuitus derivativus), not original (intuitus originarius), and therefore not an intellectual intuition. For the reason stated above, such intellectual intuition seems to belong solely to the primordial being, and can never be ascribed to a dependent being, dependent in its existence as well as in its intuition, and which through that intuition determines its existence solely in relation to given objects. This latter remark, however, must be taken only as an illustration of our aesthetic theory, not as forming part of the proof. Conclusion of the Transcendental Aesthetic Here, then, in pure a priori intuitions, space and time, we have one of the factors required for solution of the general P 091 problem of transcendental philosophy: how are synthetic a priori judgments possible? When in a priori judgment we seek to go out beyond the given concept, we come in the a priori intuitions upon that which cannot be discovered in the concept but which is certainly found a priori in the in- tuition corresponding to the concept, and can be connected with it synthetically. Such judgments, however, thus based on intuition, can never extend beyond objects of the senses; they are valid only for objects of possible experience. P 092 TRANSCENDENTAL DOCTRINE OF ELEMENTS SECOND PART TRANSCENDENTAL LOGIC INTRODUCTION IDEA OF A TRANSCENDENTAL LOGIC I LOGIC IN GENERAL OUR knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (receptivity for impressions), the second is the power of know- ing an object through these representations (spontaneity [in the production] of concepts). Through the first an object is given to us, through the second the object is thought in relation to that [given] representation (which is a mere determination of the mind). Intuition and concepts constitute, therefore, the ele- ments of all our knowledge, so that neither concepts without an intuition in some way corresponding to them, nor intuition with- out concepts, can yield knowledge. Both may be either pure or empirical. When they contain sensation (which presupposes the actual presence of the object), they are empirical. When there is no mingling of sensation with the representation,they are pure. Sensation may be entitled the material of sensible knowledge. Pure intuition, therefore, contains only the form under which something is intuited; the pure concept only the form of the thought of an object in general. Pure intuitions or pure con- cepts alone are possible a priori, empirical intuitions and empirical concepts only a posteriori. P 093 If the receptivity of our mind, its power of receiving re- presentations in so far as it is in any wise affected, is to be entitled sensibility, then the mind's power of producing repre- sentations from itself, the spontaneity of knowledge, should be called the understanding. Our nature is so constituted that our intuition can never be other than sensible; that is, it con- tains only the mode in which we are affected by objects. The faculty, on the other hand, which enables us to think the object of sensible intuition is the understanding. To neither of these powers may a preference be given over the other. Without sensibility no object would be given to us, without understanding no object would be thought. Thoughts without content are empty, intuitions without concepts are blind. It is, therefore, just as necessary to make our concepts sensible, that is, to add the object to them in intuition, as to make our intuitions intelligible, that is, to bring them under con- cepts. These two powers or capacities cannot exchange their functions. The understanding can intuit nothing, the senses can think nothing. Only through their union can know- ledge arise. But that is no reason for confounding the contribution of either with that of the other; rather is it a strong reason for carefully separating and distinguishing the one from the other. We therefore distinguish the science of the rules of sensibility in general, that is, aesthetic, from the science of the rules of the understanding in general, that is, logic. Logic, again, can be treated in a twofold manner, either as logic of the general or as logic of the special employment of the understanding. The former contains the absolutely necessary rules of thought without which there can be no employment whatsoever of the understanding. It therefore treats of understanding without any regard to difference in the objects to which the understanding may be directed. The logic of the special employment of the understanding contains the rules of correct thinking as regards a certain kind of objects. The former may be called the logic of elements, the latter the organon of this or that science. The latter is com- monly taught in the schools as a propaedeutic to the sciences, though, according to the actual procedure of human reason, it is what is obtained last of all, when the particular science P 094 under question has been already brought to such completion that it requires only a few finishing touches to correct and perfect it. For the objects under consideration must already be known fairly completely before it can be possible to pre- scribe the rules according to which a science of them is to be obtained. General logic is either pure or applied. In the former we abstract from all empirical conditions under which our under- standing is exercised, i.e. from the influence of the senses, the play of imagination, the laws of memory, the force of habit, inclination, etc. , and so from all sources of prejudice, indeed from all causes from which this or that knowledge may arise or seem to arise. For they concern the understanding only in so far as it is being employed under certain circumstances, and to become acquainted with these circumstances experi- ence is required. Pure general logic has to do, therefore, only with principles a priori, and is a canon of understanding and of reason, but only in respect of what is formal in their em- ployment, be the content what it may, empirical or tran- scendental. General logic is called applied, when it is directed to the rules of the employment of understanding under the subjective empirical conditions dealt with by psychology. Applied logic has therefore empirical principles, although it is still indeed in so far general that it refers to the employ- ment of the understanding without regard to difference in the objects. Consequently it is neither a canon of the under- standing in general nor an organon of special sciences, but merely a cathartic of the common understanding. In general logic, therefore, that part which is to constitute the pure doctrine of reason must be entirely separated from that which constitutes applied (though always still general) logic. The former alone is, properly speaking, a science, though indeed concise and dry, as the methodical exposition of a doctrine of the elements of the understanding is bound to be. There are therefore two rules which logicians must always bear in mind, in dealing with pure general logic: 1. As general logic, it abstracts from all content of the knowledge of understanding and from all differences in its objects, and deals with nothing but the mere form of thought. P 095 2. As pure logic, it has nothing to do with empirical prin- ciples, and does not, as has sometimes been supposed, borrow anything from psychology, which therefore has no influence whatever on the canon of the understanding. Pure logic is a body of demonstrated doctrine, and everything in it must be certain entirely a priori. What I call applied logic (contrary to the usual meaning of this title, according to which it should contain certain exercises for which pure logic gives the rules) is a representa- tion of the understanding and of the rules of its necessary employment in concreto, that is, under the accidental sub- jective conditions which may hinder or help its application, and which are all given only empirically. It treats of attention, its impediments and consequences, of the source of error, of the state of doubt, hesitation, and conviction, etc. Pure general logic stands to it in the same relation as pure ethics, which contains only the necessary moral laws of a free will in general, stands to the doctrine of the virtues strictly so called -- the doctrine which considers these laws under the limitations of the feelings, inclinations, and passions to which men are more or less subject. Such a doctrine can never furnish a true and demonstrated science, because, like applied logic, it depends on empirical and psychological principles. II TRANSCENDENTAL LOGIC General logic, as we have shown, abstracts from all con- tent of knowledge, that is, from all relation of knowledge to the object, and considers only the logical form in the relation of any knowledge to other knowledge; that is, it treats of the form of thought in general. But since, as the Transcendental Aes- thetic has shown, there are pure as well as empirical intuitions, a distinction might likewise be drawn between pure and em- pirical thought of objects. In that case we should have a logic in which we do not abstract from the entire content of know- ledge. This other logic, which should contain solely the rules of the pure thought of an object, would exclude only those P 096 modes of knowledge which have empirical content. It would also treat of the origin of the modes in which we know objects, in so far as that origin cannot be attributed to the objects. General logic, on the other hand, has nothing to do with the origin of knowledge, but only considers representations, be they originally a priori in ourselves or only empirically given, according to the laws which the understanding employs when, in thinking, it relates them to one another. It deals therefore only with that form which the understanding is able to impart to the representations, from whatever source they may have arisen. And here I make a remark which the reader must bear well in mind, as it extends its influence over all that follows. Not every kind of knowledge a priori should be called tran- scendental, but that only by which we know that -- and how -- certain representations (intuitions or concepts) can be em- ployed or are possible purely a priori. The term 'transcend- ental', that is to say, signifies such knowledge as concerns the a priori possibility of knowledge, or its a priori employment. Neither space nor any a priori geometrical determination of it is a transcendental representation; what can alone be entitled transcendental is the knowledge that these representations are not of empirical origin, and the possibility that they can yet relate a priori to objects of experience. The application of space to objects in general would likewise be transcendental, but, if restricted solely to objects of sense, it is empirical. The distinction between the transcendental and the empirical belongs therefore only to the critique of knowledge; it does not concern the relation of that knowledge to its objects. In the expectation, therefore, that there may perhaps be concepts which relate a priori to objects, not as pure or sen- sible intuitions, but solely as acts of pure thought -- that is, as concepts which are neither of empirical nor of aesthetic origin -- we form for ourselves by anticipation the idea of a science of the knowledge which belongs to pure understanding and reason, whereby we think objects entirely a priori. Such a science, which should determine the origin, the scope, and P 097 the objective validity of such knowledge, would have to be called transcendental logic, because, unlike general logic, which has to deal with both empirical and pure knowledge of reason, it concerns itself with the laws of understanding and of reason solely in so far as they relate a priori to objects. III THE DIVISION OF GENERAL LOGIC INTO ANALYTIC AND DIALECTIC The question, famed of old, by which logicians were supposed to be driven into a corner, obliged either to have recourse to a pitiful sophism, or to confess their ignorance and consequently the emptiness of their whole art, is the question: What is truth? The nominal definition of truth, that it is the agreement of knowledge with its object, is assumed as granted; the question asked is as to what is the general and sure criterion of the truth of any and every knowledge. To know what questions may reasonably be asked is already a great and necessary proof of sagacity and insight. For if a question is absurd in itself and calls for an answer where none is required, it not only brings shame on the pro- pounder of the question, but may betray an incautious listener into absurd answers, thus presenting, as the ancients said, the ludicrous spectacle of one man milking a he-goat and the other holding a sieve underneath. If truth consists in the agreement of knowledge with its object, that object must thereby be distinguished from other objects; for knowledge is false, if it does not agree with the object to which it is related, even although it contains some- thing which may be valid of other objects. Now a general criterion of truth must be such as would be valid in each and every instance of knowledge, however their objects may vary. It is obvious, however, that such a criterion [being general] cannot take account of the [varying] content of knowledge (relation to its [specific] object). But since truth concerns just this very content, it is quite impossible, and indeed absurd, to ask for a P 098 general test of the truth of such content. A sufficient and at the same time general criterion of truth cannot possibly be given. Since we have already entitled the content of knowledge its matter, we must be prepared to recognise that of the truth of knowledge, so far as its matter is concerned, no general criterion can be demanded. Such a criterion would by its very nature be self-contradictory. But, on the other hand, as regards knowledge in respect of its mere form (leaving aside all content), it is evident that logic, in so far as it expounds the universal and necessary rules of the understanding, must in these rules furnish criteria of truth. Whatever contradicts these rules is false. For the understanding would thereby be made to contradict its own general rules of thought, and so to contradict itself. These criteria, however, concern only the form of truth, that is, of thought in general; and in so far they are quite correct, but are not by themselves sufficient. For although our knowledge may be in complete accordance with logical demands, that is, may not contradict itself, it is still possible that it may be in contradiction with its object. The purely logical criterion of truth, namely, the agreement of knowledge with the general and formal laws of the understanding and reason, is a conditio sine qua non, and is therefore the negative condition of all truth. But further than this logic cannot go. It has no touch- stone for the discovery of such error as concerns not the form but the content. General logic resolves the whole formal procedure of the understanding and reason into its elements, and exhibits them as principles of all logical criticism of our knowledge. This part of logic, which may therefore be entitled analytic, yields what is at least the negative touchstone of truth. Its rules must be applied in the examination and appraising of the form of all knowledge before we proceed to determine whether their content contains positive truth in respect to their object. But since the mere form of knowledge, however completely it may be in agreement with logical laws, is far from being sufficient to determine the material (objective) truth of know- ledge, no one can venture with the help of logic alone to judge regarding objects, or to make any assertion. We must first, independently of logic, obtain reliable information; only P 099 then are we in a position to enquire, in accordance with logical laws, into the use of this information and its connection in a coherent whole, or rather to test it by these laws. There is, however, something so tempting in the possession of an art so specious, through which we give to all our knowledge, how- ever uninstructed we may be in regard to its content, the form of understanding, that general logic, which is merely a canon of judgment, has been employed as if it were an organon for the actual production of at least the semblance of objective assertions, and has thus been misapplied. General logic, when thus treated as an organon, is called dialectic. However various were the significations in which the ancients used 'dialectic' as the title for a science or art, we can safely conclude from their actual employment of it that with them it was never anything else than the logic of illusion. It was a sophistical art of giving to ignorance, and indeed to intentional sophistries, the appearance of truth, by the device of imitat- ing the methodical thoroughness which logic prescribes, and of using its 'topic' to conceal the emptiness of its pretensions. Now it may be noted as a sure and useful warning, that general logic, if viewed as an organon, is always a logic of illusion, that is, dialectical. For logic teaches us nothing whatsoever regarding the content of knowledge, but lays down only the formal conditions of agreement with the understanding; and since these conditions can tell us nothing at all as to the objects concerned, any attempt to use this logic as an instru- ment (organon) that professes to extend and enlarge our knowledge can end in nothing but mere talk -- in which, with a certain plausibility, we maintain, or, if such be our choice, attack, any and every possible assertion. Such instruction is quite unbecoming the dignity of philo- sophy. The title 'dialectic' has therefore come to be otherwise employed, and has been assigned to logic, as a critique of dialectical illusion. This is the sense in which it is to be under- stood in this work. P 100 IV THE DIVISION OF TRANSCENDENTAL LOGIC INTO TRANSCENDENTAL ANALYTIC AND DIALECTIC In a transcendental logic we isolate the understanding -- as above, in the Transcendental Aesthetic, the sensibility -- separating out from our knowledge that part of thought which has its origin solely in the understanding. The employment of this pure knowledge depends upon the condition that objects to which it can be applied be given to us in intuition. In the absence of intuition all our knowledge is without objects, and therefore remains entirely empty. That part of transcen- dental logic which deals with the elements of the pure know- ledge yielded by understanding, and the principles without which no object can be thought, is transcendental analytic. It is a logic of truth. For no knowledge can contradict it without at once losing all content, that is, all relation to any object, and therefore all truth. But since it is very tempting to use these pure modes of knowledge of the understanding and these prin- ciples by themselves, and even beyond the limits of experience, which alone can yield the matter (objects) to which those pure concepts of understanding can be applied, the understanding is led to incur the risk of making, with a mere show of rationality, a material use of its pure and merely formal principles, and of passing judgments upon objects without distinction -- upon objects which are not given to us, nay, perhaps cannot in any way be given. Since, properly, this transcendental analytic should be used only as a canon for passing judgment upon the empirical employment of the understanding, it is misapplied if appealed to as an organon of its general and unlimited application, and if consequently we venture, with the pure understanding alone, to judge synthetically, to affirm, and to decide regarding objects in general. The employment of the pure understanding then becomes dialectical. The second part of transcendental logic must therefore form a critique of this dialectical illusion, and is called transcendental dialectic, not as an art of producing such illusion dogmatically (an art un- fortunately very commonly practised by metaphysical jugglers), but as a critique of understanding and reason in respect of P 101 their hyperphysical employment. It will expose the false, illu- sory character of those groundless pretensions, and in place of the high claims to discover and to extend knowledge merely by means of transcendental principles, it will substitute what is no more than a critical treatment of the pure understanding, for the guarding of it against sophistical illusion. P 102 TRANSCENDENTAL LOGIC FIRST DIVISION TRANSCENDENTAL ANALYTIC TRANSCENDENTAL analytic consists in the dissection of all our a priori knowledge into the elements that pure under- standing by itself yields. In so doing, the following are the points of chief concern: (1) that the concepts be pure and not empirical; (2) that they belong, not to intuition and sensibility, but to thought and understanding; (3) that they be fundamental and be carefully distinguished from those which are derivative or composite; (4) that our table of concepts be complete, covering the whole field of the pure understanding. When a science is an aggregate brought into existence in a merely experimental manner, such completeness can never be guaranteed by any kind of mere estimate. It is possible only by means of an idea of the totality of the a priori knowledge yielded by the understanding; such an idea can furnish an exact classification of the concepts which compose that totality, exhibiting their interconnection in a system. Pure understanding distinguishes itself not merely from all that is empirical but completely also from all sensibility. It is a unity self-subsistent, self-sufficient, and not to be increased by any additions from without. The sum of its knowledge thus constitutes a system, comprehended and determined by one idea. The completeness and articulation of this system can at the same time yield a criterion of the correctness and genuine- ness of all its components. This part of transcendental logic requires, however, for its complete exposition, two books, the one containing the concepts, the other the principles of pure understanding. P 103 TRANSCENDENTAL ANALYTIC BOOK I ANALYTIC OF CONCEPTS By 'analytic of concepts' I do not understand their ana- lysis, or the procedure usual in philosophical investigations, that of dissecting the content of such concepts as may present themselves, and so of rendering them more distinct; but the hitherto rarely attempted dissection of the faculty of the under- standing itself, in order to investigate the possibility of con- cepts a priori by looking for them in the understanding alone, as their birthplace, and by analysing the pure use of this faculty. This is the proper task of a transcendental philosophy; anything beyond this belongs to the logical treatment of con- cepts in philosophy in general. We shall therefore follow up the pure concepts to their first seeds and dispositions in the human understanding, in which they lie prepared, till at last, on the occasion of experience, they are developed, and by the same understanding are exhibited in their purity, freed from the empirical conditions attaching to them. P 104 ANALYTIC OF CONCEPTS CHAPTER I THE CLUE TO THE DISCOVERY OF ALL PURE CONCEPTS OF THE UNDERSTANDING WHEN we call a faculty of knowledge into play, then, as the occasioning circumstances differ, various concepts stand forth and make the faculty known, and allow of their being collected with more or less completeness, in proportion as observation has been made of them over a longer time or with greater acuteness. But when the enquiry is carried on in this mechanical fashion, we can never be sure whether it has been brought to completion. Further, the con- cepts which we thus discover only as opportunity offers, ex- hibit no order and systematic unity, but are in the end merely arranged in pairs according to similarities, and in series accord- ing to the amount of their contents, from the simple on to the more composite -- an arrangement which is anything but sys- tematic, although to a certain extent methodically instituted. Transcendental philosophy, in seeking for its concepts, has the advantage and also the duty of proceeding according to a single principle. For these concepts spring, pure and unmixed, out of the understanding which is an absolute unity; and must therefore be connected with each other according to one con- cept or idea. Such a connection supplies us with a rule, by which we are enabled to assign its proper place to each pure concept of the understanding, and by which we can determine in an a priori manner their systematic completeness. Other- wise we should be dependent in these matters on our own discretionary judgment or merely on chance. P 105 THE TRANSCENDENTAL CLUE TO THE DISCOVERY OF ALL PURE CONCEPTS OF THE UNDERSTANDING Section I THE LOGICAL EMPLOYMENT OF THE UNDERSTANDING The understanding has thus far been explained merely negatively, as a non-sensible faculty of knowledge. Now since without sensibility we cannot have any intuition, understand- ing cannot be a faculty of intuition. But besides intuition there is no other mode of knowledge except by means of concepts. The knowledge yielded by understanding, or at least by the human understanding, must therefore be by means of concepts, and so is not intuitive, but discursive. Whereas all intuitions, as sensible, rest on affections, concepts rest on functions. By 'function' I mean the unity of the act of bringing various repre- sentations under one common representation. Concepts are based on the spontaneity of thought, sensible intuitions on the receptivity of impressions. Now the only use which the under- standing can make of these concepts is to judge by means of them. Since no representation, save when it is an intuition, is in immediate relation to an object, no concept is ever related to an object immediately, but to some other representa- tion of it, be that other representation an intuition, or itself a concept. Judgment is therefore the mediate knowledge of an object, that is, the representation of a representation of it. In every judgment there is a concept which holds of many repre- sentations, and among them of a given representation that is immediately related to an object. Thus in the judgment, 'all bodies are divisible', the concept of the divisible applies to various other concepts, but is here applied in particular to the concept of body, and this concept again to certain appear- ances that present themselves to us. These objects, therefore, are mediately represented through the concept of divisibility. Accordingly, all judgments are functions of unity among our P 106 representations; instead of an immediate representation, a higher representation, which comprises the immediate repre- sentation and various others, is used in knowing the object, and thereby much possible knowledge is collected into one. Now we can reduce all acts of the understanding to judg- ments, and the understanding may therefore be represented as a faculty of judgment. For, as stated above, the under- standing is a faculty of thought. Thought is knowledge by means of concepts. But concepts, as predicates of possible judgments, relate to some representation of a not yet deter- mined object. Thus the concept of body means something, for instance, metal, which can be known by means of that con- cept. It is therefore a concept solely in virtue of its com- prehending other representations, by means of which it can relate to objects. It is therefore the predicate of a possible judgment, for instance, 'every metal is a body'. The functions of the understanding can, therefore, be discovered if we can give an exhaustive statement of the functions of unity in judgments. That this can quite easily be done will be shown in the next section. THE CLUE TO THE DISCOVERY OF ALL PURE CONCEPTS OF THE UNDERSTANDING Section 2 $9 THE LOGICAL FUNCTION OF THE UNDERSTANDING IN JUDGMENTS If we abstract from all content of a judgment, and con- sider only the mere form of understanding, we find that the function of thought in judgment can be brought under four heads, each of which contains three moments. They may be conveniently represented in the following table: P 107 I Quantity of Judgments Universal Particular Singular II III Quality Relation Affirmative Categorical Negative Hypothetical Infinite Disjunctive IV Modality Problematic Assertoric Apodeictic As this division appears to depart in some, though not in any essential respects, from the technical distinctions ordin- arily recognised by logicians, the following observations may serve to guard against any possible misunderstanding. 1. Logicians are justified in saying that, in the employ- ment of judgments in syllogisms, singular judgments can be treated like those that are universal. For, since they have no extension at all, the predicate cannot relate to part only of that which is contained in the concept of the subject, and be excluded from the rest. The predicate is valid of that concept, without any such exception, just as if it were a general concept and had an extension to the whole of which the predicate applied. If, on the other hand, we compare a singular with a universal judgment, merely as knowledge, in respect of quantity, the singular stands to the universal as unity to infinity, and is therefore in itself essentially different from the universal. If, therefore, we estimate a singular judg- ment (judicium singulare), not only according to its own inner validity, but as knowledge in general, according to its quantity in comparison with other knowledge, it is certainly different from general judgments (judicia communia), and in a com- plete table of the moments of thought in general deserves a separate place -- though not, indeed, in a logic limited to the use of judgments in reference to each other. P 108 2. In like manner infinite judgments must, in trans- cendental logic, be distinguished from those that are affirm- ative, although in general logic they are rightly classed with them, and do not constitute a separate member of the division. General logic abstracts from all content of the predicate (even though it be negative); it enquires only whether the predicate be ascribed to the subject or opposed to it. But transcendental logic also considers what may be the worth or content of a logical affirmation that is thus made by means of a merely negative predicate, and what is thereby achieved in the way of addition to our total knowledge. If I should say of the soul, 'It is not mortal', by this negative judgment I should at least have warded off error. Now by the proposition, 'The soul is non-mortal', I have, so far as the logical form is concerned, really made an affirmation. I locate the soul in the unlimited sphere of non-mortal beings. Since the mortal constitutes one part of the whole extension of possible beings, and the non-mortal the other, nothing more is said by my proposition than that the soul is one of the infinite number of things which remain over when I take away all that is mortal. The infinite sphere of all that is possible is thereby only so far limited that the mortal is excluded from it, and that the soul is located in the remaining part of its extension. But, even allowing for such exclusion, this extension still remains infinite, and several more parts of it may be taken away without the con- cept of the soul being thereby in the least increased, or de- termined in an affirmative manner. These judgments, though infinite in respect of their logical extension, are thus, in respect of the content of their knowledge, limitative only, and cannot therefore be passed over in a transcendental table of all moments of thought in judgments, since the function of the understanding thereby expressed may perhaps be of import- ance in the field of its pure a priori knowledge. 3. All relations of thought in judgments are (a) of the predicate to the subject, (b) of the ground to its consequence, (c) of the divided knowledge and of the members of the division, taken together, to each other. In the first kind of P 109 judgments we consider only two concepts, in the second two judgments, in the third several judgments in their relation to each other. The hypothetical proposition, 'If there is a perfect justice, the obstinately wicked are punished', really contains the relation of two propositions, namely, 'There is a perfect justice', and 'The obstinately wicked are punished'. Whether both these propositions are in themselves true, here remains undetermined. It is only the logical sequence which is thought by this judgment. Finally, the disjunctive judgment contains a relation of two or more propositions to each other, a relation not, however, of logical sequence, but of logical opposition, in so far as the sphere of the one excludes the sphere of the other, and yet at the same time of community, in so far as the propositions taken together occupy the whole sphere of the knowledge in question. The disjunctive judg- ment expresses, therefore, a relation of the parts of the sphere of such knowledge, since the sphere of each part is a com- plement of the sphere of the others, yielding together the sum-total of the divided knowledge. Take, for instance, the judgment, 'The world exists either through blind chance, or through inner necessity, or through an external cause'. Each of these propositions occupies a part of the sphere of the possible knowledge concerning the existence of a world in general; all of them together occupy the whole sphere. To take the knowledge out of one of these spheres means placing it in one of the other spheres, and to place it in one sphere means taking it out of the others. There is, therefore, in a disjunctive judging a certain community of the known constitutes, such that they mutually exclude each other, and yet thereby determine in their totality the true know- ledge. For, when taken together, they constitute the whole content of one given knowledge. This is all that need here be considered, so far as concerns what follows. 4. The modality of judgments is a quite peculiar function. Its distinguishing characteristic is that it contributes nothing to the content of the judgment (for, besides quantity, quality, and relation, there is nothing that constitutes the content of a judgment), but concerns only the value of the copula in relation to thought in general. Problematic judgments are those in which affirmation or negation is taken as merely P 110 possible (optional). In assertoric judgments affirmation or negation is viewed as real (true), and in apodeictic judgments as necessary. Thus the two judgments, the relation of which constitutes the hypothetical judgment (antecedens et con- sequens), and likewise the judgments the reciprocal relation of which forms the disjunctive judgment (members of the division), are one and all problematic only. In the above example, the proposition, 'There is a perfect justice', is not stated assertorically, but is thought only as an optional judg- ment, which it is possible to assume; it is only the logical sequence which is assertoric. Such judgments may therefore be obviously false, and yet, taken problematically, may be con- ditions of the knowledge of truth. Thus the judgment 'The world exists by blind chance', has in the disjunctive judgment only problematic meaning, namely, as a proposition that may for a moment be assumed. At the same time, like the indica- tion of a false road among the number of all those roads that can be taken, it aids in the discovery of the true proposition. The problematic proposition is therefore that which expresses only logical (which is not objective) possibility -- a free choice of admitting such a proposition, and a purely optional admission of it into the understanding. The assertoric pro- position deals with logical reality or truth. Thus, for instance, in a hypothetical syllogism the antecedent is in the major premiss problematic, in the minor assertoric, and what the syllogism shows is that the consequence follows in accordance with the laws of the understanding. The apodeictic proposi- tion thinks the assertoric as determined by these laws of the understanding, and therefore as affirming a priori; and in this manner it expresses logical necessity. Since everything is thus incorporated in the understanding step by step -- inas- much as we first judge something problematically, then maintain its truth assertorically, and finally affirm it as in- separably united with the understanding, that is, as necessary and apodeictic -- we are justified in regarding these three functions of modality as so many moments of thought. Just as if thought were in the problematic a function of the understanding; in the assertoric, of the faculty of judgment; in the apodeictic, of reason. This is a remark which will be explained in the sequel. P 111 THE CLUE TO THE DISCOVERY OF ALL PURE CONCEPTS OF THE UNDERSTANDING Section 3 $10 THE PURE CONCEPTS OF THE UNDERSTANDING, OR CATEGORIES General logic, as has been repeatedly said, abstracts from all content of knowledge, and looks to some other source, whatever that may be, for the representations which it is to transform into concepts by process of analysis. Tran- scendental logic, on the other hand, has lying before it a mani- fold of a priori sensibility, presented by transcendental aes- thetic, as material for the concepts of pure understanding. In the absence of this material those concepts would be with- out any content, therefore entirely empty. Space and time contain a manifold of pure a priori intuition, but at the same time are conditions of the receptivity of our mind -- conditions under which alone it can receive representations of objects, and which therefore must also always affect the concept of these objects. But if this manifold is to be known, the spontaneity of our thought requires that it be gone through in a certain way, taken up, and connected. This act I name synthesis. By synthesis, in its most general sense, I understand the act of putting different representations together, and of grasp- ing what is manifold in them in one [act of] knowledge. Such a synthesis is pure, if the manifold is not empirical but is given a priori, as is the manifold in space and time. Before we can analyse our representations, the representations must them- selves be given, and therefore as regards content no concepts can first arise by way of analysis. Synthesis of a manifold (be it given empirically or a priori) is what first gives rise to know- ledge. This knowledge may, indeed, at first, be crude and con- fused, and therefore in need of analysis. Still the synthesis is that which gathers the elements for knowledge, and unites them to [form] a certain content. It is to synthesis, therefore, P 112 that we must first direct our attention, if we would determine the first origin of our knowledge. Synthesis in general, as we shall hereafter see, is the mere result of the power of imagination, a blind but indispensable function of the soul, without which we should have no know- ledge whatsoever, but of which we are scarcely ever conscious. To bring this synthesis to concepts is a function which belongs to the understanding, and it is through this function of the understanding that we first obtain knowledge properly so called. Pure synthesis, represented in its most general aspect, gives the pure concept of the understanding. By this pure syn- thesis I understand that which rests upon a basis of a priori synthetic unity. Thus our counting, as is easily seen in the case of larger numbers, is a synthesis according to concepts, be- cause it is executed according to a common ground of unity, as, for instance, the decade. In terms of this concept, the unity of the synthesis of the manifold is rendered necessary. By means of analysis different representations are brought under one concept -- a procedure treated of in general logic. What transcendental logic, on the other hand, teaches, is how we bring to concepts, not representations, but the pure syn- thesis of representations. What must first be given -- with a view to the a priori knowledge of all objects -- is the manifold of pure intuition; the second factor involved is the synthesis of this manifold by means of the imagination. But even this does not yet yield knowledge. The concepts which give unity to this pure synthesis, and which consist solely in the representation of this necessary synthetic unity, furnish the third requisite for the knowledge of an object; and they rest on the under- standing. The same function which gives unity to the various repre- sentations in a judgment also gives unity to the mere syn- thesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure con- cept of the understanding. The same understanding, through the same operations by which in concepts, by means of ana- lytical unity, it produced the logical form of a judgment, also introduces a transcendental content into its representa- tions, by means of the synthetic unity of the manifold in intui- P 113 tion in general. On this account we are entitled to call these representations pure concepts of the understanding, and to regard them as applying a priori to objects -- a conclusion which general logic is not in a position to establish. In this manner there arise precisely the same number of pure concepts of the understanding which apply a priori to objects of intuition in general, as, in the preceding table, there have been found to be logical functions in all possible judg- ments. For these functions specify the understanding com- pletely, and yield an exhaustive inventory of its powers. These concepts we shall, with Aristotle, call categories, for our primary purpose is the same as his, although widely diverging from it in manner of execution. TABLE OF CATEGORIES I Of Quantity Unity Plurality Totality II III Of Quality Of Relation Reality Of Inherence and Subsistence Negation (substantia et accidens) Limitation Of Causality and Dependence (cause and effect) Of Community (reciprocity between agent and patient) IV Of Modality Possibility -- Impossibility Existence -- Non-existence Necessity -- Contingency This then is the list of all original pure concepts of syn- thesis that the understanding contains within itself a priori. P 114 Indeed, it is because it contains these concepts that it is called pure understanding; for by them alone can it under- stand anything in the manifold of intuition, that is, think an object of intuition. This division is developed systematically from a common principle, namely, the faculty of judgment (which is the same as the faculty of thought). It has not arisen rhapsodically, as the result of a haphazard search after pure concepts, the complete enumeration of which as based on induction only, could never be guaranteed. Nor could we, if this were our procedure, discover why just these concepts, and no others, have their seat in the pure understanding. It was an enterprise worthy of an acute thinker like Aristotle to make search for these fundamental concepts. But as he did so on no principle, he merely picked them up as they came his way, and at first procured ten of them, which he called categories (predicaments). Afterwards he believed that he had discovered five others, which he added under the name of post-predica- ments. But his table still remained defective. Besides, there are to be found in it some modes of pure sensibility (quando, ubi, situs, also prius, simul), and an empirical concept (motus), none of which have any place in a table of the concepts that trace their origin to the understanding. Aristotle's list also enumerates among the original concepts some derivative con- cepts (actio, passio); and of the original concepts some are entirely lacking. In this connection, it is to be remarked that the categories, as the true primary concepts of the pure understanding, have also their pure derivative concepts. These could not be passed over in a complete system of transcendental philosophy, but in a merely critical essay the simple mention of the fact may suffice. I beg permission to entitle these pure but derivative con- cepts of the understanding the predicables of the pure under- standing -- to distinguish them from the predicaments [i.e. the categories]. If we have the original and primitive concepts, it is easy to add the derivative and subsidiary, and so to give a complete picture of the family tree of the [concepts of] pure understanding. Since at present we are concerned not with the completeness of the system, but only with the principles to be followed in its construction, I reserve this supplementary work P 115 for another occasion. It can easily be carried out, with the aid of the ontological manuals -- for instance, by placing under the category of causality the predicables of force, action, passion; under the category of community the predicables of presence, resistance; under the predicaments of modality the predicables of coming to be, ceasing to be, change, etc. The categories, when combined with the modes of pure sen- sibility, or with one another, yield a large number of derivative a priori concepts. To note, and, where possible, to give a com- plete inventory of these concepts, would be a useful and not unpleasant task, but it is a task from which we can here be absolved. In this treatise, I purposely omit the definitions of the cate- gories, although I may be in possession of them. I shall pro- ceed to analyse these concepts only so far as is necessary in connection with the doctrine of method which I am propound- ing. In a system of pure reason, definitions of the categories would rightly be demanded, but in this treatise they would merely divert attention from the main object of the enquiry, arousing doubts and objections which, without detriment to what is essential to our purposes, can very well be reserved for another occasion. Meanwhile, from the little that I have said, it will be obvious that a complete glossary, with all the requisite explanations, is not only a possible, but an easy task. The divi- sions are provided; all that is required is to fill them; and a systematic 'topic', such as that here given, affords sufficient guidance as to the proper location of each concept, while at the same time indicating which divisions are still empty. $II This table of categories suggests some nice points, which may perhaps have important consequences in regard to the scientific form of all modes of knowledge obtainable by reason. For that this table is extremely useful in the theoretical part of philosophy, and indeed is indispensable as supplying the com- plete plan of a whole science, so far as that science rests on a - priori concepts, and as dividing it systematically according to P 116 determinate principles, is already evident from the fact that the table contains all the elementary concepts of the under- standing in their completeness, nay, even the form of a system of them in the human understanding, and accordingly indi- cates all the momenta of a projected speculative science, and even their order, as I have elsewhere shown. P 116n * Metaphysical First Principles of Natural Science. P 116 The first of the considerations suggested by the table is that while it contains four classes of the concepts of under- standing, it may, in the first instance, be divided into two groups; those in the first group being concerned with objects of intuition, pure as well as empirical, those in the second group with the existence of these objects, in their relation either to each other or to the understanding. The categories in the first group I would entitle the mathe- matical, those in the second group the dynamical. The former have no correlates; these are to be met with only in the second group. This distinction must have some ground in the nature of the understanding. Secondly, in view of the fact that all a priori division of concepts must be by dichotomy, it is significant that in each class the number of the categories is always the same, namely, three. Further, it may be observed that the third category in each class always arises from the combination of the second category with the first. Thus allness or totality is just plurality considered as unity; limitation is simply reality combined with negation; commun- ity is the causality of substances reciprocally determining one another; lastly, necessity is just the existence which is given through possibility itself. It must not be supposed, however, that the third category is therefore merely a derivative, and not a primary, concept of the pure understanding. For the com- bination of the first and second concepts, in order that the third may be produced, requires a special act of the understand- ing, which is not identical with that which is exercised in the case of the first and the second. Thus the concept of a number (which belongs to the category of totality) is not always possible simply upon the presence of concepts of plurality and unity P 117 (for instance, in the representation of the infinite); nor can I, by simply combining the concept of a cause and that of a sub- stance, at once have understanding of influence, that is, how a substance can be the cause of something in another substance. Obviously in these cases, a separate act of the understanding is demanded; and similarly in the others. Thirdly, in the case of one category, namely, that of com- munity, which is found in the third group, its accordance with the form of a disjunctive judgment -- the form which corre- sponds to it in the table of logical functions -- is not as evident as in the case of the others. To gain assurance that they do actually accord, we must observe that in all disjunctive judgments the sphere (that is, the multiplicity which is contained in any one judgment) is represented as a whole divided into parts (the subordinate con- cepts), and that since no one of them can be contained under any other, they are thought as co-ordinated with, not sub- ordinated to, each other, and so as determining each other, not in one direction only, as in a series, but reciprocally, as in an aggregate -- if one member of the division is posited, all the rest are excluded, and conversely. Now in a whole which is made up of things, a similar com- bination is being thought; for one thing is not subordinated, as effect, to another, as cause of its existence, but, simultane- ously and reciprocally, is co-ordinated with it, as cause of the determination of the other (as, for instance, in a body the parts of which reciprocally attract and repel each other). This is a quite different kind of connection from that which is found in the mere relation of cause to effect (of ground to conse- quence), for in the latter relation the consequence does not in its turn reciprocally determine the ground, and therefore does not constitute with it a whole -- thus the world, for instance, does not with its Creator serve to constitute a whole. The procedure which the understanding follows in representing to itself the sphere of a divided concept it likewise follows when it thinks a thing as divisible; and just as, in the former case, the members of a division exclude each other, and yet are com- P 118 bined in one sphere, so the understanding represents to itself the parts of the latter as existing (as substances) in such a way that, while each exists independently of the others, they are yet combined together in one whole. $12 In the transcendental philosophy of the ancients there is included yet another chapter containing pure concepts of the understanding which, though not enumerated among the cate- gories, must, on their view, be ranked as a priori concepts of objects. This, however, would amount to an increase in the number of the categories, and is therefore not feasible. They are propounded in the proposition, so famous among the Schoolmen, quodlibet ens est unum, verum, bonum. Now, although the application of this principle has proved very meagre in consequences, and has indeed yielded only proposi- tions that are tautological, and therefore in recent times has retained its place in metaphysics almost by courtesy only, yet, on the other hand, it represents a view which, however empty it may seem to be, has maintained itself over this very long period. It therefore deserves to be investigated in respect of its origin, and we are justified in conjecturing that it has its ground in some rule of the understanding which, as often happens, has only been wrongly interpreted. These supposedly transcendental predicates of things are, in fact, nothing but logical requirements and criteria of all knowledge of things in general, and prescribe for such knowledge the categories of quantity, namely, unity, plurality, and totality. But these categories, which, properly regarded, must be taken as material, belonging to the possibility of the things themselves [empirical objects], have, in this further application, been used only in their formal meaning, as being of the nature of logical requis- ites of all knowledge, and yet at the same time have been incautiously converted from being criteria of thought to be pro- perties of things in themselves. In all knowledge of an object there is unity of concept, which may be entitled qualitative unity, so far as we think by it only the unity in the combination of the manifold of our knowledge: as, for example, the unity of the theme in a play, a speech, or a story. Secondly, there is P 119 truth, in respect of its consequences. The greater the number of true consequences that follow from a given concept, the more criteria are there of its objective reality. This might be entitled the qualitative plurality of characters, which belong to a concept as to a common ground (but are not thought in it, as quantity). Thirdly, and lastly, there is perfection, which con- sists in this, that the plurality together leads back to the unity of the concept, and accords completely with this and with no other concept. This may be entitled the qualitative complete- ness (totality). Hence it is evident that these logical criteria of the possibility of knowledge in general are the three categories of quantity, in which the unity in the production of the quantum has to be taken as homogeneous throughout; and that these categories are here being transformed so as also to yield con- nection of heterogeneous knowledge in one consciousness, by means of the quality of the knowledge as the principle of the connection. Thus the criterion of the possibility of a concept (not of an object) is the definition of it, in which the unity of the concept, the truth of all that may be immediately deduced from it, and finally, the completeness of what has been thus de- duced from it, yield all that is required for the construction of the whole concept. Similarly, the criterion of an hypothesis consists in the intelligibility of the assumed ground of explana- tion, that is, in its unity (without any auxiliary hypothesis); in the truth of the consequences that can be deduced from it (their accordance with themselves and with experience); and finally, in the completeness of the ground of explanation of these consequences, which carry us back to neither more nor less than was assumed in the hypothesis, and so in an a pos- teriori analytic manner give us back and accord with what has previously been thought in a synthetic a priori manner. We have not, therefore, in the concepts of unity, truth, and per- fection, made any addition to the transcendental table of the categories, as if it were in any respect imperfect. All that we have done is to bring the employment of these concepts under general logical rules, for the agreement of knowledge with itself -- the question of their relation to objects not being in any way under discussion. P 120 ANALYTIC OF CONCEPTS CHAPTER II THE DEDUCTION OF THE PURE CONCEPTS OF UNDERSTANDING Section 1 $13 THE PRINCIPLES OF ANY TRANSCENDENTAL DEDUCTION JURISTS, when speaking of rights and claims, distinguish in a legal action the question of right (quid juris) from the question of fact (quid facti); and they demand that both be proved. Proof of the former, which has to state the right or the legal claim, they entitle the deduction. Many empirical concepts are employed without question from anyone. Since experience is always available for the proof of their objective reality, we be- lieve ourselves, even without a deduction, to be justified in ap- propriating to them a meaning, an ascribed significance. But there are also usurpatory concepts, such as fortune, fate, which, though allowed to circulate by almost universal indul- gence, are yet from time to time challenged by the question: quid juris. This demand for a deduction involves us in con- siderable perplexity, no clear legal title, sufficient to justify their employment, being obtainable either from experience or from reason. Now among the manifold concepts which form the highly P 121 complicated web of human knowledge, there are some which are marked out for pure a priori employment, in complete in- dependence of all experience; and their right to be so em- ployed always demands a deduction. For since empirical proofs do not suffice to justify this kind of employment, we are faced by the problem how these concepts can relate to objects which they yet do not obtain from any experience. The explanation of the manner in which concepts can thus relate a priori to objects I entitle their transcendental deduction; and from it I distinguish empirical deduction, which shows the manner in which a concept is acquired through experience and through reflection upon experience, and which therefore concerns, not its legitimacy, but only its de facto mode of origination. We are already in possession of concepts which are of two quite different kinds, and which yet agree in that they relate to objects in a completely a priori manner, namely, the con- cepts of space and time as forms of sensibility, and the cate- gories as concepts of understanding. To seek an empirical de- duction of either of these types of concept would be labour entirely lost. For their distinguishing feature consists just in this, that they relate to their objects without having borrowed from experience anything that can serve in the representation of these objects. If, therefore, a deduction of such concepts is indispensable, it must in any case be transcendental. We can, however, with regard to these concepts, as with regard to all knowledge, seek to discover in experience, if not the principle of their possibility, at least the occasioning causes of their production. The impressions of the senses supplying the first stimulus, the whole faculty of knowledge opens out to them, and experience is brought into exist- ence. That experience contains two very dissimilar elements, namely, the matter of knowledge [obtained] from the senses, and a certain form for the ordering of this matter, [obtained] from the inner source of the pure intuition and thought which, on occasion of the sense-impressions, are first brought into action and yield concepts. Such an investigation of the first strivings of our faculty of knowledge, whereby it advances from particular perceptions to universal concepts, is un- doubtedly of great service. We are indebted to the celebrated P 122 Locke for opening out this new line of enquiry. But a deduc- tion of the pure a priori concepts can never be obtained in this manner; it is not to be looked for in any such direction. For in view of their subsequent employment, which has to be entirely independent of experience, they must be in a position to show a certificate of birth quite other than that of descent from experiences. Since this attempted physiological deriva- tion concerns a quaestio facti, it cannot strictly be called deduction; and I shall therefore entitle it the explanation of the possession of pure knowledge. Plainly the only deduction that can be given of this knowledge is one that is transcen- dental, not empirical. In respect to pure a priori concepts the latter type of deduction is an utterly useless enterprise which can be engaged in only by those who have failed to grasp the quite peculiar nature of these modes of know- ledge. But although it may be admitted that the only kind of deduction of pure a priori knowledge which is possible is on transcendental lines, it is not at once obvious that a deduc- tion is indispensably necessary. We have already, by means of a transcendental deduction, traced the concepts of space and time to their sources, and have explained and determined their a priori objective validity. Geometry, however, proceeds with security in knowledge that is completely a priori, and has no need to beseech philosophy for any certificate of the pure and legitimate descent of its fundamental concept of space. But the concept is employed in this science only in its reference to the outer sensible world -- of the intuition of which space is the pure form -- where all geometrical knowledge, grounded as it is in a priori intuition, possesses immediate evidence. The objects, so far as their form is concerned, are given, through the very knowledge of them, a priori in intuition. *********** otherwise; it is with them that the unavoidable demand for a transcendental deduction, not only of themselves, but also of the concept of space, first originates. For since they speak of objects through predicates not of intuition and sensibility but of pure a priori thought, they relate to objects universally, P 123 that is, apart from all conditions of sensibility. Also, not being grounded in experience, they cannot, in a priori intuition, exhibit any object such as might, prior to all experience, serve as ground for their synthesis. For these reasons, they arouse suspicion not merely in regard to the objective validity and the limits of their own employment, but owing to their tendency to employ the concept of space beyond the conditions of sensible intuition, that concept also they render ambiguous; and this, indeed, is why we have already found a transcendental deduction of it necessary. The reader must therefore be convinced of the unavoidable necessity of such a transcendental deduction before he has taken a single step in the field of pure reason. Otherwise he proceeds blindly, and after manifold wanderings must come back to the same ignorance from which he started. At the same time, if he is not to lament over obscurity in matters which are by their very nature deeply veiled, or to be too easily discouraged in the removal of obstacles, he must have a clear foreknowledge of the inevitable difficulty of the undertaking. For we must either completely surrender all claims to make judgments of pure reason in the most highly esteemed of all fields, that which transcends the limits of all possible experience, or else bring this critical enquiry to completion. We have already been able with but little difficulty to explain how the concepts of space and time, although a priori modes of knowledge, must necessarily relate to objects, and how independently of all experience they make possible a synthetic knowledge of objects. For since only by means of such pure forms of sensibility can an object appear to us, and so be an object of empirical intuition, space and time are pure intuitions which contain a priori the condition of the possibility of objects as appearances, and the synthesis which takes place in them has objective validity. The categories of understanding, on the other hand, do not represent the conditions under which objects are given in intuition. Objects may, therefore, appear to us without P 124 their being under the necessity of being related to the functions of understanding; and understanding need not, therefore, contain their a priori conditions. Thus a difficulty such as we did not meet with in the field of sensibility is here presented, namely, how subjective conditions of thought can have objective validity, that is, can furnish conditions of the possibility of all knowledge of objects. For appearances can certainly be given in intuition independently of functions of the understanding. Let us take, for instance, the concept of cause, which signifies a special kind of synthesis, whereby upon something, A, there is posited something quite different, B, according to a rule. It is not manifest a priori why appear- ances should contain anything of this kind (experiences cannot be cited in its proof, for what has to be established is the objective validity of a concept that is a priori); and it is therefore a priori doubtful whether such a concept be not perhaps altogether empty, and have no object anywhere among appearances. That objects of sensible intuition must conform to the formal conditions of sensibility which lie a priori in the mind is evident, because otherwise they would not be objects for us. But that they must likewise conform to the conditions which the understanding requires for the synthetic unity of thought, is a conclusion the grounds of which are by no means so obvious. Appearances might very well be so constituted that the understanding should not find them to be in accordance with the Conditions of its unity. Everything might be in such confusion that, for instance, in the series of appearances nothing presented itself which might yield a rule of synthesis and so answer to the concept of cause and effect. This concept would then be altogether empty, null, and meaningless. But since intuition stands in no need whatsoever of the functions of thought, appearances would none the less present objects to our intuition. If we thought to escape these toilsome enquiries by saying that experience continually presents examples of such regu- larity among appearances and so affords abundant oppor- tunity of abstracting the concept of cause, and at the same time of verifying the objective validity of such a concept, we should be overlooking the fact that the concept of cause can P 125 never arise in this manner. It must either be grounded com- pletely a priori in the understanding, or must be entirely given up as a mere phantom of the brain. For this concept makes strict demand that something, A, should be such that some- thing else, B, follows from it necessarily and in accordance with an absolutely universal rule. Appearances do indeed pre- sent cases from which a rule can be obtained according to which something usually happens, but they never prove the sequence to be necessary. To the synthesis of cause and effect there belongs a dignity which cannot be empirically expressed, namely that the effect not only succeeds upon the cause, but that it is posited through it and arises out of it. This strict universality of the rule is never a characteristic of empirical rules; they can acquire through induction only com- parative universality, that is, extensive applicability. If we were to treat pure concepts of understanding as merely em- pirical products, we should be making a complete change in [the manner of] their employment. $14 Transition to the Transcendental Deduction of the Categories There are only two possible ways in which synthetic re- presentations and their objects can establish connection, obtain necessary relation to one another, and, as it were, meet one another. Either the object alone must make the repre- sentation possible, or the representation alone must make the object possible. In the former case, this relation is only em- pirical, and the representation is never possible a priori. This is true of appearances, as regards that [element] in them which belongs to sensation. In the latter case, representation in itself does not produce its object in so far as existence is concerned, for we are not here speaking of its causality by means of the will. None the less the representation is a priori determinant of the object, if it be the case that only through P 126 the representation is it possible to know anything as an object. Now there are two conditions under which alone the know- ledge of an object is possible, first, intuition, through which it is given, though only as appearance; secondly, concept, through which an object is thought corresponding to this in- tuition. It is evident from the above that the first condition, namely, that under which alone objects can be intuited, does actually lie a priori in the mind as the formal ground of the objects. All appearances necessarily agree with this formal condition of sensibility, since only through it can they appear, that is, be empirically intuited and given. The question now arises whether a priori concepts do not also serve as ante- cedent conditions under which alone anything can be, if not intuited, yet thought as object in general. In that case all em- pirical knowledge of objects would necessarily conform to such concepts, because only as thus presupposing them is anything possible as object of experience. Now all experience does indeed contain, in addition to the intuition of the senses through which something is given, a concept of an object as being thereby given, that is to say, as appearing. Concepts of objects in general thus underlie all empirical knowledge as its a priori conditions. The objective validity of the categories as a priori concepts rests, therefore, on the fact that, so far as the form of thought is concerned, through them alone does experience become possible. They relate of necessity and a priori to objects of experience, for the reason that only by means of them can any object whatsoever of experience be thought. The transcendental deduction of all a priori concepts has thus a principle according to which the whole enquiry must be directed, namely, that they must be recognised as a priori conditions of the possibility of experience, whether of the intuition which is to be met with in it or of the thought. Con- cepts which yield the objective ground of the possibility of experience are for this very reason necessary. But the unfold- ing of the experience wherein they are encountered is not their deduction; it is only their illustration. For on any such P 127 exposition they would be merely accidental. Save through their original relation to possible experience, in which all objects of knowledge are found, their relation to any one object would be quite incomprehensible. The illustrious Locke, failing to take account of these con- siderations, and meeting with pure concepts of the understand- ing in experience, deduced them also from experience, and yet proceeded so inconsequently that he attempted with their aid to obtain knowledge which far transcends all limits of ex- perience. David Hume recognised that, in order to be able to do this, it was necessary that these concepts should have an a priori origin. But since he could not explain how it can be possible that the understanding must think concepts, which are not in themselves connected in the understanding, as being necessarily connected in the object, and since it never occurred to him that the understanding might itself, perhaps, through these concepts, be the author of the experience in which its objects are found, he was constrained to derive them from experience, namely, from a subjective necessity (that is, from custom), which arises from repeated association in experience, and which comes mistakenly to be regarded as objective. But from these premisses he argued quite consistently. It is im- possible, he declared, with these concepts and the principles to which they give rise, to pass beyond the limits of experience. *There are three original sources (capacities or faculties of the soul) which contain the conditions of the possibility of all experience, and cannot themselves be derived from any other faculty of the mind, namely, sense, imagination, and appercep- tion. Upon them are grounded (1) the synopsis of the manifold a priori through sense; (2) the synthesis of this manifold through imagination; finally (3) the unity of this synthesis through original apperception. All these faculties have a transcendental (as well as an empirical) employment which concerns the form alone, and is possible a priori. As regards sense, we have treated of this above in the first part; we shall now endeavour to comprehend the nature of the other two. P 128 Now this empirical derivation, in which both philosophers agree, cannot be reconciled with the scientific a priori know- ledge which we do actually possess, namely, pure mathematics and general science of nature; and this fact therefore suffices to disprove such derivation. While the former of these two illustrious men opened a wide door to enthusiasm -- for if reason once be allowed such rights, it will no longer allow itself to be kept within bounds by vaguely defined recommendations of moderation -- the other gave himself over entirely to scepticism, having, as he believed, discovered that what had hitherto been regarded as reason was but an all-prevalent illusion infecting our faculty of know- ledge. We now propose to make trial whether it be not possible to find for human reason safe conduct between these two rocks, assigning to her determinate limits, and yet keeping open for her the whole field of her appropriate activities. But first I shall introduce a word of explanation in regard to the categories. They are concepts of an object in general, by means of which the intuition of an object is regarded as deter- mined in respect of one of the logical functions of judgment. Thus the function of the categorical judgment is that of the relation of subject to predicate; for example, 'All bodies are divisible'. But as regards the merely logical employment of the understanding, it remains undetermined to which of the two concepts the function of the subject, and to which the function of predicate, is to be assigned. For we can also say, 'Something divisible is a body'. But when the concept of body is brought under the category of substance, it is thereby de- termined that its empirical intuition in experience must always be considered as subject and never as mere predicate. Simi- larly with all the other categories. P 129 THE DEDUCTION OF THE PURE CONCEPTS OF UNDERSTANDING Section 2 THE A PRIORI GROUNDS OF THE POSSIBILITY OF EXPERIENCE THAT a concept, although itself neither contained in the con- cept of possible experience nor consisting of elements of a possible experience, should be produced completely a priori and should relate to an object, is altogether contradictory and impossible. For it would then have no content, since no intui- tion corresponds to it; and intuitions in general, through which objects can be given to us, constitute the field, the whole ob- ject, of possible experience. An a priori concept which did not relate to experience would be only the logical form of a concept, not the concept itself through which something is thought. Pure a priori concepts, if such exist, cannot indeed con- tain anything empirical; yet, none the less, they can serve solely as a priori conditions of a possible experience. Upon this ground alone can their objective reality rest. If, therefore, we seek to discover how pure concepts of understanding are possible, we must enquire what are the a priori conditions upon which the possibility of experience rests, and which remain as its underlying grounds when every- thing empirical is abstracted from appearances. A concept which universally and adequately expresses such a normal and P 130 objective condition of experience would be entitled a pure con- cept of understanding. Certainly, once I am in possession of pure concepts of understanding, I can think objects which may be impossible, or which, though perhaps in themselves possible, cannot be given in any experience. For in the connecting of these concepts something may be omitted which yet neces- sarily belongs to the condition of a possible experience (as in the concept of a spirit). Or, it may be, pure concepts are ex- tended further than experience can follow (as with the concept of God). But the elements of all modes of a priori knowledge, even of capricious and incongruous fictions, though they cannot, indeed, be derived from experience, since in that case they would not be knowledge a priori, must none the less always contain the pure a priori conditions of a possible ex- perience and of an empirical object. Otherwise nothing would be thought through them, and they themselves, being without data, could never arise even in thought. The concepts which thus contain a priori the pure thought involved in every experience, we find in the categories. If we can prove that by their means alone an object can be thought, this will be a sufficient deduction of them, and will justify their objective validity. But since in such a thought more than simply the faculty of thought, the understanding, is brought into play, and since this faculty itself, as a faculty of knowledge that is meant to relate to objects, calls for explanation in regard to the possibility of such relation, we must first of all consider, not in their empirical but in their transcendental constitution, the subjective sources which form the a priori foundation of the possibility of experience. If each representation were completely foreign to every other, standing apart in isolation, no such thing as knowledge would ever arise. For knowledge is [essentially] a whole in which representations stand compared and connected. As sense contains a manifold in its intuition, I ascribe to it a synopsis. But to such synopsis a synthesis must always correspond; re- ceptivity can make knowledge possible only when combined with spontaneity. Now this spontaneity is the ground of a threefold synthesis which must necessarily be found in all knowledge; namely, the apprehension of representations as modifications of the mind in intuition, their reproduction in P 131 imagination, and their recognition in a concept. These point to three subjective sources of knowledge which make possible the understanding itself -- and consequently all experience as its empirical product. Preliminary Remark The deduction of the categories is a matter of such ex- treme difficulty, compelling us to penetrate so deeply into the first grounds of the possibility of our knowledge in general, that in order to avoid the elaborateness of a complete theory, and yet at the same time to omit nothing in so indispensable an enquiry, I have found it advisable in the four following pass- ages rather to prepare than to instruct the reader. System- atic exposition of these elements of the understanding is first given in Section 3, immediately following. The reader must not therefore be deterred by obscurities in these earlier sections. They are unavoidable in an enterprise never before attempted. They will, as I trust, in the section referred to, finally give way to complete insight. 1. The Synthesis of Apprehension in Intuition Whatever the origin of our representations, whether they are due to the influence of outer things, or are produced through inner causes, whether they arise a priori, or being appearances have an empirical origin, they must all, as modi- fications of the mind, belong to inner sense. All our know- ledge is thus finally subject to time, the formal condition of inner sense. In it they must all be ordered, connected, and brought into relation. This is a general observation which, throughout what follows, must be borne in mind as being quite fundamental. Every intuition contains in itself a manifold which can be represented as a manifold only in so far as the mind distin- guishes the time in the sequence of one impression upon another; for each representation, in so far as it is contained in a single moment, can never be anything but absolute unity. In order that unity of intuition may arise out of this manifold (as is required in the representation of space) it must first be run through, and held together. This act I name the synthesis of apprehension, because it is directed immediately upon intuition, which does indeed offer a manifold, but a manifold which can P 132 never be represented as a manifold, and as contained in a single representation, save in virtue of such a synthesis. This synthesis of apprehension must also be exercised a priori, that is, in respect of representations which are not empirical. For without it we should never have a priori the representations either of space or of time. They can be pro- duced only through the synthesis of the manifold which sen- sibility presents in its original receptivity. We have thus a pure synthesis of apprehension. 2. The Synthesis of Reproduction in Imagination It is a merely empirical law, that representations which have often followed or accompanied one another finally be- come associated, and so are set in a relation whereby, even in the absence of the object, one of these representations can, in accordance with a fixed rule, bring about a transition of the mind to the other. But this law of reproduction presupposes that appearances are themselves actually subject to such a rule, and that in the manifold of these representations a co- existence or sequence takes place in conformity with certain rules. Otherwise our empirical imagination would never find opportunity for exercise appropriate to its powers, and so would remain concealed within the mind as a dead and to us unknown faculty. If cinnabar were sometimes red, sometimes black, sometimes light, sometimes heavy, if a man changed sometimes into this and sometimes into that animal form, if the country on the longest day were sometimes covered with fruit, sometimes with ice and snow, my empirical imagina- tion would never find opportunity when representing red colour to bring to mind heavy cinnabar. Nor could there be an empirical synthesis of reproduction, if a certain name were sometimes given to this, sometimes to that object, or were one and the same thing named sometimes in one way, sometimes in another, independently of any rule to which appearances are in themselves subject. There must then be something which, as the a priori ground of a necessary synthetic unity of appearances, makes their reproduction possible. What that something is we P 133 soon discover, when we reflect that appearances are not things in themselves, but are the mere play of our representa- tions, and in the end reduce to determinations of inner sense. For if we can show that even our purest a priori intuitions yield no knowledge, save in so far as they contain a com- bination of the manifold such as renders a thoroughgoing synthesis of reproduction possible, then this synthesis of im- agination is likewise grounded, antecedently to all experi- ence, upon a priori principles; and we must assume a pure transcendental synthesis of imagination as conditioning the very possibility of all experience. For experience as such neces- sarily presupposes the reproducibility of appearances. When I seek to draw a line in thought, or to think of the time from one noon to another, or even to represent to myself some par- ticular number, obviously the various manifold representa- tions that are involved must be apprehended by me in thought one after the other. But if I were always to drop out of thought the preceding representations (the first parts of the line, the antecedent parts of the time period, or the units in the order represented), and did not reproduce them while advancing to those that follow, a complete representation would never be obtained: none of the above-mentioned thoughts, not even the purest and most elementary representations of space and time, could arise. The synthesis of apprehension is thus inseparably bound up with the synthesis of reproduction. And as the former con- stitutes the transcendental ground of the possibility of all modes of knowledge whatsoever -- of those that are pure a priori no less than of those that are empirical -- the repro- ductive synthesis of the imagination is to be counted among the transcendental acts of the mind. We shall therefore entitle this faculty the transcendental faculty of imagination. 3. The Synthesis of Recognition in a Concept If we were not conscious that what we think is the same as what we thought a moment before, all reproduction in the series of representations would be useless. For it would in its present state be a new representation which would not in any way belong to the act whereby it was to be gradually gener- P 134 ated. The manifold of the representation would never, there- fore, form a whole, since it would lack that unity which only consciousness can impart to it. If, in counting, I forget that the units, which now hover before me, have been added to one another in succession, I should never know that a total is being produced through this successive addition of unit to unit, and so would remain ignorant of the number. For the concept of the number is nothing but the consciousness of this unity of synthesis. The word 'concept' might of itself suggest this remark. For this unitary consciousness is what combines the mani- fold, successively intuited, and thereupon also reproduced, into one representation. This consciousness may often be only faint, so that we do not connect it with the act itself, that is, not in any direct manner with the generation of the repre- sentation, but only with the outcome [that which is thereby represented]. But notwithstanding these variations, such con- sciousness, however indistinct, must always be present; with- out it, concepts, and therewith knowledge of objects, are altogether impossible. At this point we must make clear to ourselves what we mean by the expression 'an object of representations'. We have stated above that appearances are themselves nothing but sensible representations, which, as such and in themselves, must not be taken as objects capable of existing outside our power of representation. What, then, is to be understood when we speak of an object corresponding to, and consequently also distinct from, our knowledge? It is easily seen that this object must be thought only as something in general = x, since outside our knowledge we have nothing which we could set over against this knowledge as corresponding to it. Now we find that our thought of the relation of all know- ledge to its object carries with it an element of necessity; the object is viewed as that which prevents our modes of know- ledge from being haphazard or arbitrary, and which deter- mines them a priori in some definite fashion. For in so far as they are to relate to an object, they must necessarily agree P 135 with one another, that is, must possess that unity which con- stitutes the concept of an object. But it is clear that, since we have to deal only with the manifold of our representations, and since that x (the object) which corresponds to them is nothing to us -- being, as it is, something that has to be distinct from all our representations -- the unity which the object makes necessary can be nothing else than the formal unity of consciousness in the synthesis of the manifold of representations. It is only when we have thus produced synthetic unity in the manifold of intuition that we are in a position to say that we know the object. But this unity is impossible if the intuition cannot be generated in accord- ance with a rule by means of such a function of synthesis as makes the reproduction of the manifold a priori necessary, and renders possible a concept in which it is united. Thus we think a triangle as an object, in that we are conscious of the combination of three straight lines according to a rule by which such an intuition can always be represented. This unity of rule determines all the manifold, and limits it to conditions which make unity of apperception possible. The concept of this unity is the representation of the object = x, which I think through the predicates, above mentioned, of a triangle. All knowledge demands a concept, though that concept may, indeed, be quite imperfect or obscure. But a concept is always, as regards its form, something universal which serves as a rule. The concept of body, for instance, as the unity of the manifold which is thought through it, serves as a rule in our knowledge of outer appearances. But it can be a rule for intuitions only in so far as it represents in any given appearances the necessary reproduction of their manifold, and thereby the synthetic unity in our consciousness of them. The concept of body, in the perception of something outside us, necessitates the representation of extension, and there- with representations of impenetrability, shape, etc. All necessity, without exception, is grounded in a tran- scendental condition. There must, therefore, be a transcend- ental ground of the unity of consciousness in the synthesis of the manifold of all our intuitions, and consequently also of the concepts of objects in general, and so of all objects of experience, a ground without which it would be impossible P 136 to think any object for our intuitions; for this object is no more than that something, the concept of which expresses such a necessity of synthesis. This original and transcendental condition is no other than transcendental apperception. Consciousness of self according to the determinations of our state in inner percep- tion is merely empirical, and always changing. No fixed and abiding self can present itself in this flux of inner appear- ances. Such consciousness is usually named inner sense, or empirical apperception. What has necessarily to be repre- sented as numerically identical cannot be thought as such through empirical data. To render such a transcendental presupposition valid, there must be a condition which precedes all experience, and which makes experience itself possible. There can be in us no modes of knowledge, no connection or unity of one mode of knowledge with another, without that unity of consciousness which precedes all data of intuitions, and by relation to which representation of objects is alone possible. This pure original unchangeable consciousness I shall name transcendental apperception. That it deserves this name is clear from the fact that even the purest objective unity, namely, that of the a priori concepts (space and time), is only possible through relation of the intuitions to such unity of consciousness. The numerical unity of this appercep- tion is thus the a priori ground of all concepts, just as the manifoldness of space and time is the a priori ground of the intuitions of sensibility. This transcendental unity of apperception forms out of all possible appearances, which can stand alongside one another in one experience, a connection of all these repre- sentations according to laws. For this unity of consciousness would be impossible if the mind in knowledge of the manifold could not become conscious of the identity of function whereby it synthetically combines it in one knowledge. The original and necessary consciousness of the identity of the self is thus at the same time a consciousness of an equally necessary unity of the synthesis of all appearances according to concepts, that P 137 is, according to rules, which not only make them necessarily reproducible but also in so doing determine an object for their intuition, that is, the concept of something wherein they are necessarily interconnected. For the mind could never think its identity in the manifoldness of its representations, and indeed think this identity a priori, if it did not have before its eyes the identity of its act, whereby it subordinates all synthesis of apprehension (which is empirical) to a transcend- ental unity, thereby rendering possible their interconnection according to a priori rules. Now, also, we are in a position to determine more ade- quately our concept of an object in general. All representations have, as representations, their object, and can themselves in turn become objects of other representations. Appearances are the sole objects which can be given to us immediately, and that in them which relates immediately to the object is called intuition. But these appearances are not things in themselves; they are only representations, which in turn have their object -- an object which cannot itself be intuited by us, and which may, therefore, be named the non-empirical, that is, transcend- ental object = x. The pure concept of this transcendental object, which in reality throughout all our knowledge is always one and the same, is what can alone confer upon all our empirical con- cepts in general relation to an object, that is, objective reality. This concept cannot contain any determinate intuition, and therefore refers only to that unity which must be met with in any manifold of knowledge which stands in relation to an object. This relation is nothing but the necessary unity of consciousness, and therefore also of the synthesis of the mani- fold, through a common function of the mind, which com- bines it in one representation. Since this unity must be re- garded as necessary a priori -- otherwise knowledge would be without an object -- the relation to a transcendental object, that is, the objective reality of our empirical knowledge, rests on the transcendental law, that all appearances, in so far as through them objects are to be given to us, must stand under those a priori rules of synthetical unity whereby the inter- P 138 relating of these appearances in empirical intuition is alone possible. In other words, appearances in experience must stand under the conditions of the necessary unity of apper- ception, just as in mere intuition they must be subject to the formal conditions of space and of time. Only thus can any knowledge become possible at all. 4.Preliminary Explanation of the Possibility of the Categories, as Knowledge a priori There is one single experience in which all perceptions are represented as in thoroughgoing and orderly connection, just as there is only one space and one time in which all modes of appearance and all relation of being or not being occur. When we speak of different experiences, we can refer only to the various perceptions, all of which, as such, belong to one and the same general experience. This thoroughgoing synthetic unity of perceptions is indeed the form of experience; it is nothing else than the synthetic unity of appearances in accordance with concepts. Unity of synthesis according to empirical concepts would be altogether accidental, if these latter were not based on a transcendental ground of unity. Otherwise it would be possible for appearances to crowd in upon the soul, and yet to be such as would never allow of experience. Since connection in accord- ance with universal and necessary laws would be lacking, all relation of knowledge to objects would fall away. The appear- ances might, indeed, constitute intuition without thought, but not knowledge; and consequently would be for us as good as nothing. The a priori conditions of a possible experience in general are at the same time conditions of the possibility of objects of experience. Now I maintain that the categories, above cited, are nothing but the conditions of thought in a possible experience, just as space and time are the conditions of in- tuition for that same experience. They are fundamental con- cepts by which we think objects in general for appearances, and have therefore a priori objective validity. This is exactly what we desired to prove. P 139 But the possibility, indeed the necessity, of these cate- gories rests on the relation in which our entire sensibility, and with it all possible appearances, stand to original apper- ception. In original apperception everything must necessarily conform to the conditions of the thoroughgoing unity of self- consciousness, that is, to the universal functions of synthesis, namely, of that synthesis according to concepts in which alone apperception can demonstrate a priori its complete and necessary identity. Thus the concept of a cause is nothing but a synthesis (of that which follows in the time-series, with other appearances) according to concepts; and without such unity, which has its a priori rule, and which subjects the appear- ances to itself, no thoroughgoing, universal, and therefore necessary, unity of consciousness would be met with in the manifold of perceptions. These perceptions would not then belong to any experience, consequently would be without an object, merely a blind play of representations, less even than a dream. All attempts to derive these pure concepts of understand- ing from experience, and so to ascribe to them a merely em- pirical origin, are entirely vain and useless. I need not insist upon the fact that, for instance, the concept of a cause involves the character of necessity, which no experience can yield. Experience does indeed show that one appearance customarily follows upon another, but not that this sequence is necessary, nor that we can argue a priori and with complete universality from the antecedent, viewed as a condition, to the consequent. But as regards the empirical rule of association, which we must postulate throughout when we assert that everything in the series of events is so subject to rule that nothing ever happens save in so far as something precedes it on which it universally follows -- upon what I ask, does this rule, as a law of nature, rest? How is this association itself possible? The ground of the possibility of the association of the manifold, so far as it lies in the object, is named the affinity of the manifold. I therefore ask, how are we to make comprehensible to our- selves the thoroughgoing affinity of appearances, whereby they stand and must stand under unchanging laws? On my principles it is easily explicable. All possible ap- pearances, as representations, belong to the totality of a pos- P 140 sible self-consciousness. But as self-consciousness is a tran- scendental representation, numerical identity is inseparable from it, and is a priori certain. For nothing can come to our knowledge save in terms of this original apperception. Now, since this identity must necessarily enter into the synthesis of all the manifold of appearances, so far as the synthesis is to yield empirical knowledge, the appearances are subject to a priori conditions, with which the synthesis of their apprehen- sion must be in complete accordance. The representation of a universal condition according to which a certain manifold can be posited in uniform fashion is called a rule, and, when it must be so posited, a law. Thus all appearances stand in thoroughgoing connection according to necessary laws, and therefore in a transcendental affinity, of which the empirical is a mere consequence. That nature should direct itself according to our sub- jective ground of apperception, and should indeed depend upon it in respect of its conformity to law, sounds very strange and absurd. But when we consider that this nature is not a thing in itself but is merely an aggregate of appearances, so many representations of the mind, we shall not be surprised that we can discover it only in the radical faculty of all our knowledge, namely, in transcendental apperception, in that unity on account of which alone it can be entitled object of all possible experience, that is, nature. Nor shall we be surprised that just for this very reason this unity can be known a priori, and therefore as necessary. Were the unity given in itself in- dependently of the first sources of our thought, this would never be possible. We should not then know of any source from which we could obtain the synthetic propositions assert- ing such a universal unity of nature. For they would then have to be derived from the objects of nature themselves; and as this could take place only empirically, none but a merely accidental unity could be obtained, which would fall far short of the necessary interconnection that we have in mind when we speak of nature. P 141 DEDUCTION OF THE PURE CONCEPTS OF UNDERSTANDING Section 3 THE RELATION OF THE UNDERSTANDING TO OBJECTS IN GENERAL, AND THE POSSIBILITY OF KNOWING THEM A PRIORI What we have expounded separately and singly in the preceding section, we shall now present in systematic inter- connection. There are three subjective sources of knowledge upon which rests the possibility of experience in general and of knowledge of its objects -- sense, imagination, and appercep- tion. Each of these can be viewed as empirical, namely, in its application to given appearances. But all of them are likewise a priori elements or foundations, which make this empirical employment itself possible. Sense represents appearances em- pirically in perception, imagination in association (and repro- duction), apperception in the empirical consciousness of the identity of the reproduced representations with the appear- ances whereby they were given, that is, in recognition. But all perceptions are grounded a priori in pure intuition (in time, the form of their inner intuition as representations), association in pure synthesis of imagination, and empirical consciousness in pure apperception, that is, in the thorough- going identity of the self in all possible representations. If, now, we desire to follow up the inner ground of this connection of the representations to the point upon which they have all to converge in order that they may therein for the first time acquire the unity of knowledge necessary for a possible experience, we must begin with pure appercep- tion. Intuitions are nothing to us, and do not in the least concern us if they cannot be taken up into consciousness, in which they may participate either directly or indirectly. In this way alone is any knowledge possible. We are conscious a priori of the complete identity of the self in respect of all representations which can even belong to our knowledge, as being a necessary condition of the possibility of all representa- P 142 tions. For in me they can represent something only in so far as they belong with all others to one consciousness, and therefore must be at least capable of being so connected. This principle holds a priori, and may be called the tran- scendental principle of the unity of all that is manifold in our representations, and consequently also in intuition. Since this unity of the manifold in one subject is synthetic, pure apper- ception supplies a principle of the synthetic unity of the mani- fold in all possible intuition. This synthetic unity presupposes or includes a synthesis, and if the former is to be a priori necessary, the synthesis must also be a priori. The transcendental unity of apperception thus relates to the pure synthesis of imagination, as an a priori condition of the possibility of all combination of the manifold in one knowledge. This proposition is of great importance and calls for careful consideration. All representations have a necessary relation to a possible empirical consciousness. For if they did not have this, and if it were altogether impossible to become conscious of them, this would practically amount to the admission of their non-existence. But all empirical consciousness has a necessary relation to a tran- scendental consciousness which precedes all special experience, namely, the consciousness of myself as original apperception. It is therefore absolutely necessary that in my knowledge all conscious- ness should belong to a single consciousness, that of myself. Here, then, is a synthetic unity of the manifold (of consciousness), which is known a priori, and so yields the ground for synthetic a priori propositions which concern pure thought, just as do space and time for the propositions which refer to the form of pure intuition. The synthetic proposition, that all the variety of empirical consciousness must be combined in one single self-consciousness, is the abso- lutely first and synthetic principle of our thought in general. But it must not be forgotten that the bare representation 'I' in relation to all other representations (the collective unity of which it makes possible) is transcendental consciousness. Whether this representa- tion is clear (empirical consciousness) or obscure, or even whether it ever actually occurs, does not here concern us. But the possibility of the logical form of all knowledge is necessarily conditioned by relation to this apperception as a faculty. P 142 But only the productive synthesis of the P 143 imagination can take place a priori; the reproductive rests upon empirical conditions. Thus the principle of the necessary unity of pure (productive) synthesis of imagination, prior to apperception, is the ground of the possibility of all know- ledge, especially of experience. We entitle the synthesis of the manifold in imagination transcendental, if without distinction of intuitions it is directed exclusively to the a priori combination of the manifold; and the unity of this synthesis is called transcendental, if it is repre- sented as a priori necessary in relation to the original unity of apperception. Since this unity of apperception underlies the possibility of all knowledge, the transcendental unity of the synthesis of imagination is the pure form of all possible knowledge; and by means of it all objects of possible experi- ence must be represented a priori. The unity of apperception in relation to the synthesis of imagination is the understanding; and this same unity, with reference to the transcendental synthesis of the imagination, the pure understanding. In the understanding there are then pure a priori modes of knowledge which contain the neces- sary unity of the pure synthesis of imagination in respect of all possible appearances. These are the categories, that is, the pure concepts of understanding. The empirical faculty of know- ledge in man must therefore contain an understanding which relates to all objects of the senses, although only by means of intuition and of its synthesis through imagination. All appear- ances, as data for a possible experience, are subject to this understanding. This relation of appearances to possible ex- perience is indeed necessary, for otherwise they would yield no knowledge and would not in any way concern us. We have, therefore, to recognise that pure understanding, by means of the categories, is a formal and synthetic principle of all ex- periences, and that appearances have a necessary relation to the understanding. We will now, starting from below, namely, with the em- pirical, strive to make clear the necessary connection in which understanding, by means of the categories, stands to appear- ances. What is first given to us is appearance. When combined with consciousness, it is called perception. (Save through its P 144 relation to a consciousness that is at least possible, appear- ance could never be for us an object of knowledge, and so would be nothing to us; and since it has in itself no objective reality, but exists only in being known, it would be nothing at all. ) Now, since every appearance contains a manifold, and since different perceptions therefore occur in the mind separately and singly, a combination of them, such as they cannot have in sense itself, is demanded. There must therefore exist in us an active faculty for the synthesis of this manifold. To this faculty I give the title, imagination. Its action, when immediately directed upon perceptions, I entitle apprehen- sion. Since imagination has to bring the manifold of intuition into the form of an image, it must previously have taken the impressions up into its activity, that is, have apprehended them. But it is clear that even this apprehension of the manifold would not by itself produce an image and a connection of the impressions, were it not that there exists a subjective ground which leads the mind to reinstate a preceding perception alongside the subsequent perception to which it has passed, and so to form whole series of perceptions. This is the repro- ductive faculty of imagination, which is merely empirical. If, however, representations reproduced one another in any order, just as they happened to come together, this would not lead to any determinate connection of them, but only to acci- dental collocations; and so would not give rise to any know- ledge. Their reproduction must, therefore, conform to a rule, in accordance with which a representation connects in the imagination with some one representation in preference to another. This subjective and empirical ground of repro- duction according to rules is what is called the association of representations. Psychologists have hitherto failed to realise that imagination is a necessary ingredient of perception itself. This is due partly to the fact that that faculty has been limited to reproduction, partly to the belief that the senses not only supply impressions but also com- bine them so as to generate images of objects. For that purpose some- thing more than the mere receptivity of impressions is undoubtedly required, namely, a function for the synthesis of them. P 144 Now if this unity of association had not also an objective P 145 ground which makes it impossible that appearances should be apprehended by the imagination otherwise than under the condition of a possible synthetic unity of this apprehension, it would be entirely accidental that appearances should fit into a connected whole of human knowledge. For even though we should have the power of associating perceptions, it would remain entirely undetermined and accidental whether they would themselves be associable; and should they not be associ- able, there might exist a multitude of perceptions, and indeed an entire sensibility, in which much empirical consciousness would arise in my mind, but in a state of separation, and without belonging to a consciousness of myself. This, however, is im- possible. For it is only because I ascribe all perceptions to one consciousness (original apperception) that I can say of all per- ceptions that I am conscious of them. There must, therefore, be an objective ground (that is, one that can be comprehended a priori, antecedently to all empirical laws of the imagination) upon which rests the possibility, nay, the necessity, of a law that extends to all appearances -- a ground, namely, which constrains us to regard all appearances as data of the senses that must be associable in themselves and subject to universal rules of a thoroughgoing connection in their reproduction. This objective ground of all association of appearances I entitle their affinity. It is nowhere to be found save in the principle of the unity of apperception, in respect of all know- ledge which is to belong to me. According to this principle all appearances, without exception, must so enter the mind or be apprehended, that they conform to the unity of appercep- tion. Without synthetic unity in their connection, this would be impossible; and such synthetic unity is itself, therefore, objectively necessary. The objective unity of all empirical consciousness in one consciousness, that of original apperception, is thus the neces- sary condition of all possible perception; and [this being recog- nised we can prove that] the affinity of all appearances, near or remote, is a necessary consequence of a synthesis in imagina- tion which is grounded a priori on rules. Since the imagination is itself a faculty of a priori syn- thesis, we assign to it the title, productive imagination. In so far as it aims at nothing but necessary unity in the synthesis of P 146 what is manifold in appearance, it may be entitled the tran- scendental function of imagination. That the affinity of appear- ances, and with it their association, and through this, in turn, their reproduction according to laws, and so [as involving these various factors] experience itself, should only be possible by means of this transcendental function of imagination, is indeed strange, but is none the less an obvious consequence of the preceding argument. For without this transcendental func- tion no concepts would together make up a unitary experience. The abiding and unchanging 'I' (pure apperception) forms the correlate of all our representations in so far as it is to be at all possible that we should become conscious of them. All consciousness as truly belongs to an all-comprehensive pure apperception, as all sensible intuition, as representation, does to a pure inner intuition, namely, to time. It is this apperception which must be added to pure imagination, in order to render its function intellectual. For since the syn- thesis of imagination connects the manifold only as it appears in intuition, as, for instance, in the shape of a triangle, it is, though exercised a priori, always in itself sensible. And while concepts, which belong to the understanding, are brought into play through relation of the manifold to the unity of apper- ception, it is only by means of the imagination that they can be brought into relation to sensible intuition. A pure imagination, which conditions all a priori know- ledge, is thus one of the fundamental faculties of the human soul. By its means we bring the manifold of intuition on the one side, into connection with the condition of the necessary unity of pure apperception on the other. The two extremes, namely sensibility and understanding, must stand in neces- sary connection with each other through the mediation of this transcendental function of imagination, because otherwise the former, though indeed yielding appearances, would supply no objects of empirical knowledge, and consequently no experi- ence. Actual experience, which is consitituted by apprehension, association (reproduction), and finally recognition of appear- ances, contains in recognition, the last and highest of these P 147 merely empirical elements of experience, certain concepts which render possible the formal unity of experience, and therewith all objective validity (truth) of empirical knowledge. These grounds of the recognition of the manifold, so far as they concern solely the form of an experience in general, are the categories. Upon them is based not only all formal unity in the [transcendental] synthesis of imagination, but also, thanks to that synthesis, all its empirical employment (in recogni- tion, reproduction, association, apprehension) in connection with the appearances. For only by means of these funda- mental concepts can appearances belong to knowledge or even to our consciousness, and so to ourselves. Thus the order and regularity in the appearances, which we entitle nature, we ourselves introduce. We could never find them in appearances, had no we ourselves, or the nature of our mind, originally set them there. For this unity of nature has to be a necessary one, that is, has to be an a priori certain unity of the connection of appearances; and such synthetic unity could not be established a priori if there were not sub- jective grounds of such unity contained a priori in the original cognitive powers of our mind, and if these subjective condi- tions, inasmuch as they are the grounds of the possibility of knowing any object whatsoever in experience, were not at the same time objectively valid. We have already defined the understanding in various different ways: as a spontaneity of knowledge (in distinction from the receptivity of sensibility), as a power of thought, as a faculty of concepts, or again of judgments. All these defini- tions, when they are adequately understood, are identical. We may now characterise it as the faculty of rules. This dis- tinguishing mark is more fruitful, and approximates more closely to its essential nature. Sensibility gives us forms (of intuition), but understanding gives us rules. The latter is always occupied in investigating appearances, in order to detect some rule in them. Rules, so far as they are objective, and therefore necessarily depend upon the knowledge of the object, are called laws. Although we learn many laws through P 148 experience, they are only special determinations of still higher laws, and the highest of these, under which the others all stand, issue a priori from the understanding itself. They are not borrowed from experience; on the contrary, they have to confer upon appearances their conformity to law, and so to make experience possible. Thus the understanding is some- thing more than a power of formulating rules through com- parison of appearances; it is itself the lawgiver of nature. Save through it, nature, that is, synthetic unity of the mani- fold of appearances according to rules, would not exist at all (for appearances, as such, cannot exist outside us -- they exist only in our sensibility); and this nature, as object of knowledge in an experience, with everything which it may contain, is only possible in the unity of apperception. The unity of apperception is thus the transcendental ground of the necessary conformity to law of all appearances in one ex- perience. This same unity of apperception in respect to a manifold of representations (determining it out of a unity) acts as the rule, and the faculty of these rules is the under- standing. All appearances, as possible experiences, thus lie a priori in the understanding, and receive from it their formal possibility, just as, in so far as they are mere in- tuitions, they lie in the sensibility, and are, as regards their form, only possible through it. However exaggerated and absurd it may sound, to say that the understanding is itself the source of the laws of nature, and so of its formal unity, such an assertion is none the less correct, and is in keeping with the object to which it refers, namely, experience. Certainly, empirical laws, as such, can never derive their origin from pure understanding. That is as little possible as to understand completely the inexhaust- ible multiplicity of appearances merely by reference to the pure form of sensible intuition. But all empirical laws are only special determinations of the pure laws of understanding, under which, and according to the norm of which, they first become possible. Through them appearances take on an orderly character, just as these same appearances, despite P 149 the differences of their empirical form, must none the less always be in harmony with the pure form of sensibility. Pure understanding is thus in the categories the law of the synthetic unity of all appearances, and thereby first and originally makes experience, as regards its form, possible. This is all that we were called upon to establish in the tran- scendental deduction of the categories, namely, to render comprehensible this relation of understanding to sensibility, and, by means of sensibility, to all objects of experience. The objective validity of the pure a priori concepts is thereby made intelligible, and their origin and truth determined. Summary Representation of the Correctness of this Deduction of the Pure Concepts of Understanding, and of its being the only Deduction possible If the objects with which our knowledge has to deal were things in themselves, we could have no a priori concepts of them. For from what source could we obtain the concepts? If we derived them from the object (leaving aside the question how the object could become known to us), our concepts would be merely empirical, not a priori. And if we derived them from the self, that which is merely in us could not determine the character of an object distinct from our representations, that is, could not be a ground why a thing should exist character- ised by that which we have in our thought, and why such a representation should not, rather, be altogether empty. But if, on the other hand, we have to deal only with appearances, it is not merely possible, but necessary, that certain a priori concepts should precede empirical knowledge of objects. For since a mere modification of our sensibility can never be met with outside us, the objects, as appearances, constitute an object which is merely in us. Now to assert in this manner, that all these appearances, and consequently all objects with which we can occupy ourselves, are one and all in me, that is, are determinations of my identical self, is only another way of saying that there must be a complete unity of them in one and the same apperception. But this unity of possible consciousness also constitutes the form of all knowledge of objects; through it the manifold is thought as belonging to a P 150 single object. Thus the mode in which the manifold of sensible representation (intuition) belongs to one consciousness pre- cedes all knowledge of the object as the intellectual form of such knowledge, and itself constitutes a formal a priori know- ledge of all objects, so far as they are thought (categories). The synthesis of the manifold through pure imagination, the unity of all representations in relation to original apper- ception, precede all empirical knowledge. Pure concepts of understanding are thus a priori possible, and, in relation to experience, are indeed necessary; and this for the reason that our knowledge has to deal solely with appearances, the possibility of which lies in ourselves, and the connection and unity of which (in the representation of an object) are to be met with only in ourselves. Such connection and unity must therefore precede all experience, and are required for the very possibility of it in its formal aspect. From this point of view, the only feasible one, our deduction of the categories has been developed. P 151 DEDUCTION OF THE PURE CONCEPTS OF THE UNDERSTANDING Section 2 TRANSCENDENTAL DEDUCTION OF THE PURE CONCEPTS OF THE UNDERSTANDING $15 The Possibility of Combination in General THE manifold of representations can be given in an intuition which is purely sensible, that is, nothing but receptivity; and the form of this intuition can lie a priori in our faculty of representation, without being anything more than the mode in which the subject is affected. But the combination (conjunctio) of a manifold in general can never come to us through the senses, and cannot, therefore, be already contained in the pure form of sensible intuition. For it is an act of spontaneity of the faculty of representation; and since this faculty, to distinguish it from sensibility, must be entitled understanding, all com- bination -- be we conscious of it or not, be it a combination of the manifold of intuition, empirical or non-empirical, or of various concepts -- is an act of the understanding. To this act the general title 'synthesis' may be assigned, as indicating that we cannot represent to ourselves anything as combined in the object which we have not ourselves previously combined, and that of all representations combination is the only one which P 152 cannot be given through objects. Being an act of the self- activity of the subject, it cannot be executed save by the sub- ject itself. It will easily be observed that this action is originally one and is equipollent for all combination, and that is dis- solution, namely, analysis, which appears to be its opposite, yet always presupposes it. For where the understanding has not previously combined, it cannot dissolve, since only as having been combined by the understanding can anything that allows of analysis be given to the faculty of representation. But the concept of combination includes, besides the con- cept of the manifold and of its synthesis, also the concept of the unity of the manifold. Combination is representation of the synthetic unity of the manifold. The representation of this unity cannot, therefore, arise out of the combination. On the contrary, it is what, by adding itself to the representation of the manifold, first makes possible the concept of the combina- tion. This unity, which precedes a priori all concepts of com- bination, is not the category of unity ($10); for all categories are grounded in logical functions of judgment, and in these functions combination, and therefore unity of given concepts, is already thought. Thus the category already presupposes combination. We must therefore look yet higher for this unity (as qualitative, $12), namely in that which itself contains the ground of the unity of diverse concepts in judgment, and there- fore of the possibility of the understanding, even as regards its logical employment. $16 The Original Synthetic Unity of Apperception It must be possible for the 'I think' to accompany all my representations; for otherwise something would be represented P 153 in me which could not be thought at all, and that is equivalent to saying that the representation would be impossible, or at least would be nothing to me. P 152 Whether the representations are in themselves identical, and whether, therefore, one can be analytically thought through the other, is not a question that here arises. The consciousness of the one, when the manifold is under consideration, has always to be dis- tinguished from the consciousness of the other; and it is with the synthesis of this (possible) consciousness that we are here alone concerned. P 153 That representation which can be given prior to all thought is entitled intuition. All the manifold of intuition has, therefore, a necessary relation to the 'I think' in the same subject in which this manifold is found. But this representation is an act of spontaneity, that is, it cannot be regarded as belonging to sensibility. I call it pure apperception, to distinguish it from empirical apperception, or, again, origninal apperception, because it is that self-consious- ness which, while generating the representation 'I think' (a representation which must be capable of accompanying all other representations, and which in all consciousness is one and the same), cannot itself be accompanied by any further repre- sentation. The unity of this apperception I likewise entitle the transcendental unity of self-consciousness, in order to indicate the possibility of a priori knowledge arising from it. For the manifold representations, which are given in an intuition, would not be one and all my representations, if they did not all belong to one self-consciousness. As my representa- tions (even if I am not conscious of them as such) they must conform to the condition under which alone they can stand together in one universal self-consciousness, because otherwise they would not all without exception belong to me. From this original combination many consequences follow. This thoroughgoing identity of the apperception of a manifold which is given in intuition contains a synthesis of representations, and is possible only through the conscious- ness of this synthesis. For the empirical consciousness, which accompanies different representations, is in itself diverse and without relation to the identity of the subject. That relation comes about, not simply through my accompanying each re- presentation with consciousness, but only in so far as I conjoin one representation with another, and am conscious of the syn- thesis of them. Only in so far, therefore, as I can unite a manifold of given representations in one consciousness, is it possible for me to represent to myself the identity of the con- sciousness in [i.e. throughout] these representations. In other P 154 words, the analytic unity of apperception is possible only under the presupposition of a certain synthetic unity. The thought that the representations given in intuition one and all belong to me, is therefore equivalent to the thought that I unite them in one self-consciousness, or can at least so unite them; and although this thought is not itself the consciousness of the synthesis of the representations, it pre- supposes the possibility of that synthesis. In other words, only in so far as I can grasp the manifold of the representations in one consciousness, do I call them one and all mine. For other- wise I should have as many-coloured and diverse a self as I have representations of which I am conscious to myself. Syn- thetic unity of the manifold of intuitions, as generated a - priori, is thus the ground of the identity of apperception itself, which precedes a priori all my determinate thought. Com- bination does not, however, lie in the objects, and cannot be borrowed from them, and so, through perception, first taken up into the understanding. On the contrary, it is an affair of the understanding alone, which itself is nothing but the faculty of combining a priori, and of bringing the manifold of given representations under the unity of apperception. The principle of apperception is the highest principle in the whole sphere of human knowledge. This principle of the necessary unity of apperception is ++ The analytic unity of consciousness belongs to all general con- cepts, as such. If, for instance, I think red in general, I thereby repre- sent to myself a property which (as a characteristic) can be found in something, or can he combined with other representations; that is, only by means of a presupposed possible synthetic unity can I repre- sent to myself the analytic unity. A representation which is to be thought as common to different representations is regarded as be- longing to such as have, in addition to it, also something different. Consequently it must previously be thought in synthetic unity with other (though, it may be, only possible) representations, before I can think in it the analytic unity of consciousness, which makes it a con- ceptus communis. The synthetic unity of apperception is therefore that highest point, to which we must ascribe all employment of the understanding, even the whole of logic, and conformably therewith, transcendental philosophy. Indeed this faculty of apperception is the understanding itself. P 155 itself, indeed, an identical, and therefore analytic, proposi- tion; nevertheless it reveals the necessity of a synthesis of the manifold given in intuition, without which the thoroughgoing identity of self-consciousness cannot be thought. For through the 'I', as simple representation, nothing manifold is given; only in intuition, which is distinct from the 'I', can a manifold be given; and only through combination in one conscious- ness can it be thought. An understanding in which through self-consciousness all the manifold would eo ipso be given, would be intuitive; our understanding can only think, and for intuition must look to the senses. I am conscious of the self as identical in respect of the manifold of representations that are given to me in an intuition, because I call them one and all my representations, and so apprehend them as con- stituting one intuition. This amounts to saying, that I am conscious to myself a priori of a necessary synthesis of re- presentations -- to be entitled the original synthetic unity of apperception -- under which all representations that are given to me must stand, but under which they have also first to be brought by means of a synthesis. $17 The Principle of the Synthetic Unity is the Supreme Principle of all Employment of the Understanding The supreme principle of the possibility of all intuition in its relation to sensibility is, according to the Transcendental Aesthetic, that all the manifold of intuition should be subject to the formal conditions of space and time. The supreme prin- ciple of the same possibility, in its relation to understanding, is that all the manifold of intuition should be subject to con- ditions of the original synthetic unity of apperception. Space and time, and all their parts, are intuitions, and are, therefore, with the manifold which they contain, singular representa- tions (vide the Transcendental Aesthetic). Consequently they are not mere concepts through which one and the same consciousness is found to be contained in a number of representations. On the con- trary, through them many representations are found to be contained in one representation, and in the consciousness of that representa- tion ; and they are thus composite. The unity of that consciousness P 156n is therefore synthetic and yet is also original. The singularity of such intuitions is found to have important consequences (vide $25). P 155 In so P 156 far as the manifold representations of intuition are given to us, they are subject to the former of these two principles; in so far as they must allow of being combined in one consciousness, they are subject to the latter. For without such combination nothing can be thought or known, since the given repre- sentations would not have in common the act of the apper- ception 'I think', and so could not be apprehended together in knowledge. This knowledge consists in the determinate re- lation of given representations to an object; and an object is that in the concept of which the manifold of a given intuition is united. Now all unification of representations demands unity of consciousness in the synthesis of them. Consequently it is the unity of consciousness that alone constitutes the relation of representations to an object, and therefore their objective validity and the fact that they are modes of know- ledge; and upon it therefore rests the very possibility of the understanding. The first pure knowledge of understanding, then, upon which all the rest of its employment is based, and which also at the same time is completely independent of all conditions of sensible intuition, is the principle of the original synthetic unity of apperception. Thus the mere form of outer sensible intuition, space, is not yet [by itself] knowledge; it supplies only the manifold of a priori intuition for a possible know- ledge. To know anything in space (for instance, a line), I must draw it, and thus synthetically bring into being a de- terminate combination of the given manifold, so that the unity of this act is at the same time the unity of consciousness (as in the concept of a line); and it is through this unity of con- sciousness that an object (a determinate space) is first known. The synthetic unity of consciousness is, therefore, an objective condition of all knowledge. It is not merely a condition that I myself require in knowing an object, but is a condition under which every intuition must stand in order to become an object for me. For otherwise, in the absence of this P 157 synthesis, the manifold would not be united in one con- sciousness. Although this proposition makes synthetic unity a con- dition of all thought, it is, as already stated, itself analytic. For it says no more than that all my representations in any given intuition must be subject to that condition under which alone I can ascribe them to the identical self as my representa- tions, and so can comprehend them as synthetically com- bined in one apperception through the general expression, 'I think'. This principle is not, however, to be taken as applying to every possible understanding, but only to that understand- ing through whose pure apperception, in the representation 'I am', nothing manifold is given. An understanding which through its self-consciousness could supply to itself the mani- fold of intuition -- an understanding, that is to say, through whose representation the objects of the representation should at the same time exist -- would not require, for the unity of consciousness, a special act of synthesis of the manifold. For the human understanding, however, which thinks only, and does not intuit, that act is necessary. It is indeed the first principle of the human understanding, and is so indispensable to it that we cannot form the least conception of any other possible understanding, either of such as is itself intuitive or of any that may possess an underlying mode of sensible in- tuition which is different in kind from that in space and time. $18 The Objective Unity of Self-Consciousness The transcendental unity of apperception is that unity through which all the manifold given in an intuition is united in a concept of the object. It is therefore entitled objective, and must be distinguished from the subjective unity of con- sciousness, which is a determination of inner sense -- through which the manifold of intuition for such [objective] combina- tion is empirically given. Whether I can become empirically conscious of the manifold as simultaneous or as successive depends on circumstances or empirical conditions. Therefore P 158 the empirical unity of consciousness, through association of representations, itself concerns an appearance, and is wholly contingent. But the pure form of intuition in time, merely as intuition in general, which contains a given manifold, is subject to the original unity of consciousness, simply through the necessary relation of the manifold of the intuition to the one 'I think', and so through the pure synthesis of understanding which is the a priori underlying ground of the empirical synthesis. Only the original unity is objectively valid; the empirical unity of apperception, upon which we are not here dwelling, and which besides is merely derived from the former under given conditions in concreto, has only subjective validity. To one man, for instance, a certain word suggests one thing, to another some other thing; the unity of consciousness in that which is empirical is not, as regards what is given, necessarily and universally valid. $19 The Logical Form of all Judgments consists in the Objective Unity of the Apperception of the Concepts which they contain I have never been able to accept the interpretation which logicians give of judgment in general. It is, they declare, the representation of a relation between two concepts. I do not here dispute with them as to what is defective in this interpretation -- that in any case it applies only to categorical, not to hypothetical and disjunctive judgments (the two latter containing a relation not of concepts but of judgments), an oversight from which many troublesome consequences have followed. I need only point out that the definition does not determine in what the asserted relation consists. The lengthy doctrine of the four syllogistic figures concerns categorical syllogisms only; and although it is indeed nothing more than an artificial method of securing, through the surreptitious introduction of immediate inferences (consequentiae immediatae) among the premisses of a pure syllogism, the appearance that there are more kinds of inference than that of the first figure, this would hardly have met with such remarkable acceptance, had not its authors succeeded in bringing categorical judgments into such P 159n exclusive respect, as being those to which all others must allow of being reduced -- teaching which, as indicated in $9, is none the less erroneous. P 159 But if I investigate more precisely the relation of the given modes of knowledge in any judgment, and distinguish it, as belonging to the understanding, from the relation accord- ing to laws of the reproductive imagination, which has only subjective validity, I find that a judgment is nothing but the manner in which given modes of knowledge are brought to the objective unity of apperception. This is what is intended by the copula 'is'. It is employed to distinguish the objective unity of given representations from the sub- jective. It indicates their relation to original apperception, and its necessary unity. It holds good even if the judgment is itself empirical, and therefore contingent, as, for example, in the judgment, 'Bodies are heavy'. I do not here assert that these representations necessarily belong to one another in the empirical intuition, but that they belong to one another in virtue of the necessary unity of apperception in the synthesis of intuitions, that is, according to principles of the object- ive determination of all representations, in so far as know- ledge can be acquired by means of these representations -- principles which are all derived from the fundamental prin- ciple of the transcendental unity of apperception. Only in this way does there arise from this relation a judgment, that is, a relation which is objectively valid, and so can be adequately distinguished from a relation of the same representations that would have only subjective validity -- as when they are connected according to laws of association. In the latter case, all that I could say would be, 'If I support a body, I feel an impression of weight'; I could not say, 'It, the body, is heavy'. Thus to say 'The body is heavy' is not merely to state that the two representations have always been conjoined in my perception, however often that perception be repeated; what we are asserting is that they are combined in the object, no matter what the state of the subject may be. P 160 $20 All Sensible Intuitions are subject to the Categories, as Con- ditions under which alone their Manifold can come to- gether in one Consciousness The manifold given in a sensible intuition is necessarily subject to the original synthetic unity of apperception, be- cause in no other way is the unity of intuition possible ($17). But that act of understanding by which the manifold of given representations (be they intuitions or concepts) is brought under one apperception, is the logical function of judgment (cf. $19). All the manifold, therefore, so far as it is given in a single empirical intuition, is determined in respect of one of the logical functions of judgment, and is thereby brought into one consciousness. Now the categories are just these functions of judgment, in so far as they are employed in determination of the manifold of a given intuition (cf. $13). Consequently, the manifold in a given intuition is necessarily subject to the categories. $21 Observation A manifold, contained 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 is effected by means of the category. This [requirement of a] category therefore shows that the empirical consciousness of a given manifold in a single intuition is subject to a pure self- consciousness a priori, just as is empirical intuition to a pure sensible intuition, which likewise takes place a priori. Thus in the above proposition a beginning is made of a deduction of the pure concepts of understanding; The proof of this rests on the represented unity of intuition, by which an object is given. This unity of intuition always includes in itself a synthesis of the manifold given for an intuition, and so already contains the relation of this manifold to the unity of apper- ception. P 160 and in this deduction, since the categories have their source in the understanding alone, independently of sensibility, I must abstract from the P 161 mode in which the manifold for an empirical intuition is given, and must direct attention solely to the unity which, in terms of the category, and by means of the understanding, enters into the intuition. In what follows (cf. $26) it will be shown, from the mode in which the empirical intuition is given in sensibil- ity, that its unity is no other than that which the category (according to $20) prescribes to the manifold of a given in- tuition in general. Only thus, by demonstration of the a priori validity of the categories in respect of all objects of our senses, will the purpose of the deduction be fully attained. But in the above proof there is one feature from which I could not abstract, the feature, namely, that the manifold to be intuited must be given prior to the synthesis of understanding, and independently of it. How this takes place, remains here undetermined. For were I to think an understanding which is itself intuitive (as, for example, a divine understanding which should not represent to itself given objects, but through whose representation the objects should themselves be given or pro- duced), the categories would have no meaning whatsoever in respect of such a mode of knowledge. They are merely rules for an understanding whose whole power consists in thought, con- sists, that is, in the act whereby it brings the synthesis of a mani- fold, given to it from elsewhere in intuition, to the unity of ap- perception -- a faculty, therefore, which by itself knows nothing whatsoever, but merely combines and arranges the material of knowledge, that is, the intuition, which must be given to it by the object. This peculiarity of our understanding, that it can produce a priori unity of apperception solely by means of the categories, and only by such and so many, is as little capable of further explanation as why we have just these and no other functions of judgment, or why space and time are the only forms of our possible intuition. $22 The Category has no other Application in Knowledge than to Objects of Experience To think an object and to know an object are thus by no means the same thing. Knowledge involves two factors: first, P 162 the concept, through which an object in general is thought (the category); and secondly, the intuition, through which it is given. For if no intuition could be given corresponding to the concept, the concept would still indeed be a thought, so far as its form is concerned, but would be without any object, and no knowledge of anything would be possible by means of it. So far as I could know, there would be nothing, and could be nothing, to which my thought could be applied. Now, as the Aesthetic has shown, the only intuition possible to us is sens- ible; consequently, the thought of an object in general, by means of a pure concept of understanding, can become know- ledge for us only in so far as the concept is related to objects of the senses. Sensible intuition is either pure intuition (space and time) or empirical intuition of that which is immediately represented, through sensation, as actual in space and time. Through the determination of pure intuition we can acquire a priori knowledge of objects, as in mathematics, but only in regard to their form, as appearances; whether there can be things which must be intuited in this form, is still left unde- cided. Mathematical concepts are not, therefore, by themselves knowledge, except on the supposition that there are things which allow of being presented to us only in accordance with the form of that pure sensible intuition. Now things in space and time are given only in so far as they are perceptions (that is, representations accompanied by sensation) -- therefore only through empirical representation. Consequently, the pure concepts of understanding, even when they are applied to a - priori intuitions, as in mathematics, yield knowledge only in so far as these intuitions -- and therefore indirectly by their means the pure concepts also -- can be applied to empirical in- tuitions. Even, therefore, with the aid of [pure] intuition, the categories do not afford us any knowledge of things; they do so only through their possible application to empirical intui- tion. In other words, they serve only for the possibility of em- pirical knowledge; and such knowledge is what we entitle experience. Our conclusion is therefore this: the categories, as yielding knowledge of things, have no kind of application, save only in regard to things which may be objects of possible experience. P 163 $23 The above proposition is of the greatest importance; for it determines the limits of the employment of the pure concepts of understanding in regard to objects, just as the Transcen- dental Aesthetic determined the limits of the employment of the pure form of our sensible intuition. Space and time, as con- ditions under which alone objects can possibly be given to us, are valid no further than for objects of the senses, and there- fore only for experience. Beyond these limits they represent nothing; for they are only in the senses, and beyond them have no reality. The pure concepts of understanding are free from this limitation, and extend to objects of intuition in general, be the intuition like or unlike ours, if only it be sensible and not intellectual. But this extension of concepts beyond our sensible intuition is of no advantage to us. For as concepts of objects they are then empty, and do not even enable us to judge of their objects whether or not they are possible. They are mere forms of thought, without objective reality, since we have no intuition at hand to which the synthetic unity of apperception, which constitutes the whole content of these forms, could be applied, and in being so applied determine an object. Only our sensible and empirical intuition can give to them body and meaning. If we suppose an object of a non-sensible intuition to be given, we can indeed represent it through all the predicates which are implied in the presupposition that it has none of the characteristics proper to sensible intuition; that it is not ex- tended or in space, that its duration is not a time, that no change (succession of determinations in time) is to be met with in it, etc. But there is no proper knowledge if I thus merely in- dicate what the intuition of an object is not, without being able to say what it is that is contained in the intuition. For I have not then shown that the object which I am thinking through my pure concept is even so much as possible, not being in a position to give any intuition corresponding to the concept, and being able only to say that our intuition is not applicable to it. But what has chiefly to be noted is this, that to such a some- thing [in general] not a single one of all the categories could P 164 be applied. We could not, for instance, apply to it the concept of substance, meaning something which can exist as subject and never as mere predicate. For save in so far as empirical intuition provides the instance to which to apply it, I do not know whether there can be anything that corresponds to such a form of thought. But of this more hereafter. $24 The Application of the Categories to Objects of the Senses in General The pure concepts of understanding relate, through the mere understanding, to objects of intuition in general, whether that intuition be our own or any other, provided only it be sensible. The concepts are, however, for this very reason, mere forms of thought, through which alone no determinate object is known. The synthesis or combination of the manifold in them relates only to the unity of apperception, and is thereby the ground of the possibility of a priori knowledge, so far as such knowledge rests on the understanding. This synthesis, there- fore, is at once transcendental and also purely intellectual. But since there lies in us a certain form of a priori sensible intui- tion, which depends on the receptivity of the faculty of repre- sentation (sensibility), the understanding, as spontaneity, is able to determine inner sense through the manifold of given repre- sentations, in accordance with the synthetic unity of apper- ception, and so to think synthetic unity of the apperception of the manifold of a priori sensible intuition -- that being the condition under which all objects of our human intuition must necessarily stand. In this way the categories, in themselves mere forms of thought, obtain objective reality, that is, ap- plication to objects which can be given us in intuition. These objects, however, are only appearances, for it is solely of appearances that we can have a priori intuition. This synthesis of the manifold of sensible intuition, which is possible and necessary a priori, may be entitled figurative synthesis (synthesis speciosa), to distinguish it from the syn- thesis which is thought in the mere category in respect of the manifold of an intuition in general, and which is entitled combination through the understanding (synthesis intellectua- P 165 lis). Both are transcendental, not merely as taking place a priori, but also as conditioning the possibility of other a priori knowledge. But the figurative synthesis, if it be directed merely to the original synthetic unity of apperception, that is, to the transcendental unity which is thought in the categories, must, in order to be distinguished from the merely intellec- tual combination, be called the transcendental synthesis of imagination. Imagination is the faculty of representing in intuition an object that is not itself present. Now since all our intuition is sensible, the imagination, owing to the subjective condition under which alone it can give to the concepts of understanding a corresponding intuition, belongs to sen- sibility. But inasmuch as its synthesis is an expression of spontaneity, which is determinative and not, like sense, deter- minable merely, and which is therefore able to determine sense a priori in respect of its form in accordance with the unity of apperception, imagination is to that extent a faculty which determines the sensibility a priori; and its synthesis of intuitions, conforming as it does to the categories, must be the transcendental synthesis of imagination. This synthesis is an action of the understanding on the sensibility; and is its first application -- and thereby the ground of all its other applications -- to the objects of our possible intuition. As figurative, it is distinguished from the intellectual synthesis, which is carried out by the understanding alone, without the aid of the imagination. In so far as imagination is spontaneity, I sometimes also entitle it the productive imagination, to dis- tinguish it from the reproductive imagination, whose synthesis is entirely subject to empirical laws, the laws, namely, of association, and which therefore contributes nothing to the explanation of the possibility of a priori knowledge. The repro- ductive synthesis falls within the domain, not of transcendental philosophy, but of psychology. * * * This is a suitable place for explaining the paradox which must have been obvious to everyone in our exposition of the P 166 form of inner sense ($6): namely, that this sense represents to consciousness even our own selves only as we appear to ourselves, not as we are in ourselves. For we intuit ourselves only as we are inwardly affected, and this would seem to be contradictory, since we should then have to be in a passive relation [of active affection] to ourselves. It is to avoid this contradiction that in systems of psychology inner sense, which we have carefully distinguished from the faculty of apperception, is commonly regarded as being identical with it. What determines inner sense is the understanding and its original power of combining the manifold of intuition, that is, of bringing it under an apperception, upon which the possi- bility of understanding itself rest. Now the understanding in us men is not a faculty of intuitions, and cannot, even if intuitions be given in sensibility, take them up into itself in such manner as to combine them as the manifold of its own intuition. Its synthesis, therefore, if the synthesis be viewed by itself alone, is nothing but the unity of the act, of which, as an act, it is conscious to itself, even without [the aid of] sensibility, but through which it is yet able to determine the sensibility. The understanding, that is to say, in respect of the manifold which may be given to it in accord- ance with the form of sensible intuition, is able to deter- mine sensibility inwardly. Thus the understanding, under the title of a transcendental synthesis of imagination, performs this act upon the passive subject, whose faculty it is, and we are therefore justified in saying that inner sense is affected thereby. Apperception and its synthetic unity is, indeed, very far from being identical with inner sense. The former, as the source of all combination, applies to the manifold of intui- tions in general, and in the guise of the categories, prior to all sensible intuition, to objects in general. Inner sense, on the other hand, contains the mere form of intuition, but without combination of the manifold in it, and therefore so far contains no determinate intuition, which is possible only through the consciousness of the determination of the manifold by the transcendental act of imagination (synthetic influence P 167 of the understanding upon inner sense), which I have entitled figurative synthesis. This we can always perceive in ourselves. We cannot think a line without drawing it in thought, or a circle without describing it. We cannot represent the three dimensions of space save by setting three lines at right angles to one another from the same point. Even time itself we cannot represent, save in so far as we attend, in the drawing of a straight line (which has to serve as the outer figurative representation of time), merely to the act of the synthesis of the manifold where- by we successively determine inner sense, and in so doing attend to the succession of this determination in inner sense. Motion, as an act of the subject (not as a determination of an object), and therefore the synthesis of the manifold in space, first produces the concept of succession -- if we abstract from this manifold and attend solely to the act through which we determine the inner sense according to its form. The understanding does not, therefore, find in inner sense such a combination of the manifold, but produces it, in that it affects that sense. How the 'I' that thinks can be distinct from the 'I' that intuits itself (for I can represent still other modes of intuition as at least possible), and yet, as being the same subject, can be identical with the latter; and how, therefore, I can say: "I, as intelligence and thinking subject, know myself as an object that is thought, in so far as I am given to myself [as some- thing other or] beyond that [I] which is [given to myself] in intuition, and yet know myself, like other phenomena, only as I appear to myself, not as I am to the understanding" -- these are questions that raise no greater nor less difficulty than how I can be an object to myself at all, and, more particularly, an object of intuition and of inner perceptions. Motion of an object in space does not belong to a pure science, and consequently not to geometry. For the fact that something is movable cannot be known a priori, but only through experience. Motion, however, considered as the describing of a space, is a pure act of the successive synthesis of the manifold in outer intuition in general by means of the productive imagination, and belongs not only to geometry, but even to transcendental philosophy. P 168 Indeed, that this is how it must be, is easily shown -- if we admit that space is merely a pure form of the appearances of outer sense -- by the fact that we cannot obtain for ourselves a representation of time, which is not an object of outer in- tuition, except under the image of a line, which we draw, and that by this mode of depicting it alone could we know the singleness of its dimension; and similarly by the fact that for all inner perceptions we must derive the determination of lengths of time or of points of time from the changes which are exhibited to us in outer things, and that the determina- tions of inner sense have therefore to be arranged as appear- ances in time in precisely the same manner in which we arrange those of outer sense in space. If, then, as regards the latter, we admit that we know objects only in so far as we are externally affected, we must also recognise, as regards inner sense, that by means of it we intuit ourselves only as we are inwardly affected by ourselves; in other words, that, so far as inner intuition is concerned, we know our own subject only as appearance, not as it is in itself. $25 On the other hand, in the transcendental synthesis of the manifold of representations in general, and therefore in the synthetic original 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 intui- tion. Now in order to know ourselves, there is required in addition to the act of thought, which brings the manifold of every possible intuition to the unity of apperception, a de- terminate mode of intuition, whereby this manifold is given; ++ I do not see why so much difficulty should be found in admit- ting that our inner sense is affected by ourselves. Such affection finds exemplification in each and every act of attention. In every act of attention the understanding determines inner sense, in accordance with the combination which it thinks, to that inner intuition which corresponds to the manifold in the synthesis of the understanding. How much the mind is usually thereby affected, everyone will be able to perceive in himself. P 168 it therefore follows that although my existence is not indeed P 169 appearance (still less mere illusion), the determination of my existence can take place only in conformity with the form of inner sense, according to the special mode in which the mani- fold, which I combine, is given in inner intuition. Accordingly I have no knowledge of myself as I am but merely as I appear to myself. The consciousness of self is thus very far from being a knowledge of the self, notwithstanding all the categories which [are being employed to] constitute the thought of an object in general, through combination of the manifold in one apperception. Just as for knowledge of an object distinct from me I require, besides the thought of an object in general (in the category), an intuition by which I determine that general concept, so for knowledge of myself I require, besides the consciousness, that is, besides the thought of myself, an intuition of the manifold in me, by which I determine this thought. I exist as an intelligence which is conscious solely of its power of combination; but in respect of the manifold which it has to combine I am subjected to a limiting condition (entitled inner sense), namely, that this combination can be made intuitable only according to relations of time, which lie entirely outside the concepts of understanding, strictly re- garded. Such an intelligence, therefore, can know itself only as it appears to itself in respect of an intuition which is not intellectual and cannot be given by the understanding itself, not as it would know itself if its intuition were intellectual. ++ The 'I think' expresses the act of determining my existence. Existence is already given thereby, but the mode in which I am to determine this existence, that is, the manifold belonging to it, is not thereby given. In order that it be given, self-intuition is required; and such intuition is conditioned by a given a priori form, namely, time, which is sensible and belongs to the receptivity of the deter- minable [in me]. Now since I do not have another self-intuition which gives the determining in me (I am conscious only of the spontaneity of it) prior to the act of determination, as time does in the case of the determinable, I cannot determine my existence as that of a self-active being; all that I can do is to represent to myself the spontaneity of my thought, that is, of the determination; and my existence is still only determinable sensibly, that is, as the existence of an appearance. But it is owing to this spontaneity that I entitle myself an intelligence. P 170 $26 Transcendental Deduction of the Universally Possible Em- ployment in experience of the Pure Concepts of the Understanding In the metaphysical deduction the a priori origin of the categories has been proved through their complete agreement with the general logical functions of thought; in the transcen- dental deduction we have shown their possibility as a priori modes of knowledge of objects of an intuition in general (cf. $$20, 21). We have now to explain the possibility of knowing a priori, by means of categories, whatever objects may present themselves to our senses, not indeed in respect of the form of their intuition, but in respect of the laws of their combination, and so, as it were, of prescribing laws to nature, and even of making nature possible. For unless the cate- gories discharged this function, there could be no explaining why everything that can be presented to our senses must be subject to laws which have their origin a priori in the under- standing alone. First of all, I may draw attention to the fact that by syn- thesis of apprehension I understand that combination of the manifold in an empirical intuition, whereby perception, that is, empirical consciousness of the intuition (as appearance), is possible. In the representations of space and time we have a priori forms of outer and inner sensible intuition; and to these the synthesis of apprehension of the manifold of appearance must always conform, because in no other way can the synthesis take place at all. But space and time are represented a priori not merely as forms of sensible intuition, but as themselves intuitions which contain a manifold [of their own], and there- fore are represented with the determination of the unity of this manifold (vide the Transcendental Aesthetic). Thus P 171 unity of the synthesis of the manifold, without or within us, and consequently also a combination to which everything that is to be represented as determined in space or in time must conform, is given a priori as the condition of the synthesis of all apprehension -- not indeed in, but with these intuitions. This synthetic unity can be no other than the unity of the combination of the manifold of a given intuition in general in an original consciousness, in accordance with the cate- gories, in so far as the combination is applied to our sensible intuition. All synthesis, therefore, even that which renders perception possible, is subject to the categories; and since experience is knowledge by means of connected perceptions, the categories are conditions of the possibility of experience, and are therefore valid a priori for all objects of experience. * * * When, for instance, by apprehension of the manifold of a house I make the empirical intuition of it into a perception, the necessary unity of space and of outer sensible intuition in general lies at the basis of my apprehension, and I draw as it were the outline of the house in conformity with this synthetic unity of the manifold in space. But if I abstract from the form of space, this same synthetic unity has its seat in the under- standing, and is the category of the synthesis of the homogene- ous in an intuition in general, that is, the category of quantity. To this category, therefore, the synthesis of apprehension, that is to say, the perception, must completely conform. P 170n ++ Space, represented as object (as we are required to do in geo- metry), contains more than mere form of intuition; it also contains combination of the manifold, given according to the form of sensi- bility, in an intuitive representation, so that the form of intuition gives only a manifold, the formal intuition gives unity of representa- tion. In the Aesthetic I have treated this unity as belonging merely P 171n to sensibility, simply in order to emphasise that it precedes any con- cept, although, as a matter of fact, it presupposes a synthesis which does not belong to the senses but through which all concepts of space and time first become possible. For since by its means (in that the understanding determines the sensibility) space and time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding (cf. $24). ++ In this manner it is proved that the synthesis of apprehension, which is empirical, must necessarily be in conformity with the syn- thesis of apperception, which is intellectual and is contained in the category completely a priori. It is one and the same spontaneity, P 172n which in the one case, under the title of imagination, and in the other case, under the title of understanding, brings combination into the manifold of intuition. P 172 When, to take another example, I perceive the freezing of water, I apprehend two states, fluidity and solidity, and these as standing to one another in a relation of time. But in time, which I place at the basis of the appearance [in so far] as [it is] inner intuition, I necessarily represent to myself synthetic unity of the manifold, without which that relation of time could not be given in an intuition as being determined in respect of time-sequence. Now this synthetic unity, as a condition a priori under which I combine the manifold of an intui- tion in general, is -- if I abstract from the constant form of my inner intuition, namely, time -- the category of cause, by means of which, when I apply it to my sensibility, I deter- mine everything that happens in accordance with the relation which it prescribes, and I do so in time in general. Thus my apprehension of such an event, and therefore the event itself, considered as a possible perception, is subject to the con- cept of the relation of effects and causes, and so in all other cases. Categories are concepts which prescribe laws a priori to appearances, and therefore to nature, the sum of all appear- ances (natura materialiter spectata). The question therefore arises, how it can be conceivable that nature should have to proceed in accordance with categories which yet are not de- rived from it, and do not model themselves upon its pattern; that is, how they can determine a priori the combination of the manifold of nature, while yet they are not derived from it. The solution of this seeming enigma is as follows. That the laws of appearances in nature must agree with the understanding and its a priori form, that is, with its faculty of combining the manifold in general, is no more surprising than that the appearances themselves must agree with the form of a priori sensible intuition. For just as appearances do not exist in themselves but only relatively to the subject in which, so far as it has senses, they inhere, so the laws do not exist in the appearances but only relatively to this same being, so far as it has understanding. Things in themselves would necessarily, P 173 apart from any understanding that knows them, conform to laws of their own. But appearances are only representations of things which are unknown as regards what they may be in themselves. As mere representations, they are subject to no law of connection save that which the connecting faculty pre- scribes. Now it is imagination that connects the manifold of sensible intuition; and imagination is dependent for the unity of its intellectual synthesis upon the understanding, and for the manifoldness of its apprehension upon sensibility. All possible perception is thus dependent upon synthesis of appre- hension, and this empirical synthesis in turn upon transcen- dental synthesis, and therefore upon the categories. Conse- quently, all possible perceptions, and therefore everything that can come to empirical consciousness, that is, all appearances of nature, must, so far as their connection is concerned, be sub- ject to the categories. Nature, considered merely as nature in general, is dependent upon these categories as the original ground of its necessary conformity to law (natura formaliter spectata). Pure understanding is not, however, in a position, through mere categories, to prescribe to appearances any a priori laws other than those which are involved in a nature in general, that is, in the conformity to law of all appearances in space and time. Special laws, as concerning those appear- ances which are empirically determined, cannot in their specific character be derived from the categories, although they are one and all subject to them. To obtain any knowledge what- soever of these special laws, we must resort to experience; but it is the a priori laws that alone can instruct us in regard to experience in general, and as to what it is that can be known as an object of experience. $27 Outcome of this Deduction of the Concepts of Understanding We cannot think an object save through categories; we cannot know an object so thought save through intuitions corresponding to these concepts. Now all our intuitions are sensible; and this knowledge, in so far as its object is given, is empirical. But empirical knowledge is experience. Conse- P 174 quently, there can be no a priori knowledge, except of objects of possible experience. But although this knowledge is limited to objects of ex- perience, it is not therefore all derived from experience. The pure intuitions [of receptivity] and the pure concepts of under- standing are elements in knowledge, and both are found in us a priori. There are only two ways in which we can account for a necessary agreement of experience with the concepts of its objects: either experience makes these concepts possible or these concepts make experience possible. The former supposition does not hold in respect of the categories (nor of pure sensible intuition); for since they are a priori concepts, and there- fore independent of experience, the ascription to them of an empirical origin would be a sort of generatio aequivoca. There remains, therefore, only the second supposition -- a system, as it were, of the epigenesis of pure reason -- namely, that the cate- gories contain, on the side of the understanding, the grounds of the possibility of all experience in general. How they make experience possible, and what are the principles of the possi- bility of experience that they supply in their application to appearances, will be shown more fully in the following chapter on the transcendental employment of the faculty of judgment. A middle course may be proposed between the two above mentioned, namely, that the categories are neither self-thought first principles a priori of our knowledge nor derived from ex- perience, but subjective dispositions of thought, implanted in us from the first moment of our existence, and so ordered by our Creator that their employment is in complete harmony with the laws of nature in accordance with which experience P 175 proceeds -- a kind of preformation-system of pure reason. P 174n ++ Lest my readers should stumble at the alarming evil con- sequences which may over-hastily be inferred from this statement, I may remind them that for thought the categories are not limited by the conditions of our sensible intuition, but have an unlimited field. It is only the knowledge of that which we think, the determining of the object, that requires intuition. In the absence of intuition, the thought of the object may still have its true and useful consequences, as regards the subject's employment of reason. The use of reason is not always directed to the determination of an object, that is, to know- ledge, but also to the determination of the subject and of its volition -- a use which cannot be here dealt with. P 175 Apart, however, from the objection that on such an hypo- thesis we can set no limit to the assumption of predetermined dispositions to future judgments, there is this decisive objec- tion against the suggested middle course, that the necessity of the categories, which belongs to their very conception, would then have to be sacrificed. The concept of cause, for instance, which expresses the necessity of an event under a presupposed condition, would be false if it rested only on an arbitrary subjective necessity, implanted in us, of connecting certain empirical representations according to the rule of causal relation. I would not then be able to say that the effect is connected with the cause in the object, that is to say, neces- sarily, but only that I am so constituted that I cannot think this representation otherwise than as thus connected. This is exactly what the sceptic most desires. For if this be the situa- tion, all our insight, resting on the supposed objective validity of our judgments, is nothing but sheer illusion; nor would there be wanting people who would refuse to admit this sub- jective necessity, a necessity which can only be felt. Certainly a man cannot dispute with anyone regarding that which de- pends merely on the mode in which he is himself organised. Brief Outline of this Deduction The deduction is the exposition of the pure concepts of the understanding, and therewith of all theoretical a priori know- ledge, as principles of the possibility of experience -- the prin- ciples being here taken as the determination of appearances in space and time in general, and this determination, in turn, as ultimately following from the original synthetic unity of apper- ception, as the form of the understanding in its relation to space and time, the original forms of sensibility. I consider the division by numbered paragraphs as neces- sary up to this point, because thus far we have had to treat of the elementary concepts. We have now to give an account of their employment, and the exposition may therefore pro- ceed in continuous fashion, without such numbering. P 176 TRANSCENDENTAL ANALYTIC BOOK II THE ANALYTIC OF PRINCIPLES GENERAL logic is constructed upon a ground plan which exactly coincides with the division of the higher faculties of knowledge. These are: understanding,judgment, and reason. In accordance with the functions and order of these mental powers, which in current speech are comprehended under the general title of understanding, logic in its analytic deals with concepts, judgments, and inferences. Since this merely formal logic abstracts from all content of knowledge, whether pure or empirical, and deals solely with the form of thought in general (that is, of discursive know- ledge), it can comprehend the canon of reason in its analytic portion. For the form of reason possesses its established rules, which can be discovered a priori, simply by analysing the actions of reason into their components, without our requir- ing to take account of the special nature of the knowledge involved. As transcendental logic is limited to a certain determinate content, namely, to the content of those modes of knowledge which are pure and a priori, it cannot follow general logic in this division. For the transcendental employment of reason is not, it would seem, objectively valid, and consequently does not belong to the logic of truth, i.e. to the Analytic. As a logic of illusion, it calls for separate location in the scholastic edifice, under the title of Transcendental Dialectic. P 177 Understanding and judgment find, therefore, in tran- scendental logic their canon of objectively valid and correct employment; they belong to its analytic portion. Reason, on the other hand, in its endeavours to determine something a - priori in regard to objects and so to extend knowledge beyond the limits of possible experience, is altogether dialectical. Its illusory assertions cannot find place in a canon such as the analytic is intended to contain. The Analytic of Principles will therefore be a canon solely for judgment, instructing it how to apply to appearances the concepts of understanding, which contain the condition for a priori rules. For this reason, while adopting as my theme the principles of the understanding, strictly so called, I shall employ the title doctrine of judgment as more accurately in- dicating the nature of our task. INTRODUCTION TRANSCENDENTAL JUDGMENT IN GENERAL If understanding in general is to be viewed as the faculty of rules, judgment will be the faculty of subsuming under rules; that is, of distinguishing whether something does or does not stand under a given rule (casus datae legis). General logic con- tains, and can contain, no rules for judgment. For since general logic abstracts from all content of knowledge, the sole task that remains to it is to give an analytical exposition of the form of knowledge [as expressed] in concepts, in judgments, and in inferences, and so to obtain formal rules for all employment of understanding. If it sought to give general instructions how we are to subsume under these rules, that is, to distinguish whether something does or does not come under them, that could only be by means of another rule. This in turn, for the very reason that it is a rule, again demands guidance from judgment. And thus it appears that, though understanding is capable of being instructed, and of being equipped with rules, judgment is a peculiar talent which can be practised only, and cannot be taught. It is the specific quality of so-called mother-wit; and its lack no school can make good. For although an abundance of rules borrowed from the insight of others may P 178 indeed be proffered to, and as it were grafted upon, a limited understanding, the power of rightly employing them must belong to the learner himself; and in the absence of such a natural gift no rule that may be prescribed to him for this pur- pose can ensure against misuse. A physician, a judge, or a ruler may have at command many excellent pathological, legal, or political rules, even to the degree that he may become a profound teacher of them, and yet, none the less, may easily stumble in their application. For, although admirable in understanding, he may be wanting in natural power of judg- ment. He may comprehend the universal in abstracto, and yet not be able to distinguish whether a case in concreto comes under it. Or the error may be due to his not having received, through examples and actual practice, adequate training for this particular act of judgment. Such sharpening of the judg- ment is indeed the one great benefit of examples. Correctness and precision of intellectual insight, on the other hand, they more usually somewhat impair. For only very seldom do they adequately fulfil the requirements of the rule (as casus in ter- minis). Besides, they often weaken that effort which is re- quired of the understanding to comprehend properly the rules in their universality, in independence of the particular circum- stances of experience, and so accustom us to use rules rather as formulas than as principles. Examples are thus the go-cart of judgment; and those who are lacking in the natural talent can never dispense with them. But although general logic can supply no rules for judg- ment, the situation is entirely different in transcendental logic. The latter would seem to have as its peculiar task the correcting and securing of judgment, by means of determinate rules, in the use of the pure understanding. ++ Deficiency in judgment is just what is ordinarily called stupid- ity, and for such a failing there is no remedy. An obtuse or narrow- minded person to whom nothing is wanting save a proper degree of understanding and the concepts appropriate thereto, may indeed be trained through study, even to the extent of becoming learned. But as such people are commonly still lacking in judgment (secunda Petri), it is not unusual to meet learned men who in the application of their scientific knowledge betray that original want, which can never be made good. P 178 For as a doctrine, that is, P 179 as an attempt to enlarge the sphere of the understanding in the field of pure a priori knowledge, philosophy is by no means necessary, and is indeed ill-suited for any such purpose, since in all attempts hitherto made, little or no ground has been won. On the other hand, if what is designed be a critique to guard against errors of judgment (lapsus judicii) in the employment of the few pure concepts of understanding that we possess, the task, merely negative as its advantages must then be, is one to which philosophy is called upon to devote all its re- sources of acuteness and penetration. Transcendental philosophy has the peculiarity that besides the rule (or rather the universal condition of rules), which is given in the pure concept of understanding, it can also specify a priori the instance to which the rule is to be applied. The advantage which in this respect it possesses over all other didactical sciences, with the exception of mathematics, is due to the fact that it deals with concepts which have to relate to objects a priori, and the objective validity of which cannot therefore be demonstrated a posteriori, since that would mean the complete ignoring of their peculiar dignity. It must formulate by means of universal but sufficient marks the con- ditions under which objects can be given in harmony with these concepts. Otherwise the concepts would be void of all content, and therefore mere logical forms, not pure concepts of the understanding. This transcendental doctrine of judgment will consist of two chapters. The first will treat of the sensible condition under which alone pure concepts of understanding can be employed, that is, of the schematism of pure understanding. The second will deal with the synthetic judgments which under these con- ditions follow a priori from pure concepts of understanding, and which lie a priori at the foundation of all other modes of knowledge -- that is, with the principles of pure understanding. P 180 TRANSCENDENTAL DOCTRINE OF JUDGMENT (OR ANALYTIC OF PRINCIPLES) CHAPTER I THE SCHEMATISM OF THE PURE CONCEPTS OF UNDERSTANDING In all subsumptions of an object under a concept the repre- sentation of the object must be homogeneous with the concept; in other words, the concept must contain something which is represented in the object that is to be subsumed under it. This, in fact, is what is meant by the expression, 'an object is contained under a concept'. Thus the empirical concept of a plate is homogeneous with the pure geometrical concept of a circle. The roundness which is thought in the latter can be intuited in the former. But pure concepts of understanding being quite hetero- geneous from empirical intuitions, and indeed from all sensible intuitions, can never be met with in any intuition. For no one will say that a category, such as that of causality, can be intuited through sense and is itself contained in appear- ance. How, then, is the subsumption of intuitions under pure concepts, the application of a category to appearances, pos- sible? A transcendental doctrine of judgment is necessary just because of this natural and important question. We must be able to show how pure concepts can be applicable to appear- ances. In none of the other sciences is this necessary. For since in these sciences the concepts through which the object is thought in [its] general [aspects] are not so utterly distinct and heterogeneous from those which represent it in concreto, P 181 as given, no special discussion of the applicability of the former to the latter is required. Obviously there must be some third thing, which is homo- geneous on the one hand with the category, and on the other hand with the appearance, and which thus makes the appli- cation of the former to the latter possible. This mediating representation must be pure, that is, void of all empirical content, and yet at the same time, while it must in one respect be intellectual, it must in another be sensible. Such a representation is the transcendental schema. The concept of understanding contains pure synthetic unity of the manifold in general. Time, as the formal con- dition of the manifold of inner sense, and therefore of the connection of all representations, contains an a priori manifold in pure intuition. Now a transcendental determination of time is so far homogeneous with the category, which con- stitutes its unity, in that it is universal and rests upon an a priori rule. But, on the other hand, it is so far homogeneous with appearance, in that time is contained in every empirical representation of the manifold. Thus an application of the category to appearances becomes possible by means of the transcendental determination of time, which, as the schema of the concepts of understanding, mediates the subsumption of the appearances under the category. After what has been proved in the deduction of the cate- gories, no one, I trust, will remain undecided in regard to the question whether these pure concepts of understanding are of merely empirical or also of transcendental employ- ment; that is, whether as conditions of a possible experience they relate a priori solely to appearances, or whether, as conditions of the possibility of things in general, they can be extended to objects in themselves, without any restriction to our sensibility. For we have seen that concepts are alto- gether impossible, and can have no meaning, if no object is given for them, or at least for the elements of which they are composed. They cannot, therefore, be viewed as appli- cable to things in themselves, independent of all question as to whether and how these may be given to us. We P 182 have also proved that the only manner in which objects can be given to us is by modification of our sensibility; and finally, that pure a priori concepts, in addition to the function of understanding expressed in the category, must contain a priori certain formal conditions of sensibility, namely, those of inner sense. These conditions of sensibility constitute the universal condition under which alone the category can be applied to any object. This formal and pure condition of sensibility to which the employment of the concept of under- standing is restricted, we shall entitle the schema of the concept. The procedure of understanding in these schemata we shall entitle the schematism of pure understanding. The schema is in itself always a product of imagination. Since, however, the synthesis of imagination aims at no special intuition, but only at unity in the determination of sensibility, the schema has to be distinguished from the image. If five points be set alongside one another, thus, . . . . . , I have an image of the number five. But if, on the other hand, I think only a number in general, whether it be five or a hundred, this thought is rather the representation of a method whereby a multiplicity, for instance a thousand, may be re- presented in an image in conformity with a certain concept, than the image itself. For with such a number as a thousand the image can hardly be surveyed and compared with the concept. This representation of a universal procedure of imagination in providing an image for a concept, I entitle the schema of this concept. Indeed it is schemata, not images of objects, which underlie our pure sensible concepts. No image could ever be adequate to the concept of a triangle in general. It would never attain that universality of the concept which renders it valid of all triangles, whether right-angled, obtuse-angled, or acute- angled; it would always be limited to a part only of this sphere. The schema of the triangle can exist nowhere but in thought. It is a rule of synthesis of the imagination, in respect to pure figures in space. Still less is an object of experience or its image ever adequate to the empirical concept; for this latter always stands in immediate relation to the schema of imagina- tion, as a rule for the determination of our intuition, in accord- ance with some specific universal concept. The concept 'dog' P 183 signifies a rule according to which my imagination can delineate the figure of a four-footed animal in a general manner, without limitation to any single determinate figure such as experience, or any possible image that I can repre- sent in concreto, actually presents. This schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to have open to our gaze. This much only we can assert: the image is a product of the empirical faculty of reproductive imagination; the schema of sensible concepts, such as of figures in space, is a product and, as it were, a monogram, of pure a priori imagination, through which, and in accordance with which, images themselves first become possible. These images can be connected with the concept only by means of the schema to which they belong. In themselves they are never completely congruent with the concept. On the other hand, the schema of a pure concept of understanding can never be brought into any image whatso- ever. It is simply the pure synthesis, determined by a rule of that unity, in accordance with concepts, to which the category gives expression. It is a transcendental product of imagina- tion, a product which concerns the determination of inner sense in general according to conditions of its form (time), in respect of all representations, so far as these representations are to be connected a priori in one concept in conformity with the unity of apperception. That we may not be further delayed by a dry and tedious analysis of the conditions demanded by transcendental schemata of the pure concepts of understanding in general, we shall now expound them according to the order of the categories and in connection with them. The pure image of all magnitudes (quantorum) for outer sense is space; that of all objects of the senses in general is time. But the pure schema of magnitude (quantitatis), as a concept of the understanding, is number, a representation which comprises the successive addition of homogeneous P 184 units. Number is therefore simply the unity of the synthesis of the manifold of a homogeneous intuition in general, a unity due to my generating time itself in the apprehension of the intuition. Reality, in the pure concept of understanding, is that which corresponds to a sensation in general; it is that, there- fore, the concept of which in itself points to being (in time). Negation is that the concept of which represents not-being (in time). The opposition of these two thus rests upon the distinction of one and the same time as filled and as empty. Since time is merely the form of intuition, and so of objects as appearances, that in the objects which corresponds to sensation is not the transcendental matter of all objects as things in themselves (thinghood, reality). Now every sensa- tion has a degree or magnitude whereby, in respect of its representation of an object otherwise remaining the same, it can fill out one and the same time, that is, occupy inner sense more or less completely, down to its cessation in nothingness (= 0 = 1negatio). There therefore exists a relation and connection between reality and negation, or rather a transition from the one to the other, which makes every reality representable as a quantum. The schema of a reality, as the quantity of something in so far as it fills time, is just this con- tinuous and uniform production of that reality in time as we successively descend from a sensation which has a certain degree to its vanishing point, or progressively ascend from its negation to some magnitude of it. The schema of substance is permanence of the real in time, that is, the representation of the real as a substrate of empirical determination of time in general, and so as abiding while all else changes. (The existence of what is transitory passes away in time but not time itself. To time, itself non-transitory and abiding, there corresponds in the [field of] appearance what is non-transitory in its existence, that is, substance. Only in [relation to] substance can the succession and coexistence of appearances be determined in time. ) P 185 The schema of cause, and of the causality of a thing in general, is the real upon which, whenever posited, something else always follows. It consists, therefore, in the succession of the manifold, in so far as that succession is subject to a rule. The schema of community or reciprocity, the reciprocal causality of substances in respect of their accidents, is the co- existence, according to a universal rule, of the determinations of the one substance with those of the other. The schema of possibility is the agreement of the synthesis of different representations with the conditions of time in general. Opposites, for instance, cannot exist in the same thing at the same time, but only the one after the other. The schema is therefore the determination of the representation of a thing at some time or other. The schema of actuality is existence in some determinate time. The schema of necessity is existence of an object at all times. We thus find that the schema of each category contains and makes capable of representation only a determination of time. The schema of magnitude is the generation (synthesis) of time itself in the successive apprehension of an object. The schema of quality is the synthesis of sensation or perception with the representation of time; it is the filling of time. The schema of relation is the connecting of perceptions with one another at all times according to a rule of time-determination. Finally the schema of modality and of its categories is time itself as the correlate of the determination whether and how an object belongs to time. The schemata are thus nothing but a priori determinations of time in accordance with rules. These rules relate in the order of the categories to the time- series, the time-content, the time-order, and lastly to the scope of time in respect of all possible objects. It is evident, therefore, that what the schematism of under- standing effects by means of the transcendental synthesis of P 186 imagination is simply the unity of all the manifold of intuition in inner sense, and so indirectly the unity of apperception which as a function corresponds to the receptivity of inner sense. The schemata of the pure concepts of understanding are thus the true and sole conditions under which these concepts ob- tain relation to objects and so possess significance. In the end, therefore, the categories have no other possible employment than the empirical. As the grounds of an a priori necessary unity that has its source in the necessary combination of all consciousness in one original apperception, they serve only to subordinate appearances to universal rules of synthesis, and thus to fit them for thoroughgoing connection in one ex- perience. All our knowledge falls within the bounds of possible ex- perience, and just in this universal relation to possible experi- ence consists that transcendental truth which precedes all empirical truth and makes it possible. But it is also evident that although the schemata of sensi- bility first realise the categories, they at the same time restrict them, that is, limit them to conditions which lie outside the understanding, and are due to sensibility. The schema is, pro- perly, only the phenomenon, or sensible concept, of an object in agreement with the category. (Numerus est quantitas phaeno- menon, sensatio realitas phaenomenon, constans et perdurabile rerum substantia phaenomenon, aeternitas necessitas phaeno- menon, etc. ) If we omit a restricting condition, we would seem to extend the scope of the concept that was previously limited. Arguing from this assumed fact, we conclude that the cate- gories in their pure significance, apart from all conditions of sensibility, ought to apply to things in general, as they are, and not, like the schemata, represent them only as they appear. They ought, we conclude, to possess a meaning independent of all schemata, and of much wider application. Now there certainly does remain in the pure concepts of understanding, even after elimination of every sensible condition, a meaning; but it is purely logical, signifying only the bare unity of the representations. The pure concepts can find no object, and so P 187 can acquire no meaning which might yield a concept of some object. Substance, for instance, when the sensible determina- tion of permanence is omitted, would mean simply a something which can be thought only as subject, never as a predicate of something else. Such a representation I can put to no use, for it tells me nothing as to the nature of that which is thus to be viewed as a primary subject. The categories, therefore, without schemata, are merely functions of the understanding for concepts; and represent no object. This [objective] mean- ing they acquire from sensibility, which realises the under- standing in the very process of restricting it. P 188 TRANSCENDENTAL DOCTRINE OF JUDGMENT (OR ANALYTIC OF PRINCIPLES) CHAPTER II SYSTEM OF ALL PRINCIPLES OF PURE UNDERSTANDING In the preceding chapter we have considered transcendental judgment with reference merely to the universal conditions under which it is alone justified in employing pure concepts of understanding for synthetic judgments. Our task now is to exhibit, in systematic connection, the judgments which understanding, under this critical provision, actually achieves a priori. There can be no question that in this enquiry our table of categories is the natural and the safe guide. For since it is through the relation of the categories to possible experi- ence that all pure a priori knowledge of understanding has to be constituted, their relation to sensibility in general will exhibit completely and systematically all the transcendental principles of the use of the understanding. Principles a priori are so named not merely because they contain in themselves grounds of other judgements, but also because they are not themselves grounded in higher and more universal modes of knowledge. But this characteristic does not remove them beyond the sphere of proof. This proof cannot, indeed, be carried out in any objective fashion, since such principles [do not rest on objective considerations but] lie at the foundation of all knowledge of objects. This does not, however, prevent our attempting a proof, from the subjective sources of the possibility of knowledge of an object in general. Such proof is, indeed, indispensable, if the propositions are not to incur the suspicion of being merely surreptitious assertions. P 189 Secondly, we shall limit ourselves merely to those prin- ciples which stand in relation to the categories. The principles of the Transcendental Aesthetic, according to which space and time are the conditions of the possibility of all things as ap- pearances, and likewise the restriction of these principles, namely, that they cannot be applied to things in themselves, are matters which do not come within the range of our present enquiry. For similar reasons mathematical principles form no part of this system. They are derived solely from intuition, not from the pure concept of understanding. Nevertheless, since they too are synthetic a priori judgments, their possi- bility must receive recognition in this chapter. For though their correctness and apodeictic certainty do not indeed re- quire to be established, their possibility, as cases of evident a priori knowledge, has to be rendered conceivable, and to be deduced. We shall also have to treat of the principle of analytic judgments, in so far as it stands in contrast with that of syn- thetic judgments with which alone strictly we have to deal. For by thus contrasting them we free the theory of synthetic judgments from all misunderstanding, and have them in their own peculiar nature clear before us. THE SYSTEM OF THE PRINCIPLES OF PURE UNDERSTANDING Section 1 THE HIGHEST PRINCIPLE OF ALL ANALYTIC JUDGMENTS The universal, though merely negative, condition of all our judgments in general, whatever be the content of our know- ledge, and however it may relate to the object, is that they be not self-contradictory; for if self-contradictory, these judgments are in themselves, even without reference to the object, null and void. But even if our judgment contains no contradiction, it may connect concepts in a manner not borne out by the object, or else in a manner for which no ground is given, either a priori or a posteriori, sufficient to justify such judgment, and so may P 190 still, in spite of being free from all inner contradiction, be either false or groundless. The proposition that no predicate contradictory of a thing can belong to it, is entitled the principle of contradiction, and is a universal, though merely negative, criterion of all truth. For this reason it belongs only to logic. It holds of knowledge, merely as knowledge in general, irrespective of content; and asserts that the contradiction completely cancels and in- validates it. But it also allows of a positive employment, not merely, that is, to dispel falsehood and error (so far as they rest on contradiction), but also for the knowing of truth. For, if the judgment is analytic, whether negative or affirmative, its truth can always be adequately known in accordance with the principle of contradiction. The reverse of that which as con- cept is contained and is thought in the knowledge of the object, is always rightly denied. But since the opposite of the concept would contradict the object, the concept itself must neces- sarily be affirmed of it. The principle of contradiction must therefore be recognised as being the universal and completely sufficient principle of all analytic knowledge; but beyond the sphere of analytic knowledge it has, as a sufficient criterion of truth, no authority and no field of application. The fact that no knowledge can be contrary to it without self-nullification, makes this prin- ciple a conditio sine qua non, but not a determining ground, of the truth of our [non-analytic] knowledge. Now in our critical enquiry it is only with the synthetic portion of our knowledge that we are concerned; and in regard to the truth of this kind of knowledge we can never look to the above principle for any positive information, though, of course, since it is inviolable, we must always be careful to conform to it. Although this famous principle is thus without content and merely formal, it has sometimes been carelessly formulated in a manner which involves the quite unnecessary admixture of a synthetic element. The formula runs: It is impossible that something should at one and the same time both be and not be. Apart from the fact that the apodeictic certainty, expressed through the word 'impossible', is superfluously added -- since P 191 it is evident of itself from the [very nature of the] proposition -- the proposition is modified by the condition of time. It then, as it were, asserts: A thing = A, which is something = B, can- not at the same time be not-B, but may very well in succession be both B and not-B. For instance, a man who is young cannot at the same time be old, but may very well at one time be young and at another time not-young, that is, old. The principle of contradiction, however, as a merely logical principle, must not in any way limit its assertions to time-relations. The above formula is therefore completely contrary to the intention of the principle. The misunderstanding results from our first of all separating a predicate of a thing from the concept of that thing, and afterwards connecting this predicate with its op- posite -- a procedure which never occasions a contradiction with the subject but only with the predicate which has been syn- thetically connected with that subject, and even then only when both predicates are affirmed at one and the same time. If I say that a man who is unlearned is not learned, the con- dition, at one and the same time, must be added; for he who is at one time unlearned can very well at another be learned. But if I say, no unlearned man is learned, the proposition is analytic, since the property, unlearnedness, now goes to make up the concept of the subject, and the truth of the negative judgment then becomes evident as an immediate consequence of the principle of contradiction, without requiring the supple- mentary condition, at one and the same time. This, then, is the reason why I have altered its formulation, namely, in order that the nature of an analytic proposition be clearly expressed through it. THE SYSTEM OF THE PRINCIPLES OF PURE UNDERSTANDING Section 2 THE HIGHEST PRINCIPLE OF ALL SYNTHETIC JUDGMENTS The explanation of the possibility of synthetic judgments is a problem with which general logic has nothing to do. It need not even so much as know the problem by name. But in P 192 transcendental logic it is the most important of all questions; and indeed, if in treating of the possibility of synthetic a priori judgments we also take account of the conditions and scope of their validity, it is the only question with which it is concerned. For upon completion of this enquiry, transcendental logic is in a position completely to fulfil its ultimate purpose, that of determining the scope and limits of pure understanding. In the analytic judgment we keep to the given concept, and seek to extract something from it. If it is to be affirmative, I ascribe to it only what is already thought in it. If it is to be negative, I exclude from it only its opposite. But in synthetic judgments I have to advance beyond the given concept, viewing as in relation with the concept something altogether different from what was thought in it. This relation is con- sequently never a relation either of identity or of contradiction; and from the judgment, taken in and by itself, the truth or falsity of the relation can never be discovered. Granted, then, that we must advance beyond a given concept in order to compare it synthetically with another, a third something is necessary, as that wherein alone the syn- thesis of two concepts can be achieved. What, now, is this third something that is to be the medium of all synthetic judgments? There is only one whole in which all our re- presentations are contained, namely, inner sense and its a priori form, time. The synthesis of representations rests on imagination; and their synthetic unity, which is required for judgment, on the unity of apperception. In these, therefore, [in inner sense, imagination, and apperception], we must look for the possibility of synthetic judgments; and since all three contain the sources of a priori representations, they must also account for the possibility of pure synthetic judg- ments. For these reasons they are, indeed, indispensably necessary for any knowledge of objects, which rests entirely on the synthesis of representations. If knowledge is to have objective reality, that is, to re- late to an object, and is to acquire meaning and significance in respect to it, the object must be capable of being in some P 193 manner given. Otherwise the concepts are empty; through them we have indeed thought, but in this thinking we have really known nothing; we have merely played with repre- sentations. That an object be given (if this expression be taken, not as referring to some merely mediate process, but as signifying immediate presentation in intuition), means simply that the representation through which the object is thought relates to actual or possible experience. Even space and time, however free their concepts are from everything empirical, and however certain it is that they are represented in the mind completely a priori, would yet be without objective validity, senseless and meaningless, if their necessary application to the objects of experience were not established. Their repre- sentation is a mere schema which always stands in relation to the reproductive imagination that calls up and assembles the objects of experience. Apart from these objects of ex- perience, they would be devoid of meaning. And so it is with concepts of every kind. The possibility of experience is, then, what gives objective reality to all our a priori modes of knowledge. Experience, however, rests on the synthetic unity of appearances, that is, on a synthesis according to concepts of an object of appear- ances in general. Apart from such synthesis it would not be knowledge, but a rhapsody of perceptions that would not fit into any context according to rules of a completely intercon- nected (possible) consciousness, and so would not conform to the transcendental and necessary unity of apperception. Ex- perience depends, therefore, upon a priori principles of its form, that is, upon universal rules of unity in the synthesis of appearances. Their objective reality, as necessary conditions of experience, and indeed of its very possibility, can always be shown in experience. Apart from this relation synthetic a priori principles are completely impossible. For they have then no third something, that is, no object, in which the synthetic unity can exhibit the objective reality of its concepts. Although we know a priori in synthetic judgments a great deal regarding space in general and the figures which produc- P 194 tive imagination describes in it, and can obtain such judg- ments without actually requiring any experience, yet even this knowledge would be nothing but a playing with a mere fig- ment of the brain, were it not that space has to be regarded as a condition of the appearances which constitute the material for outer experience. Those pure synthetic judgments there- fore relate, though only mediately, to possible experience, or rather to the possibility of experience; and upon that alone is founded the objective validity of their synthesis. Accordingly, since experience, as empirical synthesis, is, in so far as such experience is possible, the one species of knowledge which is capable of imparting reality to any non- empirical synthesis, this latter [type of synthesis], as know- ledge a priori, can possess truth, that is, agreement with the object, only in so far as it contains nothing save what is necessary to synthetic unity of experience in general. The highest principle of all synthetic judgments is there- fore this: every object stands under the necessary conditions of synthetic unity of the manifold of intuition in a possible ex- perience. Synthetic a priori judgements are thus possible when we re- late the formal conditions of a priori intuition, the synthesis of imagination and the necessary unity of this synthesis in a tran- scendental apperception, to a possible empirical knowledge in general. We then assert that the conditions of the possibility of experience in general are likewise conditions of the possi- bility of the objects of experience, and that for this reason they have objective validity in a synthetic a priori judgment. THE SYSTEM OF THE PRINCIPLES OF PURE UNDERSTANDING Section 3 SYSTEMATIC REPRESENTATION OF ALL THE SYNTHETIC PRINCIPLES OF PURE UNDERSTANDING That there should be principles at all is entirely due to the pure understanding. Not only is it the faculty of rules in re- P 195 spect of that which happens, but is itself the source of principles according to which everything that can be presented to us as an object must conform to rules. For without such rules ap- pearances would never yield knowledge of an object corre- sponding to them. Even natural laws, viewed as principles of the empirical employment of understanding, carry with them an expression of necessity, and so contain at least the sugges- tion of a determination from grounds which are valid a priori and antecedently to all experience. The laws of nature, in- deed, one and all, without exception, stand under higher prin- ciples of understanding. They simply apply the latter to special cases [in the field] of appearance. These principles alone supply the concept which contains the condition, and as it were the exponent, of a rule in general. What experience gives is the instance which stands under the rule. There can be no real danger of our regarding merely em- pirical principles as principles of pure understanding, or con- versely. For the necessity according to concepts which distin- guishes the principles of pure understanding, and the lack of which is evident in every empirical proposition, however general its application, suffices to make this confusion easily preventable. But there are pure a priori principles that we may not properly ascribe to the pure understanding, which is the faculty of concepts. For though they are mediated by the understanding, they are not derived from pure concepts but from pure intuitions. We find such principles in mathematics. The question, however, of their application to experience, that is, of their objective validity, nay, even the deduction of the possibility of such synthetic a priori knowledge, must always carry us back to the pure understanding. While, therefore, I leave aside the principles of mathe- matics, I shall none the less include those [more fundamental] principles upon which the possibility and a priori objective validity of mathematics are grounded. These latter must be regarded as the foundation of all mathematical principles. They proceed from concepts to intuition, not from intuition to concepts. In the application of pure concepts of understanding to P 196 possible experience, the employment of their synthesis is either mathematical or dynamical; for it is concerned partly with the mere intuition of an appearance in general, partly with its existence. The a priori conditions of intuition are absolutely necessary conditions of any possible experience; those of the existence of the objects of a possible empirical intuition are in themselves only accidental. The principles of mathematical employment will therefore be unconditionally necessary, that is, apodeictic. Those of dynamical employment will also in- deed possess the character of a priori necessity, but only under the condition of empirical thought in some experience, there- fore only mediately and indirectly. Notwithstanding their un- doubted certainty throughout experience, they will not con- tain that immediate evidence which is peculiar to the former. But of this we shall be better able to judge at the conclusion of this system of principles. The table of categories is quite naturally our guide in the construction of the table of principles. For the latter are simply rules for the objective employment of the former. All principles of pure understanding are therefore -- 1 Axioms of intuition. 2 Anticipations of perception. P 196 3 Analogies of experience. 4 Postulates of empirical thought in general. P 196 These titles I have intentionally chosen in order to give prominence to differences in the evidence and in the applica- tion of the principles. It will soon become clear that the principles involved in the a priori determination of appear- ances according to the categories of quantity and of quality (only the formal aspect of quantity and quality being con- sidered) allow of intuitive certainty, alike as regards their evidential force and as regards their a priori application to P 197 appearances. They are thereby distinguished from those of the other two groups, which are capable only of a merely discursive certainty. This distinction holds even while we recognise that the certainty is in both cases complete. I shall therefore entitle the former principles mathematical, and the latter dynamical. But it should be noted that we are as little concerned in the one case with the principles of mathe- matics as in the other with the principles of general physical dynamics. We treat only of the principles of pure understand- ing in their relation to inner sense (all differences among the given representations being ignored). It is through these principles of pure understanding that the special principles of mathematics and of dynamics become possible. I have named them, therefore, on account rather of their application than of their content. I now proceed to discuss them in the order in which they are given in the above table. 1 AXIOMS OF INTUITION Their principle is: All intuitions are extensive magnitudes. Proof ++ The Axioms of intuition. Principle of the pure understanding: All appearances are, in their intuition, extensive magnitudes. ++ All combination (conjunctio) is either com- position (compositio) or connection (nexus). The former is the syn- thesis of the manifold where its constituents do not necessarily be- long to one another. For example, the two triangles into which a square is divided by its diagonal do not necessarily belong to one another. Such also is the synthesis of the homogeneous in everything which can be mathematically treated. This synthesis can itself be divided into that of aggregation and that of coalition, the former P 198n applying to extensive and the latter to intensive quantities. P 197 Appearances, in their formal aspect, contain an intuition in space and time, which conditions them, one and all, P 198 a priori. They cannot be apprehended, that is, taken up into empirical consciousness, save through that synthesis of the manifold whereby the representations of a determinate space or time are generated, that is, through combination of the homogeneous manifold and consciousness of its synthetic unity. Consciousness of the synthetic unity of the manifold [and] homogeneous in intuition in general, in so far as the representation of an object first becomes possible by means of it, is, however, the concept of a magnitude (quantum). Thus even the perception of an object, as appearance, is only possible through the same synthetic unity of the manifold of the given sensible intuition as that whereby the unity of the combination of the manifold [and] homogeneous is thought in the concept of a magnitude. In other words, appearances are all without exception magnitudes, indeed extensive mag- nitudes. As intuitions in space or time, they must be repre- sented through the same synthesis whereby space and time in general are determined. I entitle a magnitude extensive when the representation of the parts makes possible, and therefore necessarily precedes, the representation of the whole. I cannot represent to myself a line, however small, without drawing it in thought, that is, generating from a point all its parts one after another. Only in this way can the intuition be obtained. Similarly with all times, however small. In these I think to myself only that successive advance from one moment to another, whereby through the parts of time and their addition a de- terminate time-magnitude is generated. ++The second mode of combination (nexus) is the synthesis of the manifold so far as its constituents necessarily belong to one another, as, for example, the accident to some substance, or the effect to the cause. It is therefore synthesis of that which, though heterogeneous, is yet represented as combined a priori. This combination, as not being arbitrary and as concerning the connection of the existence of the manifold, I entitle dynamical. Such connection can itself, in turn, be divided into the physical connection of the appearances with one another, and their metaphysical connection in the a priori faculty of knowledge. P 198 As the [element of] P 199 pure intuition in all appearances is either space or time, every appearance is as intuition an extensive magnitude; only through successive synthesis of part to part in [the process of] its apprehension can it come to be known. All appearances are consequently intuited as aggregates, as complexes of previously given parts. This is not the case with magnitudes of every kind, but only with those magnitudes which are represented and apprehended by us in this extensive fashion. The mathematics of space (geometry) is based upon this successive synthesis of the productive imagination in the generation of figures. This is the basis of the axioms which formulate the conditions of sensible a priori intuition under which alone the schema of a pure concept of outer appear- ance can arise -- for instance, that between two points only one straight line is possible, or that two straight lines cannot enclose a space, etc. These are the axioms which, strictly, relate only to magnitudes (quanta) as such. As regards magnitude (quantitas), that is, as regards the answer to be given to the question, 'What is the magnitude of a thing? ' there are no axioms in the strict meaning of the term, although there are a number of propositions which are synthetic and immediately certain (indemonstrabilia). The propositions, that if equals be added to equals the wholes are equal, and if equals be taken from equals the remainders are equal, are analytic propositions; for I am immediately conscious of the identity of the production of the one magni- tude with the production of the other. [Consequently, they are not] axioms, [for these] have to be a priori synthetic pro- positions. On the other hand, the evident propositions of numerical relation are indeed synthetic, but are not general like those of geometry, and cannot, therefore, be called axioms but only numerical formulas. The assertion that 7 & 5 is equal to 12 is not an analytic proposition. For neither in the repre- sentation of 7, nor in that of 5, nor in the representation of the combination of both, do I think the number 12. (That I must do so in the addition of the two numbers is not to the point, since in the analytic proposition the question is only whether I actually think the predicate in the representation of the subject. ) But although the proposition is synthetic, it is also P 200 only singular. So far as we are here attending merely to the synthesis of the homogeneous (of units), that synthesis can take place only in one way, although the employment of these numbers is general. If I assert that through three lines, two of which taken together are greater than the third, a triangle can be described, I have expressed merely the function of productive imagination whereby the lines can be drawn greater or smaller, and so can be made to meet at any and every possible angle. The number 7, on the other hand, is possible only in one way. So also is the number 12, as thus generated through the synthesis of 7 with 5. Such propositions must not, therefore, be called axioms (that would involve recognition of an infinite number of axioms), but numerical formulas. This transcendental principle of the mathematics of ap- pearances greatly enlarges our a priori knowledge. For it alone can make pure mathematics, in its complete precision, appli- cable to objects of experience. Without this principle, such application would not be thus self-evident; and there has indeed been much confusion of thought in regard to it. Appear- ances are not things in themselves. Empirical intuition is possible only by means of the pure intuition of space and of time. What geometry asserts of pure intuition is therefore undeniably valid of empirical intuition. The idle objections, that objects of the senses may not conform to such rules of construction in space as that of the infinite divisibility of lines or angles, must be given up. For if these objections hold good, we deny the objective validity of space, and consequently of all mathematics, and no longer know why and how far mathematics can be applicable to appearances. The synthesis of spaces and times, being a synthesis of the essential forms of all intuition, is what makes possible the apprehension of appearance, and consequently every outer experience and all knowledge of the objects of such experience. Whatever pure mathematics establishes in regard to the synthesis of the form of apprehension is also necessarily valid of the objects appre- hended. All objections are only the chicanery of a falsely P 201 instructed reason, which, erroneously professing to isolate the objects of the senses from the formal condition of our sen- sibility, represents them, in spite of the fact that they are mere appearances, as objects in themselves, given to the understand- ing. Certainly, on that assumption, no synthetic knowledge of any kind could be obtained of them a priori, and nothing therefore could be known of them synthetically through pure concepts of space. Indeed, the science which determines these concepts, namely geometry, would not itself be possible. 2 ANTICIPATIONS OF PERCEPTION In all appearances, the real that is an object of sensation has intensive magnitude, that is, a degree. Proof Perception is empirical consciousness, that is, a conscious- ness in which sensation is to be found. Appearances, as objects of perception, are not pure, merely formal, intuitions, like space and time. For in and by themselves these latter cannot be per- ceived. Appearances contain in addition to intuition the matter for some object in general (whereby something existing in space or time is represented); they contain, that is to say, the real of sensation as merely subjective representation, which gives us only the consciousness that the subject is affected, and which we relate to an object in general. Now from empirical consciousness to pure consciousness a graduated transition is possible, the real in the former completely vanishing and a merely formal a priori consciousness of the manifold in space and time remaining. ++ The Anticipations of Perception The principle which anticipates all perceptions, as such, is as follows: In all appearances sensation, and the real which corresponds to it in the object (realitas phaenomenon), has an intensive magnitude, that is, a degree. P 201 Consequently there is also possible a P 202 synthesis in the process of generating the magnitude of a sen- sation from its beginning in pure intuition = 0, up to any required magnitude. Since, however, sensation is not in itself an objective representation, and since neither the intuition of space nor that of time is to be met with in it, its mag- nitude is not extensive but intensive. This magnitude is generated in the act of apprehension whereby the empirical consciousness of it can in a certain time increase from nothing = 0 to the given measure. Corresponding to this intensity of sensation, an intensive magnitude, that is, a degree of influence on the sense [i.e. on the special sense involved], must be ascribed to all objects of perception, in so far as the perception contains sensation. All knowledge by means of which I am enabled to know and determine a priori what belongs to empirical knowledge may be entitled an anticipation; and this is undoubtedly the sense in which Epicurus employed the term prolepsis. But as there is an element in the appearances (namely, sensation, the matter of perception) which can never be known a priori, and which therefore constitutes the distinctive difference between empirical and a priori knowledge, it follows that sensation is just that element which cannot be anticipated. On the other hand, we might very well entitle the pure determinations in space and time, in respect of shape as well as of magnitude, anticipations of appearances, since they represent a priori that which may always be given a posteriori in experience. If, however, there is in every sensation, as sensation in general (that is, without a particular sensation having to be given), something that can be known a priori, this will, in a quite especial sense, deserve to be named anticipation. For it does indeed seem surprising that we should forestall experience, precisely in that which concerns what is only to be obtained through it, namely, its matter. Yet, none the less, such is actually the case. Apprehension by means merely of sensation occupies only an instant, if, that is, I do not take into account the succes- sion of different sensations. As sensation is that element in P 203 the [field of] appearance the apprehension of which does not involve a successive synthesis proceeding from parts to the whole representation, it has no extensive magnitude. The absence of sensation at that instant would involve the re- presentation of the instant as empty, therefore as = 0. Now what corresponds in empirical intuition to sensation is reality (realitas phaenomenon); what corresponds to its absence is negation = 0. Every sensation, however, is capable of diminu- tion, so that it can decrease and gradually vanish. Between reality in the [field of] appearance and negation there is there- fore a continuity of many possible intermediate sensations, the difference between any two of which is always smaller than the difference between the given sensation and zero or com- plete negation. In other words, the real in the [field of] ap- pearance has always a magnitude. But since its apprehension by means of mere sensation takes place in an instant and not through successive synthesis of different sensations, and there- fore does not proceed from the parts to the whole, the mag- nitude is to be met with only in the apprehension. The real has therefore magnitude, but not extensive magnitude. A magnitude which is apprehended only as unity, and in which multiplicity can be represented only through ap- proximation to negation = 0, I entitle an intensive magnitude. Every reality in the [field of] appearance has therefore inten- sive magnitude or degree. If this reality is viewed as cause, either of sensation or of some other reality in the [field of] appearance, such as change, the degree of the reality as cause is then entitled a moment, the moment of gravity. It is so named for the reason that degree signifies only that magnitude the apprehension of which is not successive, but instan- taneous. This, however, I touch on only in passing; for with causality I am not at present dealing. Every sensation, therefore, and likewise every reality in the [field of] appearance, however small it may be, has a degree, that is, an intensive magnitude which can always be diminished. Between reality and negation there is a con- tinuity of possible realities and of possible smaller perceptions. P 204 Every colour, as for instance red, has a degree which, how- ever small it may be, is never the smallest; and so with heat, the moment of gravity, etc. The property of magnitudes by which no part of them is the smallest possible, that is, by which no part is simple, is called their continuity. Space and time are quanta continua, because no part of them can be given save as enclosed between limits (points or instants), and therefore only in such fashion that this part is itself again a space or a time. Space therefore consists solely of spaces, time solely of times. Points and instants are only limits, that is, mere positions which limit space and time. But positions always presuppose the intuitions which they limit or are intended to limit; and out of mere positions, viewed as constituents capable of being given prior to space or time, neither space nor time can be constructed. Such mag- nitudes may also be called flowing, since the synthesis of productive imagination involved in their production is a pro- gression in time, and the continuity of time is ordinarily designated by the term flowing or flowing away. All appearances, then, are continuous magnitudes, alike in their intuition, as extensive, and in their mere perception (sensation, and with it reality) as intensive. If the synthesis of the manifold of appearance is interrupted, we have an aggre- gate of different appearances, and not appearance as a genuine quantum. Such an aggregate is not generated by continuing without break productive synthesis of a certain kind, but through repetition of an ever-ceasing synthesis. If I called thirteen thalers a quantum of money, I should be correct, pro- vided my intention is to state the value of a mark of fine silver. For this is a continuous magnitude in which no part is the smallest, and in which every part can constitute a piece of coin that always contains material for still smaller pieces. But if I understand by the phrase thirteen round thalers, so many coins, quite apart from the question of what their silver standard may be, I then use the phrase, quantum of thalers, inappropriately. It ought to be entitled an aggregate, that is, a number of pieces of money. But as unity must be presup- posed in all number, appearance as unity is a quantum, and as a quantum is always a continum. P 205 Since all appearances, alike in their extensive and in their intensive aspect, are thus continuous magnitudes, it might seem to be an easy matter to prove with mathematical con- clusiveness the proposition that all alteration (transition of a thing from one state to another), is continuous. But the caus- ality of an alteration in general, presupposing, as it does, em- pirical principles, lies altogether outside the limits of a tran- scendental philosophy. For upon the question as to whether a cause capable of altering the state of a thing, that is, of determining it to the opposite of a certain given state, may be possible, the a priori understanding casts no light; and this not merely because it has no insight into its possibility (such insight is lacking to us in many other cases of a priori knowledge), but because alterableness is to be met with only in certain determinations of appearances, and because, whereas [in fact] the cause of these determinations lies in the unalterable, experience alone can teach what they are. Since in our present enquiry we have no data of which we can make use save only the pure fundamental concepts of all possible experience, in which there must be absolutely nothing that is empirical, we cannot, without destroying the unity of our system, anticipate general natural science, which is based on certain primary experiences. At the same time, there is no lack of proofs of the great value of our principle in enabling us to anticipate perceptions, and even to some extent to make good their absence, by placing a check upon all false inferences which might be drawn from their absence. If all reality in perception has a degree, between which and negation there exists an infinite gradation of ever smaller degrees, and if every sense must likewise possess some par- ticular degree of receptivity of sensations, no perception, and consequently no experience, is possible that could prove, either immediately or mediately (no matter how far-ranging the reasoning may be), a complete absence of all reality in the [field of] appearance. In other words, the proof of an empty space or of an empty time can never be derived from experi- ence. For, in the first place, the complete absence of reality P 206 from a sensible intuition can never be itself perceived; and, secondly, there is no appearance whatsoever and no difference in the degree of reality of any appearance from which it can be inferred. It is not even legitimate to postulate it in order to explain any difference. For even if the whole intuition of a certain determinate space or time is real through and through, that is, though no part of it is empty, none the less, since every reality has its degree, which can diminish to nothing (the void) through infinite gradations without in any way altering the extensive magnitude of the appearance, there must be infinite different degrees in which space and time may be filled. Intensive magnitude can in different appearances be smaller or greater, although the extensive magnitude of the intuition remains one and the same. Let us give an example. Almost all natural philosophers, observing -- partly by means of the moment of gravity or weight, partly by means of the moment of opposition to other matter in motion -- a great difference in the quantity of various kinds of matter in bodies that have the same volume, unani- mously conclude that this volume, which constitutes the ex- tensive magnitude of the appearance, must in all material bodies be empty in varying degrees. Who would ever have dreamt of believing that these students of nature, most of whom are occupied with problems in mathematics and mechanics, would base such an inference solely on a meta- physical presupposition -- the sort of assumption they so stoutly profess to avoid? They assume that the real in space (I may not here name it impenetrability or weight, since these are empirical concepts) is everywhere uniform and varies only in extensive magnitude, that is, in amount. Now to this pre- supposition, for which they could find no support in experi- ence, and which is therefore purely metaphysical, I oppose a transcendental proof, which does not indeed explain the difference in the filling of spaces, but completely destroys the supposed necessity of the above presupposition, that the difference is only to be explained on the assumption of empty space. My proof has the merit at least of freeing the under- standing, so that it is at liberty to think this difference in some other manner, should it be found that some other hypothesis is required for the explanation of the natural P 207 appearances. For we then recognise that although two equal spaces can be completely filled with different kinds of matter, so that there is no point in either where matter is not present, nevertheless every reality has, while keeping its quality un- changed, some specific degree (of resistance or weight) which can, without diminution of its extensive magnitude or amount, become smaller and smaller in infinitum, before it passes into the void and [so] vanishes [out of existence]. Thus a radiation which fills a space, as for instance heat, and similarly every other reality in the [field of] appearance, can diminish in its degree in infinitum, without leaving the smallest part of this space in the least empty. It may fill the space just as completely with these smaller degrees as another appearance does with greater degrees. I do not at all intend to assert that this is what actually occurs when material bodies differ in specific gravity, but only to establish from a principle of pure understanding that the nature of our per- ceptions allows of such a mode of explanation, that we are not justified in assuming the real in appearances to be uniform in degree, differing only in aggregation and extensive magni- tude, and that we are especially in error when we claim that such interpretation can be based on an a priori principle of the understanding. This anticipation of perception must always, however appear somewhat strange to anyone trained in transcend- ental reflection, and to any student of nature who by such teaching has been trained to circumspection. The assertion that the understanding anticipates such a synthetic principle, ascribing a degree to all that is real in the appearances, and so asserting the possibility of an internal distinction in sensa- tion itself (abstraction being made of its empirical quality), awakens doubts and difficulties. It is therefore a question not unworthy of solution, how the understanding can thus in a priori fashion pronounce synthetically upon appearances, and can indeed anticipate in that which in itself is merely empirical and concerns only sensation. The quality of sensation, as for instance in colours, taste, etc. , is always merely empirical, and cannot be represented P 208 a priori. But the real, which corresponds to sensations in general, as opposed to negation = 0, represents only that something the very concept of which includes being, and signifies nothing but the synthesis in an empirical conscious- ness in general. Empirical consciousness can in inner sense be raised from 0 to any higher degree, so that a certain ex- tensive magnitude of intuition, as for instance of illuminated surface, may excite as great a sensation as the combined aggregate of many such surfaces has illuminated. [Since the extensive magnitude of the appearance thus varies independ- ently], we can completely abstract from it, and still represent in the mere sensation in any one of its moments a synthesis that advances uniformly from 0 to the given empirical con- sciousness. Consequently, though all sensations as such are given only a posteriori, their property of possessing a degree can be known a priori. It is remarkable that of magnitudes in general we can know a priori only a single quality, namely, that of continuity, and that in all quality (the real in appear- ances) we can know a priori nothing save [in regard to] their intensive quantity, namely that they have degree. Everything else has to be left to experience. 3 ANALOGIES OF EXPERIENCE The principle of the analogies is: Experience is possible only through the representation of a necessary connection of perceptions. Proof Experience is an empirical knowledge, that is, a know- ledge which determines an object through perceptions. ++ The Analogies of Experience The general principle of the analogies is: All appearances are, as regards their existence, subject a priori to rules deter- mining their relation to one another in one time. P 209 It is a synthesis of perceptions, not contained in perception but itself containing in one consciousness the synthetic unity of the manifold of perceptions. This synthetic unity constitutes the essential in any knowledge of objects of the senses, that is, in experience as distinguished from mere intuition or sensa- tion of the senses. In experience, however, perceptions come together only in accidental order, so that no necessity deter- mining their connection is or can be revealed in the perceptions themselves. For apprehension is only a placing together of the manifold of empirical intuition; and we can find in it no re- presentation of any necessity which determines the appearances thus combined to have connected existence in space and time. But since experience is a knowledge of objects through percep- tions, the relation [involved] in the existence of the manifold has to be represented in experience, not as it comes to be constructed in time but as it exists objectively in time. Since time, however, cannot itself be perceived, the determination of the existence of objects in time can take place only through their relation in time in general, and therefore only through concepts that con- nect them a priori. Since these always carry necessity with them, it follows that experience is only possible through a re- presentation of necessary connection of perceptions. The three modes of time are duration, succession, and co- existence. There will, therefore, be three rules of all relations of appearances in time, and these rules will be prior to all ex- perience, and indeed make it possible. By means of these rules the existence of every appearance can be determined in respect of the unity of all time. The general principle of the three analogies rests on the necessary unity of apperception, in respect of all possible em- pirical consciousness, that is, of all perception, at every [instant of] time. And since this unity lies a priori at the foundation of empirical consciousness, it follows that the above principle rests on the synthetic unity of all appearances as regards their relation in time. For the original apperception stands in rela- tion to inner sense (the sum of all representations), and indeed a priori to its form, that is, to the time-order of the manifold empirical consciousness. All this manifold must, as regards its time-relations, be united in the original apperception. This P 210 is demanded by the a priori transcendental unity of appercep- tion, to which everything that is to belong to my knowledge (that is, to my unified knowledge), and so can be an object for me, has to conform. This synthetic unity in the time-relations of all perceptions, as thus determined a priori, is the law, that all empirical time-determinations must stand under rules of universal time-determination. The analogies of experience, with which we are now to deal, must be rules of this description. These principles have this peculiarity, that they are not concerned with appearances and the synthesis of their em- pirical intuition, but only with the existence of such appearances and their relation to one another in respect of their existence. The manner in which something is apprehended in appear- ance can be so determined a priori that the rule of its synthesis can at once give, that is to say, can bring into being, this [element of] a priori intuition in every example that comes before us empirically. The existence of appearances cannot, however, be thus known a priori; and even granting that we could in any such manner contrive to infer that something exists, we could not know it determinately, could not, that is, anticipate the features through which its empirical intuition is distinguished from other intuitions. The two previous principles, which, as justifying the ap- plication of mathematics to appearances, I entitled the mathe- matical, referred to the possibility of appearances, and taught how, alike as regards their intuition and the real in their per- ception, they can be generated according to rules of a mathe- matical synthesis. Both principles justify us in employing numerical magnitudes, and so enable us to determine appear- ance as magnitude. For instance, I can determine a priori, that is, can construct, the degree of sensations of sunlight by com- bining some 20,000 illuminations of the moon. These first principles may therefore be called constitutive. It stands quite otherwise with those principles which seek to bring the existence of appearances under rules a priori. For since existence cannot be constructed, the principles can apply only to the relations of existence, and can yield only re- gulative principles. We cannot, therefore, expect either axioms P 211 or anticipations. If, however, a perception is given in a time- relation to some other perception, then even although this latter is indeterminate, and we consequently cannot decide what it is, or what its magnitude may be, we may none the less assert that in its existence it is necessarily connected with the former in this mode of time. In philosophy analogies signify something very different from what they represent in mathematics. In the latter they are formulas which express the equality of two quantitative relations, and are always con- stitutive; so that if three members of the proportion are given, the fourth is likewise given, that is, can be constructed. But in philosophy the analogy is not the equality of two quantitative but of two qualitative relations; and from three given mem- bers we can obtain a priori knowledge only of the relation to a fourth, not of the fourth member itself. The relation yields, how- ever, a rule for seeking the fourth member in experience, and a mark whereby it can be detected. An analogy of experience is, therefore, only a rule according to which a unity of experi- ence may arise from perception. It does not tell us how mere perception or empirical intuition in general itself comes about. It is not a principle constitutive of the objects, that is, of the appearances, but only regulative. The same can be asserted of the postulates of empirical thought in general, which concern the synthesis of mere intuition (that is, of the form of appear- ance), of perception (that is, of the matter of perception), and of experience (that is, of the relation of these perceptions). They are merely regulative principles, and are distinguished from the mathematical, which are constitutive, not indeed in certainty -- both have certainty a priori -- but in the nature of their evidence, that is, as regards the character of the intuitive (and consequently of the demonstrative) factors peculiar to the latter. In this connection what has been said of all principles that are synthetic must be specially emphasised, namely, that these analogies have significance and validity only as principles of the empirical, not of the transcendental, employment of under- standing; that only as such can they be established; and that appearances have therefore to be subsumed, not simply under P 212 the categories, but under their schemata. For if the objects to which these principles are to be related were things in them- selves, it would be altogether impossible to know anything of them synthetically a priori. They are, however, nothing but appearances; and complete knowledge of them, in the further- ance of which the sole function of a priori principles must ultimately consist, is simply our possible experience of them. The principles can therefore have no other purpose save that of being the conditions of the unity of empirical knowledge in the synthesis of appearances. But such unity can be thought only in the schema of the pure concept of understanding. The category expresses a function which is restricted by no sensible condition, and contains the unity of this schema, [in so far only] as [it is the schema] of a synthesis in general. By these principles, then, we are justified in combining appearances only according to what is no more than an analogy with the logical and universal unity of concepts. In the principle itself we do indeed make use of the category, but in applying it to appearances we substitute for it its schema as the key to its employment, or rather set it alongside the category, as its re- stricting condition, and as being what may be called its formula. A FIRST ANALOGY Principle of Permanence of Substance In all change of appearances substance is permanent; its quantum in nature is neither increased nor diminished. ++ All appearances contain the permanent (substance) as the object itself, and the transitory as its mere determination that is, as a way in which the object exists. P 213 Proof All appearances are in time; and in it alone, as substratum (as permanent form of inner intuition), can either coexistence or succession be represented. Thus the time in which all change of appearances has to be thought, remains and does not change. For it is that in which, and as determinations of which, succession or coexistence can alone be represented. Now time cannot by itself be perceived. Consequently there must be found in the objects of perception, that is, in the appearances, the substratum which represents time in general; and all change or coexistence must, in being apprehended, be perceived in this substratum, and through relation of the appearances to it. But the substratum of all that is real, that is, of all that belongs to the existence of things, is substance; and all that belongs to existence can be thought only as a determination of substance. Consequently the permanent, in relation to which alone all time-relations of appearances can be determined, is substance in the [field of] appearance, that is, the real in appearance, and as the substrate of all change remains ever the same. And as it is thus unchangeable in its existence, its quantity in nature can be neither increased nor diminished. Our apprehension of the manifold of appearance is always successive, and is therefore always changing. Through it alone we can never determine whether this manifold, as object of experience, is coexistent or successive. For such determination we require an underlying ground which exists at all times, that is, something abiding and permanent, of which all change and coexistence are only so many ways (modes of time) in which the permanent exists. ++ Proof of this first Analogy All appearances are in time. Time can determine them as existing in a twofold manner, either as in succession to one another or as coexisting. Time, in respect of the former, is viewed as time-series, in respect of the latter as time-volume. P 214 And simultaneity and succession being the only relations in time, it follows tha t only in the permanent are relations of time possible. In other words, the permanent is the substratum of the empirical representa- tion of time itself; in it alone is any determination of time possible. Permanence, as the abiding correlate of all existence of appearances, of all change and of all concomitance, ex- presses time in general. For change does not affect time itself, but only appearances in time. (Coexistence is not a mode of time itself; for none of the parts of time coexist; they are all in succession to one another. ) If we ascribe succession to time itself, we must think yet another time, in which the sequence would be possible. Only through the permanent does existence in different parts of the time-series acquire a magnitude which can be entitled duration. For in bare succession existence is always vanishing and recommencing, and never has the least magnitude. Without the permanent there is therefore no time- relation. Now time cannot be perceived in itself; the permanent in the appearances is therefore the substratum of all deter- mination of time, and, as likewise follows, is also the condition of the possibility of all synthetic unity of perceptions, that is, of experience. All existence and all change in time have thus to be viewed as simply a mode of the existence of that which remains and persists. In all appearances the permanent is the object itself, that is, substance as phenomenon; everything, on the other hand, which changes or can change belongs only to the way in which substance or substances exist, and therefore to their determinations. I find that in all ages, not only philosophers, but even the common understanding, has recognised this permanence as a substratum of all change of appearances, and always assume it to be indubitable. The only difference in this matter between the common understanding and the philosopher is that the latter expresses himself somewhat more definitely, asserting that throughout all changes in the world substance remains, and that only the accidents change. But I nowhere find even the attempt at a proof of this obviously synthetic proposition. Indeed, it is very seldom placed, where it truly belongs, at the head of those laws of nature which are pure and completely a priori. Certainly the proposition, that sub- stance is permanent, is tautological. For this permanence is P 215 our sole ground for applying the category of substance to appearance; and we ought first to have proved that in all appearances there is something permanent, and that the tran- sitory is nothing but determination of its existence. But such a proof cannot be developed dogmatically, that is, from con- cepts, since it concerns a synthetic a priori proposition. Yet as it never occurred to anyone that such propositions are valid only in relation to possible experience, and can therefore be proved only through a deduction of the possibility of ex- perience, we need not be surprised that though the above principle is always postulated as lying at the basis of ex- perience (for in empirical knowledge the need of it is felt), it has never itself been proved. A philosopher, on being asked how much smoke weighs, made reply: "Subtract from the weight of the wood burnt the weight of the ashes which are left over, and you have the weight of the smoke". He thus presupposed as undeniable that even in fire the matter (substance) does not vanish, but only suffers an alteration of form. The proposition, that noth- ing arises out of nothing, is still another consequence of the principle of permanence, or rather of the ever-abiding exist- ence, in the appearances, of the subject proper. For if that in the [field of] appearance which we name substance is to be the substratum proper of all time-determination, it must follow that all existence, whether in past or in future time, can be determined solely in and by it. We can therefore give an appearance the title 'substance' just for the reason that we presuppose its existence throughout all time, and that this is not adequately expressed by the word permanence, a term which applies chiefly to future time. But since the inner necessity of persisting is inseparably bound up with the necessity of always having existed, the expression [principle of permanence] may be allowed to stand. Gigni de nihilo nihil, in nihilum nil posse reverti, were two propositions which the ancients al- ways connected together, but which are now sometimes mis- takenly separated owing to the belief that they apply to things in themselves, and that the first would run counter to the dependence of the world -- even in respect of its substance -- upon a supreme cause. But such apprehension is unneces- sary. For we have here to deal only with appearances in the P 216 field of experience; and the unity of experience would never be possible if we were willing to allow that new things, that is, new substances, could come into existence. For we should then lose that which alone can represent the unity of time, namely, the identity of the substratum, wherein alone all change has thoroughgoing unity. This permanence is, however, simply the mode in which we represent to ourselves the existence of things in the [field of] appearance. The determinations of a substance, which are nothing but special ways in which it exists, are called accidents. They are always real, because they concern the existence of substance. (Negations are only determinations which assert the non- existence of something in substance. ) If we ascribe a special [kind of] existence to this real in substance (for instance, to motion, as an accident of matter), this existence is entitled inherence, in distinction from the existence of substance which is entitled subsistence. But this occasions many misunder- standings; it is more exact and more correct to describe an accident as being simply the way in which the existence of a substance is positively determined. But since it is unavoid- able, owing to the conditions of the logical employment of our understanding, to separate off, as it were, that which in the existence of a substance can change while the substance still remains, and to view this variable element in relation to the truly permanent and radical, this category has to be assigned a place among the categories of relation, but rather as the condition of relations than as itself containing a relation. The correct understanding of the concept of alteration is also grounded upon [recognition of] this permanence. Coming to be and ceasing to be are not alterations of that which comes to be or ceases to be. Alteration is a way of existing which follows upon another way of existing of the same object. All that alters persists, and only its state changes. Since this change thus concerns only the determinations, which can cease to be or begin to be, we can say, using what may seem a somewhat paradoxical expression, that only the permanent P 217 (substance) is altered, and that the transitory suffers no alteration but only a change, inasmuch as certain determina- tions cease to be and others begin to be. Alteration can therefore be perceived only in substances. A coming to be or ceasing to be that is not simply a determination of the permanent but is absolute, can never be a possible per- ception. For this permanent is what alone makes possible the representation of the transition from one state to another, and from not-being to being. These transitions can be empirically known only as changing determinations of that which is per- manent. If we assume that something absolutely begins to be, we must have a point of time in which it was not. But to what are we to attach this point, if not to that which already exists? For a preceding empty time is not an object of perception. But if we connect the coming to be with things which pre- viously existed, and which persist in existence up to the moment of this coming to be, this latter must be simply a de- termination of what is permanent in that which precedes it. Similarly also with ceasing to be; it presupposes the empirical representation of a time in which an appearance no longer exists. Substances, in the [field of] appearance, are the substrata of all determinations of time. If some of these substances could come into being and others cease to be, the one condition of the empirical unity of time would be removed. The appear- ances would then relate to two different times, and existence would flow in two parallel streams -- which is absurd. There is only one time in which all different times must be located not as coexistent but as in succession to one another. Permanence is thus a necessary condition under which alone appearances are determinable as things or objects in a possible experience. We shall have occasion in what follows to make such observations as may seem necessary in regard to the empirical criterion of this necessary permanence -- the criterion, consequently, of the substantiality of appearances. P 218 B SECOND ANALOGY Principle of Succession in Time, in accordance with the Law of Causality All alterations take place in conformity with the law of the connection of cause and effect. Proof (The preceeding principle has shown that all appearances of succession in time are one and all only alterations, that is a successive being and not-being of the determinations of substance which abides; and therefore that the being of substance as following on its not-being, or its not-being as following upon its being cannot be admitted -- in other words, that there is no coming into being or passing away of sub- stance itself. Still otherwise expressed the principle is, that all change (succession) of appearances is merely alteration. Coming into being and passing away of substance are not alterations of it, since the concept of alteration presupposes one and the same subject as existing with two opposite deter- minations, and therefore as abiding. With this preliminary reminder, we pass to the proof. ) I perceive that appearances follow one another, that is, that there is a state of things at one time the opposite of which was in the preceding time. Thus I am really connecting two percep- tions in time. Now connection is not the work of mere sense and intuition, but is here the product of a synthetic faculty of imagination, which determines inner sense in respect of the time-relation. ++ Principle of Production Everything that happens, that is, begins to be, presupposes something upon which it follows according to a rule. P 218 But imagination can connect these two states P 219 in two ways, so that either the one or the other precedes in time. For time cannot be perceived in itself, and what precedes and what follows cannot, therefore, by relation to it, be em- pirically determined in the object. I am conscious only that my imagination sets the one state before and the other after, not that the one state precedes the other in the object. In other words, the objective relation of appearances that follow upon one another is not to be determined through mere perception. In order that this relation be known as determined, the rela- tion between the two states must be so thought that it is there- by determined as necessary which of them must be placed before, and which of them after, and that they cannot be placed in the reverse relation. But the concept which carries with it a necessity of synthetic unity can only be a pure concept that lies in the understanding, not in perception; and in this case it is the concept of the relation of cause and effect, the former of which determines the latter in time, as its consequence -- not as in a sequence that may occur solely in the imagination (or that may not be perceived at all). Experience itself -- in other words, empirical knowledge of appearances -- is thus possible only in so far as we subject the succession of appearances, and therefore all alteration, to the law of causality; and, as likewise follows, the appear- ances, as objects of experience, are themselves possible only in conformity with the law. The apprehension of the manifold of appearance is always successive. The representations of the parts follow upon one another. Whether they also follow one another in the object is a point which calls for further reflection, and which is not decided by the above statement. Everything, every repre- sentation even, in so far as we are conscious of it, may be entitled object. But it is a question for deeper enquiry what the word 'object' ought to signify in respect of appearances when these are viewed not in so far as they are (as representa- tions) objects, but only in so far as they stand for an object. The appearances, in so far as they are objects of consciousness simply in virtue of being representations, are not in any way distinct from their apprehension, that is, from their recep- tion in the synthesis of imagination; and we must therefore P 220 agree that the manifold of appearances is always generated in the mind successively. Now if appearances were things in them- selves, then since we have to deal solely with our representations, we could never determine from the succession of the representa- tions how their manifold may be connected in the object. How things may be in themselves, apart from the representations through which they affect us, is entirely outside our sphere of knowledge. In spite, however, of the fact that the appearances are not things in themselves, and yet are what alone can be given to us to know, in spite also of the fact that their repre- sentation in apprehension is always successive, I have to show what sort of a connection in time belongs to the manifold in the appearances themselves. For instance, the apprehen- sion of the manifold in the appearance of a house which stands before me is successive. The question then arises, whether the manifold of the house is also in itself suc- cessive. This, however, is what no one will grant. Now im- mediately I unfold the transcendental meaning of my concepts of an object, I realise that the house is not a thing in itself, but only an appearance, that is, a representation, the tran- scendental object of which is unknown. What, then, am I to understand by the question: how the manifold may be con- nected in the appearance itself, which yet is nothing in itself? That which lies in the successive apprehension is here viewed as representation, while the appearance which is given to me, notwithstanding that it is nothing but the sum of these representations, is viewed as their object; and my concept, which I derive from the representations of apprehension, has to agree with it. Since truth consists in the agreement of knowledge with the object, it will at once be seen that we can here enquire only regarding the formal conditions of empirical truth, and that appearance, in contradistinction to the repre- sentations of apprehension, can be represented as an object distinct from them only if it stands under a rule which dis- tinguishes it from every other apprehension and necessitates some one particular mode of connection of the manifold. The object is that in the appearance which contains the condition of this necessary rule of apprehension. Let us now proceed to our problem. That something happens, i.e. that something, or some state which did not pre- P 221 viously exist, comes to be, cannot be perceived unless it is preceded by an appearance which does not contain in itself this state. For an event which should follow upon an empty time, that is, a coming to be preceded by no state of things, is as little capable of being apprehended as empty time itself. Every apprehension of an event is therefore a perception that fol- lows upon another perception. But since, as I have above illustrated by reference to the appearance of a house, this like- wise happens in all synthesis of apprehension, the apprehen- sion of an event is not yet thereby distinguished from other apprehensions. But, as I also note, in an appearance which contains a happening (the preceding state of the percep- tion we may entitle A, and the succeeding B) B can be apprehended only as following upon A; the perception A cannot follow upon B but only precede it. For instance, I see a ship move down stream. My perception of its lower position follows upon the perception of its position higher up in the stream, and it is impossible that in the appre- hension of this appearance the ship should first be per- ceived lower down in the stream and afterwards higher up. The order in which the perceptions succeed one another in apprehension is in this instance determined, and to this order apprehension is bound down. In the previous example of a house my perceptions could begin with the apprehension of the roof and end with the basement, or could begin from below and end above; and I could similarly apprehend the manifold of the empirical intuition either from right to left or from left to right. In the series of these perceptions there was thus no determinate order specifying at what point I must begin in order to connect the manifold empirically. But in the percep- tion of an event there is always a rule that makes the order in which the perceptions (in the apprehension of this appearance) follow upon one another a necessary order. In this case, therefore, we must derive the subjective suc- cession of apprehension from the objective succession of ap- pearances. Otherwise the order of apprehension is entirely undetermined, and does not distinguish one appearance from another. Since the subjective succession by itself is altogether P 222 arbitrary, it does not prove anything as to the manner in which the manifold is connected in the object. The objective succession will therefore consist in that order of the manifold of appearance according to which, in conformity with a rule, the apprehension of that which happens follows upon the apprehension of that which precedes. Thus only can I be justified in asserting, not merely of my apprehension, but of appearance itself, that a succession is to be met with in it. This is only another way of saying that I cannot arrange the apprehension otherwise than in this very succession. In conformity with such a rule there must lie in that which precedes an event the condition of a rule according to which this event invariably and necessarily follows. I cannot reverse this order, proceeding back from the event to determine through apprehension that which precedes. For appearance never goes back from the succeeding to the preceding point of time, though it does indeed stand in relation to some pre- ceding point of time. The advance, on the other hand, from a given time to the determinate time that follows is a neces- sary advance. Therefore, since there certainly is something that follows [i.e. that is apprehended as following], I must refer it necessarily to something else which precedes it and upon which it follows in conformity with a rule, that is, of necessity. The event, as the conditioned, thus affords reliable evidence of some condition, and this condition is what determines the event. Let us suppose that there is nothing antecedent to an event, upon which it must follow according to rule. All succession of perception would then be only in the apprehension, that is, would be merely subjective, and would never enable us to de- termine objectively which perceptions are those that really precede and which are those that follow. We should then have only a play of representations, relating to no object; that is to say, it would not be possible through our percep- tion to distinguish one appearance from another as regards relations of time. For the succession in our apprehension would always be one and the same, and there would be nothing in the appearance which so determines it that a certain se- quence is rendered objectively necessary. I could not then assert that two states follow upon one another in the [field of] P 223 appearance, but only that one apprehension follows upon the other. That is something merely subjective, determining no object; and may not, therefore, be regarded as knowledge of any object, not even of an object in the [field of] appearance. If, then, we experience that something happens, we in so doing always presuppose that something precedes it, on which it follows according to a rule. Otherwise I should not say of the object that it follows. For mere succession in my apprehension, if there be no rule determining the succession in relation to something that precedes, does not justify me in assuming any succession in the object. I render my sub- jective synthesis of apprehension objective only by reference to a rule in accordance with which the appearances in their succession, that is, as they happen, are determined by the pre- ceding state. The experience of an event [i.e. of anything as happening] is itself possible only on this assumption. This may seem to contradict all that has hitherto been taught in regard to the procedure of our understanding. The accepted view is that only through the perception and compari- son of events repeatedly following in a uniform manner upon preceding appearances are we enabled to discover a rule according to which certain events always follow upon certain appearances, and that this is the way in which we are first led to construct for ourselves the concept of cause. Now the con- cept, if thus formed, would be merely empirical, and the rule which it supplies, that everything which happens has a cause, would be as contingent as the experience upon which it is based. Since the universality and necessity of the rule would not be grounded a priori, but only on induction, they would be merely fictitious and without genuinely universal validity. It is with these, as with other pure a priori representations -- for instance, space and time. We can extract clear concepts of them from experience, only because we have put them into experience, and because experience is thus itself brought about only by their means. Certainly, the logical clearness of this representation of a rule determining the series of events is possible only after we have employed it in experience. Never- P 224 theless, recognition of the rule, as a condition of the synthetic unity of appearances in time, has been the ground of ex- perience itself, and has therefore preceded it a priori. We have, then, to show, in the case under consideration, that we never, even in experience, ascribe succession (that is, the happening of some event which previously did not exist) to the object, and so distinguish it from subjective sequence in our apprehension, except when there is an underlying rule which compels us to observe this order of perceptions rather than any other; nay, that this compulsion is really what first makes possible the representation of a succession in the object. We have representations in us, and can become conscious of them. But however far this consciousness may extend, and however careful and accurate it may be, they still remain mere representations, that is, inner determinations of our mind in this or that relation of time. How, then, does it come about that we posit an object for these representations, and so, in addition to their subjective reality, as modifications, ascribe to them some mysterious kind of objective reality. Objective meaning cannot consist in the relation to another representa- tion (of that which we desire to entitle object), for in that case the question again arises, how this latter representation goes out beyond itself, acquiring objective meaning in addition to the subjective meaning which belongs to it as determination of the mental state. If we enquire what new character relation to an object confers upon our representations, what dignity they thereby acquire, we find that it results only in subjecting the representations to a rule, and so in necessitating us to connect them in some one specific manner; and conversely, that only in so far as our representations are necessitated in a certain order as regards their time-relations do they acquire objective meaning. In the synthesis of appearances the manifold of representa- tions is always successive. Now no object is hereby represented, since through this succession, which is common to all appre- hensions, nothing is distinguished from anything else. But immediately I perceive or assume that in this succession there is a relation to the preceding state, from which the representa- P 225 tion follows in conformity with a rule, I represent something as an event, as something that happens; that is to say, I appre- hend an object to which I must ascribe a certain determinate position in time -- a position which, in view of the preceding state, cannot be otherwise assigned. When, therefore, I per- ceive that something happens, this representation first of all contains [the consciousness] that there is something preceding, because only by reference to what precedes does the appear- ance acquire its time-relation, namely, that of existing after a preceding time in which it itself was not. But it can acquire this determinate position in this relation of time only in so far as something is presupposed in the preceding state upon which it follows invariably, that is, in accordance with a rule. From this there results a twofold consequence. In the first place, I cannot reverse the series, placing that which happens prior to that upon which it follows. And secondly, if the state which precedes is posited, this determinate event follows inevitably and necessarily. The situation, then, is this: there is an order in our representations in which the present, so far as it has come to be, refers us to some preceding state as a correlate of the event which is given; and though this correlate is, indeed, indeterminate, it none the less stands in a determining relation to the event as its consequence, connecting the event in neces- sary relation with itself in the time-series. If, then, it is a necessary law of our sensibility, and there- fore a formal condition of all perceptions, that the preceding time necessarily determines the succeeding (since I cannot ad- vance to the succeeding time save through the preceding), it is also an indispensable law of empirical representation of the time-series that the appearances of past time determine all existences in the succeeding time, and that these latter, as events, can take place only in so far as the appearances of past time determine their existence in time, that is, determine them according to a rule. For only in appearances can we empirically apprehend this continuity in the connection of times. Understanding is required for all experience and for its possibility. Its primary contribution does not consist in making the representation of objects distinct, but in making the repre- P 226 sentation of an object possible at all. This it does by carrying the time-order over into the appearances and their existence. For to each of them, [viewed] as [a] consequent, it assigns, through relation to the preceding appearances, a position de- termined a priori in time. Otherwise, they would not accord with time itself, which [in] a priori [fashion] determines the position of all its parts. Now since absolute time is not an ob- ject of perception, this determination of position cannot be de- rived from the relation of appearances to it. On the contrary, the appearances must determine for one another their position in time, and make their time-order a necessary order. In other words, that which follows or happens must follow in con- formity with a universal rule upon that which was contained in the preceding state. A series of appearances thus arises which, with the aid of the understanding, produces and makes neces- sary the same order and continuous connection in the series of possible perceptions as is met with a priori in time -- the form of inner intuition wherein all perceptions must have a position. That something happens is, therefore, a perception which belongs to a possible experience. This experience becomes actual when I regard the appearance as determined in its posi- tion in time, and therefore as an object that can always be found in the connection of perceptions in accordance with a rule. This rule, by which we determine something according to succession of time, is, that the condition under which an event invariably and necessarily follows is to be found in what pre- cedes the event. The principle of sufficient reason is thus the ground of possible experience, that is, of objective knowledge of appearances in respect of their relation in the succession of time. The proof of this principle rests on the following considera- tions. All empirical knowledge involves the synthesis of the manifold by the imagination. This synthesis is always succes- sive, that is, the representations in it are always sequent upon one another. In the imagination this sequence is not in any way determined in its order, as to what must precede and what must follow, and the series of sequent representations P 227 can indifferently be taken either in backward or in forward order. But if this synthesis is a synthesis of apprehension of the manifold of a given appearance, the order is determined in the object, or, to speak more correctly, is an order of suc- cessive synthesis that determines an object. In accordance with this order something must necessarily precede, and when this antecedent is posited, something else must necessarily follow. If, then, my perception is to contain knowledge of an event, of something as actually happening, it must be an empirical judgment in which we think the sequence as deter- mined; that is, it presupposes another appearance in time, upon which it follows necessarily, according to a rule. Were it not so, were I to posit the antecedent and the event were not to follow necessarily thereupon, I should have to regard the succession as a merely subjective play of my fancy; and if I still represented it to myself as something objective, I should have to call it a mere dream. Thus the relation of appearances (as possible perceptions) according to which the subsequent event, that which happens, is, as to its existence, necessarily determined in time by something preceding in conformity with a rule -- in other words, the relation of cause to effect -- is the condition of the objective validity of our empirical judg- ments, in respect of the series of perceptions, and so of their empirical truth; that is to say, it is the condition of experience. The principle of the causal relation in the sequence of appear- ances is therefore also valid of all objects of experience ([in so far as they are] under the conditions of succession), as being itself the ground of the possibility of such experience. At this point a difficulty arises with which we must at once deal. The principle of the causal connection among ap- pearances is limited in our formula to their serial succession, whereas it applies also to their coexistence, when cause and effect are simultaneous. For instance, a room is warm while the outer air is cool. I look around for the cause, and find a heated stove. Now the stove, as cause, is simultaneous with its effect, the heat of the room. Here there is no serial succession in time between cause and effect. They are simultaneous, and P 228 yet the law is valid. The great majority of efficient natural causes are simultaneous with their effects, and the sequence in time of the latter is due only to the fact that the cause cannot achieve its complete effect in one moment. But in the moment in which the effect first comes to be, it is in- variably simultaneous with the causality of its cause. If the cause should have ceased to exist a moment before, the effect would never have come to be. Now we must not fail to note that it is the order of time, not the lapse of time, with which we have to reckon; the relation remains even if no time has elapsed. The time between the causality of the cause and its immediate effect may be [a] vanishing [quantity], and they may thus be simultaneous; but the relation of the one to the other will always still remain determinable in time. If I view as a cause a ball which impresses a hollow as it lies on a stuffed cushion, the cause is simultaneous with the effect. But I still distinguish the two through the time-relation of their dynamical connection. For if I lay the ball on the cushion, a hollow follows upon the previous flat smooth shape; but if (for any reason) there previously exists a cushion, a leaden ball does not follow upon it. The sequence in time is thus the sole empirical criterion of an effect in its relation to the causality of the cause which precedes it. A glass [filled with water] is the cause of the rising of the water above its horizontal surface, although both appearances are simultaneous. For immediately I draw off water from a larger vessel into the glass, something follows, namely the alteration from the horizontal position which the water then had to the concave form which it assumes in the glass. Causality leads to the concept of action, this in turn to the concept of force, and thereby to the concept of substance. As my critical scheme, which is concerned solely with the sources of synthetic a priori knowledge, must not be compli- cated through the introduction of analyses which aim only at the clarification, not at the extension, of concepts, I leave detailed exposition of my concepts to a future system of pure reason. Such an analysis has already, indeed, been developed in considerable detail in the text-books. But I must not leave unconsidered the empirical criterion of a substance, P 229 in so far as substance appears to manifest itself not through permanence of appearance, but more adequately and easily through action. Wherever there is action -- and therefore activity and force -- there is also substance, and it is in substance alone that the seat of this fruitful source of appearances must be sought. This is, so far, well said; but when we seek to explain what is to be understood by substance, and in so doing are careful to avoid the fallacy of reasoning in a circle, the discovery of an answer is no easy task. How are we to conclude directly from the action to the permanence of that which acts? For that is an essential and quite peculiar characteristic of sub- stance (as phenomenon). But while according to the usual pro- cedure, which deals with concepts in purely analytic fashion, this question would be completely insoluble, it presents no such difficulty from the standpoint which we have been formulating. Action signifies the relation of the subject of causality to its effect. Since, now, every effect consists in that which happens, and so in the transitory, which signifies time in its character of succession, its ultimate subject, as the substratum of everything that changes, is the permanent, that is, substance. For according to the principle of causality actions are always the first ground of all change of appearances, and cannot therefore be found in a subject which itself changes, because in that case other actions and another subject would be re- quired to determine this change. For this reason action is a sufficient empirical criterion to establish the substantiality of a subject, without my requiring first to go in quest of its permanence through the comparison of perceptions. Besides, by such method (of comparison) we could not achieve the completeness required for the magnitude and strict univer- sality of the concept. That the first subject of the causality of all coming to be and ceasing to be cannot itself, in the field of appearances, come to be and cease to be, is an assured conclusion which leads to [the concept of] empirical necessity and permanence in existence, and so to the concept of a sub- stance as appearance. When something happens, the mere coming to be, apart from all question of what it is that has come to be, is already in P 230 itself a matter for enquiry. The transition from the not-being of a state to this state, even supposing that this state [as it occurs] in the [field of] appearance exhibited no quality, of itself demands investigation. This coming to be, as was shown above in the First Analogy, does not concern substance, which does not come to be out of nothing. For if coming to be out of nothing is regarded as effect of a foreign cause, it has to be entitled creation, and that cannot be admitted as an event among appearances since its mere possibility would destroy the unity of experience. On the other hand, when I view all things not as phenomena but as things in themselves, and as objects of the mere understanding, then despite their being substances they can be regarded, in respect of their existence, as depending upon a foreign cause. But our terms would then carry with them quite other meanings, and would not apply to appearances as possible objects of experience. How anything can be altered, and how it should be possible that upon one state in a given moment an opposite state may follow in the next moment -- of this we have not, a priori, the least conception. For that we require knowledge of actual forces, which can only be given empirically, as, for instance, of the moving forces, or what amounts to the same thing, of certain successive appearances, as motions, which indicate [the presence of] such forces. But apart from all question of what the content of the alteration, that is, what the state which is altered, may be, the form of every alteration, the condition under which, as a coming to be of another state, it can alone take place, and so the succession of the states themselves (the happening), can still be considered a priori according to the law of causality and the conditions of time. If a substance passes from one state, a, to another, b, the point of time of the second is distinct from that of the first, and follows upon it. ++ It should be carefully noted that I speak not of the alteration of certain relations in general, but of alteration of state. Thus, when a body moves uniformly, it does not in any way alter its state (of motion); that occurs only when its motion increases or diminishes. P 231 Similarly, the second state as reality in the [field of] appearance differs from the first wherein it did not exist, as b from zero. That is to say, even if the state b differed from the state a only in magnitude, the alteration would be a coming to be of b - a, which did not exist in the previous state, and in respect of which it = 0. The question therefore arises how a thing passes from one state = a to another = b. Between two instants there is al- ways a time, and between any two states in the two instants there is always a difference which has magnitude. For all parts of appearances are always themselves magnitudes. All transi- tion from one state to another therefore occurs in a time which is contained between two instants, of which the first deter- mines the state from which the thing arises, and the second that into which it passes. Both instants, then, are limits of the time of a change, and so of the intermediate state between the two states, and therefore as such form part of the total alteration. Now every alteration has a cause which evinces its causality in the whole time in which the alteration takes place. This cause, therefore, does not engender the alteration suddenly, that is, at once or in one instant, but in a time; so that, as the time in- creases from the initial instant a to its completion in b, the magnitude of the reality (b - a) is in like manner generated through all smaller degrees which are contained between the first and the last. All alteration is thus only possible through a continuous action of the causality which, so far as it is uniform, is entitled a moment. The alteration does not consist of these moments, but is generated by them as their effect. That is the law of the continuity of all alteration. Its ground is this: that neither time nor appearance in time consists of parts which are the smallest [possible], and that, nevertheless, the state of a thing passes in its alteration through all these parts, as elements, to its second state. In the [field of] appearance there is no difference of the real that is the smallest, just as in the magnitude of times there is no time that is the smallest; and the new state of reality accordingly proceeds from the first wherein this reality was not, through all the infinite de- grees, the differences of which from one another are all smaller than that between 0 and a. P 232 While we are not concerned to enquire what utility this principle may have in the investigation of nature, what does imperatively call for investigation is the question how such a principle, which seems to extend our knowledge of nature, can be possible completely a priori. Such an enquiry cannot be dis- pensed with, even though direct inspection may show the prin- ciple to be true and [empirically] real, and though the question, how it should be possible, may therefore be considered super- fluous. For there are so many ungrounded claims to the extension of our knowledge through pure reason, that we must take it as a universal principle that any such pretension is of itself a ground for being always mistrustful, and that, in the absence of evidence afforded by a thoroughgoing deduction, we may not believe and assume the justice of such claims, no matter how clear the dogmatic proof of them may appear to be. All increase in empirical knowledge, and every advance of perception, no matter what the objects may be, whether ap- pearances or pure intuitions, is nothing but an extension of the determination of inner sense, that is, an advance in time. This advance in time determines everything, and is not in itself deter- mined through anything further. That is to say, its parts are given only in time, and only through the synthesis of time; they are not given antecedently to the synthesis. For this reason every transition in perception to something which follows in time is a determination of time through the generation of this perception, and since time is always and in all its parts a mag- nitude, is likewise the generation of a perception as a magnitude through all degrees of which no one is the smallest, from zero up to its determinate degree. This reveals the possibility of knowing a priori a law of alterations, in respect of their form. We are merely anticipating our own apprehension, the formal condition of which, since it dwells in us prior to all appearance that is given, must certainly be capable of being known a priori. In the same manner, therefore, in which time contains the sensible a priori condition of the possibility of a continuous advance of the existing to what follows, the understanding, by virtue of the unity of apperception, is the a priori condi- tion of the possibility of a continuous determination of all posi- tions for the appearances in this time, through the series of P 233 causes and effects, the former of which inevitably lead to the existence of the latter, and so render the empirical knowledge of the time-relations valid universally for all time, and there- fore objectively valid. C THIRD ANALOGY Principle of Coexistence, in accordance with the Law of Reciprocity or Community All substances, in so far as they can be perceived to coexist in space, are in thoroughgoing reciprocity. Proof Things are coexistent when in empirical intuition the perceptions of them can follow upon one another recipro- cally, which, as has been shown in the proof of the second principle, cannot occur in the succession of appearances. Thus I can direct my perception first to the moon and then to the earth, or, conversely, first to the earth and then to the moon; and because the perceptions of these objects can follow each other reciprocally, I say that they are coexistent. Now coexistence is the existence of the manifold in one and the same time. But time itself cannot be perceived, and we are not, therefore, in a position to gather, simply from things being set in the same time, that their perceptions can follow each other reciprocally. The synthesis of imagination in apprehension would only reveal that the one perception is in the subject when the other is not there, and vice versa, but not that the objects are coexistent, that is, that if the one exists the other exists at the same time, and that it is only because they thus coexist that the perceptions are able to follow one another re ciprocally. ++ Principle of Community All substances, so far as they coexist, stand in thorough- going community, that is, in mutual interaction. P 234 Consequently, in the case of things which coexist externally to one another, a pure concept of the reciprocal sequence of their determinations is required, if we are to be able to say that the reciprocal sequence of the perceptions is grounded in the object, and so to represent the coexistence as objective. But the relation of substances in which the one contains determinations the ground of which is contained in the other is the relation of influence; and when each substance reciprocally contains the ground of the determinations in the other, the relation is that of community or reciprocity. Thus the coexistence of substances in space cannot be known in experience save on the assumption of their reciprocal interaction. This is therefore the condition of the possibility of the things themselves as objects of experience. Things are coexistent so far as they exist in one and the same time. But how do we know that they are in one and the same time? We do so when the order in the synthesis of ap- prehension of the manifold is a matter of indifference, that is, whether it be from A through B, C, D to E, or reversewise from E to A. For if they were in succession to one another in time, in the order, say, which begins with A and ends in E, it is impossible that we should begin the apprehension in the perception of E and proceed backwards to A, since A belongs to past time and can no longer be an object of appre- hension. Now assuming that in a manifold of substances as appear- ances each of them is completely isolated, that is, that no one acts on any other and receives reciprocal influences in return, I maintain that their coexistence would not be an object of a possible perception and that the existence of one could not lead by any path of empirical synthesis to the existence of another. For if we bear in mind that they would be separated by a completely empty space, the perception which advances from one to another in time would indeed, by means of a succeeding perception, determine the existence of the latter, but would not be able to distinguish whether it follows object- P 235 ively upon the first or whether it is not rather coexistent with it. There must, therefore, besides the mere existence of A and B, be something through which A determines for B, and also reversewise B determines for A, its position in time, because only on this condition can these substances be empirically represented as coexisting. Now only that which is the cause of another, or of its determinations, determines the position of the other in time. Each substance (inasmuch as only in respect of its determinations can it be an effect) must therefore contain in itself the causality of certain determinations in the other substance, and at the same time the effects of the causality of that other; that is, the substances must stand, immediately or mediately, in dynamical community, if their coexistence is to be known in any possible experience. Now, in respect to the objects of experience, everything without which the experi- ence of these objects would not itself be possible is necessary. It is therefore necessary that all substances in the [field of] appearance, so far as they coexist, should stand in thorough- going community of mutual interaction. The word community is in the German language ambigu- ous. It may mean either communio or commercium. We here employ it in the latter sense, as signifying a dynamical com- munity, without which even local community (communio spatii) could never be empirically known. We may easily recognise from our experiences that only the continuous influences in all parts of space can lead our senses from one object to another. The light, which plays between our eye and the celestial bodies, produces a mediate community between us and them, and thereby shows us that they coexist. We cannot empirically change our position, and perceive the change, unless matter in all parts of space makes perception of our position possible to us. For only thus by means of their reciprocal influence can the parts of matter establish their simultaneous existence, and thereby, though only mediately, their coexistence, even to the most remote objects. Without community each percep- tion of an appearance in space is broken off from every other, and the chain of empirical representations, that is, experience, P 236 would have to begin entirely anew with each new object, without the least connection with the preceding representation, and without standing to it in any relation of time. I do not by this argument at all profess to disprove void space, for it may exist where perceptions cannot reach, and where there is, therefore, no empirical knowledge of coexistence. But such a space is not for us an object of any possible experience. The following remarks may be helpful in [further] elucida- tion [of my argument]. In our mind, all appearances, since they are contained in a possible experience, must stand in community (communio) of apperception, and in so far as the objects are to be represented as coexisting in connection with each other, they must mutually determine their position in one time, and thereby constitute a whole. If this subjective community is to rest on an objective ground, or is to hold of appearances as substances, the perception of the one must as ground make possible the perception of the other, and reversewise -- in order that the succession which is always found in the perceptions, as apprehensions, may not be as- cribed to the objects, and in order that, on the contrary, these objects may be represented as coexisting. But this is a re- ciprocal influence, that is, a real community (commercium) of substances; without it the empirical relation of coexistence could not be met with in experience. Through this com- mercium the appearances, so far as they stand outside one another and yet in connection, constitute a composite (com- positum reale), and such composites are possible in many different ways. The three dynamical relations, from which all others spring, are therefore inherence, consequence, and composition. *** These, then, are the three analogies of experience. They are simply principles of the determination of the existence of ap- pearances in time, according to all its three modes, viz. the rela- tion to time itself as a magnitude (the magnitude of existence, that is, duration), the relation in time as a successive series, and finally the relation in time as a sum of all simultaneous exist- ence. This unity of time-determination is altogether dynamical. P 237 For time is not viewed as that wherein experience immedi- ately determines position for every existence. Such deter- mination is impossible, inasmuch as absolute time is not an object of perception with which appearances could be con- fronted. What determines for each appearance its position in time is the rule of the understanding through which alone the existence of appearances can acquire synthetic unity as regards relations of time; and that rule consequently determines the position [in a manner that is] a priori and valid for each and every time. By nature, in the empirical sense, we understand the con- nection of appearances as regards their existence according to necessary rules, that is, according to laws. There are certain laws which first make a nature possible, and these laws are a priori. Empirical laws can exist and be discovered only through experience, and indeed in consequence of those original laws through which experience itself first becomes possible. Our analogies therefore really portray the unity of nature in the connection of all appearances under certain exponents which express nothing save the relation of time (in so far as time comprehends all existence) to the unity of apperception -- such unity being possible only in synthesis according to rules. Taken together, the analogies thus declare that all appearances lie, and must lie, in one nature, because without this a priori unity no unity of experience, and therefore no determination of objects in it, would be possible. As to the mode of proof of which we have made use in these transcendental laws of nature, and as to their peculiar character, an observation has to be made which must likewise be of very great importance as supplying a rule to be followed in every other attempt to prove a priori propositions that are intellectual and at the same time synthetic. Had we attempted to prove these analogies dogmatically; had we, that is to say, attempted to show from concepts that everything which exists is to be met with only in that which is permanent, that every event presupposes something in the preceding state upon which it follows in conformity with a rule; and finally, that in the manifold which is coexistent the states coexist in rela- tion to one another in conformity with a rule and so stand in P 238 community, all our labour would have been wasted. For through mere concepts of these things, analyse them as we may, we can never advance from one object and its existence to the exist- ence of another or to its mode of existence. But there is an alternative method, namely, to investigate the possibility of experience as a knowledge wherein all objects -- if their repre- sentation is to have objective reality for us -- must finally be capable of being given to us. In this third [medium], the essential form of which consists in the synthetic unity of the apperception of all appearances, we have found a priori con- ditions of complete and necessary determination of time for all existence in the [field of] appearance, without which even empirical determination of time would be impossible. In it we have also found rules of synthetic unity a priori, by means of which we can anticipate experience. For lack of this method, and owing to the erroneous assumption that synthetic proposi- tions, which the empirical employment of the understanding recommends as being its principles, may be proved dogmatic- ally, the attempt has, time and again, been made, though always vainly, to obtain a proof of the principle of sufficient reason. And since the guiding-thread of the categories, which alone can reveal and make noticeable every gap in the under- standing, alike in regard to concepts and to principles, has hitherto been lacking, no one has so much as thought of the other two analogies, although use has always tacitly been made of them. ++ The unity of the world-whole, in which all appearances have to be connected, is evidently a mere consequence of the tacitly assumed principle of the community of all substances which are coexistent. For if they were isolated, they would not as parts con- stitute a whole. And if their connection (the reciprocal action of the manifold) were not already necessary because of their coexistence, we could not argue from this latter, which is a merely ideal relation to the former, which is a real relation. We have, however, in the proper context, shown that community is really the ground of the possibility of an empirical knowledge of coexistence, and that the inference, rightly regarded, is simply from this empirical knowledge to community as its condition. P 239 4 THE POSTULATES OF EMPIRICAL THOUGHT IN GENERAL 1. That which agrees with the formal conditions of ex- perience, that is, with the conditions of intuition and of con- cepts, is possible. 2. That which is bound up with the material conditions of experience, that is, with sensation, is actual. 3. That which in its connection with the actual is deter- mined in accordance with universal conditions of experience, is (that is, exists as) necessary. Explanation The categories of modality have the peculiarity that, in determining an object, they do not in the least enlarge the concept to which they are attached as predicates. They only express the relation of the concept to the faculty of knowledge. Even when the concept of a thing is quite complete, I can still enquire whether this object is merely possible or is also actual, or if actual, whether it is not also necessary. No additional determinations are thereby thought in the object itself; the question is only how the object, together with all its deter- minations, is related to understanding and its empirical em- ployment, to empirical judgment, and to reason in its appli- cation to experience. Just on this account also the principles of modality are nothing but explanations of the concepts of possibility, actual- ity, and necessity, in their empirical employment; at the same time they restrict all categories to their merely empirical em- ployment, and do not approve or allow their transcendental employment. For if they are not to have a purely logical sig- nificance, analytically expressing the form of thought, but are to refer to the possibility, actuality, or necessity of things, they must concern possible experience and its synthetic unity, in which alone objects of knowledge can be given. The postulate of the possibility of things requires that the concept of the things should agree with the formal con- ditions of an experience in general. But this, the objective form of experience in general, contains all synthesis that is P 240 required for knowledge of objects. A concept which contains a synthesis is to be regarded as empty and as not related to any object, if this synthesis does not belong to experience either as being derived from it, in which case it is an empirical concept, or as being an a priori condition upon which experi- ence in general in its formal aspect rests, in which case it is a pure concept. In the latter case it still belongs to experience, inasmuch as its object is to be met with only in experience. For whence shall we derive the character of the possibility of an object which is thought through a synthetic a priori con- cept, if not from the synthesis which constitutes the form of the empirical knowledge of objects? It is, indeed, a necessary logical condition that a concept of the possible must not con- tain any contradiction; but this is not by any means sufficient to determine the objective reality of the concept, that is, the pos- sibility of such an object as is thought through the concept. Thus there is no contradiction in the concept of a figure which is enclosed within two straight lines, since the concepts of two straight lines and of their coming together contain no negation of a figure. The impossibility arises not from the concept in itself, but in connection with its construction in space, that is, from the conditions of space and of its determination. And since these contain a priori in themselves the form of experi- ence in general, they have objective reality, that is, they apply to possible things. We shall now proceed to show the far-reaching utility and influence of this postulate of possibility. If I represent to my- self a thing which is permanent, so that everything in it which changes belongs only to its state, I can never know from such a concept that a thing of this kind is possible. Or if I represent to myself something which is so constituted that if it is posited something else invariably and inevitably follows from it, this may certainly be so thought without contradiction; but this thought affords no means of judging whether this property (causality) is to be met with in any possible thing. Lastly, I can represent to myself diverse things (substances), which are so constituted that the state of the one carries with it some consequence in the state of the other, and this reciprocally; but I can never determine from these concepts, which contain a merely arbitrary synthesis, whether a relation of this kind P 241 can belong to any [possible] things. Only through the fact that these concepts express a priori the relations of perceptions in every experience, do we know their objective reality, that is their transcendental truth, and this, indeed, independently of experience, though not independently of all relation to the form of an experience in general, and to the synthetic unity in which alone objects can be empirically known. But if we should seek to frame quite new concepts of sub- stances, forces, reciprocal actions, from the material which perception presents to us, without experience itself yielding the example of their connection, we should be occupying our- selves with mere fancies, of whose possibility there is absolutely no criterion since we have neither borrowed these concepts [directly] from experience, nor have taken experience as our instructress in their formation. Such fictitious concepts, un- like the categories, can acquire the character of possibility not in a priori fashion, as conditions upon which all experience depends, but only a posteriori as being concepts which are given through experience itself. And, consequently, their pos- sibility must either be known a posteriori and empirically, or it cannot be known at all. A substance which would be per- manently present in space, but without filling it (like that mode of existence intermediate between matter and thinking being which some would seek to introduce), or a special ulti- mate mental power of intuitively anticipating the future (and not merely inferring it), or lastly a power of standing in com- munity of thought with other men, however distant they may be -- are concepts the possibility of which is altogether ground- less, as they cannot be based on experience and its known laws; and without such confirmation they are arbitrary combinations of thoughts, which, although indeed free from contradiction, can make no claim to objective reality, and none, therefore, as to the possibility of an object such as we here profess to think. As regards reality, we obviously cannot think it in concreto, without calling experience to our aid. For reality is bound up with sensation, the matter of experience, not with that form of relation in regard to which we can, if we so choose, resort to a playful inventiveness. But I leave aside everything the possibility of which can P 242 be derived only from its actuality in experience, and have here in view only the possibility of things through a priori concepts; and I maintain the thesis that their possibility can never be established from such concepts taken in and by themselves, but only when the concepts are viewed as formal and objective conditions of experience in general. It does, indeed, seem as if the possibility of a triangle could be known from its concept in and by itself (the concept is cer- tainly independent of experience), for we can, as a matter of fact, give it an object completely a priori, that is, can construct it. But since this is only the form of an object, it would remain a mere product of imagination, and the possibility of its object would still be doubtful. To determine its possibility, something more is required, namely, that such a figure be thought under no conditions save those upon which all objects of experience rest. That space is a formal a priori condition of outer experi- ences, that the formative synthesis through which we con- struct a triangle in imagination is precisely the same as that which we exercise in the apprehension of an appearance, in making for ourselves an empirical concept of it -- these are the considerations that alone enable us to connect the representa- tion of the possibility of such a thing with the concept of it. Similarly, since the concepts of continuous magnitudes, indeed of magnitudes in general, are one and all synthetic, the possi- bility of such magnitudes is never clear from the concepts them- selves, but only when they are viewed as formal conditions of the determination of objects in experience in general. And where, indeed, should we seek for objects corresponding to these concepts if not in experience, through which alone ob- jects are given to us? We can, indeed, prior to experience itself, know and characterise the possibility of things, merely by reference to the formal conditions under which in experi- ence anything whatsoever is determined as object, and therefore can do so completely a priori. But, even so, this is possible only in relation to experience and within its limits. The postulate bearing on the knowledge of things as actual does not, indeed, demand immediate perception (and, therefore, sensation of which we are conscious) of the object whose existence is to be known. What we do, however, P 243 require is the connection of the object with some actual perception, in accordance with the analogies of experi- ence, which define all real connection in an experience in general. In the mere concept of a thing no mark of its existence is to be found. For though it may be so complete that nothing which is required for thinking the thing with all its inner deter- minations is lacking to it, yet existence has nothing to do with all this, but only with the question whether such a thing be so given us that the perception of it can, if need be, precede the concept. For that the concept precedes the perception signi- fies the concept's mere possibility; the perception which sup- plies the content to the concept is the sole mark of actuality. We can also, however, know the existence of the thing prior to its perception and, consequently, comparatively speaking, in an a priori manner, if only it be bound up with certain percep- tions, in accordance with the principles of their empirical con- nection (the analogies). For the existence of the thing being thus bound up with our perceptions in a possible experience, we are able in the series of possible perceptions and under the guidance of the analogies to make the transition from our actual perception to the thing in question. Thus from the per- ception of the attracted iron filings we know of the existence of a magnetic matter pervading all bodies, although the con- stitution of our organs cuts us off from all immediate percep- tion of this medium. For in accordance with the laws of sensi- bility and the context of our perceptions, we should, were our senses more refined, come also in an experience upon the im- mediate empirical intuition of it. The grossness of our senses does not in any way decide the form of possible experience in general. Our knowledge of the existence of things reaches, then, only so far as perception and its advance according to empirical laws can extend. If we do not start from ex- perience, or do not proceed accordance with laws of the em- P 244 pirical connection of appearances, our guessing or enquiring into the existence of anything will only be an idle pretence. Idealism raises, however, what is a serious objection to these rules for proving existence mediately; and this is the proper place for its refutation. *** Refutation of Idealism Idealism -- meaning thereby material idealism -- is the theory which declares the existence of objects in space out- side us either to be merely doubtful and indemonstrable or to be false and impossible. The former is the problematic ideal- ism of Descartes, which holds that there is only one empirical assertion that is indubitably certain, namely, that 'I am'. The latter is the dogmatic idealism of Berkeley. He maintains that space, with all the things of which it is the inseparable condi- tion, is something which is in itself impossible; and he there- fore regards the things in space as merely imaginary entities. Dogmatic idealism is unavoidable, if space be interpreted as a property that must belong to things in themselves. For in that case space, and everything to which it serves as condition, is a non-entity. The ground on which this idealism rests has al- ready been undermined by us in the Transcendental Aesthetic. Problematic idealism, which makes no such assertion, but merely pleads incapacity to prove, through immediate experi- ence, any existence except our own, is, in so far as it allows of no decisive judgment until sufficient proof has been found, reasonable and in accordance with a thorough and philo- sophical mode of thought. The required proof must, therefore, show that we have experience, and not merely imagination of outer things; and this, it would seem, cannot be achieved save by proof that even our inner experience, which for Descartes is indubitable, is possible only on the assumption of outer ex- perience. P 245 THESIS The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me. Proof I am conscious of my own existence as determined in time. All determination of time presupposes something per- manent in perception. This permanent cannot, however, be something in me, since it is only through this per- manent that my existence in time can itself be deter- mined. Thus perception of this permanent is possible only through a thing outside me and not through the mere re- presentation of a thing outside me; and consequently the determination of my existence in time is possible only through the existence of actual things which I perceive outside me. Now consciousness [of my existence] in time is necessarily bound up with consciousness of the [condition of the] possi- bility of this time-determination; and it is therefore necessarily bound up with the existence of things outside me, as the condition of the time-determination. In other words, the con- sciousness of my existence is at the same time an immediate consciousness of the existence of other things outside me. Note 1. It will be observed that in the foregoing proof the game played by idealism has been turned against itself, and with greater justice. Idealism assumed that the only immediate experience is inner experience, and that from it we can only infer outer things -- and this, moreover, only in an untrustworthy manner, as in all cases where we are inferring from given effects to determinate causes. In this particular case, the cause of the representations, which we ascribe, perhaps falsely, to outer things, may lie in ourselves. But in the above proof it has been shown that outer experience is really P 246 immediate, and that only by means of it is inner experience -- not indeed the consciousness of my own existence, but the determination of it in time -- possible. Certainly, the repre- sentation 'I am', which expresses the consciousness that can accompany all thought, immediately includes in itself the existence of a subject; but it does not so include any knowledge of that subject, and therefore also no empirical knowledge, that is, no experience of it. For this we require, in addition to the thought of something existing, also intuition, and in this case inner intuition, in respect of which, that is, of time, the subject must be determined. But in order so to determine it, outer objects are quite indispensable; and it therefore follows that inner experience is itself possible only mediately, and only through outer experience. Note 2. With this thesis all employment of our cognitive faculty in experience, in the determination of time, entirely agrees. Not only are we unable to perceive any deter- mination of time save through change in outer relations (motion) relatively to the permanent in space (for instance, the motion of the sun relatively to objects on the earth), we have nothing permanent on which, as intuition, we can base the concept of a substance, save only matter; and even this permanence is not obtained from outer experience, but is presupposed a priori as a necessary condition of determina- tion of time, and therefore also as a determination of inner sense in respect of [the determination of] our own existence through the existence of outer things. ++ The immediate consciousness of the existence of outer things is, in the preceding thesis, not presupposed, but proved, be the possibility of this consciousness understood by us or not. The ques- tion as to its possibility would be this: whether we have an inner sense only, and no outer sense, but merely an outer imagination. It is clear, however, that in order even only to imagine something as outer, that is, to present it to sense in intuition, we must already have an outer sense, and must thereby immediately distinguish the mere receptivity of an outer intuition from the spontaneity which characterises every act of imagination. For should we merely be imagining an outer sense, the faculty of intuition, which is to be determined by the faculty of imagination, would itself be annulled. P 246 The consciousness of myself in the representation 'I' is not an intuition, but a P 247 merely intellectual representation of the spontaneity of a thinking subject. This 'I' has not, therefore, the least pre- dicate of intuition, which, as permanent, might serve as cor- relate for the determination of time in inner sense -- in the manner in which, for instance, impenetrability serves in our empirical intuition of matter. Note 3. From the fact that the existence of outer things is required for the possibility of a determinate consciousness of the self, it does not follow that every intuitive representa- tion of outer things involves the existence of these things, for their representation can very well be the product merely of the imagination (as in dreams and delusions). Such re- presentation is merely the reproduction of previous outer perceptions, which, as has been shown, are possible only through the reality of outer objects. All that we have here sought to prove is that inner experience in general is possible only through outer experience in general. Whether this or that supposed experience be not purely imaginary, must be ascer- tained from its special determinations, and through its con- gruence with the criteria of all real experience. *** Lastly, as regards the third postulate, it concerns material necessity in existence, and not merely formal and logical necessity in the connection of concepts. Since the existence of any object of the senses cannot be known completely a priori, but only comparatively a priori, relatively to some other pre- viously given existence; and since, even so, we can then arrive only at such an existence as must somewhere be contained in the context of the experience, of which the given perception is a part, the necessity of existence can never be known from concepts, but always only from con- nection with that which is perceived, in accordance with universal laws of experience. Now there is no existence that can be known as necessary under the condition of other given appearances, save the existence of effects from given causes, P 248 in accordance with laws of causality. It is not, therefore, the existence of things (substances) that we can know to be neces- sary, but only the existence of their state; and this necessity of the existence of their state we can know only from other states, which are given in perception, in accordance with empirical laws of causality. It therefore follows that the cri- terion of necessity lies solely in the law of possible experience, the law that everything which happens is determined a priori through its cause in the [field of] appearance. We thus know the necessity only of those effects in nature the causes of which are given to us, and the character of necessity in existence extends no further than the field of possible experience, and even in this field is not applicable to the existence of things as substances, since substances can never be viewed as empirical effects -- that is, as happening and coming to be. Necessity con- cerns only the relations of appearances in conformity with the dynamical law of causality and the possibility grounded upon it of inferring a priori from a given existence (a cause) to another existence (the effect). That everything which happens is hypothetically necessary is a principle which subordinates alteration in the world to a law, that is, to a rule of necessary existence, without which there would be nothing that could be entitled nature. The proposition that nothing happens through blind chance (in mundo non datur casus) is therefore an a - priori law of nature. So also is the proposition that no neces- sity in nature is blind, but always a conditioned and therefore intelligible necessity (non datur fatum). Both are laws through which the play of alterations is rendered subject to a nature of things (that is, of things as appearances), or what amounts to the same thing, to the unity of understanding, in which alone they can belong to one experience, that is, to the syn- thetic unity of appearances. Both belong to the class of dynamical principles. The first is really a consequence of the principle of causality, and so belongs to the analogies of experience. The second is a principle of modality; but this modality, while adding the concept of necessity to causal determination, itself stands under a rule of understanding. The principle of continuity forbids any leap in the series of appearances, that is, of alterations (in mundo non datur saltus); P 249 it also forbids, in respect of the sum of all empirical intuitions in space, any gaps or cleft between two appearances (non datur hiatus); for so we may express the proposition, that nothing which proves a vacuum, or which even admits it as a part of empirical synthesis, can enter into experience. As regards a void which may be conceived to lie beyond the field of possible experience, that is, outside the world, such a question does not come within the jurisdiction of the mere understanding -- which decides only upon questions that concern the use to be made of given appearances for the obtaining of empirical know- ledge. It is a problem for that ideal reason which goes out beyond the sphere of a possible experience and seeks to judge of that which surrounds and limits it; and is a problem which will therefore have to be considered in the Transcendental Dialectic. These four propositions (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum), like all principles of transcendental origin, we can easily ex- hibit in their order, that is, in accordance with the order of the categories, and so assign to each its proper place. But the reader has now had sufficient practice to allow of his doing this for himself, or of easily discovering the guiding principle for so doing. They are all entirely at one in this, that they allow of nothing in the empirical synthesis which may do violence or detriment to the understanding and to the con- tinuous connection of all appearances -- that is, to the unity of the concepts of the understanding. For in the understanding alone is possible the unity of experience, in which all percep- tions must have their place. To enquire whether the field of possibility is larger than the field which contains all actuality, and this latter, again, larger than the sum of that which is necessary, is to raise somewhat subtle questions which demand a synthetic solution and yet come under the jurisdiction of reason alone. For they are tantamount to the enquiry whether things as appearances one and all belong to the sum and context of a single experience, of which every given perception is a part, a part which there- fore cannot be connected with any other [series of] appearances, or whether my perceptions can belong, in their general con- nection, to more than one possible experience. The under- P 250 standing, in accordance with the subjective and formal con- ditions of sensibility as well as of apperception, prescribes a priori to experience in general the rules which alone make experience possible. Other forms of intuition than space and time, other forms of understanding than the discursive forms of thought, or of knowledge through concepts, even if they should be possible, we cannot render in any way conceivable and comprehensible to ourselves; and even assuming that we could do so, they still would not belong to experience -- the only kind of knowledge in which objects are given to us. Whether other perceptions than those belonging to our whole possible experience, and therefore a quite different field of matter, may exist, the understanding is not in a position to decide. It can deal only with the synthesis of that which is given. Moreover, the poverty of the customary inferences through which we throw open a great realm of possibility, of which all that is actual (the objects of experience) is only a small part, is patently obvious. Everything actual is possible; from this proposition there naturally follows, in accordance with the logical rules of conversion, the merely particular proposition, that some possible is actual; and this would seem to mean that much is possible which is not actual. It does indeed seem as if we were justified in extending the number of possible things beyond that of the actual, on the ground that something must be added to the possible to constitute the actual. But this [alleged] process of adding to the pos- sible I refuse to allow. For that which would have to be added to the possible, over and above the possible, would be impossible. What can be added is only a relation to my understanding, namely that in addition to agreement with the formal conditions of experience there should be connect- tion with some perception. But whatever is connected with perception in accordance with empirical laws is actual, even although it is not immediately perceived. That yet another series of appearances in thoroughgoing connection with that which is given in perception, and consequently that more than one all-embracing experience is possible, cannot be in- ferred from what is given; and still less can any such infer- ence be drawn independently of anything being given -- since P 251 without material nothing whatsoever can be thought. What is possible only under conditions which themselves are merely possible is not in all respects possible. But such [absolute] possibility is in question when it is asked whether the possi- bility of things extends further than experience can reach. I have made mention of these questions only in order to omit nothing which is ordinarily reckoned among the concepts of understanding. But as a matter of fact absolute possibility, that which is in all respects valid, is no mere concept of understanding, and can never be employed empirically. It belongs exclusively to reason, which transcends all possible empirical employment of the understanding. We have there- fore had to content ourselves with some merely critical re- marks; the matter must otherwise be left in obscurity until we come to the proper occasion for its further treatment. Before concluding this fourth section, and therewith the system of all principles of pure understanding, I must explain why I have entitled the principles of modality postulates. I interpret this expression not in the sense which some recent philosophical writers, wresting it from its proper mathematical significance, have given to it, namely, that to postulate should mean to treat a proposition as immediately certain, with- out justification or proof. For if, in dealing with synthetic propositions, we are to recognise them as possessing un- conditioned validity, independently of deduction, on the evi- dence [merely] of their own claims, then no matter how evident they may be, all critique of understanding is given up. And since there is no lack of audacious pretensions, and these are supported by common belief (though that is no credential of their truth), the understanding lies open to every fancy, and is in no position to withhold approval of those assertions which, though illegitimate, yet press upon us, in the same confident tone, their claims to be accepted as actual axioms. Whenever, therefore, an a priori determination is synthetically added to the concept of a thing, it is indispensable that, if not a proof, at least a deduction of the legitimacy of such an assertion should be supplied. The principles of modality are not, however, objectively synthetic. For the predicates of possibility, actuality, and P 252 necessity do not in the least enlarge the concept of which they are affirmed, adding something to the representation of the object. But since they are none the less synthetic, they are so subjectively only, that is, they add to the concept of a thing (of something real), of which otherwise they say nothing, the cog- nitive faculty from which it springs and in which it has its seat. Thus if it is in connection only with the formal conditions of experience, and so merely in the understanding, its object is called possible. If it stands in connection with perception, that is, with sensation as material supplied by the senses, and through perception is determined by means of the understanding, the object is actual. If it is determined through the connection of per- ceptions according to concepts, the object is entitled necessary. The principles of modality thus predicate of a concept nothing but the action of the faculty of knowledge through which it is generated. Now in mathematics a postulate means the prac- tical proposition which contains nothing save the synthesis through which we first give ourselves an object and generate its concept -- for instance, with a given line, to describe a circle on a plane from a given point. Such a proposition cannot be proved, since the procedure which it demands is exactly that through which we first generate the concept of such a figure. With exactly the same right we may postulate the principles of modality, since they do not increase our concept of things, but only show the manner in which it is connected with the faculty of knowledge. General Note on the System of the Principles That the possibility of a thing cannot be determined from the category alone, and that in order to exhibit the objective reality of the pure concept of understanding we must always have an intuition, is a very noteworthy fact. ++ Through the actuality of a thing I certainly posit more than the possibility of it, but not in the thing. For it can never contain more in its actuality than is contained in its complete possibility. But while possibility is merely a positing of the thing in relation to the understanding (in its empirical employment), actuality is at the same time a connection of it with perception. P 253 Take, for instance, the categories of relation. We cannot determine from mere concepts how (1) something can exist as subject only, and not as a mere determination of other things, that is, how a thing can be substance, or (2) how, because something is, something else must be, and how, therefore, a thing can be a cause, or (3) when several things exist, how because one of them is there, something follows in regard to the others and vice versa, and how in this way there can be a community of substances. This likewise applies to the other categories; for example, how a thing can be equal to a number of things taken together, that is, can be a quantity. So long as intuition is lacking, we do not know whether through the categories we are thinking an object, and whether indeed there can anywhere be an object suited to them. In all these ways, then, we obtain confirmation that the categories are not in themselves knowledge, but are merely forms of thought for the making of knowledge from given intuitions. For the same reason it follows that no synthetic proposi- tion can be made from mere categories. For instance, we are not in a position to say that in all existence there is substance, that is, something which can exist only as subject and not as mere predicate; or that everything is a quantum, etc. For if intuition be lacking, there is nothing which can enable us to go out beyond a given concept, and to connect another with it. No one, therefore, has ever yet succeeded in proving a syn- thetic proposition merely from pure concepts of the under- standing -- as, for instance, that everything which exists con- tingently has a cause. We can never get further than proving, that without this relation we are unable to comprehend the existence of the contingent, that is, are unable a priori through the understanding to know the existence of such a thing -- from which it does not, however, follow that this is also a con- dition of the possibility of the things themselves. If the reader will go back to our proof of the principle of causality -- that everything which happens, that is, every event, presupposes a cause -- he will observe that we were able to prove it only of objects of possible experience; and even so, not from pure con- cepts, but only as a principle of the possibility of experience, and therefore of the knowledge of an object given in empirical P 254 intuition. We cannot, indeed, deny that the proposition, that everything contingent must have a cause, is patent to every- one from mere concepts. But the concept of the contingent is then being apprehended as containing, not the category of modality (as something the not-being of which can be thought), but that of relation (as something which can exist only as consequence of something else); and it is then, of course, an identical proposition -- that which can exist only as consequence has a cause. As a matter of fact, when we are required to cite examples of contingent existence, we invari- ably have recourse to alterations, and not merely to the possi- bility of entertaining the opposite in thought. Now alteration is an event which, as such, is possible only through a cause, and the not-being of which is therefore in itself possible. In other words, we recognise contingency in and through the fact that something can exist only as the effect of a cause; and if, there- fore, a thing is assumed to be contingent, it is an analytic pro- position to say that it has a cause. But it is an even more noteworthy fact, that in order to understand the possibility of things in conformity with the categories, and so to demonstrate the objective reality of the latter, we need, not merely intuitions, but intuitions that are in all cases outer intuitions. When, for instance, we take the pure concepts of relation, we find, firstly, that in order to obtain something permanent in intuition corresponding to the con- cept of substance, and so to demonstrate the objective reality of this concept, we require an intuition in space (of matter). ++ We can easily think the non-existence of matter. From this the ancients did not, however, infer its contingency. Even the change from being to not-being of a given state of a thing, in which all alteration consists, does not prove the contingency of this state, on the ground of the reality of its opposite. For instance, that a body should come to rest after having been in motion does not prove the contingency of the motion as being the opposite of the state of rest. For this opposite is opposed to the other only logically, not realiter. To prove the contingency of its motion, we should have to prove that instead of the motion at the preceding moment, it was possible for the body to have been then at rest, not that it is after- wards at rest; for in the latter case the opposites are quite consistent with each other. P 255 For space alone is determined as permanent, while time, and therefore everything that is in inner sense, is in constant flux. Secondly, in order to exhibit alteration as the intuition corre- sponding to the concept of causality, we must take as our example motion, that is, alteration in space. Only in this way can we obtain the intuition of alterations, the possibility of which can never be comprehended through any pure under- standing. For alteration is combination of contradictorily opposed determinations in the existence of one and the same thing. Now how it is possible that from a given state of a thing an opposite state should follow, not only cannot be conceived by reason without an example, but is actually incomprehensible to reason without intuition. The intuition required is the in- tuition of the movement of a point in space. The presence of the point in different locations (as a sequence of opposite de- terminations) is what alone first yields to us an intuition of alteration. For in order that we may afterwards make inner alterations likewise thinkable, we must represent time (the form of inner sense) figuratively as a line, and the inner alteration through the drawing of this line (motion), and so in this manner by means of outer intuition make compre- hensible the successive existence of ourselves in different states. The reason of this is that all alteration, if it is to be perceived as alteration, presupposes something permanent in intuition, and that in inner sense no permanent intuition is to be met with. Lastly, the possibility of the category of community cannot be comprehended through mere reason alone; and consequently its objective reality is only to be de- termined through intuition, and indeed through outer intuition in space. For how are we to think it to be possible, when several substances exist, that, from the existence of one, something (as effect) can follow in regard to the existence of the others, and vice versa; in other words, that because there is something in the one there must also in the others be something which is not to be understood solely from the existence of these others? For this is what is required in order that there be com- munity; community is not conceivable as holding between things each of which, through its subsistence, stands in com- plete isolation. Leibniz, in attributing to the substances of the P 256 world, as thought through the understanding alone, a com- munity, had therefore to resort to the mediating intervention of a Deity. For, as he justly recognised, a community of sub- stances is utterly inconceivable as arising simply from their existence. We can, however, render the possibility of com- munity -- of substances as appearances -- perfectly compre- hensible, if we represent them to ourselves in space, that is, in outer intuition. For this already contains in itself a priori formal outer relations as conditions of the possibility of the real relations of action and reaction, and therefore of the possibility of community. Similarly, it can easily be shown that the possibility of things as quantities, and therefore the objective reality of quantity, can be exhibited only in outer intuition, and that only through the mediation of outer intuition can it be applied also to inner sense. But, to avoid prolixity, I must leave the reader to supply his own examples of this. These remarks are of great importance, not only in con- firmation of our previous refutation of idealism, but even more, when we come to treat of self-knowledge by mere inner consciousness, that is, by determination of our nature without the aid of outer empirical intuitions -- as showing us the limits of the possibility of this kind of knowledge. The final outcome of this whole section is therefore this: all principles of the pure understanding are nothing more than principles a priori of the possibility of experience, and to experience alone do all a priori synthetic propositions relate -- indeed, their possibility itself rests entirely on this relation. P 257 TRANSCENDENTAL DOCTRINE OF JUDGMENT (ANALYTIC OF PRINCIPLES) CHAPTER III THE GROUND OF THE DISTINCTION OF ALL OBJECTS IN GENERAL INTO PHENOMENA AND NOUMENA WE have now not merely explored the territory of pure under- standing, and carefully surveyed every part of it, but have also measured its extent, and assigned to everything in it its rightful place. This domain is an island, enclosed by nature itself within unalterable limits. It is the land of truth -- en- chanting name! -- surrounded by a wide and stormy ocean, the native home of illusion, where many a fog bank and many a swiftly melting iceberg give the deceptive appearance of farther shores, deluding the adventurous seafarer ever anew with empty hopes, and engaging him in enterprises which he can never abandon and yet is unable to carry to com- pletion. Before we venture on this sea, to explore it in all directions and to obtain assurance whether there be any ground for such hopes, it will be well to begin by casting a glance upon the map of the land which we are about to leave, and to enquire, first, whether we cannot in any case be satisfied with what it contains -- are not, indeed, under compulsion to be satisfied, inasmuch as there may be no other territory upon which we can settle; and, secondly, by what title we possess even this domain, and can consider ourselves as secured against all opposing claims. Although we have already given a sufficient answer to these questions in the course of the Analytic, a summary statement of its solutions may nevertheless help to strengthen our conviction, by focussing the various considerations in their bearing on the questions now before us. P 258 We have seen that everything which the understanding derives from itself is, though not borrowed from experience, at the disposal of the understanding solely for use in experi- ence. The principles of pure understanding, whether con- stitutive a priori, like the mathematical principles, or merely regulative, like the dynamical, contain nothing but what may be called the pure schema of possible experience. For experience obtains its unity only from the synthetic unity which the understanding originally and of itself confers upon the synthesis of imagination in its relation to apper- ception; and the appearances, as data for a possible know- ledge, must already stand a priori in relation to, and in agree- ment with, that synthetic unity. But although these rules of understanding are not only true a priori, but are indeed the source of all truth (that is, of the agreement of our know- ledge with objects), inasmuch as they contain in themselves the ground of the possibility of experience viewed as the sum of all knowledge wherein objects can be given to us, we are not satisfied with the exposition merely of that which is true, but likewise demand that account be taken of that which we desire to know. If, therefore, from this critical enquiry we learn nothing more than what, in the merely empirical em- ployment of understanding, we should in any case have practised without any such subtle enquiry, it would seem as if the advantage derived from it by no means repays the labour expended. The reply may certainly be made that in the endeavour to extend our knowledge a meddlesome curiosity is far less injurious than the habit of always insisting, before entering on any enquiries, upon antecedent proof of the utility of the enquiries -- an absurd demand, since prior to completion of the enquiries we are not in a position to form the least conception of this utility, even if it were placed before our eyes. There is, however, one advantage which may be made comprehensible and of interest even to the most re- fractory and reluctant learner, the advantage, that while the understanding, occupied merely with its empirical employ- ment, and not reflecting upon the sources of its own know- ledge, may indeed get along quite satisfactorily, there is yet one task to which it is not equal, that, namely, of determining the limits of its employment, and of knowing what it is that P 259 may lie within and what it is that lies without its own proper sphere. This demands just those deep enquiries which we have instituted. If the understanding in its empirical employment cannot distinguish whether certain questions lie within its horizon or not, it can never be assured of its claims or of its possessions, but must be prepared for many a humiliating disillusionment, whenever, as must unavoidably and con- stantly happen, it oversteps the limits of its own domain, and loses itself in opinions that are baseless and mis- leading. If the assertion, that the understanding can employ its various principles and its various concepts solely in an em- pirical and never in a transcendental manner, is a proposition which can be known with certainty, it will yield important consequences. The transcendental employment of a concept in any principle is its application to things in general and in themselves; the empirical employment is its application merely to appearances; that is, to objects of a possible experience. That the latter application of concepts is alone feasible is evident from the following considerations. We demand in every con- cept, first, the logical form of a concept (of thought) in general, and secondly, the possibility of giving it an object to which it may be applied. In the absence of such object, it has no meaning and is completely lacking in content, though it may still contain the logical function which is required for making a concept out of any data that may be presented. Now the object cannot be given to a concept otherwise than in intui- tion; for though a pure intuition can indeed precede the object a priori, even this intuition can acquire its object, and there- fore objective validity, only through the empirical intuition of which it is the mere form. Therefore all concepts, and with them all principles, even such as are possible a priori, relate to empirical intuitions, that is, to the data for a possible experience. Apart from this relation they have no objective validity, and in respect of their representations are a mere play of imagination or of understanding. Take, for instance, the concepts of mathematics, considering them first of all in their pure intuitions. Space has three dimensions; between two points there can be only one straight line, etc. Although all these principles, and the representation of the P 260 object with which this science occupies itself, are generated in the mind completely a priori, they would mean nothing, were we not always able to present their meaning in appear- ances, that is, in empirical objects. We therefore demand that a bare concept be made sensible, that is, that an object corresponding to it be presented in intuition. Otherwise the concept would, as we say, be without sense, that is, without meaning. The mathematician meets this demand by the con- struction of a figure, which, although produced a priori, is an appearance present to the senses. In the same science the concept of magnitude seeks its support and sensible meaning in number, and this in turn in the fingers, in the beads of the abacus, or in strokes and points which can be placed before the eyes. The concept itself is always a priori in origin, and so likewise are the synthetic principles or formulas derived from such concepts; but their employment and their relation to their professed objects can in the end be sought nowhere but in experience, of whose possibility they contain the formal conditions. That this is also the case with all categories and the prin- ciples derived from them, appears from the following con- sideration. We cannot define any one of them in any real fashion, that is, make the possibility of their object under- standable, without at once descending to the conditions of sensibility, and so to the form of appearances -- to which, as their sole objects, they must consequently be limited. For if this condition be removed, all meaning, that is, relation to the object, falls away; and we cannot through any example make comprehensible to ourselves what sort of a thing is to be meant by such a concept. ++ In the above statement of the table of categories, we relieved ourselves of the task of defining each of them, as our purpose, which concerned only their synthetic employment, did not require such definition, and we are not called upon to incur any responsibility through unnecessary undertakings from which we can be relieved. P 261 The concept of magnitude in general can never be explained except by saying that it is that determination of a thing whereby we are enabled to think how many times a unit is posited in it. But this how-many-times is based on successive repetition, and therefore on time and the synthesis of the homogeneous in time. Reality, in contradistinction to negation, can be ex- plained only if we think time (as containing all being) as either filled with being or as empty. If I leave out permanence (which is existence in all time), nothing remains in the concept of sub- stance save only the logical representation of a subject -- a re- presentation which I endeavour to realise by representing to myself something which can exist only as subject and never as predicate. ++ It was no evasion but an important prudential maxim, not to embark upon the task of definition, attempting or professing to attain completeness and precision in the determination of a concept, so long as we can achieve our end with one or other of its properties, without requiring a complete enumeration of all those that constitute the com- plete concept. But we now perceive that the ground of this precaution lies still deeper. We realise that we are unable to define them even if we wished. For if we remove all those conditions of sensibility which mark them out as concepts of possible empirical employment, and view them as concepts of things in general and therefore of transcendental employment, all that we can then do with them is to regard the logical function in judgments [to which they give expression] as the condition of the possibility of the things themselves, without in the least being able to show how they can have application to an object, that is, how in pure understanding, apart from sensibility, they can have meaning and objective validity. ++ I here mean real definition -- which does not merely substitute for the name of a thing other more intelligible words, but contains a clear property by which the defined object can always be known with certainty, and which makes the explained concept serviceable in application. Real explanation would be that which makes clear not only the concept but also its objective reality. Mathematical explanations which present the object in intuition, in conformity with the concept, are of this latter kind. P 262 But not only am I ignorant of any conditions under which this logical pre-eminence may belong to anything; I can neither put such a concept to any use, nor draw the least inference from it. For no object is thereby determined for its employment, and consequently we do not know whether it signifies anything whatsoever. If I omit from the concept of cause the time in which something follows upon some- thing else in conformity with a rule, I should find in the pure category nothing further than that there is something from which we can conclude to the existence of something else. In that case not only would we be unable to distinguish cause and effect from one another, but since the power to draw such in- ferences requires conditions of which I know nothing, the con- cept would yield no indication how it applies to any object. The so-called principle, that everything accidental has a cause, presents itself indeed somewhat pompously, as self-sufficing in its own high dignity. But if I ask what is understood by accidental, and you reply, "That the not-being of which is possible," I would gladly know how you can determine this possibility of its not-being, if you do not represent a succession in the series of appearances and in it a being which follows upon not-being (or reversewise), that is, a change. For to say that the not-being of a thing does not contradict itself, is a lame appeal to a logical condition, which, though necessary to the concept, is very far from being sufficient for real possibility. I can remove in thought every existing substance without contradicting myself, but I cannot infer from this their objec- tive contingency in existence, that is, that their non-existence is possible. As regards the concept of community, it is easily seen that inasmuch as the pure categories of substance and causality admit of no explanation determinant of the object, neither is any such explanation possible of reciprocal causality in the relation of substances to one another (com- mercium). So long as the definition of possibility, existence, and necessity is sought solely in pure understanding, they can- not be explained save through an obvious tautology. For to substitute the logical possibility of the concept (namely, that the concept does not contradict itself) for the transcendental possibility of things (namely, that an object corresponds to P 263 the concept) can deceive and leave satisfied only the simple- minded. ++ There is something strange and even absurd in the asser- tion that there should be a concept which possesses a meaning and yet is not capable of any explanation. But the categories have this peculiar feature, that only in virtue of the general condition of sensibility can they possess a determinate mean- ing and relation to any object. Now when this condition has been omitted from the pure category, it can contain nothing but the logical function for bringing the manifold under a concept. By means of this function or form of the concept, thus taken by itself, we cannot in any way know and distinguish what object comes under it, since we have abstracted from the sens- ible condition through which alone objects can come under it. Consequently, the categories require, in addition to the pure concept of understanding, determinations of their application to sensibility in general (schemata). Apart from such application they are not concepts through which an object is known and distinguished from others, but only so many modes of think- ing an object for possible intuitions, and of giving it meaning, under the requisite further conditions, in conformity with some function of the understanding, that is, of defining it. But they cannot themselves be defined. The logical functions of judg- ments in general, unity and plurality, assertion and denial, subject and predicate, cannot be defined without perpetrat- ing a circle, since the definition must itself be a judgment, and so must already contain these functions. The pure categories are nothing but representations of things in general, so far as the manifold of their intuition must be thought through one or other of these logical functions. ++ In a word, if all sensible intuition, the only kind of intuition which we possess, is removed, not one of these concepts can in any fashion verify itself, so as to show its real possibility. Only logical possibility then remains, that is, that the concept or thought is pos- sible. That, however, is not what we are discussing, but whether the concept relates to an object and so signifies something. P 264 From all this it undeniably follows that the pure concepts of understanding can never admit of transcendental but always only of empirical employment, and that the principles of pure understanding can apply only to objects of the senses under the universal conditions of a possible experience, never to things in general without regard to the mode in which we are able to intuit them. Accordingly the Transcendental Analytic leads to this important conclusion, that the most the understanding can achieve a priori is to anticipate the form of a possible experi- ence in general. And since that which is not appearance can- not be an object of experience, the understanding can never transcend those limits of sensibility within which alone objects can be given to us. Its principles are merely rules for the ex- position of appearances; and the proud name of an Ontology that presumptuously claims to supply, in systematic doctrinal form, synthetic a priori knowledge of things in general (for instance, the principle of causality) must, therefore, give place to the modest title of a mere Analytic of pure understanding. Thought is the act which relates given intuition to an object. If the mode of this intuition is not in any way given, the object is merely transcendental, and the concept of understanding has only transcendental employment, namely, as the unity of the thought of a manifold in general. Thus no object is determined through a pure category in which ab- straction is made of every condition of sensible intuition -- the only kind of intuition possible to us. P 263 Magnitude is the determination P 264 which can be thought only through a judgment which has quantity (judicium commune); reality is that determination which can be thought only through an affirmative judgment; substance is that which, in relation to intuition, must be the last subject of all other determinations. But what sort of a thing it is that demands one of these functions rather than another, remains altogether undetermined. Thus the cate- gories, apart from the condition of sensible intuition, of which they contain the synthesis, have no relation to any determinate object, cannot therefore define any object, and so do not in themselves have the validity of objective concepts. P 264 It then expresses only the P 265 thought of an object in general, according to different modes. Now the employment of a concept involves a function of judg- ment whereby an object is subsumed under the concept, and so involves at least the formal condition under which some- thing can be given in intuition. If this condition of judgment (the schema) is lacking, all subsumption becomes impossible. For in that case nothing is given that could be subsumed under the concept. The merely transcendental employment of the cate- gories is, therefore, really no employment at all, and has no determinate object, not even one that is determinable in its mere form. It therefore follows that the pure category does not suffice for a synthetic a priori principle, that the principles of pure understanding are only of empirical, never of tran- scendental employment, and that outside the field of possible experience there can be no synthetic a priori principles. It may be advisable, therefore, to express the situation as follows. The pure categories, apart from formal conditions of sensibility, have only transcendental meaning; nevertheless they may not be employed transcendentally, such employment being in itself impossible, inasmuch as all conditions of any employment in judgments are lacking to them, namely, the formal conditions of the subsumption of any ostensible object under these concepts. Since, then, as pure categories merely, they are not to be employed empirically, and cannot be em- ployed transcendentally, they cannot, when separated from all sensibility, be employed in any manner whatsoever, that is, they cannot be applied to any ostensible object. They are the pure form of the employment of understanding in respect of objects in general, that is, of thought; but since they are merely its form, through them alone no object can be thought or determined. ++ Appearances, so far as they are thought as objects accord- ing to the unity of the categories, are called phaenomena. But if I postulate things which are mere objects of understanding, and which, nevertheless, can be given as such to an intuition, P 266 although not to one that is sensible -- given therefore coram intuitu intellectuali -- such things would be entitled noumena (intelligibilia). P 266 But we are here subject to an illusion from which it is difficult to escape. The categories are not, as regards their origin, grounded in sensibility, like the forms of intuition, space and time; and they seem, therefore, to allow of an application extending beyond all objects of the senses. As a matter of fact they are nothing but forms of thought, which contain the merely logical faculty of uniting a priori in one con- sciousness the manifold given in intuition; and apart, therefore, from the only intuition that is possible to us, they have even less meaning than the pure sensible forms. Through these forms an object is at least given, whereas a mode of com- bining the manifold -- a mode peculiar to our understanding -- by itself, in the absence of that intuition wherein the mani- fold can alone be given, signifies nothing at all. At the same time, if we entitle certain objects, as appearances, sensible entities (phenomena), then since we thus distin- guish the mode in which we intuit them from the nature that belongs to them in themselves, ++ Now we must bear in mind that the concept of appear- ances, as limited by the Transcendental Aesthetic, already of itself establishes the objective reality of noumena and justifies the division of objects into phaenomena and noumena, and so of the world into a world of the senses and a world of the under- standing (mundus sensibilis et intelligibilis), and indeed in such manner that the distinction does not refer merely to the logical form of our knowledge of one and the same thing, ac- cording as it is indistinct or distinct, but to the difference in the manner in which the two worlds can be first given to our knowledge, and in conformity with this difference, to the manner in which they are in themselves generically distinct from one another. For if the senses represent to us something merely as it appears, this something must also in itself be a P 267 thing, and an object of a non-sensible intuition, that is, of the understanding. P 267 it is implied in this distinction that we place the latter, considered in their own nature, although we do not so intuit them, or that we place other possible things, which are not objects of our senses but are thought as objects merely through the understanding, in opposition to the former, and that in so doing we entitle them intelligible entities (noumena). The question then arises, whether our pure concepts of understanding have meaning in respect of these latter, and so can be a way of knowing them. At the very outset, however, we come upon an ambiguity which may occasion serious misapprehension. The under- standing, when it entitles an object in a [certain] relation mere phenomenon, at the same time forms, apart from that relation, a representation of an object in itself, and so comes to represent itself as also being able to form con- cepts of such objects. ++ In other words, a [kind of] knowledge must be possible, in which there is no sensibility, and which alone has reality that is absolutely objective. Through it objects will be represented as they are, whereas in the empirical employment of our understanding things will be known only as they appear. If this be so, it would seem to follow that we cannot assert, what we have hitherto maintained, that the pure modes of knowledge yielded by our understanding are never anything more than principles of the exposition of appearance, and that even in their a priori application they relate only to the formal possibility of experience. On the contrary, we should have to recognise that in addition to the empirical employment of the categories, which is limited to sensible conditions, there is like- wise a pure and yet objectively valid employment. For a field quite different from that of the senses would here lie open to us, a world which is thought as it were in the spirit (or even perhaps intuited), and which would therefore be for the under- standing a far nobler, not a less noble, object of contemplation. P 267 And since the understanding yields no concepts additional to the categories, it also supposes that the object in itself must at least be thought through these P 268 pure concepts, and so is misled into treating the entirely indeterminate concept of an intelligible entity, namely, of a something in general outside our sensibility, as being a de- terminate concept of an entity that allows of being known in a certain [purely intelligible] manner by means of the under- standing. If by 'noumenon' we mean a thing so far as it is not an object of our sensible intuition, and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term. But if we understand by it an object of a non-sensible intuition, we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. This would be 'noumenon' in the positive sense of the term. The doctrine of sensibility is likewise the doctrine of the noumenon in the negative sense, that is, of things which the understanding must think without this reference to our mode of intuition, therefore not merely as appearances but as things in themselves. ++ All our representations are, it is true, referred by the under- standing to some object; and since appearances are nothing but representations, the understanding refers them to a some- thing, as the object of sensible intuition. But this something, thus conceived, is only the transcendental object; and by that is meant a something = X, of which we know, and with the present constitution of our understanding can know, nothing whatsoever, but which, as a correlate of the unity of apper- ception, can serve only for the unity of the manifold in sensible intuition. By means of this unity the understanding combines the manifold into the concept of an object. This transcendental object cannot be separated from the sense data, for nothing is then left through which it might be thought. Consequently it is not in itself an object of knowledge, but only the representa- tion of appearances under the concept of an object in general -- a concept which is determinable through the manifold of these appearances. P 268 At the same time the understanding is P 269 well aware that in viewing things in this manner, as thus apart from our mode of intuition, it cannot make any use of the categories. For the categories have meaning only in rela- tion to the unity of intuition in space and time; and even this unity they can determine, by means of general a priori con- necting concepts, only because of the mere ideality of space and time. In cases where this unity of time is not to be found, and therefore in the case of the noumenon, all employment, and indeed the whole meaning of the categories, entirely vanishes; for we have then no means of determining whether things in harmony with the categories are even possible. On this point I need only refer the reader to what I have said in the opening sentences of the General Note appended to the preceding chapter. The possibility of a thing can never be proved merely from the fact that its concept is not self-con- tradictory, but only through its being supported by some corresponding intuition. P 268a Just for this reason the categories represent no special ob- ject, given to the understanding alone, but only serve to determine P 269a the transcendental object, which is the concept of some- thing in general, through that which is given in sensibility, in order thereby to know appearances empirically under concepts of objects. The cause of our not being satisfied with the substrate of sensibility, and of our therefore adding to the phenomena nou- mena which only the pure understanding can think, is simply as follows. The sensibility (and its field, that of the appear- ances) is itself limited by the understanding in such fashion that it does not have to do with things in themselves but only with the mode in which, owing to our subjective constitution, they appear. The Transcendental Aesthetic, in all its teaching, has led to this conclusion; and the same conclusion also, of course, follows from the concept of an appearance in general; namely, that something which is not in itself appearance must cor- respond to it. For appearance can be nothing by itself, outside our mode of representation. Unless, therefore, we are to move constantly in a circle, the word appearance must be recognised as already indicating a relation to something, the immediate P 270a representation of which is, indeed, sensible, but which, even apart from the constitution of our sensibility (upon which the form of our intuition is grounded), must be something in itself, that is, an object independent of sensibility. P 269 If, therefore, we should attempt to apply the categories to objects which are not viewed as being appearances, we should have to postulate an intuition other P 270 than the sensible, and the object would thus be a noumenon in the positive sense. Since, however, such a type of intuition, intellectual intuition, forms no part whatsoever of our faculty of knowledge, it follows that the employment of the categories can never extend further than to the objects of experience. Doubtless, indeed, there are intelligible entities corresponding to the sensible entities; there may also be in- telligible entities to which our sensible faculty of intuition has no relation whatsoever; but our concepts of understand- ing, being mere forms of thought for our sensible intuition, could not in the least apply to them. That, therefore, which we entitle 'noumenon' must be understood as being such only in a negative sense. If I remove from empirical knowledge all thought (through categories), no knowledge of any object remains. For through mere intuition nothing at all is thought, and the fact that this affection of sensibility is in me does not [by itself] amount to a relation of such representation to any object. But if, on the other hand, I leave aside all intuition, the form of thought still remains ++ There thus results the concept of a noumenon. It is not of anything, but signifies only the thought of something in general, in which I abstract from everything that belongs to the form of sensible intuition. But in order that a noumenon may signify a true object, distinguishable from all phenomena, it is not enough that I free my thought from all conditions of sensible intuition; I must likewise have ground for assuming another kind of intuition, different from the sensible, in which such an object may be given. For otherwise my thought, while indeed without contradictions, is none the less empty. We have not, indeed, been able to prove that sensible intuition is the only possible intuition, but only that it is so for us. But neither have we been able to prove that another kind of intuition is possible. P 271 -- that is, the mode of determining an object for the manifold of a possible intuition. The categories accord- ingly extend further than sensible intuition, since they think objects in general, without regard to the special mode (the sensibility) in which they may be given. But they do not thereby determine a greater sphere of objects. For we cannot assume that such objects can be given, without presupposing the possibility of another kind of intuition than the sensible; and we are by no means justified in so doing. If the objective reality of a concept cannot be in any way known, while yet the concept contains no contradiction and also at the same time is connected with other modes of knowledge that involve given concepts which it serves to limit, I entitle that concept problematic. The concept of a noumenon -- that is, of a thing which is not to be thought as object of the senses but as a thing in itself, solely through a pure understanding -- is not in any way contradictory. For we cannot assert of sensi- bility that it is the sole possible kind of intuition. P 270a Consequently, although our thought can abstract from all P 271a ++ sensibility, it is still an open question whether the notion of a noumenon be not a mere form of a concept, and whether, when this separation has been made, any object whatsoever is left. The object to which I relate appearance in general is the transcendental object, that is, the completely indeter- minate thought of something in general. This cannot be entitled the noumenon; for I know nothing of what it is in itself, and have no concept of it save as merely the object of a sensible intuition in general, and so as being one and the same for all appearances. I cannot think it through any cate- gory; for a category is valid [only] for empirical intuition, as bringing it under a concept of object in general. A pure use of the category is indeed possible [logically], that is, without con- tradiction; but it has no objective validity, since the category is not then being applied to any intuition so as to impart to it the unity of an object. For the category is a mere function of thought, through which no object is given to me, and by which I merely think that which may be given in intuition. P 272 Further, the concept of a noumenon is necessary, to prevent sensible intuition from being extended to things in themselves, and thus to limit the objective validity of sensible knowledge. The remaining things, to which it does not apply, are entitled noumena, in order to show that this knowledge cannot extend its domain over everything which the understanding thinks. But none the less we are unable to comprehend how such noumena can be possible, and the domain that lies out beyond the sphere of appearances is for us empty. That is to say, we have an understanding which problematically extends further, but we have no intuition, indeed not even the concept of a possible intuition, through which objects outside the field of sensibility can be given, and through which the under- standing can be employed assertorically beyond that field. The concept of a noumenon is thus a merely limiting concept, the function of which is to curb the pretensions of sensibility; and it is therefore only of negative employment. At the same time it is no arbitrary invention; it is bound up with the limitation of sensibility, though it cannot affirm any- thing positive beyond the field of sensibility. The division of objects into phenomena and noumena, and the world into a world of the senses and a world of the under- standing, is therefore quite inadmissible in the positive sense although the distinction of concepts as sensible and intellectual is certainly legitimate. For no object can be determined for the latter concepts, and consequently they cannot be asserted to be objectively valid. If we abandon the senses, how shall we make it conceivable that our categories, which would be the sole re- maining concepts for noumena, should still continue to signify something, since for their relation to any object more must be given than merely the unity of thought -- namely, in addition, a possible intuition, to which they may be applied. None the less, if the concept of a noumenon be taken in a merely prob- lematic sense, it is not only admissible, but as setting limits to sensibility is likewise indispensable. But in that case a nou- menon is not for our understanding a special [kind of] object, namely, an intelligible object; the [sort of] understanding to which it might belong is itself a problem. For we cannot in P 273 the least represent to ourselves the possibility of an under- standing which should know its object, not discursively through categories, but intuitively in a non-sensible intuition. What our understanding acquires through this concept of a noumenon, is a negative extension; that is to say, under- standing is not limited through sensibility; on the contrary, it itself limits sensibility by applying the term noumena to things in themselves (things not regarded as appearances). But in so doing it at the same time sets limits to itself, recog- nising that it cannot know these noumena through any of the categories, and that it must therefore think them only under the title of an unknown something. In the writings of modern philosophers I find the expres- sions mundus sensibilis and intelligibilis used with a mean- ing altogether different from that of the ancients -- a meaning which is easily understood, but which results merely in an empty play upon words. According to this usage, some have thought good to entitle the sum of appearances, in so far as they are intuited, the world of the senses, and in so far as their connection is thought in conformity with laws of understand- ing, the world of the understanding. Observational astronomy, which teaches merely the observation of the starry heavens, would give an account of the former; theoretical astronomy, on the other hand, as taught according to the Copernican system, or according to Newton's laws of gravitation, would give an account of the second, namely, of an intelligible world. But such a twisting of words is a merely sophistical subterfuge; it seeks to avoid a troublesome question by changing its meaning to suit our own convenience. Under- standing and reason are, indeed, employed in dealing with appearances; ++ We must not, in place of the expression mundus intelligibilis, use the expression 'an intellectual world', as is commonly done in German exposition. For only modes of knowledge are either intellectual or sensuous. What can only be an object of the one or the other kind of intuition must be entitled (however harsh- sounding) intelligible or sensible. P 273 but the question to be answered is whether they have also yet another employment, when the object is not a P 274 phenomenon (that is, is a noumenon); and it is in this latter sense that the object is taken, when it is thought as merely intelligible, that is to say, as being given to the understanding alone, and not to the senses. The question, therefore, is whether in addition to the empirical employment of the understanding -- to its employment even in the Newtonian account of the structure of the universe -- there is likewise possible a tran- scendental employment, which has to do with the noumenon as an object. This question we have answered in the negative. When, therefore, we say that the senses represent objects as they appear, and the understanding objects as they are, the latter statement is to be taken, not in the transcendental, but in the merely empirical meaning of the terms, namely as meaning that the objects must be represented as objects of experience, that is, as appearances in thoroughgoing inter- connection with one another, and not as they may be apart from their relation to possible experience (and consequently to any senses), as objects of the pure understanding. Such objects of pure understanding will always remain unknown to us; we can never even know whether such a transcen- dental or exceptional knowledge is possible under any con- ditions -- at least not if it is to be the same kind of know- ledge as that which stands under our ordinary categories. Understanding and sensibility, with us, can determine objects only when they are employed in conjunction. When we separ- ate them, we have intuitions without concepts, or concepts without intuitions -- in both cases, representations which we are not in a position to apply to any determinate object. If, after all these explanations, any one still hesitates to abandon the merely transcendental employment of the cate- gories, let him attempt to obtain from them a synthetic pro- position. An analytic proposition carries the understanding no further; for since it is concerned only with what is already thought in the concept, it leaves undecided whether this con- cept has in itself any relation to objects, or merely signifies the unity of thought in general -- complete abstraction being made from the mode in which an object may be given. The understanding [in its analytic employment] is concerned only to know what lies in the concept; it is indifferent as to the P 275 object to which the concept may apply. The attempt must therefore be made with a synthetic and professedly tran- scendental principle, as, for instance, 'Everything that exists, exists as substance, or as a determination inherent in it', or 'Everything contingent exists as an effect of some other thing, namely, of its cause'. Now whence, I ask, can the understand- ing obtain these synthetic propositions, when the concepts are to be applied, not in their relation to possible experience, but to things in themselves (noumena)? Where is here that third something, which is always required for a synthetic proposi- tion, in order that, by its mediation, the concepts which have no logical (analytic) affinity may be brought into connection with one another? The proposition can never be established, nay, more, even the possibility of any such pure assertion can- not be shown, without appealing to the empirical employment of the understanding, and thereby departing completely from the pure and non-sensible judgment. Thus the concept of pure and merely intelligible objects is completely lacking in all principles that might make possible its application. For we cannot think of any way in which such intelligible objects might be given. The problematic thought which leaves open a place for them serves only, like an empty space, for the limitation of empirical principles, without itself containing or revealing any other object of knowledge beyond the sphere of those principles. P 276 APPENDIX THE AMPHIBOLY OF CONCEPTS OF REFLECTION ARISING FROM THE CONFUSION OF THE EMPIRICAL WITH THE TRANSCENDENTAL EMPLOYMENT OF UNDERSTANDING Reflection (reflexio) does not concern itself with objects them- selves with a view to deriving concepts from them directly, but is that state of mind in which we first set ourselves to discover the subjective conditions under which [alone] we are able to arrive at concepts. It is the consciousness of the re- lation of given representations to our different sources of know- ledge; and only by way of such consciousness can the relation of the sources of knowledge to one another be rightly deter- mined. Prior to all further treatment of our representations, this question must first be asked: In which of our cognitive faculties are our representations connected together? Is it the understanding, or is it the senses, by which they are combined or compared? Many a judgment is accepted owing to custom or is grounded in inclination; but since no reflection precedes it, or at least none follows critically upon it, it is taken as having originated in the understanding. An examination (i.e. the direction of our attention to the grounds of the truth of a judgment) is not indeed required in every case; for if the judgment is immediately certain (for instance, the judgment that between two points there can only be one straight line), there can be no better evidence of its truth than the judgment itself. All judgments, however, and indeed all comparisons, require reflection, i.e. distinction of the cognitive faculty to which the given concepts belong. The act by which I confront P 277 the comparison of representations with the cognitive faculty to which it belongs, and by means of which I distinguish whether it is as belonging to the pure understanding or to sensible intuition that they are to be compared with each other, I call transcendental reflection. Now the relations in which concepts in a state of mind can stand to one another are those of identity and difference, of agreement and opposition, of the inner and the outer, and finally of the determinable and the determination (matter and form). The right determining of the relation depends on the answer to the question, in which faculty of knowledge they belong together subjectively -- in the sensibility or in the understanding. For the difference between the faculties makes a great difference to the mode in which we have to think the relations. Before constructing any objective judgment we compare the concepts to find in them identity (of many representa- tions under one concept) with a view to universal judgments, difference with a view to particular judgments, agreement with a view to affirmative judgments, opposition with a view to negative judgments, etc. For this reason we ought, it seems, to call the above-mentioned concepts, concepts of comparison (conceptus comparationis). If, however, the question is not about the logical form, but about the content of the concepts, i.e. whether things are themselves identical or different, in agreement or in opposition, etc. , then since the things can have a twofold relation to our faculty of knowledge, namely, to sensi- bility and to understanding, it is the place to which they belong in this regard that determines the mode in which they belong to one another. For this reason the interrelations of given re- presentations can be determined only through transcendental reflection, that is, through [consciousness of] their relation to one or other of the two kinds of knowledge. Whether things are identical or different, in agreement or in opposition, etc. , can- not be established at once from the concepts themselves by mere comparison (comparatio), but solely by means of tran- scendental consideration (reflexio), through distinction of the cognitive faculty to which they belong. We may therefore say P 278 that logical reflection is a mere act of comparison; for since we take no account whatsoever of the faculty of knowledge to which the given representations belong, the representations must be treated as being, so far as their place in the mind is concerned, all of the same order. Transcendental reflection, on the other hand, since it bears on the objects themselves, con- tains the ground of the possibility of the objective comparison of representations with each other, and is therefore altogether different from the former type of reflection. Indeed they do not even belong to the same faculty of knowledge. This trans- cendental consideration is a duty from which nobody who wishes to make any a priori judgments about things can claim exemption. We shall now take it in hand, and in so doing shall obtain no little light for the determining of the real business of the understanding. 1. Identity and Difference. -- If an object is presented to us on several occasions but always with the same inner determina- tions (qualitas et quantitas), then if it be taken as object of pure understanding, it is always one and the same, only one thing (numerica identitas), not many. But if it is appearance, we are not concerned to compare concepts; even if there is no difference whatever as regards the concepts, difference of spatial position at one and the same time is still an adequate ground for the numerical difference of the object, that is, of the object of the senses. Thus in the case of two drops of water we can abstract altogether from all internal difference (of quality and quantity), and the mere fact that they have been intuited simultaneously in different spatial positions is suffi- cient justification for holding them to be numerically different. Leibniz took the appearances for things-in-themselves, and so for intelligibilia, i.e. objects of the pure understanding (al- though, on account of the confused character of our represen- tations of them, he still gave them the name of phenomena), and on that assumption his principle of the identity of indis- cernibles (principium identitatis indiscernibilium) certainly could not be disputed. But since they are objects of sensibility, in relation to which the employment of the understanding is not pure but only empirical, plurality and numerical difference are already given us by space itself, the condition of outer P 279 appearances. For one part of space, although completely simi- lar and equal to another part, is still outside the other, and for this very reason is a different part, which when added to it constitutes with it a greater space. The same must be true of all things which exist simultaneously in the different spatial positions, however similar and equal they may otherwise be. 2. Agreement and Opposition. -- If reality is represented only by the pure understanding (realitas noumenon), no oppo- sition can be conceived between the realities, i.e. no relation of such a kind that, when combined in the same subject, they cancel each other's consequences and take a form like 3 - 3 = 0. On the other hand, the real in appearance (realitas phaeno- menon) may certainly allow of opposition. When such realities are combined in the same subject, one may wholly or partially destroy the consequences of another, as in the case of two moving forces in the same straight line, in so far as they either attract or impel a point in opposite directions, or again in the case of a pleasure counterbalancing pain. 3. The Inner and the Outer. -- In an object of the pure understanding that only is inward which has no relation what- soever (so far as its existence is concerned) to anything different from itself. It is quite otherwise with a substantia phaenomenon in space; its inner determinations are nothing but relations, and it itself is entirely made up of mere relations. We are acquainted with substance in space only through forces which are active in this and that space, either bringing other objects to it (at- traction), or preventing them penetrating into it (repulsion and impenetrability). We are not acquainted with any other properties constituting the concept of the substance which appears in space and which we call matter. As object of pure understanding, on the other hand, every substance must have inner determinations and powers which pertain to its inner reality. But what inner accidents can I entertain in thought, save only those which my inner sense presents to me? They must be something which is either itself a thinking or ana- logous to thinking. For this reason Leibniz, regarding sub- stances as noumena, took away from them, by the manner in which he conceived them, whatever might signify outer re- lation, including also, therefore, composition, and so made P 280 them all, even the constituents of matter, simple subjects with powers of representation -- in a word, MONADS. 4. Matter and Form. -- These two concepts underlie all other reflection, so inseparably are they bound up with all employment of the understanding. The one [matter] signifies the determinable in general, the other [form] its determina- tion -- both in the transcendental sense, abstraction being made from all differences in that which is given and from the mode in which it is determined Logicians formerly gave the name 'matter' to the universal, and the name 'form' to the specific difference. In any judgment we can call the given concepts logical matter (i.e. matter for the judgment), and their relation (by means of the copula) the form of the judg- ment. In every being the constituent elements of it (essentialia) are the matter, the mode in which they are combined in one thing the essential form. Also as regards things in general unlimited reality was viewed as the matter of all possibility, and its limitation (negation) as being the form by which one thing is distinguished from others according to transcendental concepts. The understanding, in order that it may be in a posi- tion to determine anything in definite fashion, demands that something be first given, at least in concept. Consequently in the concept of the pure understanding matter is prior to form; and for this reason Leibniz first assumed things (monads), and within them a power of representation, in order after- wards to found on this their outer relation and the community of their states (i.e. of the representations). Space and time -- the former through the relation of substances, the latter through the connection of their determinations among them- selves -- were thus, on this view, possible as grounds and con- sequents. This, in fact, is how it would necessarily be, if the pure understanding could be directed immediately to objects, and if space and time were determinations of things-in-them- selves. But if they are only sensible intuitions, in which we determine all objects merely as appearances, then the form of intuition (as a subjective property of sensibility) is prior to all matter (sensations); space and time come before all appear- ances and before all data of experience, and are indeed what make the latter at all possible. The intellectualist philo- sopher could not endure to think of the form as preceding P 281 the things themselves and determining their possibility -- a perfectly just criticism on the assumption that we intuit things as they really are, although in confused representation. But since sensible intuition is a quite specific subjective condition, which lies a priori at the foundation of all perception, as its original form, it follows that the form is given by itself, and that so far is the matter (or the things themselves which appear) from serving as the foundation (as we should have to judge if we followed mere concepts) that on the contrary its own possibility presupposes a formal intuition (time and space) as antecedently given. NOTE TO THE AMPHIBOLY 0F CONCEPTS OF REFLECTION Let me call the place which we assign to a concept, either in sensibility or in pure understanding, its transcendental location. Thus the decision as to the place which belongs to every concept according to difference in the use to which it is put, and the directions for determining this place for all concepts according to rules, is a transcendental topic. This doctrine, in distinguishing the cognitive faculty to which in each case the concepts properly belong, will provide a sure safeguard against the surreptitious employment of pure under- standing and the delusions which arise therefrom. We may call every concept, every heading, under which many items of knowledge fall, a logical location. On this is based the logical topic of Aristotle, of which teachers and orators could make use in order under given headings of thought to find what would best suit the matter in hand, and then, with some appearance of thoroughness, to argue or be eloquent about it. The transcendental topic, on the other hand, contains no more than the above-mentioned four headings of all com- parison and distinction. They are distinguished from cate- gories by the fact that they do not present the object accord- ing to what constitutes its concept (quantity, reality), but only serve to describe in all its manifoldness the comparison of the representations which is prior to the concept of things. But this comparison requires in the first place a reflection, that is, a determination of the location to which the repre- P 282 sentations of the things that are being compared belong, namely, whether they are thought by the pure understanding or given in appearance by sensibility. Concepts can be compared logically without our troubling to which faculty their objects belong, that is, as to whether their objects are noumena for the understanding, or are phenomena for the sensibility. But if we wish to advance to the objects with these concepts, we must first resort to tran- scendental reflection, in order to determine for which cognitive faculty they are to be objects, whether for pure understanding or for sensibility. In the absence of such reflection, the use of these concepts is very unsafe, giving birth to alleged synthetic principles, which the critical reason cannot recognise, and which are based on nothing better than a transcendental amphiboly, that is, a confounding of an object of pure under- standing with appearance. Having no such transcendental topic, and being therefore deceived by the amphiboly of the concepts of reflection, the celebrated Leibniz erected an intellectual system of the world, or rather believed that he could obtain knowledge of the inner nature of things by comparing all objects merely with the understanding and with the separated, formal concepts of its thought. Our table of concepts of reflection gives us the unexpected advantage of putting before our eyes the distinct- ive features of his system in all its parts, and at the same time the chief ground of this peculiar way of thinking, which indeed rested on nothing but a misunderstanding. He compared all things with each other by means of concepts alone, and natur- ally found no other differences save those through which the understanding distinguishes its pure concepts from one another. The conditions of sensible intuition, which carry with them their own differences, he did not regard as original, sensibility being for him only a confused mode of representa- tion, and not a separate source of representations. Appear- ance was, on his view, the representation of the thing in itself. Such representation is indeed, as he recognised, different in logical form from knowledge through the under- standing, since, owing to its usual lack of analysis, it intro- duces a certain admixture of accompanying representations P 283 into the concept of the thing, an admixture which the under- standing knows how to separate from it. In a word, Leibniz intellectualised appearances, just as Locke, according to his system of noogony (if I may be allowed the use of such ex- pressions), sensualised all concepts of the understanding, i.e. interpreted them as nothing more than empirical or abstracted concepts of reflection. Instead of seeking in understanding and sensibility two sources of representations which, while quite different, can supply objectively valid judgments of things only in conjunction with each other, each of these great men holds to one only of the two, viewing it as in immediate relation to things in themselves. The other faculty is then regarded as serving only to confuse or to order the represen- tations which this selected faculty yields. Leibniz therefore compared the objects of the senses with each other merely in regard to understanding, taking them as things in general. First, he compared them in so far as they are to be judged by understanding to be identical or to be different. And since he had before him only their con- cepts and not their position in intuition (wherein alone the objects can be given), and left entirely out of account the transcendental place of these concepts (whether the object is to be reckoned among appearances or things in themselves), it inevitably followed that he should extend his principle of the identity of indiscernibles, which is valid only of concepts of things in general, to cover also the objects of the senses (mundus phaenomenon), and that he should believe that in so doing he had advanced our knowledge of nature in no small degree. Certainly, if I know a drop of water in all its internal determinations as a thing in itself, and if the whole concept of any one drop is identical with that of every other, I cannot allow that any drop is different from any other. But if the drop is an appearance in space, it has its location not only in understanding (under concepts) but in sensible outer intuition (in space), and the physical locations are there quite indifferent to the inner determinations of the things. A loca- tion b can contain a thing which is completely similar and equal to another in a location a, just as easily as if the things were inwardly ever so different. Difference of locations, with- out any further conditions, makes the plurality and distinction P 284 of objects, as appearances, not only possible but also neces- sary. Consequently, the above so-called law is no law of nature. It is only an analytic rule for the comparison of things through mere concepts. Secondly, the principle that realities (as pure assertions) never logically conflict with each other is an entirely true proposition as regards the relation of concepts, but has not the least meaning in regard either to nature or to anything in itself. For real conflict certainly does take place; there are cases where A - B = 0, that is, where two realities combined in one subject cancel one another's effects. This is brought before our eyes incessantly by all the hindering and counter- acting processes in nature, which, as depending on forces, must be called realitates phaenomena. General mechanics can indeed give the empirical condition of this conflict in an a - priori rule, since it takes account of the opposition in the direction of forces, a condition totally ignored by the tran- scendental concept of reality. Although Herr von Leibniz did not indeed announce the above proposition with all the pomp of a new principle, he yet made use of it for new assertions, and his successors expressly incorporated it into their Leib- nizian - Wolffian system. Thus, according to this principle all evils are merely consequences of the limitations of created beings, that is, negations, since negations alone conflict with reality. (This is indeed the case as regards the mere concept of a thing in general, but not as regards things as appearances. ) Similarly his disciples consider it not only pos- sible, but even natural, to combine all reality in one being, without fear of any conflict. For the only conflict which they recognise is that of contradiction, whereby the concept of a thing is itself removed. They do not admit the conflict of re- ciprocal injury, in which each of two real grounds destroys the effect of the other -- a conflict which we can represent to our- selves only in terms of conditions presented to us in sensibility. Thirdly, Leibniz's monadology has no basis whatsoever save his mode of representing the distinction of inner and outer merely in relation to the understanding. Substances in general must have some internal nature, which is therefore free from all outer relations, and consequently also from com- P 285 position. The simple is therefore the basis of that which is inner in things-in-themselves. But that which is inner in the state of a substance cannot consist in place, shape, contact, or motion (these determinations being all outer relations), and we can therefore assign to substances no inner state save that through which we ourselves inwardly determine our sense, namely, the state of the representations. This, therefore, com- pleted the conception of the monads, which, though they have to serve as the basic material of the whole universe, have no other active power save only that which consists in representa- tions, the efficacy of which is confined, strictly speaking, to themselves. For this very reason his principle of the possible reciprocal community of substances had to be a pre-established harmony, and could not be a physical influence. For since everything is merely inward, i.e. concerned with its own representations, the state of the representations of one substance could not stand in any effective connection whatever with that of another. There had to be some third cause, determining all substances whatsoever, and so making their states correspond to each other, not indeed by an occasional special intervention in each particular case (systema assistentiae), but by the unity of the idea of a cause valid for all substances, and in which they must one and all obtain their existence and permanence, and consequently also their reciprocal correspondence, according to universal laws. Fourthly, Leibniz's famous doctrine of time and space, in which he intellectualised these forms of sensibility, owed its origin entirely to this same fallacy of transcendental reflec- tion. If I attempt, by the mere understanding, to represent to myself outer relations of things, this can only be done by means of a concept of their reciprocal action; and if I seek to connect two states of one and the same thing, this can only be in the order of grounds and consequences. Accordingly, Leibniz conceived space as a certain order in the community of sub- stances, and time as the dynamical sequence of their states. That which space and time seem to possess as proper to them- selves, in independence of things, he ascribed to the confusion in their concepts, which has led us to regard what is a mere P 286 form of dynamical relations as being a special intuition, self- subsistent and antecedent to the things themselves. Thus space and time were for him the intelligible form of the connection of things (substances and their states) in themselves; and the things were intelligible substances (substantiae noumena). And since he allowed sensibility no mode of intuition peculiar to itself but sought for all representation of objects, even the empirical, in the understanding, and left to the senses nothing but the despicable task of confusing and distorting the repre- sentations of the former, he had no option save to treat the [intellectualised] concepts as being likewise valid of appear- ances. But even if we could by pure understanding say anything synthetically in regard to things-in-themselves (which, how- ever, is impossible), it still could not be applied to appear- ances, which do not represent things-in-themselves. In dealing with appearances I shall always be obliged to compare my concepts, in transcendental reflection, solely under the con- ditions of sensibility; and accordingly space and time will not be determinations of things-in-themselves but of appearances. What the things-in-themselves may be I do not know, nor do I need to know, since a thing can never come before me except in appearance. The remaining concepts of reflection have to be dealt with in the same manner. Matter is substantia phaenomenon. That which inwardly belongs to it I seek in all parts of the space which it occupies, and in all effects which it exercises, though admittedly these can only be appearances of outer sense. I have therefore nothing that is absolutely, but only what is comparatively inward and is itself again composed of outer relations. The absolutely inward [nature] of matter, as it would have to be conceived by pure understanding, is nothing but a phantom; for matter is not among the objects of pure understanding, and the transcendental object which may be the ground of this appearance that we call matter is a mere something of which we should not understand what it is, even if someone were in a position to tell us. For we can understand only that which brings with it, in intuition, something corre- sponding to our words. If by the complaints -- that we have no P 287 insight whatsoever into the inner [nature] of things -- it be meant that we cannot conceive by pure understanding what the things which appear to us may be in themselves, they are entirely illegitimate and unreasonable. For what is demanded is that we should be able to know things, and therefore to intuit them, without senses, and therefore that we should have a faculty of knowledge altogether different from the human, and this not only in degree but as regards intuition likewise in kind -- in other words, that we should be not men but beings of whom we are unable to say whether they are even possible, much less how they are constituted. Through ob- servation and analysis of appearances we penetrate to nature's inner recesses, and no one can say how far this knowledge may in time extend. But with all this knowledge, and even if the whole of nature were revealed to us, we should still never be able to answer those transcendental questions which go beyond nature. The reason of this is that it is not given to us to observe our own mind with any other intuition than that of inner sense; and that it is yet precisely in the mind that the secret of the source of our sensibility is located. The rela- tion of sensibility to an object and what the transcendental ground of this [objective] unity may be, are matters undoubtedly so deeply concealed that we, who after all know even ourselves only through inner sense and therefore as appearance, can never be justified in treating sensibility as being a suitable instrument of investigation for discovering anything save always still other appearances -- eager as we yet are to explore their non-sensible cause. What makes this critique of conclusions based merely on acts of reflection so exceedingly useful is that it renders mani- fest the nullity of all conclusions about objects which are compared with each other solely in the understanding, and at the same time confirms our principal contention, namely, that although appearances are not included as things-in-them- selves among the objects of pure understanding, they are yet the only objects in regard to which our knowledge can possess objective reality, that is, in respect of which there is an in- tuition corresponding to the concepts. If we reflect in a merely logical fashion, we are only com- P 288 paring our concepts with each other in the understanding, to find whether both have the same content, whether they are contradictory or not, whether something is contained within the concept or is an addition from outside, which of the two is given and which should serve only as a mode of thinking what is given. But if I apply these concepts to an object in general (in the transcendental sense), without determining whether it be an object of sensible or of intellectual intuition, limitations are at once revealed in the very notion of this object which forbid any non-empirical employment of the concepts, and by this very fact prove that the representation of an object as a thing in general is not only insufficient, but, when taken without sensible determination, and independ- ently of any empirical condition, self-contradictory. The con- clusion is that we must either abstract from any and every object (as in logic), or, if we admit an object, must think it under the conditions of sensible intuition. For the intelligible would require a quite peculiar intuition which we do not possess, and in the absence of this would be for us nothing at all; and, on the other hand, it is also evident that appearances could not be objects in themselves. If I think to myself merely things in general, the difference in their outer relations cannot constitute a difference in the things themselves; on the con- trary, it presupposes this difference. And if there is no inward difference between the concept of the one and the concept of the other, I am only positing one and the same thing in different relations. Further, the addition of one sheer affirmation (reality) to another increases the positive in them; nothing is withdrawn or inhibited; accordingly the real in things cannot be in conflict with itself -- and so on. *** As we have shown, the concepts of reflection, owing to a certain misinterpretation, have exercised so great an influence upon the employment of the understanding that they have misled even one of the most acute of all philosophers into a supposititious system of intellectual knowledge, which under- P 289 takes to determine its objects without any assistance from the senses. For this reason the exposition of the cause of what is deceptive -- occasioning these false principles -- in the amphi- boly of these concepts, is of great utility as a reliable method of determining and securing the limits of the understanding. It is indeed true that whatever universally agrees with or contradicts a concept also agrees with or contradicts every particular which is contained under it (dictum de omni et nullo); but it would be absurd to alter this logical principle so as to read: -- what is not contained in a universal concept is also not included in the particular concepts which stand under it. For these are particular concepts just because they include in themselves more than is thought in the universal. Nevertheless it is upon this latter principle that the whole intellectual sys- tem of Leibniz is based; and with this principle it therefore falls, together with all the ambiguities (in the employment of the understanding) that have thence arisen. The principle of the identity of indiscernibles is really based on the presupposition, that if a certain distinction is not found in the concept of a thing in general, it is also not to be found in the things themselves, and consequently that all things which are not distinguishable from one another in their con- cepts (in quality or quantity) are completely identical (numero eadem). Because in the mere concept of a thing in general we abstract from the many necessary conditions of its intuition, the conditions from which we have abstracted are, with strange presumption, treated as not being there at all, and nothing is allowed to the thing beyond what is contained in its concept. The concept of a cubic foot of space, wherever and how- ever often I think it, is in itself throughout one and the same. But two cubic feet are nevertheless distinguished in space by the mere difference of their locations (numero diversa); these locations are conditions of the intuition wherein the object of this concept is given; they do not, however, belong to the con- cept but entirely to sensibility. Similarly there is no conflict in the concept of a thing unless a negative statement is com- bined with an affirmative; merely affirmative concepts cannot, when combined, produce any cancellation. But in the sensible P 290 intuition, wherein reality (e.g. motion) is given, there are conditions (opposite directions), which have been omitted in the concept of motion in general, that make possible a conflict (though not indeed a logical one), namely, as producing from what is entirely positive a zero (=0). We are not, therefore, in a position to say that since conflict is not to be met with in the concepts of reality, all reality is in agreement with itself. According to mere concepts the inner is the substratum of all relational or outer determinations. If, therefore, I abstract from all conditions of intuition and confine myself to the con- cept of a thing in general, I can abstract from all outer rela- tion, and there must still be left a concept of something which signifies no relation, but inner determinations only. From this it seems to follow that in whatever is a thing (substance) there is something which is absolutely inward and precedes all outer determinations, inasmuch as it is what first makes them possible; and consequently, that this substratum, as no longer containing in itself any outer relations, is simple. (Corporeal things are never anything save relations only, at least of their parts external to each other. ) And since we know of no determinations which are absolutely inner except those [given] through our inner sense, this substratum is not only simple; it is likewise (in analogy with our inner sense) determined through representations; in other words, all things are really monads, simple beings endowed with representations. These contentions would be entirely justified, if beyond the con- cept of a thing in general there were no further conditions under which alone objects of outer intuition can be given us -- those from which the pure concept has [as a matter of fact] made abstraction. ++ If we here wished to resort to the usual subterfuge, maintaining as regards realitates noumena that they at least do not act in opposi- tion to each other, it would be incumbent on us to produce an ex- ample of such pure and non-sensuous reality, that it may be dis- cerned whether such a concept represents something or nothing. But no example can be obtained otherwise than from experience, which never yields more than phenomena. This proposition has therefore no further meaning than that a concept which only in- cludes affirmation includes no negation -- a proposition which we have never doubted. P 291 For under these further conditions, as we find, an abiding appearance in space (impenetrable extension) can contain only relations and nothing at all that is absolutely inward, and yet be the primary substratum of all outer per- ception. Through mere concepts I cannot, indeed, think what is outer without thinking something that is inner; and this for the sufficient reason that concepts of relation presuppose things which are absolutely [i.e. independently] given, and without these are impossible. But something is contained in intuition which is not to be met with in the mere concept of a thing; and this yields the substratum, which could never be known through mere concepts, namely, a space which with all that it contains consists solely of relations, formal or, it may be, also real. Because, without an absolutely inner element, a thing can never be represented by mere concepts, I may not therefore claim that there is not also in the things themselves which are subsumed under these concepts, and in their intuition, some- thing external that has no basis in anything wholly inward. Once we have abstracted from all conditions of intuition, there is, I admit, nothing left in the mere concept but the inner in general and its interrelations, through which alone the ex- ternal is possible. But this necessity, which is founded solely on abstraction, does not arise in the case of things as given in intuition with determinations that express mere relations, with- out having anything inward as their basis; for such are not things in themselves but merely appearances. All that we know in matter is merely relations (what we call the inner determinations of it are inward only in a comparative sense), but among these relations some are self-subsistent and per- manent, and through these we are given a determinate object. The fact that, if I abstract from these relations, there is no- thing more left for me to think does not rule out the concept of a thing as appearance, nor indeed the concept of an object in abstracto. What it does remove is all possibility of an object determinable through mere concepts, that is, of a noumenon. It is certainly startling to hear that a thing is to be taken as consisting wholly of relations. Such a thing is, however, mere appearance, and cannot be thought through pure categories; P 292 what it itself consists in is the mere relation of something in general to the senses. Similarly, if we begin with mere con- cepts, we cannot think the relations of things in abstracto in any other manner than by regarding one thing as the cause of determinations in another, for that is how our understanding conceives of relations. But since we are in that case disregard- ing all intuition, we have ruled ourselves out from any kind of recognition of the special mode in which the different elements of the manifold determine each other's positions, that is, of the form of sensibility (space), which yet is presupposed in all empirical causality. If by merely intelligible objects we mean those things which are thought through pure categories, without any schema of sensibility, such objects are impossible. For the condition of the objective employment of all our concepts of understanding is merely the mode of our sensible intuition, by which objects are given us; if we abstract from these objects, the con- cepts have no relation to any object. Even if we were willing to assume a kind of intuition other than this our sensible kind, the functions of our thought would still be without meaning in respect to it. If, however, we have in mind only objects of a non-sensible intuition, in respect of which our categories are admittedly not valid, and of which therefore we can never have any knowledge whatsoever (neither in- tuition nor concept), noumena in this purely negative sense must indeed be admitted. For this is no more than saying that our kind of intuition does not extend to all things, but only to objects of our senses, that consequently its objective validity is limited, and that a place therefore remains open for some other kind of intuition, and so for things as its objects. But in that case the concept of a noumenon is problem- atic, that is, it is the representation of a thing of which we can neither say that it is possible nor that it is impossible; for we are acquainted with no kind of intuition but our own sensible kind and no kind of concepts but the categories, and neither of these is appropriate to a non-sensible object. We cannot, therefore, positively extend the sphere of the objects of our thought beyond the conditions of our sensibility, and assume besides appearances objects of pure thought, that is, P 293 noumena, since such objects have no assignable positive meaning. For in regard to the categories we must admit that they are not of themselves adequate to the knowledge of things in themselves, and that without the data of sensibility they would be merely subjective forms of the unity of under- standing, having no object. Thought is in itself, indeed, no product of the senses, and in so far is also not limited by them; but it does not therefore at once follow that it has a pure employment of its own, unaided by sensibility, since it is then without an object. We cannot call the noumenon such an object; signifying, as it does, the problematic concept of an object for a quite different intuition and a quite different understanding from ours, it is itself a problem. The concept of the noumenon is, therefore, not the concept of an object, but is a problem unavoidably bound up with the limitation of our sensibility -- the problem, namely, as to whether there may not be objects entirely disengaged from any such kind of intuition. This is a question which can only be answered in an indeterminate manner, by saying that as sensible in- tuition does not extend to all things without distinction, a place remains open for other and different objects; and con- sequently that these latter must not be absolutely denied, though -- since we are without a determinate concept of them (inasmuch as no category can serve that purpose) -- neither can they be asserted as objects for our understanding. Understanding accordingly limits sensibility, but does not thereby extend its own sphere. In the process of warning the latter that it must not presume to claim applicability to things-in-themselves but only to appearances, it does indeed think for itself an object in itself, but only as transcendental object, which is the cause of appearance and therefore not itself appearance, and which can be thought neither as quan- tity nor as reality nor as substance etc. (because these concepts always require sensible forms in which they determine an object). We are completely ignorant whether it is to be met with in us or outside us, whether it would be at once removed with the cessation of sensibility, or whether in the absence of sensibility it would still remain. If we are pleased to name this object noumenon for the reason that its representation is not sensible, we are free to do so. But since we can apply P 294 to it none of the concepts of our understanding, the repre- sentation remains for us empty, and is of no service except to mark the limits of our sensible knowledge and to leave open a space which we can fill neither through possible ex- perience nor through pure understanding. The critique of this pure understanding, accordingly, does not permit us to create a new field of objects beyond those which may be presented to it as appearances, and so to stray into intelligible worlds; nay, it does not allow of our entertain- ing even the concept of them. The error, which quite obvi- ously is the cause of this mistaken venture, and which indeed excuses though it does not justify it, lies in employing the understanding, contrary to its vocation, transcendentally, and in making objects, that is, possible intuitions, conform to con- cepts, not concepts to possible intuitions, on which alone their objective validity rests. This error, in turn, is due to the fact that apperception, and with it thought, precedes all possible determinate ordering of representations. Consequently what we do is to think something in general; and while on the one hand we determine it in sensible fashion, on the other hand we distinguish from this mode of intuiting it the universal object represented in abstracto. What we are then left with is a mode of determining the object by thought alone -- a merely logical form without content, but which yet seems to us to be a mode in which the object exists in itself (noumenon) without regard to intuition, which is limited to our senses. Before we leave the Transcendental Analytic we must add some remarks which, although in themselves not of special importance, might nevertheless be regarded as re- quisite for the completeness of the system. The supreme concept with which it is customary to begin a transcendental philosophy is the division into the possible and the impossible. But since all division presupposes a concept to be divided, a still higher one is required, and this is the concept of an object in general, taken problematically, without its having been decided whether it is something or nothing. As the categories are the only concepts which refer to objects in general, the P 295 distinguishing of an object, whether it is something or nothing, will proceed according to the order and under the guidance of the categories. I. To the concepts of all, many, and one there is opposed the concept which cancels everything, that is, none. Thus the object of a concept to which no assignable intuition whatso- ever corresponds is = nothing. That is, it is a concept without an object (ens rationis), like noumena, which cannot be reckoned among the possibilities, although they must not for that reason be declared to be also impossible; or like certain new fundamental forces, which though entertained in thought without self-contradiction are yet also in our thinking un- supported by any example from experience, and are therefore not to be counted as possible. 2. Reality is something; negation is nothing, namely, a concept of the absence of an object, such as shadow, cold (nihil privativum). 3. The mere form of intuition, without substance, is in itself no object, but the merely formal condition of an object (as appearance), as pure space and pure time (ens imagina- rium). These are indeed something, as forms of intuition, but are not themselves objects which are intuited. 4. The object of a concept which contradicts itself is nothing, because the concept is nothing, is the impossible, e.g. a two-sided rectilinear figure (nihil negativum). The table of this division of the concept of nothing would therefore have to be drawn up as follows. (The corresponding division of something follows directly from it): Nothing, as I Empty concept without object, ens rationis. 2 Empty object of a concept, nihil privativum. P 295 3 Empty intuition without object, ens imaginarium. 4 Empty object without concept, nihil negativum. P 296 We see that the ens rationis (1) is distinguished from the nihil negativum (4), in that the former is not to be counted among possibilities because it is mere fiction (although not self-contradictory), whereas the latter is opposed to possi- bility in that the concept cancels itself. Both, however, are empty concepts. On the other hand, the nihil privativum (2) and the ens imaginarium (3) are empty data for concepts. If light were not given to the senses we could not represent dark- ness, and if extended beings were not perceived we could not represent space. Negation and the mere form of intuition, in the absence of a something real, are not objects.