Front Page Titles (by Subject) IV: Preliminary Explanation of the Possibility of the Categories as Knowledge a priori - Critique of Pure Reason
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IV: Preliminary Explanation of the Possibility of the Categories as Knowledge a priori - Friedrich Max Müller, Critique of Pure Reason 
Immanuel Kant’s Critique of Pure Reason. In Commemoration of the Centenary of its First Publication. Translated into English by F. Max Mueller (2nd revised ed.) (New York: Macmillan, 1922).
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Preliminary Explanation of the Possibility of the Categories as Knowledge a priori
There is but one experience in which all perceptions are represented as in permanent and regular connection, as there is but one space and one time in which all forms of phenomena and all relations of being or not being take place. If we speak of different experiences, we only mean different perceptions so far as they belong to one and the same general experience. It is the permanent and synthetical unity of perceptions that constitutes the form of experience, and experience is nothing but the synthetical unity of phenomena according to concepts.
Unity of synthesis, according to empirical concepts, would be purely accidental, nay, unless these [p. 111] were founded on a transcendental ground of unity, a whole crowd of phenomena might rush into our soul, without ever forming real experience. All relation between our knowledge and its objects would be lost at the same time, because that knowledge would no longer be held together by general and necessary laws; it would therefore become thoughtless intuition, never knowledge, and would be to us the same as nothing.
The conditions a priori of any possible experience in general are at the same time conditions of the possibility of any objects of our experience. Now I maintain that the categories of which we are speaking are nothing but the conditions of thought which make experience possible, as much as space and time contain the conditions of that intuition which forms experience. These categories therefore are also fundamental concepts by which we think objects in general for the phenomena, and have therefore a priori objective validity. This is exactly what we wish to prove.
The possibility, nay the necessity of these categories rests on the relation between our whole sensibility, and therefore all possible phenomena, and that original apperception in which everything must be necessarily subject to the conditions of the permanent unity of self-consciousness, that is, must submit to the general functions [p. 112] of that synthesis which we call synthesis according to concepts, by which alone our apperception can prove its permanent and necessary identity a priori. Thus the concept of cause is nothing but a synthesis of that which follows in temporal succession, with other phenomena, but a synthesis according to concepts: and without such a unity which rests on a rule a priori, and subjects all phenomena to itself, no permanent and general, and therefore necessary unity of consciousness would be formed in the manifold of our perceptions. Such perceptions would then belong to no experience at all, they would be without an object, a blind play of representations, — less even than a dream.
All attempts therefore at deriving those pure concepts of the understanding from experience, and ascribing to them a purely empirical origin, are perfectly vain and useless. I shall not dwell here on the fact that a concept of cause, for instance, contains an element of necessity, which no experience can ever supply, because experience, though it teaches us that after one phenomenon something else follows habitually, can never teach us that it follows necessarily, nor that we could a priori, and without any limitation, derive from it, as a condition, any conclusion as to what must follow. And thus I ask with reference to that empirical rule of association, which must always be admitted if we say that everything in the succession of events is so entirely subject to rules that nothing [p. 113] ever happens without something preceding it on which it always follows, — What does it rest on, if it is a law of nature, nay, how is that very association possible? You call the ground for the possibility of the association of the manifold, so far as it is contained in the objects themselves, the affinity of the manifold. I ask, therefore, how do you make that permanent affinity by which phenomena stand, nay, must stand, under permanent laws, conceivable to yourselves?
According to my principles it is easily conceivable. All possible phenomena belong, as representations, to the whole of our possible self-consciousness. From this, as a transcendental representation, numerical identity is inseparable and a priori certain, because nothing can become knowledge except by means of that original apperception. As this identity must necessarily enter into the synthesis of the whole of the manifold of phenomena, if that synthesis is to become empirical knowledge, it follows that the phenomena are subject to conditions a priori to which their synthesis (in apprehension) must always conform. The representation of a general condition according to which something manifold can be arranged (with uniformity) is called a rule, if it must be so arranged, a law. All phenomena therefore stand in a permanent connection according to necessary laws, and thus possess [p. 114] that transcendental affinity of which the empirical is a mere consequence.
It sounds no doubt very strange and absurd that nature should have to conform to our subjective ground of apperception, nay, be dependent on it, with respect to her laws. But if we consider that what we call nature is nothing but a whole of phenomena, not a thing by itself, but a number of representations in our soul, we shall no longer be surprised that we only see her through the fundamental faculty of all our knowledge, namely, the transcendental apperception, and in that unity without which it could not be called the object (or the whole) of all possible experience, that is, nature. We shall thus also understand why we can recognise this unity a priori, and therefore as necessary, which would be perfectly impossible if it were given by itself and independent of the first sources of our own thinking. In that case I could not tell whence we should take the synthetical propositions of such general unity of nature. They would have to be taken from the objects of nature themselves, and as this could be done empirically only, we could derive from it none but an accidental unity, which is very different from that necessary connection which we mean when speaking of nature.
Of the Relation of the Understanding to Objects in General, and the Possibility of Knowing Them a priori [p. 115]
What in the preceding section we have discussed singly and separately we shall now try to treat in connection with each other and as a whole. We saw that there are three subjective sources of knowledge on which the possibility of all experience and of the knowledge of its objects depends, namely, sense, imagination, and apperception. Each of them may be considered as empirical in its application to given phenomena; all, however, are also elements or grounds a priori which render their empirical application possible. Sense represents phenomena empirically in perception, imagination in association (and reproduction), apperception in the empirical consciousness of the identity of these reproductive representations with the phenomena by which they were given; therefore in recognition.
The whole of our perception rests a priori on pure intuition (if the perception is regarded as representation, then on time, as the form of our internal intuition), the association of it (the whole) on the pure syn- [p. 116] thesis of imagination, and our empirical consciousness of it on pure apperception, that is, on the permanent identity of oneself in the midst of all possible representations.
If we wish to follow up the internal ground of this connection of representations to that point towards which they must all converge, and where they receive for the first time that unity of knowledge which is requisite for every possible experience, we must begin with pure apperception. Intuitions are nothing to us, and do not concern us in the least, if they cannot be received into our consciousness, into which they may enter either directly or indirectly. Knowledge is impossible in any other way. We are conscious a priori of our own permanent identity with regard to all representations that can ever belong to our knowledge, as forming a necessary condition of the possibility of all representations (because these could not represent anything in me, unless they belonged with everything else to one consciousness and could at least be connected within it). This principle stands firm a priori, and may be called the transcendental principle of the unity of all the manifold of our representations (therefore also of intuition). This unity of the manifold in one subject is synthetical; the pure apperception therefore supplies us with a principle of the synthetical unity of [p. 117] the manifold in all possible intuitions.1
This synthetical unity, however, presupposes [p. 118] or involves a synthesis, and if that unity is necessary a priori, the synthesis also must be a priori. The transcendental unity of apperception therefore refers to the pure synthesis of imagination as a condition a priori of the possibility of the manifold being united in one knowledge. Now there can take place a priori the productive synthesis of imagination only, because the reproductive rests on conditions of experience. The principle therefore of the necessary unity of the pure (productive) synthesis of imagination, before all apperception, constitutes the ground of the possibility of all knowledge, nay, of all experience.
The synthesis of the manifold in imagination is called transcendental, if, without reference to the difference of intuitions, it affects only the a priori conjunction of the manifold; and the unity of that synthesis is called transcendental if, with reference to the original unity of apperception, it is represented as a priori necessary. As the possibility of all knowledge depends on the unity of that apperception, it follows that the transcendental unity of the synthesis of imagination is the pure form of all possible knowledge through which therefore all objects of possible experience must be represented a priori.
This unity of apperception with reference to [p. 119] the synthesis of imagination is the understanding, and the same unity with reference to the transcendental synthesis of the imagination, the pure understanding. It must be admitted therefore that there exist in the understanding pure forms of knowledge a priori, which contain the necessary unity of the pure synthesis of the imagination in reference to all possible phenomena. These are the categories, that is, the pure concepts of the understanding. The empirical faculty of knowledge of man contains therefore by necessity an understanding which refers to all objects of the senses, though by intuition only, and by its synthesis through imagination, and all phenomena, as data of a possible experience, must conform to that understanding. As this relation of phenomena to a possible experience is likewise necessary, (because, without it, we should receive no knowledge through them, and they would not in the least concern us), it follows that the pure understanding constitutes by the means of the categories a formal and synthetical principle of all experience, and that phenomena have thus a necessary relation to the understanding.
We shall now try to place the necessary connection of the understanding with the phenomena by means of the categories more clearly before the reader, by beginning with the beginning, namely, with the empirical.
The first that is given us is the phenomenon, [p. 120] which, if connected with consciousness, is called perception. (Without its relation to an at least possible consciousness, the phenomenon could never become to us an object of knowledge. It would therefore be nothing to us; and because it has no objective reality in itself, but exists only in being known, it would be nothing altogether.) As every phenomenon contains a manifold, and different perceptions are found in the mind singly and scattered, a connection of them is necessary, such as they cannot have in the senses by themselves. There exists therefore in us an active power for the synthesis of the manifold which we call imagination, and the function of which, as applied to perceptions, I call apprehension.1 This imagination is meant to change the manifold of intuition into an image, it must therefore first receive the impressions into its activity, which I call to apprehend.
It must be clear, however, that even this apprehension [p. 121] of the manifold could not alone produce a coherence of impressions or an image, without some subjective power of calling one perception from which the mind has gone over to another back to that which follows, and thus forming whole series of perceptions. This is the reproductive faculty of imagination which is and can be empirical only.
If representations, as they happen to meet with one another, could reproduce each other at haphazard, they would have no definite coherence, but would form irregular agglomerations only, and never produce knowledge. It is necessary therefore that their reproduction should be subject to a rule by which one representation connects itself in imagination with a second and not with a third. It is this subjective and empirical ground of reproduction according to rules, which is called the association of representations.
If this unity of association did not possess an objective foundation also, which makes it impossible that phenomena should be apprehended by imagination in any other way but under the condition of a possible synthetical unity of that apprehension, it would be a mere accident that phenomena lend themselves to a certain connection in human knowledge. Though we might have the power of associating perceptions, it would still be a matter of [p. 122] uncertainty and chance whether they themselves are associable; and, in case they should not be so, a number of perceptions; nay, the whole of our sensibility, might possibly contain a great deal of empirical consciousness, but in a separate state, nay, without belonging to the one consciousness of myself, which, however, is impossible. Only by ascribing all perceptions to one consciousness (the original apperception) can I say of all of them that I am conscious of them. It must be therefore an objective ground, that is, one that can be understood as existing a priori, and before all empirical laws of imagination, on which alone the possibility, nay, even the necessity of a law can rest, which pervades all phenomena, and which makes us look upon them all, without exception, as data of the senses, associable by themselves, and subject to general rules of a permanent connection in their reproduction. This objective ground of all association of phenomena I call their affinity, and this can nowhere be found except in the principle of the unity of apperception applied to all knowledge which is to belong to me. According to it all phenomena, without exception, must so enter into the mind or be apprehended as to agree with the unity of apperception. This, without a synthetical unity in their connection, which is therefore necessary objectively also, would be impossible.
We have thus seen that the objective unity [p. 123] of all (empirical) consciousness in one consciousness (that of the original apperception) is the necessary condition even of all possible perception, while the affinity of all phenomena (near or remote) is a necessary consequence of a synthesis in imagination which is a priori founded on rules.
Imagination is therefore likewise the power of a synthesis a priori which is the reason why we called it productive imagination, and so far as this aims at nothing but the necessary unity in the synthesis of all the manifold in phenomena, it may be called the transcendental function of imagination. However strange therefore it may appear at first, it must nevertheless have become clear by this time that the affinity of phenomena and with it their association, and through that, lastly, their reproduction also according to laws, that is, the whole of our experience, becomes possible only by means of that transcendental function of imagination, without which no concepts of objects could ever come together in one experience.
It is the permanent and unchanging Ego (or pure apperception) which forms the correlative of all our representations, if we are to become conscious of them, and all consciousness belongs quite as much to such an all-embracing pure apperception as all sensuous intuitions belongs, as a representation, to a pure internal [p. 124] intuition, namely, time. This apperception it is which must be added to pure imagination, in order to render its function intellectual. For by itself, the synthesis of imagination, though carried out a priori, is always sensuous, and only connects the manifold as it appears in intuition, for instance, the shape of a triangle. But when the manifold is brought into relation with the unity of apperception, concepts which belong to the understanding become possible, but only as related to sensuous intuition through imagination.
We have therefore a pure imagination as one of the fundamental faculties of the human soul, on which all knowledge a priori depends. Through it we bring the manifold of intuition on one side in connection with the condition of the necessary unity of pure apperception on the other. These two extreme ends, sense and understanding, must be brought into contact with each other by means of the transcendental function of imagination, because, without it, the senses might give us phenomena, but no objects of empirical knowledge, therefore no experience. Real experience, which is made up of apprehension, association (reproduction), and lastly recognition of phenomena, contains in this last and highest [p. 125] (among the purely empirical elements of experience) concepts, which render possible the formal unity of experience, and with it, all objective validity (truth) of empirical knowledge. These grounds for the recognition of the manifold, so far as they concern the form only of experience in general, are our categories. On them is founded the whole formal unity in the synthesis of imagination and, through it, of1 the whole empirical use of them (in recognition, reproduction, association, and apprehension) down to the very phenomena, because it is only by means of those elements of knowledge that the phenomena can belong to our consciousness and therefore to ourselves.
It is we therefore who carry into the phenomena which we call nature, order and regularity, nay, we should never find them in nature, if we ourselves, or the nature of our mind, had not originally placed them there. For the unity of nature is meant to be a necessary and a priori certain unity in the connection of all phenomena. And how should we a priori have arrived at such a synthetical unity, if the subjective grounds of such unity were not contained a priori in the original sources of our knowledge, and if those subjective conditions did not at the same time possess objective validity, as being the grounds on which alone an object becomes possible in [p. 126] our experience?
We have before given various definitions of the understanding, by calling it the spontaneity of knowledge (as opposed to the receptivity of the senses), or the faculty of thinking, or the faculty of concepts or of judgments; all of these explanations, if more closely examined, coming to the same. We may now characterise it as the faculty of rules. This characteristic is more significant, and approaches nearer to the essence of the understanding. The senses give us forms (of intuition), the understanding rules, being always busy to examine phenomena, in order to discover in them some kind of rule. Rules, so far as they are objective (therefore necessarily inherent in our knowledge of an object), are called laws. Although experience teaches us many laws, yet these are only particular determinations of higher laws, the highest of them, to which all others are subject, springing a priori from the understanding; not being derived from experience, but, on the contrary, imparting to the phenomena their regularity, and thus making experience possible. The understanding therefore is not only a power of making rules by a comparison of phenomena, it is itself the lawgiver of nature, and without the understanding nature, that is, a synthetical unity of the manifold of phenomena, [p. 127] according to rules, would be nowhere to be found, because phenomena, as such, cannot exist without us, but exist in our sensibility only. This sensibility, as an object of our knowledge in any experience, with everything it may contain, is possible only in the unity of apperception, which unity of apperception is transcendental ground of the necessary order of all phenomena in an experience. The same unity of apperception with reference to the manifold of representations (so as to determine it out of one)1 forms what we call the rule, and the faculty of these rules I call the understanding. As possible experience therefore, all phenomena depend in the same way a priori on the understanding, and receive their formal possibility from it as, when looked upon as mere intuitions, they depend on sensibility, and become possible through it, so far as their form is concerned.
However exaggerated therefore and absurd it may sound, that the understanding is itself the source of the laws of nature, and of its formal unity, such a statement is nevertheless correct and in accordance with experience. It is quite true, no doubt, that empirical laws, as such, cannot derive their origin from the pure understanding, as little as the infinite manifoldness of phenomena could be sufficiently comprehended through the pure form of sensuous intuition. But all empirical laws are only particular determinations of the pure laws of the [p. 128] understanding, under which and according to which the former become possible, and phenomena assume a regular form, quite as much as all phenomena, in spite of the variety of their empirical form, must always submit to the conditions of the pure form of sensibility.
The pure understanding is therefore in the categories the law of the synthetical unity of all phenomena, and thus makes experience, so far as its form is concerned, for the first time possible. This, and no more than this, we were called upon to prove in the transcendental deduction of the categories, namely, to make the relation of the understanding to our sensibility, and through it to all objects of experience, that is the objective validity of the pure concepts a priori of the understanding, conceivable, and thus to establish their origin and their truth.
If the objects with which our knowledge has to deal were things by themselves, we could have no concepts a priori of them. For where should we take them? If we took them from the object (without asking even the question, how that object could be known to us) our [p. 129] concepts would be empirical only, not concepts a priori. If we took them from within ourselves, then that which is within us only, could not determine the nature of an object different from our representations, that is, supply a ground why there should be a thing to which something like what we have in our thoughts really belongs, and why all this representation should not rather be altogether empty. But if, on the contrary, we have to deal with phenomena only, then it becomes not only possible, but necessary, that certain concepts a priori should precede our empirical knowledge of objects. For being phenomena, they form an object that is within us only, because a mere modification of our sensibility can never exist outside us. The very idea that all these phenomena, and therefore all objects with which we have to deal, are altogether within me, or determinations of my own identical self, implies by itself the necessity of a permanent unity of them in one and the same apperception. In that unity of a possible consciousness consists also the form of all knowledge of objects, by which the manifold is thought as belonging to one object. The manner therefore in which the manifold of sensuous representation (intuition) belongs to our consciousness, precedes all knowledge of an object, as its intellectual form, and constitutes a kind of formal a priori knowledge of all objects in general, if they are to be thought (categories). Their synthesis [p. 130] by means of pure imagination, and the unity of all representations with reference to the original apperception, precede all empirical knowledge. Pure concepts of the understanding are therefore a priori possible, nay, with regard to experience, necessary, for this simple reason because our knowledge has to deal with nothing but phenomena, the possibility of which depends on ourselves, and the connection and unity of which (in the representation of an object) can be found in ourselves only, as antecedent to all experience, nay, as first rendering all experience possible, so far as its form is concerned. On this ground, as the only possible one, our deduction of the categories has been carried out.]
ANALYTIC OF PRINCIPLES
General logic is built up on a plan that coincides accurately with the division of the higher faculties of knowledge. These are, Understanding, Judgment, and Reason. Logic therefore treats in its analytical portion of concepts, judgments, and syllogisms corresponding with the functions and the order of the above-named faculties [p. 131] of the mind, which are generally comprehended under the vague name of the understanding.
As formal logic takes no account of the contents of our knowledge (pure or empirical), but treats of the form of thought only (discursive knowledge), it may well contain in its analytical portion the canon of reason also, reason being, according to its form, subject to definite rules which, without reference to the particular nature of the knowledge to which they are applied, can be found out a priori by a mere analysis of the acts of reasoning into their component parts.
Transcendental logic, being limited to a certain content, namely, to pure knowledge a priori, cannot follow general logic in this division; for it is clear that the transcendental use of reason cannot be objectively valid, and cannot therefore belong to the logic of truth, that is, to Analytic, but must be allowed to form a separate part of our scholastic system, as a logic of illusion, under the name of transcendental Dialectic.
Understanding and judgment have therefore a canon of their objectively valid, and therefore true use in transcendental logic, and belong to its analytical portion. But reason, in its attempts to determine anything a priori with reference to objects, and to extend knowledge beyond the limits of possible experience, is altogether dialectical, and its illusory assertions have no place in a canon [p. 132] such as Analytic demands.
Our Analytic of principles therefore will be merely a canon of the faculty of judgment, teaching it how to apply to phenomena the concepts of the understanding, which contain the condition of rules a priori. For this reason, and in order to indicate my purpose more clearly, I shall use the name of doctrine of the faculty of judgment, while treating of the real principles of the understanding.
If the understanding is explained as the faculty of rules, the faculty of judgment consists in performing the subsumption under these rules, that is, in determining whether anything falls under a given rule (casus datæ legis) or not. General logic contains no precepts for the faculty of judgment and cannot contain them. For as it takes no account of the contents of our knowledge, it has only to explain analytically the mere form of knowledge in concepts, judgments, and syllogisms, and thus [p. 133] to establish formal rules for the proper employment of the understanding. If it were to attempt to show in general how anything should be arranged under these rules, and how we should determine whether something falls under them or not, this could only take place by means of a new rule. This, because it is a new rule, requires a new precept for the faculty of judgment, and we thus learn that, though the understanding is capable of being improved and instructed by means of rules, the faculty of judgment is a special talent which cannot be taught, but must be practised. This is what constitutes our so-called mother-wit, the absence of which cannot be remedied by any schooling. For although the teacher may offer, and as it were graft into a narrow understanding, plenty of rules borrowed from the experience of others, the faculty of using them rightly must belong to the pupil himself, and without that talent no precept that may be given is safe from abuse.1 A physician, therefore, a judge, or [p. 134] a politician, may carry in his head many beautiful pathological, juridical, or political rules, nay, he may even become an accurate teacher of them, and he may yet in the application of these rules commit many a blunder, either because he is deficient in judgment, though not in understanding, knowing the general in the abstract, but unable to determine whether a concrete case falls under it; or, it may be, because his judgment has not been sufficiently trained by examples and practical experience. It is the one great advantage of examples that they sharpen the faculty of judgment, but they are apt to impair the accuracy and precision of the understanding, because they fulfil but rarely the conditions of the rule quite adequately (as casus in terminis). Nay, they often weaken the effort of the understanding in comprehending rules according to their general adequacy, and independent of the special circumstances of experience, and accustom us to use those rules in the end as formulas rather than as principles. Examples may thus be called the go-cart of the judgment, which those who are deficient in that natural talent1 can never do without.
But although general logic can give no precepts [p. 135] to the faculty of judgment, the case is quite different with transcendental logic, so that it even seems as if it were the proper business of the latter to correct and to establish by definite rules the faculty of the judgment in the use of the pure understanding. For as a doctrine and a means of enlarging the field of pure knowledge a priori for the benefit of the understanding, philosophy does not seem necessary, but rather hurtful, because, in spite of all attempts that have been hitherto made, hardly a single inch of ground has been gained by it. For critical purposes, however, and in order to guard the faculty of judgment against mistakes (lapsus judicii) in its use of the few pure concepts of the understanding which we possess, philosophy (though its benefits may be negative only) has to employ all the acuteness and penetration at its command.
What distinguishes transcendental philosophy is, that besides giving the rules (or rather the general condition of rules) which are contained in the pure concept of the understanding, it can at the same time indicate a priori the case to which each rule may be applied. The superiority which it enjoys in this respect over all other sciences, except mathematics, is due to this, that it treats of concepts which are meant to refer to their objects a priori, so that their objective validity cannot be proved [p. 136] a posteriori, because this would not affect their own peculiar dignity. It must show, on the contrary, by means of general but sufficient marks, the conditions under which objects can be given corresponding to those concepts; otherwise these would be without any contents, mere logical forms, and not pure concepts of the understanding.
Our transcendental doctrine of the faculty of judgment will consist of two chapters. The first will treat of the sensuous condition under which alone pure concepts of the understanding can be used. This is what I call the schematism of the pure understanding. The second will treat of the synthetical judgments, which can be derived a priori under these conditions from pure concepts of the understanding, and on which all knowledge a priori depends. It will treat, therefore, of the principles of the pure understanding.
OF THE SCHEMATISM OF THE PURE CONCEPTS OF THE UNDERSTANDING [p. 137]
In comprehending any object under a concept, the representation of the former must be homogeneous with the latter,1 that is, the concept must contain that which is represented in the object to be comprehended under it, for this is the only meaning of the expression that an object is comprehended under a concept. Thus, for instance, the empirical concept of a plate is homogeneous with the pure geometrical concept of a circle, the roundness which is conceived in the first forming an object of intuition in the latter.
Now it is clear that pure concepts of the understanding, as compared with empirical or sensuous impressions in general, are entirely heterogeneous, and can never be met with in any intuition. How then can the latter be comprehended under the former, or how can the categories be applied to phenomena, as no one is likely to say that causality, for instance, could be seen through the senses, and was contained in the phenomenon? It is [p. 138] really this very natural and important question which renders a transcendental doctrine of the faculty of judgment necessary, in order to show how it is possible that any of the pure concepts of the understanding can be applied to phenomena. In all other sciences in which the concepts by which the object is thought in general are not so heterogeneous or different from those which represent it in concreto, and as it is given, there is no necessity to enter into any discussions as to the applicability of the former to the latter.
In our case there must be some third thing homogeneous on the one side with the category, and on the other with the phenomenon, to render the application of the former to the latter possible. This intermediate representation must be pure (free from all that is empirical) and yet intelligible on the one side, and sensuous on the other. Such a representation is the transcendental schema.
The concept of the understanding contains pure synthetical unity of the manifold in general. Time, as the formal condition of the manifold in the internal sense, consequently of the conjunction of all representations, contains a manifold a priori in pure intuition. A transcendental determination of time is so far homogeneous with the category (which constitutes its unity) that it is general and founded on a rule a priori; and it is on the other hand so far homogeneous with the phenomenon, [p. 139] that time must be contained in every empirical representation of the manifold. The application of the category to phenomena becomes possible therefore by means of the transcendental determination of time, which, as a schema of the concepts of the understanding, allows the phenomena to be comprehended under the category.
After what has been said in the deduction of the categories, we hope that nobody will hesitate in answering the question whether these pure concepts of the understanding allow only of an empirical or also of a transcendental application, that is, whether, as conditions of a possible experience, they refer a priori to phenomena only, or whether, as conditions of the possibility of things in general, they may be extended to objects by themselves (without restriction to our sensibility). For there we saw that concepts are quite impossible, and cannot have any meaning unless there be an object given either to them or, at least, to some of the elements of which they consist, and that they can never refer to things by themselves (without regard as to whether and how things may be given to us). We likewise saw that the only way in which objects can be given to us, consists in a modification of our sensibility, and lastly, that pure concepts a priori must contain, besides the function of the understanding in the category itself, formal conditions a priori of sensibility (particularly [p. 140] of the internal sense) which form the general condition under which alone the category may be applied to any object. We shall call this formal and pure condition of sensibility, to which the concept of the understanding is restricted in its application, its schema; and the function of the understanding in these schemata, the schematism of the pure understanding.
The schema by itself is no doubt a product of the imagination only, but as the synthesis of the imagination does not aim at a single intuition, but at some kind of unity alone in the determination of sensibility, the schema ought to be distinguished from the image. Thus, if I place five points, one after the other . . . . . , this is an image of the number five. If, on the contrary, I think of a number in general, whether it be five or a hundred, this thinking is rather the representation of a method of representing in one image a certain quantity (for instance a thousand) according to a certain concept, than the image itself, which, in the case of a thousand, I could hardly take in and compare with the concept. This representation of a general procedure of the imagination by which a concept receives its image, I call the schema of such concept.
The fact is that our pure sensuous concepts do not depend on images of objects, but on schemata. [p. 141] No image of a triangle in general could ever be adequate to its concept. It would never attain to that generality of the concept, which makes it applicable to all triangles, whether right-angled, or acute-angled, or anything else, but would always be restricted to one portion only of the sphere of the concept. The schema of the triangle can exist nowhere but in thought, and is in fact a rule for the synthesis of imagination with respect to pure forms in space. Still less does an object of experience or its image ever cover the empirical concept, which always refers directly to the schema of imagination as a rule for the determination of our intuitions, according to a certain general concept. The concept of dog means a rule according to which my imagination can always draw a general outline of the figure of a four-footed animal, without being restricted to any particular figure supplied by experience or to any possible image which I may draw in the concrete. This schematism of our understanding applied to phenomena and their mere form is an art hidden in the depth of the human soul, the true secrets of which we shall hardly ever be able to guess and reveal. So much only we can say, that the image is a product of the empirical faculty of the productive imagination, while the schema of sensuous concepts (such as of figures in space) is a product and so to say a monogram of [p. 142] the pure imagination a priori, through which and according to which images themselves become possible, though they are never fully adequate to the concept, and can be connected with it by means of their schema only. The schema of a pure concept of the understanding, on the contrary, is something which can never be made into an image; for it is nothing but the pure synthesis determined by a rule of unity, according to concepts, a synthesis as expressed by the category, and represents a transcendental product of the imagination, a product which concerns the determination of the internal sense in general, under the conditions of its form (time), with reference to all representations, so far as these are meant to be joined a priori in one concept, according to the unity of apperception.
Without dwelling any longer on a dry and tedious determination of all that is required for the transcendental schemata of the pure concepts of the understanding in general, we shall proceed at once to represent them according to the order of the categories, and in connection with them.
The pure image of all quantities (quanta) before the external sense, is space; that of all objects of the senses in general, time. The pure schema of quantity (quantitas), however, as a concept of the understanding, is number, a representation which comprehends the successive addition of one to one (homogeneous). Number therefore is nothing but the unity of the synthesis [p. 143] of the manifold (repetition) of a homogeneous intuition in general, I myself producing the time in the apprehension of the intuition.
Reality is, in the pure concept of the understanding, that which corresponds to a sensation in general: that, therefore, the concept of which indicates by itself being (in time), while negation is that the concept of which represents not-being (in time). The opposition of the two takes place therefore by a distinction of one and the same time, as either filled or empty. As time is only the form of intuition, that is, of objects as phenomena, that which in the phenomena corresponds to sensation, constitutes the transcendental matter of all objects, as things by themselves (reality, Sachheit). Every sensation, however, has a degree of quantity by which it can fill the same time (that is, the internal sense, with reference to the same representation of an object), more or less, till it vanishes into nothing (equal to nought or negation). There exists, therefore, a relation and connection, or rather a transition from reality to negation, which makes every reality representable as a quantum; and the schema of a reality, as the quantity of something which fills time, is this very continuous and uniform production of reality in time; while we either descend from the sensation which has a certain degree, to its vanishing in time, or ascend from the negation of sensation to some quantity of it.
The schema of substance is the permanence [p. 144] of the real in time, that is, the representation of it as a substratum for the empirical determination of time in general, which therefore remains while everything else changes. (It is not time that passes, but the existence of the changeable passes in time. What corresponds therefore in the phenomena to time, which in itself is unchangeable and permanent, is the unchangeable in existence, that is, substance; and it is only in it that the succession and the coexistence of phenomena can be determined according to time.)
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. [p. 145]
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 [p. 146] 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 phaenomenon, constans et perdurabile rerum substantia phaenomenon — 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, [p. 147] 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.
SYSTEM OF ALL PRINCIPLES OF THE PURE UNDERSTANDING [p. 148]
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 [p. 149] 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 [p. 150] 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.
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 [p. 151] 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, because 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, [p. 152] 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 [p. 153] 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.
Of the Highest Principle of all Synthetical Judgments [p. 154]
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 [p. 155] 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 [p. 156] 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, [p. 157] 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 knowledge 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 [p. 158] 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.
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 [p. 159] (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.
There can hardly be any danger of our mistaking purely empirical principles for principles of the pure understanding or vice versa, for the character of necessity which distinguishes the concepts of the pure understanding, and the absence of which can easily be perceived in every empirical proposition, however general it may seem, will always prevent their confusion. There are, however, pure principles a priori which I should not like to ascribe to the pure understanding, because they are derived, not from pure concepts, but from pure intuitions (although by means of the understanding); the [p. 160] understanding being the faculty of the concepts. We find such principles in mathematics, but their application to experience, and therefore their objective validity, nay, even the possibility of such synthetical knowledge a priori (the deduction thereof) rests always on the pure understanding.
Hence my principles will not include the principles of mathematics, but they will include those on which the possibility and objective validity a priori of those mathematical principles are founded, and which consequently are to be looked upon as the source of those principles, proceeding from concepts to intuitions, and not from intuitions to concepts.
When the pure concepts of the understanding are applied to every possible experience, their synthesis is either mathematical or dynamical, for it is directed partly to the intuition of a phenomenon only, partly to its existence. The conditions a priori of intuition are absolutely necessary with regard to every possible experience, while the conditions of the existence of the object of a possible empirical intuition are in themselves accidental only. The principles of the mathematical use of the categories will therefore be absolutely necessary, that is apodictic, while those of their dynamical use, though likewise possessing the character of necessity a priori, can possess such a character subject only to the condition of empirical thought in experience, that is mediately and indirectly, and cannot therefore claim that immediate evidence which belongs to the former, although their certainty with regard to experience in general remains unaffected by this. Of this we shall be better qualified to judge at [p. 161] the conclusion of this system of principles.
Our table of categories gives us naturally the best instructions for drawing up a table of principles, because these are nothing but rules for the objective use of the former.
All principles of the pure understanding are therefore,
I have chosen these names not unadvisedly, so that the difference with regard to the evidence and the application of those principles should not be overlooked. We shall soon see that, both with regard to the evidence and the a priori determination of phenomena according to the categories of quantity and quality (if we attend to the form of them only) their principles differ considerably from those of the other two classes, inasmuch as the [p. 162] former are capable of an intuitive, the latter of a merely discursive, though both of a complete certainty. I shall therefore call the former mathematical, the latter dynamical principles.1 It should be observed, however, that I do not speak here either of the principles of mathematics, or of those of general physical dynamics, but only of the principles of the pure understanding in relation to the internal sense (without any regard to the actual representations given in it). It is these through which the former become possible, and I have given them their name, more on account of their application than of their contents. I shall now proceed to consider them in the same order in which they stand in the table.
[1 ]This point is of great importance and should be carefully considered. All representations have a necessary relation to some possible empirical consciousness, for if they did not possess that relation, and if it were entirely impossible to become conscious of them, this would be the same as if they did not exist. All empirical consciousness has a necessary relation to a transcendental consciousness, which precedes all single experiences, namely, the consciousness of my own self as the original apperception. It is absolutely necessary therefore that in my knowledge all consciousness should belong to one consciousness of my own self. Here we have a synthetical unity of the manifold (consciousness) which can be known a priori, and which may thus supply a foundation for synthetical propositions a priori concerning pure thinking in the same way as space and time supply a foundation for synthetical propositions which concern the form of mere intuition.
[1 ]It has hardly struck any psychologist that this imagination is a necessary ingredient of perception. This was partly owing to their confining this faculty to reproduction, partly to our belief that the senses do not only give us impressions, but compound them also for us, thus producing pictures of objects. This, however, beyond our receptivity of impressions, requires something more, namely, a function for their synthesis.
[1 ]Of may be omitted, if we read aller empirischer Gebrauch.
[1 ]That is, out of one, or out of the unity of apperception.
[1 ]Deficiency in the faculty of judgment is really what we call stupidity, and there is no remedy for that. An obtuse and narrow mind, deficient in nothing but a proper degree of understanding and correct concepts, may be improved by study, so far as to become even learned. But as even then there is often a deficiency of judgment (secunda Petri) we often meet with very learned men, who in handling their learning betray that original deficiency which can never be mended.
[1 ]Desselben has been changed into derselben in later editions. Desselben, however, may be meant to refer to Urtheil, as contained in Urtheilskraft. The second edition has desselben.
[1 ]Read dem letzteren, as corrected by Rosenkranz, for der letzteren.
[1 ]The insertion of man, as suggested by Rosenkranz, is impossible.
[1 ]Here follows in the Second Edition, Supplement XV.