Critique of Pure Reason

by Immanuel Kant

  The schema of cause and of the causality of a thing in general is the real which, when once supposed to exist, is always followed by something else. It consists therefore in the succession of the manifold, in so far as that succession is subject to a rule.

  The schema of community (reciprocal action) or of the reciprocal causality of substances, in respect to their accidents, is the coexistence, according to a general rule, of the determinations of the one 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, as, for instance, when opposites cannot exist at the same time in the same thing, but only one after the other. It is therefore the determination of the representation of a thing at any time whatsoever.

  The schema of reality is existence at a given time.

  The schema of necessity is the existence of an object at all times.

  It is clear, therefore, if we examine all the categories, that the schema of quantity contains and represents the production (synthesis) of time itself in the successive apprehension of an object; the schema of quality, the synthesis of sensation (perception) with the representation of time or the filling-up of time; the schema of relation, the relation of perceptions to each other at all times (that is, according to a rule which determines time); lastly, the schema of modality and its categories, time itself as the correlative of the determination of an object as to whether and how it belongs to time. The schemata therefore are nothing but determinations of time a priori according to rules, and these, as applied to all possible objects, refer in the order of the categories to the series of time, the contents of time, the order of time, and lastly, the comprehension of time.

  We have thus seen that the schematism of the understanding, by means of a transcendental synthesis of imagination, amounts to nothing else but to the unity of the manifold in the intuition of the internal sense, and therefore indirectly to the unity of apperception, as an active function corresponding to the internal sense (as receptive). These schemata therefore of the pure concepts of the understanding are the true and only conditions by which these concepts can gain a relation to objects, that is, a significance, and the categories are thus in the end of no other but a possible empirical use, serving only, on account of an a priori necessary unity (the necessary connection of all consciousness in one original apperception) to subject all phenomena to general rules of synthesis, and thus to render them capable of a general connection in experience.

  All our knowledge is contained within this whole of possible experience, and transcendental truth, which precedes all empirical truth and renders it possible, consists in general relation of it to that experience.

  But although the schemata of sensibility serve thus to realise the categories, it must strike everybody that they at the same time restrict them, that is, limit them by conditions foreign to the understanding and belonging to sensibility. Hence the schema is really the phenomenon, or the sensuous concept of an object in agreement with the category numerus est quantitas phaenomenon, sensatio realitas phenomenon, constans et perdurabile rerum substantia phenomenon—aeternitas necessitas phaenomenon, etc.). If we omit a restrictive condition, it would seem that we amplify a formerly limited concept, and that therefore the categories in their pure meaning, free from all conditions of sensibility, should be valid of things in general, as they are, while their schemata represent them only as they appear, so that these categories might claim a far more extended power, independent of all schemata. And in truth we must allow to these pure concepts of the understanding, apart from all sensuous conditions, a certain significance, though a logical one only, with regard to the mere unity of representations produced by them, although these representations have no object and therefore no meaning that could give us a concept of an object. Thus substance, if we leave out the sensuous condition of permanence, would mean nothing but a something that may be conceived as a subject, without being the predicate of anything else. Of such a representation we can make nothing, because it does not teach us how that thing is determined which is thus to be considered as the first subject. Categories, therefore, without schemata are functions only of the understanding necessary for concepts, but do not themselves represent any object. This character is given to them by sensibility only, which realises the understanding by, at the same time, restricting it.

  1Read dem letzteren, as corrected by Rosenkranz, for der letzteren.

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  The Transcendental Doctine of the Faculty of Judgment or Analytic of Principles

  Chapter II

  System of all Principles of the Pure Understanding

  WE have in the preceding chapter considered the transcendental faculty of judgment with reference to those general conditions only under which it is justified in using the pure concepts of the understanding for synthetical judgments. It now becomes our duty to represent systematically those judgments which, under that critical provision, the understanding, can really produce a priori. For this purpose our table of categories will be without doubt our natural and best guide. For it is the relation of the categories to all possible experience which must constitute all pure a priori knowledge of the understanding; and their relation to sensibility in general will therefore exhibit completely and systematically all the transcendental principles of the use of the understanding.1

  Principles a priori are so called, not only because they contain the grounds for other judgments, but also because they themselves are not founded on higher and more general kinds of knowledge. This peculiarity, however, does not enable them to dispense with every kind of proof; for although this could not be given objectively, as all knowledge of any object really rests on it, this does not prevent us from attempting to produce a proof drawn from the subjective sources of the possibility of a knowledge of the object in general; nay, it may be necessary to do so, because, without it, our assertion might be suspected of being purely gratuitous.

  We shall treat, however, of those principles only which relate to the categories. We shall have nothing to do with the principles of transcendental æsthetic, according to which space and time are the conditions of the possibility of all things as phenomena, nor with the limitation of those principles, prohibiting their application to things by themselves. Mathematical principles also do not belong to this part of our discussion, because they are derived from intuition, and not from the pure concept of the understanding. As they are, however, synthetical judgments a priori, their possibility will have to be discussed, not in order to prove their correctness and apodictic certainty, which would be unnecessary, but in order to make the possibility of such self-evident knowledge a priori conceivable and intelligible.

  We shall also have to speak of the principle of analytical as opposed to synthetical judgments, the latter being the proper subject of our enquiries, because this very opposition frees the theory of the latter from all misunderstandings, and places them clearly before us in their own peculiar character.

  System of the Principles of the Pure Understanding

  Section I

  Of the Highest Principle of all Analytical Judgments

  Whatever the object of our knowledge may be, and whatever the relation between our knowledge and its object, it must always submit to that general, though only negative condition of all our judgments, that they do not contradict themselves; otherwise these judgments, without any reference to their object, are in themselves nothing. But although there may be no contradiction in our judgment, it may nevertheless connect concepts in a manner not warranted by the object, or without there being any ground, whether a priori or a posteriori, to confirm such a judgment. A judgment may therefore be false or groundless, though in itself it is free from all contradiction.

  The proposition that no subject can have a predicate which contradicts it, is called the principle of contradiction. It is a general though only negative criterion of all truth, and belongs to logic only, becau
se it applies to knowledge as knowledge only, without reference to its object, and simply declares that such contradiction would entirely destroy and annihilate it.

  Nevertheless, a positive use also may be made of that principle, not only in order to banish falsehood and error, so far as they arise from contradiction, but also in order to discover truth. For in an analytical judgment, whether negative or affirmative, its truth can always be sufficiently tested by the principle of contradiction, because the opposite of that which exists and is thought as a concept in our knowledge of an object, is always rightly negatived, while the concept itself is necessarily affirmed of it, for the simple reason that its opposite would be in contradiction with the object.

  It must therefore be admitted that the principle of contradiction is the general and altogether sufficient principle of all analytical knowledge, though beyond this its authority and utility, as a sufficient criterion of truth, must not be allowed to extend. For the fact that no knowledge can run counter to that principle, without destroying itself, makes it no doubt a conditio sine qua non, but never the determining reason of the truth of our knowledge. Now, as in our present enquiry we are chiefly concerned with the synthetical part of our knowledge, we must no doubt take great care never to offend against that inviolable principle, but we ought never to expect from it any help with regard to the truth of this kind of knowledge.

  There is, however, a formula of this famous principle—a principle merely formal and void of all contents—which contains a synthesis that has been mixed up with it from mere carelessness and without any real necessity. This formula is: It is impossible that anything should be and at the same time not be. Here, first of all, the apodictic certainty expressed by the word impossible is added unnecessarily, because it is understood by itself from the nature of the proposition; secondly, the proposition is affected by the condition of time, and says, as it were, something = A, which is something = B, cannot be at the same time not-B, but it can very well be both (B and not-B) in succession. For instance, a man who is young cannot be at the same time old, but the same man may very well be young at one time and not young, that is, old, at another. The principle of contradiction, however, as a purely logical principle, must not be limited in its application by time; and the before-mentioned formula runs therefore counter to its very nature. The misunderstanding arises from our first separating one predicate of an object from its concept, and by our afterwards joining its opposite with that predicate, which gives us a contradiction, not with the subject, but with its predicate only which was synthetically connected with it, and this again only on condition that the first and second predicate have both been applied at the same time. If I want to say that a man who is unlearned is not learned, I must add the condition 'at the same time,' for a man who is unlearned at one time may very well be learned at another. But if I say no unlearned man is learned, then the proposition is analytical, because the characteristic (unlearnedness) forms part now of the concept of the subject, so that the negative proposition becomes evident directly from the principle of contradiction, and without the necessity of adding the condition, 'at the same time.' This is the reason why I have so altered the wording of that formula that it displays at once the nature of an analytical proposition.

  System of the Principles of the Pure Understanding

  Section II

  Of the Highest Principle of all Synthetical Judgments

  The explanation of the possibility of synthetical judgments is a subject of which general logic knows nothing, not even its name, while in a transcendental logic it is the most important task of all, nay, even the only one, when we have to consider the possibility of synthetical judgments a priori, their conditions, and the extent of their validity. For when that task is accomplished, the object of transcendental logic, namely, to determine the extent and limits of the pure understanding, will have been fully attained.

  In forming an analytical judgment I remain within a given concept, while predicating something of it. If what I predicate is affirmative, I only predicate of that concept what is already contained in it; if it is negative, I only exclude from it the opposite of it. In forming synthetical judgments, on the contrary, I have to go beyond a given concept, in order to bring something together with it, which is totally different from what is contained in it. Here we have neither the relation of identity nor of contradiction, and nothing in the judgment itself by which we can discover its truth or its falsehood.

  Granted, therefore, that we must go beyond a given concept in order to compare it synthetically with another, something else is necessary in which, as in a third, the synthesis of two concepts becomes possible. What then, is that third? What is the medium of all synthetical judgments? It can only be that in which all our concepts are contained, namely, the internal sense and its a priori form, time. The synthesis of representations depends on imagination, but their synthetical unity, which is necessary for forming a judgment, depends on the unity of apperception. It is here therefore that the possibility of synthetical judgments, and (as all the three contain the sources of representations a priori) the possibility of pure synthetical judgments also, will have to be discovered; nay, they will on these grounds be necessary, if any knowledge of objects is to be obtained that rests entirely on a synthesis of representations.

  If knowledge is to have any objective reality, that is to say, if it is to refer to an object, and receive by means of it any sense and meaning, the object must necessarily be given in some way or other. Without that all concepts are empty. We have thought in them, but we have not, by thus thinking, arrived at any knowledge. We have only played with representations. To give an object, if this is not meant again as mediate only, but if it means to represent something immediately in intuition, is nothing else but to refer the representation of the object to experience (real or possible). Even space and time, however pure these concepts may be of all that is empirical, and however certain it is that they are represented in the mind entirely a priori, would lack nevertheless all objective validity, all sense and meaning, if we could not show the necessity of their use with reference to all objects of experience. Nay, their representation is is a pure schema, always referring to that reproductive imagination which calls up the objects of experience, without which objects would be meaningless. The same applies to all concepts without any distinction.

  It is therefore the possibility of experience which alone gives objective reality to all our knowledge a priori. Experience, however, depends on the synthetical unity of phenomena, that is, on a synthesis according to concepts of the object of phenomena in general. Without it, it would not even be knowledge, but only a rhapsody of perceptions, which would never grow into a connected text according to the rules of an altogether coherent (possible) consciousness, nor into a transcendental and necessary unity of apperception. Experience depends therefore on a priori principles of its form, that is, on general rules of unity in the synthesis of phenomena, and the objective reality of these (rules) can always be shown by their being the necessary conditions in all experience; nay, even in the possibility of all experience. Without such a relation synthetical propositions a priori would be quite impossible, because they have no third medium, that is, no object in which the synthetical unity of their concepts could prove their objective reality.

  Although we know therefore a great deal a priori in synthetical judgments with reference to space in general, or to the figures which productive imagination traces in it, without requiring for it any experience, this our knowledge would nevertheless be nothing but a playing with the cobwebs of our brain, if space were not to be considered as the condition of phenomena which supply the material for external experience. Those pure synthetical judgments therefore refer always, though mediately only, to possible experience, or rather to the possibility of experience, on which alone the objective validity of their synthesis is founded.

  As therefore experience, being an empirical synthesis, is in its possibility the only kind of kn
owledge that imparts reality to every other synthesis, this other synthesis, as knowledge a priori, possesses truth (agreement with its object) on this condition only, that it contains nothing beyond what is necessary for the synthetical unity of experience in general.

  The highest principle of all synthetical judgments is therefore this, that every object is subject to the necessary conditions of a synthetical unity of the manifold of intuition in a possible experience.

  Thus synthetical judgments a priori are possible, if we refer the formal conditions of intuition a priori, the synthesis of imagination, and the necessary unity of it in a transcendental apperception, to a possible knowledge in general, given in experience, and if we say that the conditions of the possibility of experience in general are at the same time conditions of the possibility of the objects of experience themselves, and thus possess objective validity in a synthetical judgment a priori.

  System of the Principles the Pure Understanding

  Section III

  Systematical Representation of all Synthetical Principles of the Understanding

  That there should be principles at all is entirely due to the pure understanding, which is not only the faculty of rules in regard to all that happens, but itself the source of principles, according to which everything (that can become an object to us) is necessarily subject to rules, because, without such, phenomena would never become objects corresponding to knowledge. Even laws of nature, if they are considered as principles of the empirical use of the understanding, carry with them a character of necessity, and thus lead to the supposition that they rest on grounds which are valid a priori and before all experience. Nay, all laws of nature without distinction are subject to higher principles of the understanding, which they apply to particular cases of experience. They alone therefore supply the concept which contains the condition, and, as it were, the exponent of a rule in general, while experience furnishes each case to which the general rule applies.