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BOOK II: ANALYTIC OF PRINCIPLES - 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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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.
[OF THE AXIOMS OF INTUITION1
All Phenomena are, with reference to their intuition, extensive quantities’]
I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, and therefore necessarily preceded by it. I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, starting [p. 163] from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all portions of time and their addition, a definite quantity of time. As in all phenomena pure intuition is either space or time, every phenomenon, as an intuition, must be an extensive quantity, because it can be known in apprehension by a successive synthesis only (of part with part). All phenomena therefore, when perceived in intuition, are aggregates (collections) of previously given parts, which is not the case with every kind of quantities, but with those only which are represented to us and apprehended as extensive.
On this successive synthesis of productive imagination in elaborating figures are founded the mathematics of extension with their axioms (geometry), containing the conditions of sensuous intuition a priori, under which alone the schema of a pure concept of an external phenomenal appearance can be produced; for instance, between two points one straight line only is possible, or two straight lines cannot enclose a space, etc. These are the axioms which properly relate only to quantities (quanta) as such.
But with regard to quantity (quantitas), that is, with regard to the answer to the question, how large something may be, there are no axioms, in the proper [p. 164] sense of the word, though several of the propositions referring to it possess synthetical and immediate certainty (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 really analytical, because I am conscious immediately of the identity of my producing the one quantity with my producing the other; axioms on the contrary must be synthetical propositions a priori. The self-evident propositions on numerical relation again are no doubt synthetical, but they are not general, like those of geometry, and therefore cannot be called axioms, but numerical formulas only. That 7+5=12 is not an analytical proposition. For neither in the representation of 7, nor in that of 5, nor in that of the combination of both, do I think the number 12. (That I am meant to think it in the addition of the two, is not the question here, for in every analytical proposition all depends on this, whether the predicate is really thought in the representation of the subject.) Although the proposition is synthetical, it is a singular proposition only. If in this case we consider only the synthesis of the homogeneous unities, then the synthesis can here take place in one way only, although afterwards the use of these numbers becomes general. If I say, a triangle can be constructed with three lines, two of which together are greater than the third, I have before me the mere function of productive imagination, which may draw the lines greater or smaller, and bring them together at various angles. The number 7, on the contrary, [p. 165] is possible in one way only, and so likewise the number 12, which is produced by the synthesis of the former with 5. Such propositions therefore must not be called axioms (for their number would be endless) but numerical formulas.
This transcendental principle of phenomenal mathematics adds considerably to our knowledge a priori. Through it alone it becomes possible to make pure mathematics in their full precision applicable to objects of experience, which without that principle would by no means be self-evident, nay, has actually provoked much contradiction. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition (of space and time), and whatever geometry says of the latter is valid without contradiction of the former. All evasions, as if objects of the senses should not conform to the rules of construction in space (for instance, to the rule of the infinite divisibility of lines or angles) must cease, for one would thus deny all objective validity to space and with it to all mathematics, and would no longer know why and how far mathematics can be applied to phenomena. The synthesis of spaces and times, as the synthesis of the essential form of all intuition, is that which renders possible at the same time the apprehension of phenomena, that is, every external [p. 166] experience, and therefore also all knowledge of its objects, and whatever mathematics, in their pure use prove of that synthesis is valid necessarily also of this knowledge. All objections to this are only the chicaneries of a falsely guided reason, which wrongly imagines that it can separate the objects of the senses from the formal conditions of our sensibility, and represents them, though they are phenomena only, as objects by themselves, given to the understanding. In this case, however, nothing could be known of them a priori, nothing could be known synthetically through pure concepts of space, and the science which determines those concepts, namely, geometry, would itself become impossible.
[Anticipations of Perception
The principle which anticipates all perceptions as such, is this: In all phenomena sensation, and the Real which corresponds to it in the object (realitas phaenomenon), has an intensive quantity, that is, a degree1 ]
All knowledge by means of which I may know and determine a priori whatever belongs to empirical knowledge, may be called an anticipation, and it is no doubt in this sense that Epicurus used the expression [p. 167] πρόληψις. But as there is always in phenomena something which can never be known a priori, and constitutes the real difference between empirical and a priori knowledge, namely, sensation (as matter of perception), it follows that this can never be anticipated. The pure determinations, on the contrary, in space and time, as regards both figure and quantity, may be called anticipations of phenomena, because they represent a priori, whatever may be given a posteriori in experience. If, however, there should be something in every sensation that could be known a priori as sensation in general, even if no particular sensation be given, this would, in a very special sense, deserve to be called anticipation, because it seems extraordinary that we should anticipate experience in that which concerns the matter of experience and can be derived from experience only. Yet such is really the case.
Apprehension, by means of sensation only, fills no more than one moment (if we do not take into account the succession of many sensations). Sensation, therefore, being that in the phenomenon the apprehension of which does not form a successive synthesis progressing from parts to a complete representation, is without any extensive quantity, and the absence of sensation in one and the same moment would represent it as empty, therefore = 0. [p. 168] What corresponds in every empirical intuition to sensation is reality (realitas phaenomenon), what corresponds to its absence is negation = 0. Every sensation, however, is capable of diminution, so that it may decrease, and gradually vanish. There is therefore a continuous connection between reality in phenomena and negation, by means of many possible intermediate sensations, the difference between which is always smaller than the difference between the given sensation and zero or complete negation. It thus follows that the real in each phenomenon has always a quantity, though it is not perceived in apprehension, because apprehension takes place by a momentary sensation, not by a successive synthesis of many sensations; it does not advance from the parts to the whole, and though it has a quantity, it has not an extensive quantity.
That quantity which can be apprehended as unity only, and in which plurality can be represented by approximation only to negation = 0, I call intensive quantity. Every reality therefore in a phenomenon has intensive quantity, that is, a degree. If this reality is considered as a cause (whether of sensation, or of any other reality in the phenomenon, for instance, of change) the degree of that reality as a cause we call a momentum, for instance, the momentum of gravity: and this because the degree indicates that quantity only, the apprehension of [p. 169] which is not successive, but momentary. This I mention here in passing, because we have not yet come to consider causality.
Every sensation, therefore, and every reality in phenomena, however small it may be, has a degree, that is, an intensive quantity which can always be diminished, and there is between reality and negation a continuous connection of possible realities, and of possible smaller perceptions. Every colour, red, for instance, has a degree, which, however small, is never the smallest; and the same applies to heat, the momentum of gravity, etc.
This peculiar property of quantities that no part of them is the smallest possible part (no part indivisible) is called continuity. Time and space are quanta continua, because there is no part of them that is not enclosed between limits (points and moments), no part that is not itself again a space or a time. Space consists of spaces only, time of times. Points and moments are only limits, mere places of limitation, and as places presupposing always those intuitions which they are meant to limit or to determine. Mere places or parts that might be given before space or time, could [p. 170] never be compounded into space or time. Such quantities can also be called flowing, because the synthesis of the productive imagination which creates them is a progression in time, the continuity of which we are wont to express by the name of flowing, or passing away.
All phenomena are therefore continuous quantities, whether according to their intuition as extensive, or according to mere perception (sensation and therefore reality) as intensive quantities. When there is a break in the synthesis of the manifold of phenomena, we get only an aggregate of many phenomena, not a phenomenon, as a real quantum; for aggregate is called that what is produced, not by the mere continuation of productive synthesis of a certain kind, but by the repetition of a synthesis (beginning and) ending at every moment. If I call thirteen thalers a quantum of money, I am right, provided I understand by it the value of a mark of fine silver. This is a continuous quantity in which no part is the smallest, but every part may constitute a coin which contains material for still smaller coins. But if I understand by it thirteen round thalers, that is, so many coins (whatever their value in silver may be), then I should be wrong in speaking of a quantum of thalers, but should call it an aggregate, that is a number of coins. As every number must be founded on some unity, every [p. 171] phenomenon, as a unity, is a quantum, and, as such, a continuum.
If then all phenomena, whether considered as extensive or intensive, are continuous quantities, it might seem easy to prove with mathematical evidence that all change also (transition of a thing from one state into another) must be continuous, if the causality of the change did not lie quite outside the limits of transcendental philosophy, and presupposed empirical principles. For the understanding a priori tells us nothing of the possibility of a cause which changes the state of things, that is, determines them to the opposite of a given state, and this not only because it does not perceive the possibility of it (for such a perception is denied to us in several kinds of knowledge a priori), but because the changeability relates to certain determinations of phenomena to be taught by experience only, while their cause must lie in that which is unchangeable. But as the only materials which we may use at present are the pure fundamental concepts of every possible experience, from which all that is empirical is excluded, we cannot here, without injuring the unity of our system, anticipate general physical science which is based upon certain fundamental experiences. [p. 172]
Nevertheless, there is no lack of evidence of the great influence which our fundamental principle exercises in anticipating perceptions, nay, even in making up for their deficiency, in so far as it (that principle) stops any false conclusions that might be drawn from this deficiency.
If therefore all reality in perception has a certain degree, between which and negation there is an infinite succession of ever smaller degrees, and if every sense must have a definite degree of receptivity of sensations, it follows that no perception, and therefore no experience, is possible, that could prove, directly or indirectly, by any roundabout syllogisms, a complete absence of all reality in a phenomenon. We see therefore that experience can never supply a proof of empty space or empty time, because the total absence of reality in a sensuous intuition can itself never be perceived, neither can it be deduced from any phenomenon whatsoever and from the difference of degree in its reality; nor ought it ever to be admitted in explanation of it. For although the total intuition of a certain space or time is real all through, no part of it being empty, yet as every reality has its degree which, while the extensive quality of the phenomenon remains unchanged, [p. 173] may diminish by infinite degrees down to the nothing or void, there must be infinitely differing degrees in which space and time are filled, and the intensive quantity in phenomena may be smaller or greater, although the extensive quantity as given in intuition remains the same.
We shall give an example. Almost all natural philosophers, perceiving partly by means of the momentum of gravity or weight, partly by means of the momentum of resistance against other matter in motion, that there is a great difference in the quantity of various kinds of matter though their volume is the same, conclude unanimously that this volume (the extensive quantity of phenomena) must in all of them, though in different degrees, contain a certain amount of empty space. Who could have thought that these mathematical and mechanical philosophers should have based such a conclusion on a purely metaphysical hypothesis, which they always profess to avoid, by assuming that the real in space (I do not wish here to call it impenetrability or weight, because these are empirical concepts) must always be the same, and can differ only by its extensive quantity, that is, by the number of parts. I meet this hypothesis, for which they could find no ground in experience, and which therefore is purely metaphysical, by a transcendental demonstration, which, though it is not intended to explain the difference in the [p. 174] filling of spaces, will nevertheless entirely remove the imagined necessity of their hypothesis which tries to explain that difference by the admission of empty spaces, and which thus restores, at least to the understanding, its liberty to explain to itself that difference in a different way, if any such hypothesis be wanted in natural philosophy.
We can easily perceive that although the same spaces are perfectly filled by two different kinds of matter, so that there is no point in either of them where matter is not present, yet the real in either, the quality being the same, has its own degrees (of resistance or weight) which, without any diminution of its extensive quantity, may grow smaller and smaller in infinitum, before it reaches the void and vanishes. Thus a certain expansion which fills a space, for instance, heat, and every other kind of phenomenal reality, may, without leaving the smallest part of space empty, diminish by degrees in infinitum, and nevertheless fill space with its smaller, quite as much as another phenomenon with greater degrees. I do not mean to say that this is really the case with different kinds of matter according to their specific of gravity. I only want to show by a fundamental principle of the pure [p. 175] understanding, that the nature of our perceptions renders such an explanation possible, and that it is wrong to look upon the real in phenomena as equal in degree, and differing only in aggregation and its extensive quantity, nay to maintain this on the pretended authority of an a priori principle of the understanding.
Nevertheless, this anticipation of perception is apt to startle1 an enquirer accustomed to and rendered cautious by transcendental disquisitions, and we may naturally wonder that the understanding should be able to anticipate2 a synthetical proposition with regard to the degree of all that is real in phenomena, and, therefore, with regard to the possibility of an internal difference of sensation itself, apart from its empirical quality; and it seems therefore a question well worthy of a solution, how the understanding can pronounce synthetically and a priori about phenomena, nay, anticipate them with regard to what, properly speaking, is empirical, namely, sensation.
The quality of sensation, colour, taste, etc., is always empirical, and cannot be conceived a priori. But the real that corresponds to sensations in general, as opposed to negation =0, does only represent something the concept of which implies being, and means nothing but the synthesis in any empirical consciousness. In the internal sense that empirical consciousness can be raised from 0 to [p. 176] any higher degree, so that an extensive quantity of intuition (for instance, an illuminated plain) excites the same amount of sensation, as an aggregate of many other less illuminated plains. It is quite possible, therefore, to take no account of the extensive quantity of a phenomenon, and yet to represent to oneself in the mere sensation in any single moment a synthesis of a uniform progression from 0 to any given empirical consciousness. All sensations, as such, are therefore given a posteriori1 only, but their quality, in so far as they must possess a degree, can be known a priori. It is remarkable that of quantities in general we can know one quality only a priori, namely, their continuity, while with regard to quality (the real of phenomena) nothing is known to us a priori, but their intensive quantity, that is, that they must have a degree. Everything else is left to experience.
[The Analogies of Experience
The general principle of them is: All phenomena, as far as their existence is concerned, are subject a priori to rules, determining their mutual relation in one and the same time2 ] [p. 177]
The three modi of time are permanence, succession, and coexistence. There will therefore be three rules of all relations of phenomena in time, by which the existence of every phenomenon with regard to the unity of time is determined, and these rules will precede all experience, nay, render experience possible.
The general principle of the three analogies depends on the necessary unity of apperception with reference to every possible empirical consciousness (perception) at every time, and, consequently, as that unity forms an a priori ground, on the synthetical unity of all phenomena, according to their relation in time. For the original apperception refers to the internal sense (comprehending all representations), and it does so a priori to its form, that is, to the relation of the manifold of the empirical consciousness in time. The original apperception is intended to combine all this manifold according to its relations in time, for this is what is meant by its transcendental unity a priori, to which all is subject which is to belong to my own and my uniform knowledge, and thus to become an object for me. This synthetical unity in the time relations of all perceptions, which is determined a priori, is expressed therefore in the law, that all empirical determinations of time must be subject to rules of the general [p. 178] determination of time; and the analogies of experience, of which we are now going to treat, are exactly rules of this kind.
These principles have this peculiarity, that they do not refer to phenomena and the synthesis of their empirical intuition, but only to the existence of phenomena and their mutual relation with regard to their existence. The manner in which something is apprehended as a phenomenon may be so determined a priori that the rule of its synthesis may give at the same time this intuition a priori in any empirical case, nay, may really render it possible. But the existence of phenomena can never be known a priori, and though we might be led in this way to infer some kind of existence, we should never be able to know it definitely, or to anticipate that by which the empirical intuition of one differs from that of others.
The principles which we considered before and which, as they enable us to apply mathematics to phenomena, I called mathematical, refer to phenomena so far only as they are possible, and showed how, with regard both to their intuition and to the real in their perception, they can be produced according to the rules of a mathematical synthesis, so that, in the one as well as in the other, we may use numerical quantities, and with them a determination of all phenomena as quantities. Thus I might, [p. 179] for example, compound the degree of sensations of the sunlight out of, say, 200,000 illuminations by the moon, and thus determine it a priori or construct it. Those former principles might therefore be called constitutive.
The case is totally different with those principles which are meant to bring the existence of phenomena under rules a priori, for as existence cannot be constructed, they can only refer to the relations of existence and become merely regulative principles. Here therefore we could not think of either axioms or anticipations, and whenever a perception is given us as related in time to some others (although undetermined), we could not say a priori what other perception or how great a perception is necessarily connected with it, but only how, if existing, it is necessarily connected with the other in a certain mode of time. In philosophy analogy means something very different to what it does in mathematics. In the latter they are formulas which state the equality of two quantitative relations, and they are always constitutive so that when three1 terms of a proposition are given, the fourth also is given by it, that is, can be constructed out of it. In philosophy, on the contrary, analogy does not consist in the equality of two quantitative, but of two qualitative relations, so that when three terms are given I may learn from them a priori the relation to a fourth only, but not that [p. 180] fourth term itself. All I can thus gain is a rule according to which I may look in experience for the fourth term, or a characteristic mark by which I may find it. An analogy of experience can therefore be no more than a rule according to which a certain unity of experience may arise from perceptions (but not how perception itself, as an empirical intuition, may arise); it may serve as a principle for objects (as phenomena1 ) not in a constitutive, but only in a regulative capacity.
Exactly the same applies to the postulates of empirical thought in general, which relate to the synthesis of mere intuition (the form of phenomena), the synthesis of perception (the matter of them), and the synthesis of experience (the relation of these perceptions). They too are regulative principles only, and differ from the mathematical, which are constitutive, not in their certainty, which is established in both a priori, but in the character of their evidence, that is, in that which is intuitive in it, and therefore in their demonstration also.
What has been remarked of all synthetical principles and must be enjoined here more particularly is this, that these analogies have their meaning and validity, not as principles of the transcendent, but only as principles [p. 181] of the empirical use of the understanding. They can be established in this character only, nor can phenomena ever be comprehended under the categories directly, but only under their schemata. If the objects to which these principles refer were things by themselves, it would be perfectly impossible to know anything of them a priori and synthetically. But they are nothing but phenomena, and our whole knowledge of them, to which, after all, all principles a priori must relate, is only our possible experience of them. Those principles therefore can aim at nothing but the conditions of the unity of empirical knowledge in the synthesis of phenomena, which synthesis is represented only in the schema of the pure concepts of the understanding, while the category contains the function, restricted by no sensuous condition, of the unity of that synthesis as synthesis in general. Those principles will therefore authorise us only to connect phenomena, according to analogy, with the logical and universal unity of concepts, so that, though in using the principle we use the category, yet in practice (in the application to phenomena) we put the schema of the category, as a practical key, in its1 place, or rather put it by the side of the category as a restrictive condition, or, as what may be called, a formula of the category.
All phenomena contain the permanent (substance) as the object itself, and the changeable as its determination only, that is, as a mode in which the object exists
Proof of the First Analogy
All phenomena take place in time. Time can determine in two ways the relation in the existence of phenomena, so far as they are either successive or coexistent. In the first case time is considered as a series, in the second as a whole.]
Our apprehension of the manifold of phenomena is always successive, and therefore always changing. By it alone therefore we can never determine whether the manifold, as an object of experience, is coexistent or successive, unless there is something in it which exists always, that is, something constant and permanent, while change and succession are nothing but so many kinds (modi) of time in which the permanent exists. Relations of time are therefore possible in the permanent only (coexistence and succession being the only relations of time) [p. 183] so that the permanent is the substratum of the empirical representation of time itself, and in it alone all determination of time is possible. Permanence expresses time as the constant correlative of all existence of phenomena, of all change and concomitancy. For change does not affect time itself, but only phenomena in time (nor is coexistence a mode of time itself, because in it no parts can be coexistent, but successive only). If we were to ascribe a succession to time itself, it would be necessary to admit another time in which such succession should be possible. Only through the permanent does existence in different parts of a series of time assume a quantity which we call duration. For in mere succession existence always comes and goes, and never assumes the slightest quantity. Without something permanent therefore no relation of time is possible. Time by itself, however, cannot be perceived, and it is therefore the permanent in phenomena that forms the substratum for all determination of time, and at the same time the condition of the possibility of all synthetical unity of perceptions, that is, of experience; while with regard to that permanent all existence and all change in time can only be taken as a mode of existence of what is permanent. In all phenomena therefore the permanent is the object itself, that is, the substance (phenomenon), while all that changes or can change [p. 184] belongs only to the mode in which substance or substances exist, therefore to their determinations.
I find that in all ages not only the philosopher, but also the man of common understanding has admitted this permanence as a substratum of all change of phenomena. It will be the same in future, only that a philosopher generally expresses himself somewhat more definitely by saying that in all changes in the world the substance remains, and only the accidents change. But I nowhere find even the attempt at a proof of this very synthetical proposition, and it occupies but seldom that place which it ought to occupy at the head of the pure and entirely a priori existing laws of nature. In fact the proposition that substance is permanent is tautological, because that permanence is the only ground why we apply the category of substance to a phenomenon, and it ought first to have been proved that there is in all phenomena something permanent, while the changeable is only a determination of its existence. But as such a proof can never be given dogmatically and as deduced from concepts, because it refers to a synthetical proposition a priori, and as no one ever thought that such propositions could be valid only in reference to possible experience, and could therefore be proved only by a deduction of the possibility of [p. 185] experience, we need not wonder that, though it served as the foundation of all experience (being felt to be indispensable for every kind of empirical knowledge), it has never been established by proof.
A philosopher was asked, What is the weight of smoke? He replied, Deduct from the weight of the wood burnt the weight of the remaining ashes, and you have the weight of the smoke. He was therefore convinced that even in fire matter (substance) does not perish, but that its form only suffers a change. The proposition also, from nothing comes nothing, was only another conclusion from the same principle of permanence, or rather of the constant presence of the real subject in phenomena. For if that which people call substance in a phenomenon is to be the true substratum for all determination in time, then all existence in the past as well as the future must be determined in it, and in it only. Thus we can only give to a phenomenon the name of substance because we admit its existence at all times, which is not even fully expressed by the word permanence, because it refers rather to future time only. The internal necessity however of permanence is inseparably connected with the necessity to have been always, and the expression may therefore stand. [p. 186] Gigni de nihilo nihil, in nihilum nil posse reverti, were two propositions which the ancients never separated, but which at present are sometimes parted, because people imagine that they refer to things by themselves, and that the former might contradict the dependence of the world on a Supreme Cause (even with regard to its substance), an apprehension entirely needless, as we are only speaking here of phenomena in the sphere of experience, the unity of which would never be possible, if we allowed that new things (new in substance) could ever arise. For in that case we should lose that which alone can represent the unity of time, namely, the identity of the substratum, in which alone all change retains complete unity. This permanence, however, is nothing but the manner in which we represent the existence of things (as phenomenal).
The different determinations of a substance, which are nothing but particular modes in which it exists, are called accidents. They are always real, because they concern the existence of a substance (negations are nothing but determinations which express the non-existence of something in the substance). If we want to ascribe a particular kind of existence to these real determinations of the substance, as, for instance, to motion, as an accident of matter, we call it inherence, in order to distinguish it from the existence of substance, which1 we call subsistence. This, however, has given rise to many misunderstandings, [p. 187] and we shall express ourselves better and more correctly, if we define the accident through the manner only in which the existence of a substance is positively determined. It is inevitable, however, according to the conditions of the logical use of our understanding, to separate, as it were, whatever can change in the existence of a substance, while the substance itself remains unchanged, and to consider it in its relation to that which is radical and truly permanent. Hence a place has been assigned to this category under the title of relations, not so much because it contains itself a relation, as because it contains their condition.
On this permanence depends also the right understanding of the concept of change. To arise and to perish are not changes of that which arises or perishes. Change is a mode of existence, which follows another mode of existence of the same object. Hence whatever changes is permanent, and its condition only changes. As this alteration refers only to determinations which may have an end or a beginning, we may use an expression that seems somewhat paradoxical and say: the permanent only (substance) is changed, the changing itself suffers no change, but only an alteration, certain determinations ceasing to exist, while others begin.
It is therefore in substances only that change [p. 188] can be perceived. Arising or perishing absolutely, and not referring merely to a determination of the permanent can never become a possible perception, because it is the permanent only which renders the representations of a transition from one state to another, from not being to being, possible, which (changes) consequently can only be known empirically, as alternating determinations of what is permanent. If you suppose that something has an absolute beginning, you must have a moment of time in which it was not. But with what can you connect that moment, if not with that which already exists? An empty antecedent time cannot be an object of perception. But if you connect this beginning with things which existed already and continue to exist till the beginning of something new, then the latter is only a determination of the former, as of the permanent. The same holds good with regard to perishing, for this would presuppose the empirical representation of a time in which a phenomenon exists no longer.
Substances therefore (as phenomena) are the true substrata of all determinations of time. If some substances could arise and others perish, the only condition of the empirical unity of time would be removed, and phenomena would then be referred to two different times, in which existence would pass side by side, which is absurd. For there is but one time in which all different times [p. 189] must be placed, not as simultaneous, but as successive.
Permanence, therefore, is a necessary condition under which alone phenomena, as things or objects, can be determined in a possible experience. What the empirical criterion of this necessary permanence, or of the substantiality of phenomena may be, we shall have to explain in the sequel.
Everything that happens (begins to be), presupposes something on which it follows according to a rule]
The apprehension of the manifold of phenomena is always successive. The representations of the parts follow one upon another. Whether they also follow one upon the other in the object is a second point for reflection, not contained in the former. We may indeed call everything, even every representation, so far as we are conscious of it, an object; but it requires a more profound investigation to discover what this word may [p. 190] mean with regard to phenomena, not in so far as they (as representations) are objects, but in so far as they only signify an object. So far as they, as representations only, are at the same time objects of consciousness, they cannot be distinguished from our apprehension, that is from their being received in the synthesis of our imagination, and we must therefore say, that the manifold of phenomena is always produced in the mind successively. If phenomena were things by themselves, the succession of the representations of their manifold would never enable us to judge how that manifold is connected in the object. We have always to deal with our representations only; how things may be by themselves (without reference to the representations by which they affect us) is completely beyond the sphere of our knowledge. Since, therefore, phenomena are not things by themselves, and are yet the only thing that can be given to us to know, I am asked to say what kind of connection in time belongs to the manifold of the phenomena itself, when the representation of it in our apprehension is always successive. Thus, for instance, the apprehension of the manifold in the phenomenal appearance of a house that stands before me, is successive. The question then arises, whether the manifold of the house itself be successive by itself, which of course no one would admit. Whenever I ask for the transcendental meaning of my concepts of an object, I find that a house is not a thing by itself, but a phenomenon [p. 191] only, that is, a representation the transcendental object of which is unknown. What then can be the meaning of the question, how the manifold in the phenomenon itself (which is not a thing by itself) may be connected? Here that which is contained in our successive apprehension is considered as representation, and the given phenomenon, though it is nothing but the whole of those representations, as their object, with which my concept, drawn from the representations of my apprehension, is to accord. As the accord between knowledge and its object is truth, it is easily seen, that we can ask here only for the formal conditions of empirical truth, and that the phenomenon, in contradistinction to the representations of our apprehension, can only be represented as the object different from them, if it is subject to a rule distinguishing it from every other apprehension, and necessitating a certain kind of conjunction of the manifold. That which in the phenomenon contains the condition of this necessary rule of apprehension is the object.
Let us now proceed to our task. That something takes place, that is, that something, or some state, which did not exist before, begins to exist, cannot be perceived empirically, unless there exists antecedently a phenomenon which does not contain that state; for a reality, following on empty time, that is a beginning of existence, [p. 192] preceded by no state of things, can be apprehended as little as empty time itself. Every apprehension of an event is therefore a perception following on another perception. But as this applies to all synthesis of apprehension, as I showed before in the phenomenal appearance of a house, that apprehension would not thereby be different from any other. But I observe at the same time, that if in a phenomenon which contains an event I call the antecedent state of perception A, and the subsequent B, B can only follow A in my apprehension, while the perception A can never follow B, but can only precede it. I see, for instance, a ship gliding down a stream. My perception of its place below follows my perception of its place higher up in the course of the stream, and it is impossible in the apprehension of this phenomenon that the ship should be perceived first below and then higher up. We see therefore that the order in the succession of perceptions in our apprehension is here determined, and our apprehension regulated by that order. In the former example of a house my perceptions could begin in the apprehension at the roof and end in the basement, or begin below and end above: they could apprehend the manifold of the empirical intuition from right to left or from left to right. There was therefore no determined order in the succession of these perceptions, determining the point where [p. 193] I had to begin in apprehension, in order to connect the manifold empirically; while in the apprehension of an event there is always a rule, which makes the order of the successive perceptions (in the apprehension of this phenomenon) necessary.
In our case, therefore, we shall have to derive the subjective succession in our apprehension from the objective succession of the phenomena, because otherwise the former would be entirely undetermined, and unable to distinguish one phenomenon from another. The former alone proves nothing as to the connection of the manifold in the object, because it is quite arbitrary. The latter must therefore consist in the order of the manifold in a phenomenon, according to which the apprehension of what is happening follows upon the apprehension of what has happened, in conformity with a rule. Thus only can I be justified in saying, not only of my apprehension, but of the phenomenon itself, that there exists in it a succession, which is the same as to say that I cannot arrange the apprehension otherwise than in that very succession.
In conformity with this, there must exist in that which always precedes an event the condition of a rule, by which this event follows at all times, and necessarily; [p. 194] but I cannot go back from the event and determine by apprehension that which precedes. For no phenomenon goes back from the succeeding to the preceding point of time, though it is related to some preceding point of time, while the progress from a given time to a determined following time is necessary. Therefore, as there certainly is something that follows, I must necessarily refer it to something else which precedes, and upon which it follows by rule, that is, by necessity. So that the event, as being conditional, affords a safe indication of some kind of condition, while that condition itself determines the event.
If we supposed that nothing precedes an event upon which such event must follow according to rule, all succession of perception would then exist in apprehension only, that is, subjectively; but it would not thereby be determined objectively, what ought properly to be the antecedent and what the subsequent in perception. We should thus have a mere play of representations unconnected with any object, that is, no phenomenon would, by our perception, be distinguished in time from any other phenomenon, because the succession in apprehension would always be uniform, and there would be nothing in the phenomena to determine the succession, so as to render a certain sequence objectively necessary. I could not say therefore that two states follow each other in a phenomenon, but only that one apprehension follows [p. 195] another, which is purely subjective, and does not determine any object, and cannot be considered therefore as knowledge of anything (even of something purely phenomenal).
If therefore experience teaches us that something happens, we always presuppose that something precedes on which it follows by rule. Otherwise I could not say of the object that it followed, because its following in my apprehension only, without being determined by rule in reference to what precedes, would not justify us in admitting an objective following.1 It is therefore always with reference to a rule by which phenomena as they follow, that is as they happen, are determined by an antecedent state, that I can give an objective character to my subjective synthesis (of apprehension); nay, it is under this supposition only that an experience of anything that happens becomes possible.
It might seem indeed as if this were in contradiction to all that has always been said on the progress of the human understanding, it having been supposed that only by a perception and comparison of many events, following in the same manner on preceding phenomena, we were led to the discovery of a rule according to which certain events always follow on certain phenomena, and that thus only we were enabled to form to ourselves the concept of a cause. If this were so, that concept would be [p. 196] empirical only, and the rule which it supplies, that everything which happens must have a cause, would be as accidental as experience itself. The universality and necessity of that rule would then be fictitious only, and devoid of any true and general validity, because not being a priori, but founded on induction only. The case is the same as with other pure representations a priori (for instance space and time), which we are only able to draw out as pure concepts from experience, because we have put them first into experience, nay, have rendered experience possible only by them. It is true, no doubt, that the logical clearness of this representation of a rule, determining the succession of events, as a concept of cause, becomes possible only when we have used it in experience, but, as the condition of the synthetical unity of phenomena in time, it was nevertheless the foundation of all experience, and consequently preceded it a priori.
It is necessary therefore to show by examples that we never, even in experience, ascribe the sequence or consequence (of an event or something happening that did not exist before) to the object, and distinguish it from the subjective sequence of our apprehension, except when there is a rule which forces us to observe a certain order of perceptions, and no other; nay, that it is this force which from the first renders the representation of a [p. 197] succession in the object possible.
We have representations within us, and can become conscious of them; but however far that consciousness may extend, and however accurate and minute it may be, yet the representations are always representations only, that is, internal determinations of our mind in this or that relation of time. What right have we then to add to these representations an object, or to ascribe to these modifications, beyond their subjective reality, another objective one? Their objective character cannot consist in their relation to another representation (of that which one wished to predicate of the object), for thus the question would only arise again, how that representation could again go beyond itself, and receive an objective character in addition to the subjective one, which belongs to it, as a determination of our mind. If we try to find out what new quality or dignity is imparted to our representations by their relation to an object, we find that it consists in nothing but the rendering necessary the connection of representations in a certain way, and subjecting them to a rule; and that on the other hand they receive their objective character only because a certain order is necessary in the time relations of our representations.
In the synthesis of phenomena the manifold [p. 198] of our representations is always successive. No object can thus be represented, because through the succession which is common to all apprehensions, nothing can be distinguished from anything else. But as soon as I perceive or anticipate that there is in this succession a relation to an antecedent state from which the representation follows by rule, then something is represented as an event, or as something that happens: that is to say, I know an object to which I must assign a certain position in time, which, after the preceding state, cannot be different from what it is. If therefore I perceive that something happens, this representation involves that something preceded, because the phenomenon receives its position in time with reference to what preceded, that is, it exists after a time in which it did not exist. Its definite position in time can only be assigned to it, if in the antecedent state something is presupposed on which it always follows by rule. It thus follows that, first of all, I cannot invert the order, and place that which happens before that on which it follows; secondly, that whenever the antecedent state is there, the other event must follow inevitably and necessarily. Thus it happens that there arises an order among our representations, in which the present state [p. 199] (as having come to be), points to an antecedent state, as a correlative of the event that is given; a correlative which, though as yet indefinite, refers as determining to the event, as its result, and connects that event with itself by necessity, in the succession of time.
If then it is a necessary law of our sensibility, and therefore a formal condition of all perception, that a preceding necessarily determines a succeeding time (because I cannot arrive at the succeeding time except through the preceding), it is also an indispensable law of the empirical representation of the series of time that the phenomena of past time determine every existence in succeeding times, nay, that these, as events, cannot take place except so far as the former determine their existence in time, that is, determine it by rule. For it is of course in phenomena only that we can know empirically this continuity in the coherence of times.
What is required for all experience and renders it possible is the understanding, and the first that is added by it is not that it renders the representation of objects clear, but that it really renders the representation of any object for the first time possible. This takes place by the understanding transferring the order of time to the phenomena and their existence, and by assigning to each of them as to a consequence a certain a priori determined place in time, with reference to antecedent phenomena, without which place phenomena would not be in [p. 200] accord with time, which determines a priori their places to all its parts. This determination of place cannot be derived from the relation in which phenomena stand to absolute time (for that can never be an object of perception); but, on the contrary, phenomena must themselves determine to each other their places in time, and render them necessary in the series of time. In other words, what happens or follows must follow according to a general rule on that which was contained in a previous state. We thus get a series of phenomena which, by means of the understanding, produces and makes necessary in the series of possible perceptions the same order and continuous coherence which exists a priori in the form of internal intuition (time), in which all perceptions must have their place.
That something happens is therefore a perception which belongs to a possible experience, and this experience becomes real when I consider the phenomenon as determined with regard to its place in time, that is to say, as an object which can always be found, according to a rule, in the connection of perceptions. This rule, by which we determine everything according to the succession of time, is this: the condition under which an event follows at all times (necessarily) is to be found in what precedes. All possible experience therefore, that is, all objective knowledge of phenomena with regard to their relation in the succession of time, depends on [p. 201] ‘the principle of sufficient reason.’
The proof of this principle rests entirely on the following considerations. All empirical knowledge requires synthesis of the manifold by imagination, which is always successive, one representation following upon the other. That succession, however, in the imagination is not at all determined with regard to the order in which something precedes and something follows, and the series of successive representations may be taken as retrogressive as well as progressive. If that synthesis, however, is a synthesis of apperception (of the manifold in a given phenomenon), then the order is determined in the object, or, to speak more accurately, there is then in it an order of successive synthesis which determines the object, and according to which something must necessarily precede, and, when it is once there, something else must necessarily follow. If therefore my perception is to contain the knowledge of an event, or something that really happens, it must consist of an empirical judgment, by which the succession is supposed to be determined, so that the event presupposes another phenomenon in time on which it follows necessarily and according to a rule. If it were different, if the antecedent phenomenon were there, and the event did not follow on it necessarily, it would become to me a mere play of my subjective imaginations, or if I thought it to be objective, I should call it a dream. It is therefore the relation of phenomena (as possible perceptions) [p. 202] according to which the existence of the subsequent (what happens) is determined in time by something antecedent necessarily and by rule, or, in other words, the relation of cause and effect, which forms the condition of the objective validity of our empirical judgments with regard to the series of perceptions, and therefore also the condition of the empirical truth of them, and of experience. The principle of the causal relation in the succession of phenomena is valid therefore for all objects of experience, also (under the conditions of succession), because that principle is itself the ground of the possibility of such experience.
Here, however, we meet with a difficulty that must first be removed. The principle of the causal connection of phenomena is restricted in our formula to their succession, while in practice we find that it applies also to their coexistence, because cause and effect may exist at the same time. There may be, for instance, inside a room heat which is not found in the open air. If I look for its cause, I find a heated stove. But that stove, as cause, exists at the same time with its effect, the heat of the room, and there is therefore no succession in time between cause and effect, but they are coexistent, and yet the law applies. The fact is, that the greater portion of the active [p. 203] causes1 in nature is coexistent with its effects, and the succession of these effects in time is due only to this, that a cause cannot produce its whole effect in one moment. But at the moment in which an effect first arises it is always coexistent with the causality of its cause, because if that had ceased one moment before, the effect would never have happened. Here we must well consider that what is thought of is the order, not the lapse of time, and that the relation remains, even if no time had lapsed. The time between the causality of the cause and its immediate effect can be vanishing (they may be simultaneous), but the relation of the one to the other remains for all that determinable in time. If I look upon a ball that rests on a soft cushion, and makes a depression in it, as a cause, it is simultaneous with its effect. But I nevertheless distinguish the two through the temporal relation of dynamical connection. For if I place the ball on a cushion, its smooth surface is followed by a depression, while, if there is a depression in the cushion (I know not whence), a leaden ball does by no means follow from it.
The succession in time is therefore the only empirical criterion of an effect with regard to the causality of the cause which precedes it. The glass is the cause of the rising of the water above its horizontal surface, [p. 204] although both phenomena are simultaneous. For as soon as I draw water in a glass from a larger vessel, something follows, namely, the change of the horizontal state which it had before into a concave state which it assumes in the glass.
This causality leads to the concept of action, that to the concept of force, and lastly, to the concept of substance. As I do not mean to burden my critical task, which only concerns the sources of synthetical knowledge a priori, with analytical processes which aim at the explanation, and not at the expansion of our concepts, I leave a fuller treatment of these to a future system of pure reason; nay, I may refer to many well-known manuals in which such an analysis may be found. I cannot pass, however, over the empirical criterion of a substance, so far as it seems to manifest itself, not so much through the permanence of the phenomenon as through action.
Wherever there is action, therefore activity and force, there must be substance, and in this alone the seat of that fertile source of phenomena can be sought. This sounds very well, but if people are asked to explain what they mean by substance, they find it by no means easy to answer without reasoning in a circle. How can [p. 205] we conclude immediately from the action to the permanence of the agent, which nevertheless is an essential and peculiar characteristic of substance (phaenomenon)? After what we have explained before, however, the answer to this question is not so difficult, though it would be impossible, according to the ordinary way of proceeding analytically only with our concepts. Action itself implies the relation of the subject of the causality to the effect. As all effect consists in that which happens, that is, in the changeable, indicating time in succession, the last subject of it is the permanent, as the substratum of all that changes, that is substance. For, according to the principle of causality, actions are always the first ground of all change of phenomena, and cannot exist therefore in a subject that itself changes, because in that case other actions and another subject would be required to determine that change. Action, therefore, is a sufficient empirical criterion to prove substantiality, nor is it necessary that I should first establish its permanency by means of compared perceptions, which indeed would hardly be possible in this way, at least with that completeness which is required by the magnitude and strict universality of the concept. That the first subject of the causality of all arising and perishing cannot itself (in the field of phenomena) arise and perish, is a safe conclusion, pointing in [p. 206] the end to empirical necessity and permanency in existence, that is, the concept of a substance as a phenomenon.
If anything happens, the mere fact of something arising, without any reference to what it is, is in itself a matter for enquiry. The transition from the not-being of a state into that state, even though it contained no quality whatever as a phenomenon, must itself be investigated. This arising, as we have shown in No. A, does not concern the substance (because a substance never arises), but its state only. It is therefore mere change, and not an arising out of nothing. When such an arising is looked upon as the effect of a foreign cause, it is called creation. This can never be admitted as an event among phenomena, because its very possibility would destroy the unity of experience. If, however, we consider all things, not as phenomena, but as things by themselves and objects of the understanding only, then, though they are substances, they may be considered as dependent in their existence on a foreign cause. Our words would then assume quite a different meaning, and no longer be applicable to phenomena, as possible objects of experience.
How anything can be changed at all, how it is possible that one state in a given time is followed by another [p. 207] at another time, of that we have not the slightest conception a priori. We want for that a knowledge of real powers, which can be given empirically only: for instance, a knowledge of motive powers, or what is the same, a knowledge of certain successive phenomena (as movements) which indicate the presence of such forces. What can be considered a priori, according to the law of causality and the conditions of time, are the form of every change, the condition under which alone, as an arising of another state, it can take place (its contents, that is, the state, which is changed, being what it may), and therefore the succession itself of the states (that which has happened).1
When a substance passes from one state a into another b, the moment of the latter is different from the moment of the former state, and follows it. Again, that second state, as a reality (in phenomena), differs from the first in which that reality did not exist, as b from zero; that is, even if the state b differed from the state a in quantity only, that change is an arising of b — a, which in the former state was non-existent, and in relation to [p. 208] which that state is = o.
The question therefore arises how a thing can pass from a state = a to another = b? Between two moments there is always a certain time, and between two states in these two moments there is always a difference which must have a certain quantity, because all parts of phenomena are always themselves quantities. Every transition therefore from one state into another takes place in a certain time between two moments, the first of which determines the state from which a thing arises, the second that at which it arrives. Both therefore are the temporal limits of a change or of an intermediate state between two states, and belong as such to the whole of the change. Every change, however, has a cause which proves its causality during the whole of the time in which the change takes place. The cause therefore does not produce the change suddenly (in one moment), but during a certain time; so that, as the time grows from the initiatory moment a to its completion in b, the quantity of reality also (b-a) is produced through all the smaller degrees between the first and the last. All change therefore is possible only through a continuous action of causality which, so far as it is uniform, is called a momentum. [p. 209] A change does not consist of such momenta, but is produced by them as their effect.
This is the law of continuity in all change, founded on this, that neither time nor a phenomenon in time consists of parts which are the smallest possible, and that nevertheless the state of a thing which is being changed passes through all these parts, as elements, to its new state. No difference of the real in phenomena and no difference in the quantity of times is ever the smallest; and thus the new state of reality grows from the first state in which that reality did not exist through all the infinite degrees thereof, the differences of which from one another are smaller than that between zero and a.
It does not concern us at present of what utility this principle may be in physical science. But how such a principle, which seems to enlarge our knowledge of nature so much, can be possible a priori, that requires a careful investigation, although we can see that it is real and true, and might thus imagine that the question how it was possible is unnecessary. For there are so many unfounded pretensions to enlarge our knowledge by pure reason that we must accept it as a general principle, to be always distrustful, and never to believe or accept anything [p. 210] of this kind without documents capable of a thorough deduction, however clear the dogmatical proof of it may appear.
All addition to our empirical knowledge and every advance in perception is nothing but an enlargement of the determinations of our internal sense, that is, a progression in time, whatever the objects may be, whether phenomena or pure intuitions. This progression in time determines everything, and is itself determined by nothing else, that is, the parts of that progression are only given in time, and through the synthesis of time, but not time before this synthesis. For this reason every transition in our perception to something that follows in time is really a determination of time through the production of that perception, and as time is always and in all its parts a quantity, the production of a perception as a quantity, through all degrees (none of them being the smallest), from zero up to its determined degree. This shows how it is possible to know a priori a law of changes, as far as their form is concerned. We are only anticipating our own apprehension, the formal condition of which, as it dwells in us before all given phenomena, may well be known a priori.
In the same manner therefore in which time contains the sensuous condition a priori of the possibility [p. 211] of a continuous progression of that which exists to that which follows, the understanding, by means of the unity of apperception, is a condition a priori of the possibility of a continuous determination of the position of all phenomena in that time, and this through a series of causes and effects, the former producing inevitably the existence of the latter, and thus rendering the empirical knowledge of the relations of time valid for all times (universally) and therefore objectively valid.
All substances, in so far as they are coexistent, stand in complete community, that is, reciprocity one to another1 ]
Things are coexistent in so far as they exist at one and the same time. But how can we know that they exist at one and the same time? Only if the order in the synthesis of apprehension of the manifold is indifferent, that is, if I may advance from A through B, C, D, to E, or contrariwise from E to A. For, if the synthesis were successive in time (in the order beginning with A and ending with E), it would be impossible to begin the apprehension with the perception of E and to go backwards to A, because A belongs to past time, and can no longer be an object of apprehension. [p. 212]
If we supposed it possible that in a number of substances, as phenomena, each were perfectly isolated, so that none influenced another or received influences from another, then the coexistence of them could never become an object of possible perception, nor could the existence of the one through any process of empirical synthesis lead us on to the existence of another. For if we imagined that they were separated by a perfectly empty space, a perception, proceeding from the one in time to the other might no doubt determine the existence of it by means of a subsequent perception, but would never be able to determine whether that phenomenon followed objectively on the other or was coexistent with it.
There must therefore be something besides their mere existence by which A determines its place in time for B, and B for A, because thus only can these two substances be represented empirically as coexistent. Nothing, however, can determine the place of anything else in time, except that which is its cause or the cause of its determinations. Therefore every substance (since it can be effect with regard to its determinations only) must contain in itself the causality of certain determinations in another substance, and, at the same time, the effects of the causality of that other substance, that is, substances must stand in dynamical communion, immediately or mediately, [p. 213] with each other, if their coexistence is to be known in any possible experience. Now, everything without which the experience of any objects would be impossible, may be said to be necessary with reference to such objects of experience; from which it follows that it is necessary for all substances, so far as they are coexistent as phenomena, to stand in a complete communion of reciprocity with each other.
The word communion (Gemeinschaft) may be used in two senses, meaning either communio or commercium. We use it here in the latter sense: as a dynamical communion without which even the local communio spatii could never be known empirically. We can easily per ceive in our experience, that continuous influences only can lead our senses in all parts of space from one object to another; that the light which plays between our eyes and celestial bodies produces a mediate communion between us and them, and proves the coexistence of the latter; that we cannot change any place empirically (perceive such a change) unless matter itself renders the perception of our own place possible to us, and that by means of its reciprocal influence only matter can evince its simultaneous existence, and thus (though mediately only) its coexistence, even to the most distant objects. Without this communion every perception (of any phenomenon [p. 214] in space) is separated from the others, and the chain of empirical representations, that is, experience itself, would have to begin de novo with every new object, without the former experience being in the least connected with it, or standing to it in any temporal relation. I do not want to say anything here against empty space. Empty space may exist where perception cannot reach, and where therefore no empirical knowledge of coexistence takes place, but, in that case, it is no object for any possible experience.
The following remarks may elucidate this. It is necessary that in our mind all phenomena, as being contained in a possible experience, must share a communion of apperception, and if the objects are to be represented as connected in coexistence, they must reciprocally determine their place in time, and thus constitute a whole. If this subjective communion is to rest on an objective ground, or is to refer to phenomena as substances, then the perception of the one as cause must render possible the perception of the other, and vice versa: so that the succession which always exists in perceptions, as apprehensions, may not be attributed to the objects, but that the objects should be represented as existing simultaneously. This is a reciprocal influence, that is a real commercium of substances, without which the empirical relation of co-existence [p. 215] would be impossible in our experience. Through this commercium, phenomena as being apart from each other and yet connected, constitute a compound (compositum reale), and such compounds become possible in many ways. The three dynamical relations, therefore, from which all others are derived, are inherence, consequence, and composition.
* * * * * * * *
These are the three analogies of experience. They are nothing but principles for determining the existence of phenomena in time, according to its three modes. First, the relation of time itself, as to a quantity (quantity of existence, that is duration). Secondly, the relation in time, as in a series (successively). And thirdly, likewise in time, as the whole of all existence (simultaneously). This unity in the determination of time is dynamical only, that is, time is not looked upon as that in which experience assigns immediately its place to every existence, for this would be impossible; because absolute time is no object of perception by which phenomena could be held together; but the rule of the understanding through which alone the existence of phenomena can receive synthetical unity in time determines the place of each of them in time, therefore a priori and as valid for all time.
By nature (in the empirical sense of the word) [p. 216] we mean the coherence of phenomena in their existence, according to necessary rules, that is, laws. There are therefore certain laws, and they exist a priori, which themselves make nature possible, while the empirical laws exist and are discovered through experience, but in accordance with those original laws which first render experience possible. Our analogies therefore represent the unity of nature in the coherence of all phenomena, under certain exponents, which express the relation of time (as comprehending all existence) to the unity of apperception, which apperception can only take place in the synthesis according to rules. The three analogies, therefore, simply say, that all phenomena exist in one nature, and must so exist because, without such unity a priori no unity of experience, and therefore no determination of objects in experience, would be possible.
With regard to the mode of proof, by which we have arrived at these transcendental laws of nature and its peculiar character, a remark must be made which will become important as a rule for any other attempt to prove intelligible, and at the same time synthetical propositions a priori. If we had attempted to prove these analogies dogmatically, that is from concepts, showing that all which exists is found only in that which is permanent, that every event [p. 217] presupposes something in a previous state on which it follows by rule, and lastly, that in the manifold which is coexistent, states coexist in relation to each other by rule, all our labour would have been in vain. For we may analyse as much as we like, we shall never arrive from one object and its existence at the existence of another, or at its mode of existence by means of the concepts of these things only. What else then remained? There remained the possibility of experience, as that knowledge in which all objects must in the end be capable of being given to us, if their representation is to have any objective reality for us. In this, namely in the synthetical unity of apperception of all phenomena, we discovered the conditions a priori of an absolute and necessary determination in time of all phenomenal existence. Without this even the empirical determinations in time would be impossible, and we thus established the rules of the synthetical unity a priori, by which we might anticipate experience. It was because people were ignorant of this method, and imagined that they could prove dogmatically synthetical propositions which the empirical use of the understanding follows as its principles, that so many and always unsuccessful attempts have been made to prove the proposition of the ‘sufficient reason.’ The other two analogies have not even been thought of, though everybody followed them unconsciously,1 because the method of the categories [p. 218] was wanting, by which alone every gap in the understanding, both with regard to concepts and principles, can be discovered and pointed out.
The Postulates of Empirical Thought in General
1. What agrees with the formal conditions of experience (in intuition and in concepts) is possible
2. What is connected with the material conditions of experience (sensation) is real
3. That which, in its connection with the real, is determined by universal conditions of experience, is (exists as) necessary
Explanation [p. 219]
The categories of modality have this peculiar character that, as determining an object, they do not enlarge in the least the concept to which they are attached as predicates, but express only a relation to our faculty of knowledge. Even when the concept of a thing is quite complete, I can still ask with reference to that object, whether it is possible only, or real also, and, if the latter, whether it is necessary? No new determinations of the object are thereby conceived, but it is only asked in what relation it (with all its determinations) stands to the understanding and its empirical employment, to the empirical faculty of judgment, and to reason, in its application to experience?
The principles of modality are therefore nothing but explanations of the concepts of possibility, reality, and necessity, in their empirical employment, confining all categories to an empirical employment only, and prohibiting their transcendental1 use. For if these categories are not to have a purely logical character, expressing the forms of thought analytically, but are to refer to things, their possibility, reality, or necessity, they must have reference to possible experience and its synthetical unity, in which alone objects of knowledge can be given.
The postulate of the possibility of things [p. 220] demands that the concept of these should agree with the formal conditions of experience in general. This, the objective form of experience in general, contains all synthesis which is required for a knowledge of objects. A concept is to be considered as empty, and as referring to no object, if the synthesis which it contains does not belong to experience, whether as borrowed from it (in which case it is called an empirical concept), or as a synthesis on which, as a condition a priori, all experience (in its form) depends, in which case it is a pure concept, but yet belonging to experience, because its object can only be found in it. For whence could the character of the possibility of an object, which can be conceived by a synthetical concept a priori, be derived, except from the synthesis which constitutes the form of all empirical knowledge of objects? It is no doubt a necessary logical condition, that such a concept must contain nothing contradictory, but this is by no means sufficient to establish the objective reality of a concept, that is, the possibility of such an object, as is conceived by a concept. Thus in the concept of a figure to be enclosed between two straight lines, there is nothing contradictory, because the concepts of two straight lines and their meeting contain no negation of a figure. [p. 221] The impossibility depends, not on the concept itself, but on its construction in space, that is, the conditions of space and its determinations, and it is these that have objective reality, or apply to possible things, because they contain a priori in themselves the form of experience in general.
And now we shall try to explain the manifold usefulness and influence of this postulate of possibility. If I represent to myself a thing that is permanent, while everything which changes belongs merely to its state, I can never know from such a concept by itself that a thing of that kind is possible. Or, if I represent to myself something so constituted that, when it is given, something else must at all times and inevitably follow upon it, this may no doubt be conceived without contradiction, but we have as yet no means of judging whether such a quality, viz. causality, is to be met with in any possible object. Lastly, I can very well represent to myself different things (substances) so constituted, that the state of the one produces an effect on the state of the other, and this reciprocally; but whether such a relation can belong to any things cannot be learned from these concepts which contain a purely arbitrary synthesis. The objective reality of these concepts is only known when we see that they [p. 222] express a priori the relations of perceptions in every kind of experience; and this objective reality, that is, their transcendental truth, though independent of all experience, is nevertheless not independent of all relation to the form of experience in general, and to that synthetical unity in which alone objects can be known empirically.
But if we should think of framing new concepts of substances, forces, and reciprocal actions out of the material supplied to us by our perceptions, without borrowing from experience the instance of their connection, we should entangle ourselves in mere cobwebs of our brain, the possibility of which could not be tested by any criteria, because in forming them we were not guided by experience, nor had borrowed these concepts from it. Such purely imaginary concepts cannot receive the character of possibility, like the categories a priori, as conditions on which all experience depends, but only a posteriori, as concepts that must be given by experience, so that their possibility can either not be known at all, or a posteriori, and empirically only. Thus, for instance, a substance supposed to be present as permanent in space, and yet not filling it (like that something between matter and the thinking subject, which some have tried to introduce), or a peculiar faculty of our mind, by which we can see (not only infer) the future, or lastly, another faculty, by which we can enter into a community of thought with other men (however distant they may be), all these are concepts the [p. 223] possibility of which has nothing to rest on, because it is not founded on experience and its known laws. Without these they are and can only be arbitrary combinations of thought which, though they contain nothing contradictory in themselves, have no claim to objective reality, or to the possibility of such an object as is to be conceived by them. With regard to reality, it stands to reason that we cannot conceive it in the concrete without the aid of experience; for reality concerns sensation only, as the material of experience, and not the form of relations, which might to a certain extent allow us to indulge in mere fancies.
I here pass by everything the possibility of which can only be learned from its reality in experience, and I only mean to consider the possibility of things through concepts a priori. Of these (concepts) I persist in maintaining that they can never exist as such concepts by themselves alone, but only as formal and objective conditions of experience in general.1
It might seem indeed as if the possibility of a triangle could be known from its concept by itself (being independent of all experience), for we can give to it an object entirely a priori, that is, we can construct it. But as this is only the form of an object, it would always remain a product of the imagination only. The possibility [p. 224] of its object would remain doubtful, because more is wanted to establish it, namely, that such a figure should really be conceived under all those conditions on which all objects of experience depend. That which alone connects with this concept the representation of the possibility of such a thing, is the fact that space is a formal condition a priori of all external experiences, and that the same formative synthesis, by which we construct a triangle in imagination, should be identical with that which we exercise in the apprehension of a phenomenon, in order to make an empirical concept of it. And thus the possibility of continuous quantities, nay, of all quantities, the concepts of which are always synthetical, can never be deduced from the concepts themselves, but only from them, as formal conditions of the determination of objects in all experience. And where indeed should we look for objects, corresponding to our concepts, except in experience, by which alone objects are given us? If we are able to know and determine the possibility of things without any previous experience, this is only with reference to those formal conditions under which anything may become an object in experience. This takes place entirely a priori, but nevertheless in constant reference to experience, and within its limits.
The postulate concerning our knowledge of [p. 225] the reality of things, requires perception, therefore sensation and consciousness of it, not indeed immediately of the object itself, the existence of which is to be known, but yet of a connection between it and some real perception, according to the analogies of experience which determine in general all real combinations in experience.
In the mere concept of a thing no sign of its existence can be discovered. For though the concept be ever so perfect, so that nothing should be wanting in it to enable us to conceive the thing with all its own determinations, existence has nothing to do with all this. It depends only on the question whether such a thing be given us, so that its perception may even precede its concept. A concept preceding experience implies its possibility only, while perception, which supplies the material of a concept, is the only characteristic of reality. It is possible, however, even before the perception of a thing, and therefore, in a certain sense, a priori, to know its existence, provided it hang together with some other perceptions, according to the principles of their empirical connection (analogies). For in that case the existence of a thing hangs together at least with our perceptions in a possible experience, and guided by our analogies we [p. 226] can, starting from our real experience, arrive at some other thing in the series of possible perceptions. Thus we know the existence of some magnetic matter pervading all bodies from the perception of the attracted iron filings, though our organs are so constituted as to render an immediate perception of that matter impossible. According to the laws of sensibility and the texture of our perceptions, we ought in our experience to arrive at an immediate empirical intuition of that magnetic matter, if only our senses were more acute, for their actual obtuseness does not concern the form of possible experience. Wherever, therefore, perception and its train can reach, according to empirical laws, there our knowledge also of the existence of things can reach. But if we do not begin with experience, or do not proceed according to the laws of the empirical connection of phenomena, we are only making a vain display, as if we could guess and discover the existence of anything.1
With reference to the third postulate we find that it refers to the material necessity in existence, and not to the merely formal and logical necessity in the connection of concepts. As it is impossible that the existence of the objects of the senses should ever be known entirely a priori, though it may be known to a certain extent a priori, namely, with reference to another already given existence, and as even in that case we can only [p. 227] arrive at such an existence as must somewhere be contained in the whole of the experience of which the given perception forms a part, it follows that the necessity of existence can never be known from concepts, but always from the connection only with what is actually perceived, according to general rules of experience.2 Now, there is no existence that can be known as necessary under the condition of other given phenomena, except the existence of effects from given causes, according to the laws of causality. It is not therefore the existence of things (substances), but the existence of their state, of which alone we can know the necessity, and this from other states only, which are given in perception, and according to the empirical laws of causality. Hence it follows that the criterium of necessity can only be found in the law of possible experience, viz. that everything that happens is determined a priori by its cause in phenomena.1 We therefore know in nature the necessity of those effects only of which the causes are given, and the character of necessity in existence never goes beyond the field of possible experience, and even there it does not apply to the existence of things, as substances, because such substances can never be looked upon as empirical effects or as something that happens and arises. Necessity, therefore, affects only the relations of phenomena [p. 228] according to the dynamical law of causality, and the possibility, dependent upon it, of concluding a priori from a given existence (of a cause) to another existence (that of an effect). Thus the principle that everything which happens is hypothetically necessary, subjects all the changes in the world to a law, that is, to a rule of necessary existence, without which there would not even be such a thing as nature. Hence the proposition that nothing happens by blind chance (in mundo non datur casus) is an a priori law of nature, and so is likewise the other, that no necessity in nature is a blind, but always a conditional and therefore an intelligible, necessity (non datur fatum). Both these are laws by which the mere play of changes is rendered subject to a nature of things (as phenomena), or what is the same, to that unity of the understanding in which alone they can belong to experience, as the synthetical unity of phenomena. Both are dynamical principles. The former is in reality a consequence of the principle of causality (the second of the analogies of experience). The latter is one of the principles of modality, which to the determination of causality adds the concept of necessity, which itself is subject to a rule of the understanding. The principle of continuity rendered every break in the series of phenomena (changes) impossible (in mundo non datur saltus), and likewise any gap between two [p. 229] phenomena in the whole of our empirical intuitions in space (non datur hiatus). For so we may express the proposition that nothing can enter into experience to prove a vacuum, or even to admit it as a possible part of empirical synthesis. For the vacuum, which one may conceive as outside the field of possible experience (the world), can never come before the tribunal of the understanding which has to decide on such questions only as concern the use to be made of given phenomena for empirical knowledge. It is in reality a problem of that ideal reason which goes beyond the sphere of a possible experience, and wants to form an opinion of that which surrounds and limits experience, and will therefore have to be considered in our transcendental Dialectic. With regard to the four propositions (in mundo non datur hiatus, non datus saltus, non datur casus, non datur fatum), it would be easy to represent each of them, as well as all principles of a transcendental origin, according to the order of the categories, and thus to assign its proper place to every one of them. But, after what has been said before, the versed and expert reader will find it easy to do this himself, and to discover the proper method for it. They all simply agree in this, that they admit nothing in our empirical synthesis that would in any way run counter to the understanding, and to the continuous cohesion of all phenomena, that is, to the unity of its concepts. For it is the understanding [p. 230] alone through which the unity of experience, in which all perceptions must have their place, becomes possible.
Whether the field of possibility be larger than the field which contains everything which is real, and whether this again be larger than the field of what is necessary, are curious questions and admitting of a synthetical solution, which questions however are to be brought before the tribunal of reason only. They really come to this, whether all things, as phenomena, belong to the sphere of one experience, of which every given perception forms a part, that could not be connected with any other phenomena, or whether my perceptions can ever belong to more than one possible experience (in its general connection). The understanding in reality does nothing but give to experience a rule a priori, according to the subjective and formal conditions of sensibility and apperception, which alone render experience possible. Other forms of intuition (different from space and time), and other forms of the understanding (different from the discursive forms of thought or conceptual knowledge), even if they were possible, we could in no wise render conceivable or intelligible to ourselves; and even if we could, they would never belong to experience, the only field of knowledge in which objects are given to us. Whether there be [p. 231] therefore other perceptions but those that belong to our whole possible experience, whether there be in fact a completely new field of matter, can never be determined by the understanding, which is only concerned with the synthesis of what is given.
The poverty of the usual arguments by which we construct a large empire of possibility of which all that is real (the objects of experience) forms but a small segment, is but too apparent. When we say that all that is real is possible, we arrive, according to the logical rules of inversion, at the merely particular proposition that some possible is real, and thus seem to imply that much is possible that is not real. Nay, it seems as if we might extend the number of things possible beyond that of things real, simply on the ground that something must be added to the possible to make it real. But this addition to the possible I cannot recognise, because what would thus be added to the possible, would be really the impossible. It is only to my understanding that anything can be added concerning the agreement with the formal conditions of experience, and what can be added is the connection with some perception; and whatever is connected with such a perception, according to empirical laws, is real, though it may not be perceived immediately. But that, in constant connection with what is given us in experience, [p. 232] there should be another series of phenomena, and therefore more than one all-embracing experience, cannot possibly be concluded from what is given us, and still less, if nothing is given us, because nothing can be thought without some kind of material. What is possible only under conditions which themselves are possible only, is not possible in the full sense of the word, not therefore in the sense in which we ask whether the possibility of things can extend beyond the limits of experience.
I have only touched on these questions in order to leave no gap in what are commonly supposed to be the concepts of the understanding. But absolute possibility (which has no regard for the formal conditions of experience) is really no concept of the understanding, and can never be used empirically, but belongs to reason alone, which goes beyond all possible empirical use of the understanding. We have therefore made these few critical remarks only, leaving the subject itself unexplained for the present.
And here, when I am on the point of concluding this fourth number and at the same time the system of all principles of the pure understanding, I think I ought to explain why I call the principles of modality postulates. I do not take this term in the sense which has [p. 233] been given to it by some modern philosophical writers, and which is opposed to the sense in which mathematicians take it, viz. that to postulate should mean to represent a proposition as certain without proof or justification; for if we were to admit with regard to synthetical propositions, however evident they may appear, that they should meet with unreserved applause, without any deduction, and on their own authority only, all criticism of the understanding would be at an end. And as there is no lack of bold assertions, which public opinion does not decline to accept, (this acceptance being, however, no credential), our understanding would be open to every fancy, and could not refuse its sanction to claims which demand admission as real axioms in the same confident tone, though without any substantial reasons. If therefore a condition a priori is to be synthetically joined to the concept of a thing, it will be indispensable that, if not a proof, at least a deduction of the legitimacy of such an assertion, should be forthcoming.
The principles of modality, however, are not objectively synthetical, because the predicates of possibility, reality, and necessity do not in the least increase the concept of which they are predicated, by adding anything to its representation. But as nevertheless they are synthetical, they are so subjectively only, i.e. they add to the [p. 234] concept of a (real) thing, without predicating anything new, the peculiar faculty of knowledge from which it springs and on which it depends, so that, if in the understanding the concept is only connected with the formal conditions of experience, its object is called possible; if it is connected with perception (sensation as the material of the senses), and through it determined by the understanding, its object is called real; while, if it is determined through the connection of perceptions, according to concepts, its object is called necessary. The principles of modality therefore predicate nothing of a concept except the act of the faculty of knowledge by which it is produced. In mathematics a postulate means a practical proposition, containing nothing but a synthesis by which we first give an object to ourselves and produce its concept, as if, for instance, we draw a circle with a given line from a given point in the plane. Such a proposition cannot be proved, because the process required for it is the very process by which we first produce the concept of such a figure. We may therefore with the same right postulate the principles of modality, because they never increase1 the concept of a thing, but indicate the manner only in which the concept was joined with our faculty of knowledge.1 [p. 235]
ON THE GROUND OF DISTINCTION OF ALL SUBJECTS INTO PHENOMENA AND NOUMENA
We have now not only traversed the whole domain of the pure understanding, and carefully examined each part of it, but we have also measured its extent, and assigned to everything in it its proper place. This domain, however, is an island and enclosed by nature itself within limits that can never be changed. It is the country of truth (a very attractive name), but surrounded by a wide and stormy ocean, the true home of illusion, where many a fog bank and ice that soon melts away tempt us to believe in new lands, while constantly deceiving the adventurous mariner with vain hopes, and involving [p. 236] him in adventures which he can never leave, and yet can never bring to an end. Before we venture ourselves on this sea, in order to explore it on every side, and to find out whether anything is to be hoped for there, it will be useful to glance once more at the map of that country which we are about to leave, and to ask ourselves, first, whether we might not be content with what it contains, nay, whether we must not be content with it, supposing that there is no solid ground anywhere else on which we could settle; secondly, by what title we possess even that domain, and may consider ourselves safe against all hostile claims. Although we have sufficiently answered these questions in the course of the analytic, a summary recapitulation of their solutions may help to strengthen our conviction, by uniting all arguments in one point.
We have seen that the understanding possesses everything which it draws from itself, without borrowing from experience, for no other purpose but for experience. The principles of the pure understanding, whether constitutive a priori (as the mathematical) or simply relative (as the dynamical), contain nothing but, as it were, the pure schema of possible experience; for that experience [p. 237] derives its unity from that synthetical unity alone which the understanding originally and spontaneously imparts to the synthesis of imagination, with reference to apperception, and to which all phenomena, as data of a possible knowledge, must conform a priori. But although these rules of the understanding are not only true a priori, but the very source of all truth, that is, of the agreement of our knowledge with objects, because containing the conditions of the possibility of experience, as the complete sphere of all knowledge in which objects can be given to us, nevertheless we do not seem to be content with hearing only what is true, but want to know a great deal more. If therefore this critical investigation does not teach us any more than what, even without such subtle researches, we should have practised ourselves in the purely empirical use of the understanding, it would seem as if the advantages derived from it were hardly worth the labour. One might reply that nothing would be more prejudicial to the enlargement of our knowledge than that curiosity which, before entering upon any researches, wishes to know beforehand the advantages likely to accrue from them, though quite unable as yet to form the least conception of such advantages, even though they were placed before our eyes. There is, however, one advantage in this transcendental investigation which can be rendered intelligible, [p. 238] nay, even attractive to the most troublesome and reluctant apprentice, namely this, that the understanding confined to its empirical use only and unconcerned with regard to the sources of its own knowledge, may no doubt fare very well in other respects, but can never determine for itself the limits of its own use and know what is inside or outside its own sphere. It is for that purpose that such profound investigations are required as we have just instituted. If the understanding cannot decide whether certain questions lie within its own horizon or not, it can never feel certain with regard to its claims and possessions, but must be prepared for many humiliating corrections, when constantly transgressing, as it certainly will, the limits of its own domain, and losing itself in follies and fancies.
That the understanding cannot make any but an empirical, and never a transcendental, use of all its principles a priori, nay, of all its concepts, is a proposition which, if thoroughly understood, leads indeed to most important consequences. What we call the transcendental use of a concept in any proposition is its being referred to things in general and to things by themselves, while its empirical use refers to phenomena only, that is, to objects of a possible experience. That the latter use alone is admissible will be clear from the following considerations. [p. 239] What is required for every concept is, first, the logical form of a concept (of thought) in general; and, secondly, the possibility of an object to which it refers. Without the latter, it has no sense, and is entirely empty, though it may still contain the logical function by which a concept can be formed out of any data. The only way in which an object can be given to a concept is in intuition, and though a pure intuition is possible a priori and before the object, yet even that pure intuition can receive its object, and with it its objective validity, by an empirical intuition only, of which it is itself nothing but the form. All concepts, therefore, and with them all principles, though they may be possible a priori, refer nevertheless to empirical intuitions, that is, to data of a possible experience. Without this, they can claim no objective validity, but are a mere play, whether of the imagination or of the understanding with their respective representations. Let us take the concepts of mathematics as an example, and, first, with regard to pure intuitions. Although such principles as ‘space has three dimensions,’ ‘between two points there can be only one straight line,’ as well as the representation of the object with which that science is occupied, may be produced in the mind a priori, they would have no meaning, if we were not able at all times [p. 240] to show their meaning as applied to phenomena (empirical objects). It is for this reason that an abstract concept is required to be made sensuous, that is, that its corresponding object is required to be shown in intuition, because, without this, the concept (as people say) is without sense, that is, without meaning. Mathematics fulfil this requirement by the construction of the figure, which is a phenomenon present to the senses (although constructed a priori). In the same science the concept of quantity finds its support and sense in number; and this in turn in the fingers, the beads of the abacus, or in strokes and points which can be presented to the eyes. The concept itself was produced a priori, together with all the synthetical principles or formulas which can be derived from such concepts; but their use and their relation to objects can nowhere be found except in experience, of which those concepts contain a priori the (formal) possibility only.
That this is the case with all categories and with all the principles drawn from them, becomes evident from the fact that we could not define any one of them (really, that is, make conceivable the possibility of their object),1 without at once having recourse to the conditions of sensibility or the form of phenomena, to which, as their only possible objects, these categories must necessarily be restricted, it being impossible, if we take away [p. 241] these conditions, to assign to them any meaning, that is, any relation to an object, or to make it intelligible to ourselves by an example what kind of thing could be intended by such concepts.
[When representing the table of the categories, we dispensed with the definition of every one of them, because at that time it seemed unnecessary for our purpose, which concerned their synthetical use only, and because entailing responsibilities which we were not bound to incur. This was not a mere excuse, but a very important prudential rule, viz. not to rush into definitions, and to attempt or pretend completeness or precision in the definition of a concept, when one or other of its characteristic marks is sufficient without a complete enumeration of all that constitute the whole concept. Now, however, we can perceive that this caution had even a deeper ground, namely, that we could not have defined them, even if we had wished;1 for, if we remove all conditions of [p. 242] sensibility, which distinguish them as the concepts of a possible empirical use, and treat them as concepts of things in general (therefore as of transcendental use), nothing remains but to regard the logical function in judgments as the condition of the possibility of the things themselves, without the slightest indication as to where they could have their application and their object, or how they could have any meaning or objective validity in the pure understanding, apart from sensibility.]2
No one can explain the concept of quantity in general, except, it may be, by saying that it is the determination of an object, by which we may know how many times the one is supposed to exist in it. But this ‘how many times’ is based on successive repetition, that is on time, and on the synthesis in it of the homogeneous.
Reality, again, can only be explained in opposition to a negation, if we think of time (as containing all being) being either filled or empty.
Were I to leave out permanence (which means existence at all times), nothing would remain of my concept of substance but the logical representation of a subject which I think I can realise by imagining something which is a subject only, without [p. 243] being a predicate of anything. But in this case we should not only be ignorant of all conditions under which this logical distinction could belong to anything, but we should be unable to make any use of it or draw any conclusions from it, because no object is thus determined for the use of this concept, and no one can tell whether such a concept has any meaning at all.
Of the concept of cause also (if I leave out time, in which something follows on something else by rule) I should find no more in the pure category than that it is something which enables us to conclude the existence of something else, so that it would not only be impossible to distinguish cause and effect from each other, but the concept of cause would possess no indication as to how it can be applied to any object, because, in order to form any such conclusion, certain conditions require to be known of which the concept itself tells us nothing. The so-called principle that everything contingent has a cause, comes no doubt before us with great solemnity and self-assumed dignity. But, if I ask what you understand by contingent and you answer, something of which the non-existence is possible, I should be glad to know how you can recognise this possibility of non-existence, if you do not represent to yourselves, in the series of phenomena, some kind of succession, and in it an existence that follows upon non-existence (or vice versa), and consequently a change? To say that the non-existence of a thing is not self-contradictory [p. 244] is but a lame appeal to a logical condition which, though it is necessary for the concept, yet is by no means sufficient for its real possibility. I can perfectly well remove in thought every existing substance, without contradicting myself, but I can by no means conclude from this as to its objective contingency in its existence, that is, the possibility of its non-existence in itself.
As regards the concept of community, it is easy to see that, as the pure categories of substance and causality admit of no explanation that would determine their object, neither could such an explanation apply to the reciprocal causality in the relation of substances to each other (commercium).
As to possibility, existence, and necessity, no one has yet been able to explain them, except by a manifest tautology, so long as their definition is to be exclusively drawn from the pure understanding. To substitute the transcendental possibility of things (when an object corresponds to a concept) for the logical possibility of the concept (when the concept does not contradict itself) is a quibble such as could deceive and satisfy the inexperienced only.
[It seems to be something strange and even illogical1 that there should be a concept which must have a meaning, and yet is incapable of any explanation. But the case of these categories is peculiar, because it is only by means of the general sensuous condition that they can acquire a definite meaning, and a reference to any objects. That condition being [p. 245] left out in the pure category, it follows that it can contain nothing but the logical function by which the manifold is brought into a concept. By means of this function, that is, the pure form of the concept, nothing can be known nor distinguished as to the object belonging to it, because the sensuous condition, under which alone objects can belong to it, has been removed. Thus we see that the categories require, besides the pure concept of the understanding, certain determinations of their application to sensibility in general (schemata). Without them, they would not be concepts by which an object can be known and distinguished from other objects, but only so many ways of thinking an object for possible intuitions, and giving to it, according to one of the functions of the understanding, its meaning (certain requisite conditions being given). They are needed to define an object, and cannot therefore be defined themselves. The logical functions of judgments in general, namely, unity and plurality, assertion and negation, subject and predicate, cannot be defined without arguing in a circle, because the definition would itself be a judgment and contain these very functions. The pure categories are nothing but representations of things in general, so far as the manifold in intuition must be thought by one or the other of these functions. Thus, magnitude is the determination which can [only be thought by a judgment possessing [p. 246] quantity (judicium commune); reality, the determination which can only be thought by an affirmative judgment; while substance is that which, in regard to intuition, must be the last subject of all other determinations. With all this it remains perfectly undetermined, what kind of things they may be with regard to which we have to use one rather than another of these functions, so that, without the condition of sensuous intuition, for which they supply the synthesis, the categories have no relation to any definite object, cannot define any object, and consequently have not in themselves the validity of objective concepts.]
From this it follows incontestably, that the pure concepts of the understanding never admit of a transcendental, but only of an empirical use, and that the principles of the pure understanding can only be referred, as general conditions of a possible experience, to objects of the senses, never to things by themselves (without regard to the manner in which we have to look at them).
Transcendental Analytic has therefore yielded us this important result, that the understanding a priori can never do more than anticipate the form of a possible experience; and as nothing can be an object of experience except the phenomenon, it follows that the understanding can never go beyond the limits of sensibility, within which alone objects are given to us. Its principles are principles [p. 247] for the exhibition of phenomena only; and the proud name of Ontology, which presumes to supply in a systematic form different kinds of synthetical knowledge a priori of things by themselves (for instance the principle of causality), must be replaced by the more modest name of a mere Analytic of the pure understanding.
Thought is the act of referring a given intuition to an object. If the mode of such intuition is not given, the object is called transcendental, and the concept of the understanding admits then of a transcendental use only, in producing a unity in the thought of the manifold in general. A pure category therefore, in which every condition of sensuous intuition, the only one that is possible for us, is left out, cannot determine an object, but only the thought of an object in general, according to different modes. Now, if we want to use a concept, we require in addition some function of the faculty of judgment, by which an object is subsumed under a concept, consequently the at least formal condition under which something can be given in intuition. If this condition of the faculty of judgment (schema) is wanting, all subsumption is impossible, because nothing is given that could be subsumed under the concept. The purely transcendental use of categories therefore is in reality of no use at all, and has no definite or even, with regard to its form only, definable object. Hence it follows that a pure category is not fit for any [p. 248] synthetical a priori principle, and that the principles of the pure understanding admit of empirical only, never of transcendental application, nay, that no synthetical principles a priori are possible beyond the field of possible experience.
It might therefore be advisable to express ourselves in the following way: the pure categories, without the formal conditions of sensibility, have a transcendental character only, but do not admit of any transcendental use, because such use in itself is impossible, as the categories are deprived of all the conditions of being used in judgments, that is, of the formal conditions of the subsumption of any possible object under these concepts. As therefore (as pure categories) they are not meant to be used empirically, and cannot be used transcendentally, they admit, if separated from sensibility, of no use at all; that is, they cannot be applied to any possible object, and are nothing but the pure form of the use of the understanding with reference to objects in general, and of thought, without ever enabling us to think or determine any object by their means alone.
[Appearances,1 so far as they are thought as objects under the unity of the categories, are called phenomena. But if I admit things which are objects of the [p. 249] understanding only, and nevertheless can be given as objects of an intuition, though not of sensuous intuition (as coram intuitu intellectuali), such things would be called Noumena (intelligibilia).
One might feel inclined to think that the concept of Phenomena, as limited by the transcendental æsthetic, suggested by itself the objective reality of the Noumena, and justified a division of objects into phenomena and noumena, and consequently of the world into a sensible and intelligible world (mundus sensibilis et intelligibilis); and this in such a way that the distinction between the two should not refer to the logical form only of a more or less clear knowledge of one and the same object, but to a difference in their original presentation to our knowledge, which makes them to differ in themselves from each other in kind. For if the senses only represent to us something as it appears, that something must by itself also be a thing, and an object of a non-sensuous intuition, i.e. of the understanding. That is, there must be a kind of knowledge in which there is no sensibility, and which alone possesses absolute objective reality, representing objects as they are, while through the empirical use of our understanding we know things only as they appear. Hence it would seem to follow that, beside the empirical [p. 250] use of the categories (limited by sensuous conditions), there was another one, pure and yet objectively valid, and that we could not say, as we have hitherto done, that our knowledge of the pure understanding contained nothing but principles for the exhibition of phenomena, which, even a priori, could not apply to anything but the formal possibility of experience. Here, in fact, quite a new field would seem to be open, a world, as it were, realised in thought (nay, according to some, even in intuition), which would be a more, and not a less, worthy object for the pure understanding.
All our representations are no doubt referred by the understanding to some sort of object, and as phenomena are nothing but representations, the understanding refers them to a something, as the object of our sensuous intuition, this something being however the transcendental object only. This means a something equal to x, of which we do not, nay, with the present constitution of our understanding, cannot know anything, but which1 can only serve, as a correlatum of the unity of apperception, for the unity of the manifold in sensuous intuition, by means of which the understanding unites the manifold into the concept of an object. This transcendental object cannot be separated from the sensuous data, because in that case nothing would remain by which it could be [p. 251] thought. It is not therefore an object of knowledge in itself, but only the representation of phenomena, under the concept of an object in general, which can be defined by the manifold of sensuous intuition.
For this very reason the categories do not represent a peculiar object, given to the understanding only, but serve only to define the transcendental object (the concept of something in general) by that which is given us through the senses, in order thus to know empirically phenomena under the concepts of objects.
What then is the cause why people, not satisfied with the substratum of sensibility, have added to the phenomena the noumena, which the understanding only is supposed to be able to realise? It is this, that sensibility and its sphere, that is the sphere of phenomena, is so limited by the understanding itself that it should not refer to things by themselves, but only to the mode in which things appear to us, in accordance with our own subjective qualification. This was the result of the whole transcendental æsthetic, and it really follows quite naturally from the concept of a phenomenon in general, that something must correspond to it, which in itself is not a phenomenon, because a phenomenon cannot be anything by itself, apart from our mode of representation. [p. 252] Unless therefore we are to move in a constant circle, we must admit that the very word phenomenon indicates a relation to something the immediate representation of which is no doubt sensuous, but which nevertheless, even without this qualification of our sensibility (on which the form of our intuition is founded) must be something by itself, that is an object independent of our sensibility.
Hence arises the concept of a noumenon, which however is not positive, nor a definite knowledge of anything, but which implies only the thinking of something, without taking any account of the form of sensuous intuition. But in order that a noumenon may signify a real object that can be distinguished from all phenomena, it is not enough that I should free my thought of all conditions of sensuous intuition, but I must besides have some reason for admitting another kind of intuition besides the sensuous, in which such an object can be given; otherwise my thought would be empty, however free it may be from contradictions. It is true that we were not able to prove that the sensuous is the only possible intuition, though it is so for us: but neither could we prove that another kind of intuition was possible; and although our thought may take no account of any sensibility, the question always remains whether, after that, it is not a mere [p. 253] form of a concept, and whether any real object would thus be left.
The object to which I refer the phenomenon in general is the transcendental object, that is, the entirely indefinite thought of something in general. This cannot be called the noumenon, for I know nothing of what it is by itself, and have no conception of it, except as the object of sensuous intuition in general, which is therefore the same for all phenomena. I cannot lay hold of it by any of the categories, for these are valid for empirical intuitions only, in order to bring them under the concept of an object in general. A pure use of the categories is no doubt possible, that is, not self-contradictory, but it has no kind of objective validity, because it refers to no intuition to which it is meant to impart the unity of an object. The categories remain for ever mere functions of thought by which no object can be given to me, but by which I can only think whatever may be given to me in intuition.]
If all thought (by means of categories) is taken away from empirical knowledge, no knowledge of any object remains, because nothing can be thought by mere intuition, and the mere fact that there is within me an affection of my sensibility, establishes in no way any relation of such a representation to any object. If, on the contrary, all intuition is taken away, there always remains [p. 254] the form of thought, that is, the mode of determining an object for the manifold of a possible intuition. In this sense the categories may be said to extend further than sensuous intuition, because they can think objects in general without any regard to the special mode of sensibility in which they may be given; but they do not thus prove a larger sphere of objects, because we cannot admit that such objects can be given, without admitting the possibility of some other but sensuous intuition, for which we have no right whatever.
I call a concept problematic, if it is not self-contradictory, and if, as limiting other concepts, it is connected with other kinds of knowledge, while its objective reality cannot be known in any way. Now the concept of a noumenon, that is of a thing which can never be thought as an object of the senses, but only as a thing by itself (by the pure understanding), is not self-contradictory, because we cannot maintain that sensibility is the only form of intuition. That concept is also necessary, to prevent sensuous intuition from extending to things by themselves; that is, in order to limit the objective validity of sensuous knowledge (for all the rest to which sensuous intuition does not extend is called noumenon, for [p. 255] the very purpose of showing that sensuous knowledge cannot extend its domain over everything that can be thought by the understanding). But, after all, we cannot understand the possibility of such noumena, and whatever lies beyond the sphere of phenomena is (to us) empty; that is, we have an understanding which problematically extends beyond that sphere, but no intuition, nay not even the conception of a possible intuition, by which, outside the field of sensibility, objects could be given to us, and our understanding could extend beyond that sensibility in its assertory use. The concept of a noumenon is therefore merely limitative, and intended to keep the claims of sensibility within proper bounds, therefore of negative use only. But it is not a mere arbitrary fiction, but closely connected with the limitation of sensibility, though incapable of adding anything positive to the sphere of the senses.
A real division of objects into phenomena and noumena, and of the world into a sensible and intelligible world (in a positive sense),1 is therefore quite inadmissible, although concepts may very well be divided into sensuous and intellectual. For no objects can be assigned to these intellectual concepts, nor can they be represented as objectively valid. If we drop the senses, how are we to make it [p. 256] conceivable that our categories (which would be the only remaining concepts for noumena) have any meaning at all, considering that, in order to refer them to any object, something more must be given than the mere unity of thought, namely, a possible intuition, to which the categories could be applied? With all this the concept of a noumenon, if taken as problematical only, remains not only admissible, but, as a concept to limit the sphere of sensibility, indispensable. In this case, however, it is not a particular intelligible object for our understanding, but an understanding to which it could belong is itself a problem, if we ask how it could know an object, not discursively by means of categories, but intuitively, and yet in a nonsensuous intuition, — a process of which we could not understand even the bare possibility. Our understanding thus acquires a kind of negative extension, that is, it does not become itself limited by sensibility, but, on the contrary, limits it, by calling things by themselves (not considered as phenomena) noumena. In doing this, it immediately proceeds to prescribe limits to itself, by admitting that it cannot know these noumena by means of the categories, but can only think of them under the name of something unknown.
In the writings of modern philosophers, however, I meet with a totally different use of the terms of mundus sensibilis and intelligibilis,1 totally different from the meaning assigned to these terms by the ancients. [p. 257] Here all difficulty seems to disappear. But the fact is, that there remains nothing but mere word-mongery. In accordance with this, some people have been pleased to call the whole of phenomena, so far as they are seen, the world of sense; but so far as their connection, according to general laws of the understanding, is taken into account, the world of the understanding. Theoretical astronomy, which only teaches the actual observation of the starry heavens, would represent the former; contemplative astronomy, on the contrary (taught according to the Copernican system, or, it may be, according to Newton’s laws of gravitation), the latter, namely, a purely intelligible world. But this twisting of words is a mere sophistical excuse, in order to avoid a troublesome question, by changing its meaning according to one’s own convenience. Understanding and reason may be applied to phenomena, but it is very questionable whether they can be applied at all to an object which is not a phenomenon, but a noumenon; and it is this, when the object is represented as purely intelligible, that is, as given to the understanding only, and not to the senses. The question therefore is whether, besides the empirical use of the understanding (even in the Newtonian view of the world), a transcendental use is possible, referring to the noumenon, as its object; and that question we have answered decidedly in the negative.
When we therefore say that the senses represent [p. 258] objects to us as they appear, and the understanding as they are, the latter is not to be taken in a transcendental, but in a purely empirical meaning, namely, as to how they, as objects of experience, must be represented, according to the regular connection of phenomena, and not according to what they may be, as objects of the pure understanding, apart from their relation to possible experience, and therefore to our senses. This will always remain unknown to us; nay, we shall never know whether such a transcendental and exceptional knowledge is possible at all, at least as comprehended under our ordinary categories. With us understanding and sensibility cannot determine objects, unless they are joined together. If we separate them, we have intuitions without concepts, or concepts without intuitions, in both cases representations which we cannot refer to any definite object.
If, after all these arguments, anybody should still hesitate to abandon the purely transcendental use of the categories, let him try an experiment with them for framing any synthetical proposition. An analytical proposition does not in the least advance the understanding, which, as in such a proposition it is only concerned with what is already thought in the concept, does not ask whether the concept in itself has any reference to objects, or expresses only the unity of thought in general [p. 259] (this completely ignoring the manner in which an object may be given). The understanding in fact is satisfied if it knows what it contained in the concept of an object; it is indifferent as to the object to which the concept may refer. But let him try the experiment with any synthetical and so-called transcendental proposition, as for instance, ‘Everything that exists, exists as a substance, or as a determination inherent in it,’ or ‘Everything contingent exists as an effect of some other thing, namely, its cause,’ etc. Now I ask, whence can the understanding take these synthetical propositions, as the concepts are to apply, not to some possible experience, but to things by themselves (noumena)? Where is that third term to be found which is always required for a synthetical proposition, in order thus to join concepts which have no logical (analytical) relation with each other? It will be impossible to prove such a proposition, nay even to justify the possibility of any such pure assertion, without appealing to the empirical use of the understanding, and thus renouncing entirely the so-called pure and nonsensuous judgment. There are no principles therefore according to which the concepts of pure and merely intelligible objects could ever be applied, because we cannot imagine any way in which they could be given, and the problematic thought, which leaves a place open to them, serves only, like empty space, to limit the sphere of empirical principles, without containing or indicating [p. 260] any other object of knowledge, lying beyond that sphere.
Reflection (reflexio) is not concerned with objects themselves, in order to obtain directly concepts of them, but is a state of the mind in which we set ourselves to discover the subjective conditions under which we may arrive at concepts. It is the consciousness of the relation of given representations to the various sources of our knowledge by which alone their mutual relation can be rightly determined. Before saying any more of our representations, the first question is, to which faculty of knowledge they may all belong; whether it is the understanding or the senses by which they are connected and compared. Many a judgment is accepted from mere habit, or made from inclination, and as no reflection precedes or even follows it critically, the judgment is supposed [p. 261] to have had its origin in the understanding. It is not all judgments that require an investigation, that is, a careful attention with regard to the grounds of their truth; for if they are immediately certain, as for instance, that between two points there can be only one straight line, no more immediately certain marks of their truth than that which they themselves convey could be discovered. But all judgments, nay, all comparisons, require reflection, that is, a discrimination of the respective faculty of knowledge to which any given concepts belong. The act by which I place in general the comparison of representations by the side of the faculty of knowledge to which that comparison belongs, and by which I determine whether these representations are compared with each other as belonging to the pure understanding or to sensuous intuition, I call transcendental reflection. The relation in which the two concepts may stand to each other in one state of the mind is that of identity and difference, of agreement and opposition, of the internal and external, and finally of the determinable and the determination (matter and form). The right determination of that relation depends on the question in which faculty of knowledge they subjectively belong to each other, whether in sensibility or in the understanding. For the proper distinction of the latter is of great importance with regard to the manner in which the former must be considered. [p. 262]
Before proceeding to form any objective judgments, we have to compare the concepts with regard to the identity (of many representations under one concept) as the foundation of general judgments, or with regard to their difference as the foundation of particular judgments, or with regard to their agreement and opposition serving as the foundations of affirmative and negative judgments, etc. For this reason it might seem that we ought to call these concepts concepts of comparison (conceptus comparationis). But as, when the contents of concepts and not their logical form must be considered, that is, whether the things themselves are identical or different, in agreement or in opposition, etc., all things may have a twofold relation to our faculty of knowledge, namely, either to sensibility or to the understanding, and as the manner in which they belong to one another depends on the place to which they belong, it follows that the transcendental reflection, that is the power of determining the relation of given representations to one or the other class of knowledge, can alone determine their mutual relation. Whether the things are identical or different, in agreement or opposition, etc., cannot be established at once by the concepts themselves by means of a mere comparison (comparatio), but first of all by a proper discrimination of that class of knowledge to which they belong, that is, by transcendental reflection. It might therefore be said, that logical reflection is a mere comparison, because it takes no account of the faculty of knowledge to which any given representations belong, and treats [p. 263] them, so far as they are all found in the mind, as homogeneous, while transcendental reflection (which refers to the objects themselves) supplies the possibility of an objective comparison of representations among themselves, and is therefore very different from the other, the faculty of knowledge to which they belong not being the same. This transcendental reflection is a duty from which no one can escape who wishes to form judgments a priori. We shall now take it in hand, and may hope thus to throw not a little light on the real business of the understanding.
Identity and Difference
When an object is presented to us several times, but each time with the same internal determinations (qualitas et quantitas), it is, so long as it is considered as an object of the pure understanding, always one and the same, one thing, not many (numerica identitas). But if it is a phenomenon, a comparison of the concepts is of no consequence, and though everything may be identical with regard to the concepts, yet the difference of the places of this phenomenon at the same time is a sufficient ground for admitting the numerical difference of the object (of the senses). Thus, though there may be no internal difference whatever (either in quality or quantity) between two drops of water, yet the fact that they may be seen [p. 264] at the same time in different places is sufficient to establish their numerical difference. Leibniz took phenomena to be things by themselves, intelligibilia, that is, objects of the pure understanding (though, on account of the confused nature of their representations, he assigned to them the name of phenomena), and from that point of view his principle of their indiscernibility (principium identitas indiscernibilium) could not be contested. As, however, they are objects of sensibility, and the use of the understanding with regard to them is not pure, but only empirical, their plurality and numerical diversity are indicated by space itself, as the condition of external phenomena. For one part of space, though it may be perfectly similar and equal to another, is still outside it, and for this very reason a part of space different from the first which, added to it, makes a larger space: and this applies to all things which exist at the same time in different parts of space, however similar or equal they may be in other respects.
Agreement and Opposition
When reality is represented by the pure understanding only (realitas noumenon), no opposition can be conceived between realities, that is, no such relation that, if connected in one subject, they should annihilate the effects one of the other, as for instance 3 - 3 = 0. The real in [p. 265] the phenomena, on the contrary (realitas phenomenon), may very well be in mutual opposition, and if connected in one subject, one may annihilate completely or in part the effect of the other, as in the case of two forces moving in the same straight line, either drawing or impelling a point in opposite directions, or in the case of pleasure, counterbalancing a certain amount of pain.
The Internal and the External
In an object of the pure understanding that only is internal which has no relation whatever (as regards its existence) to anything different from itself. The inner relations, on the contrary, of a substantia phenomenon in space are nothing but relations, and the substance itself a complex of mere relations. We only know substances in space through the forces which are active in a certain space, by either drawing others near to it (attraction) or by preventing others from penetrating into it (repulsion and impenetrability). Other properties constituting the concept of a substance appearing in space, and which we call matter, are unknown to us. As an object of the pure understanding, on the contrary, every substance must have internal determinations and forces bearing on the internal reality. But what other internal accidents can I think except those which my own internal sense presents [p. 266] to me, namely, something which is either itself thought, or something analogous to it? Hence Leibniz represented all substances (as he conceived them as noumena), even the component parts of matter (after having in thought removed from them everything implying external relation, and therefore composition also), as simple subjects endowed with powers of representation, in one word, as monads.
Matter and Form
These are two concepts which are treated as the foundation of all other reflection, so inseparably are they connected with every act of the understanding. The former denotes the determinable in general, the latter its determination (both in a purely transcendental meaning, all differences in that which is given and the mode in which it is determined being left out of consideration). Logicians formerly called the universal, matter; the specific difference, form. In every judgment the given concepts may be called the logical matter (for a judgment); their relation, by means of the copula, the form of a judgment. In every being its component parts (essentialia) are the matter; the mode in which they are connected in it, the essential form. With respect to things in general, unlimited reality was regarded as the matter of all possibility, and the limitation thereof (negation) as that form by which one [p. 267] thing is distinguished from another, according to transcendental concepts. The understanding demands first that something should be given (at least in concept) in order to be able afterwards to determine it in a certain manner. In the concept of the pure understanding therefore, matter comes before form, and Leibniz in consequence first assumed things (monads), and within them an internal power of representation, in order afterwards to found thereon their external relation, and the community of their states, that is, of their representations. In this way space and time were possible only, the former through the relation of substances, the latter through the connection of their determinations among themselves, as causes and effects. And so it would be indeed, if the pure understanding could be applied immediately to objects, and if space and time were determinations of things by themselves. But if they are sensuous intuitions only, in which we determine all objects merely as phenomena, then it follows that the form of intuition (as a subjective quality of sensibility) comes before all matter (sensations), that space and time therefore come before all phenomena, and before all data of experience, and render in fact all experience possible. As an intellectual philosopher Leibniz could not endure that this form should come before things and determine their possibility: a criticism quite just when he assumed that we see things as they are (though in a confused representation). But as sensuous intuition is a peculiar [p. 268] subjective condition on which all perception a priori depends, and the form of which is original and independent, the form must be given by itself, and so far from matter (or the things themselves which appear) forming the true foundation (as we might think, if we judged according to mere concepts), the very possibility of matter presupposes a formal intuition (space and time) as given.
NOTE ON THE AMPHIBOLY OF REFLECTIVE CONCEPTS
I beg to be allowed to call the place which we assign to a concept, either in sensibility or in the pure understanding, its transcendental place. If so, then the determination of this position which belongs to every concept, according to the difference of its use, and the directions for determining according to rules that place for all concepts, would be called transcendental topic; a doctrine which would thoroughly protect us against the subreptitious claims of the pure understanding and the errors arising from it, by always distinguishing to what faculty of knowledge each concept truly belongs. Every concept, or every title to which many kinds of knowledge belong, may be called a logical place. Upon this is based the logical topic of Aristotle, of which orators and schoolmasters avail themselves in order to find under certain titles of thought [p. 269] what would best suit the matter they have in hand, and thus to be able, with a certain appearance of thoroughness, to argue and wrangle to any extent.
Transcendental topic, on the contrary, contains no more than the above-mentioned four titles of all comparison and distinction, which differ from the categories because they do not serve to represent the object according to what constitutes its concept (quantity, reality, etc.), but only the comparison of representations, in all its variety, which precedes the concept of things. This comparison, however, requires first a reflection, that is, a determination of the place to which the representations of things which are to be compared belong, namely, whether they are thought by the pure understanding or given as phenomena by sensibility.
Concepts may be logically compared without our asking any questions as to what place their objects belong, whether as noumena to the understanding, or to sensibility as phenomena. But if with these concepts we wish to proceed to the objects themselves, a transcendental reflection is necessary first of all, in order to determine whether they are meant to be objects for the pure understanding or for sensibility. Without this reflection our use of these concepts would be very uncertain, and [p. 270] synthetical propositions would spring up which critical reason cannot acknowledge, and which are simply founded on transcendental amphiboly, that is, on our confounding an object of the pure understanding with a phenomenon.
For want of such a transcendental topic, and deceived by the amphiboly of reflective concepts, the celebrated Leibniz erected an intellectual system of the world, or believed at least that he knew the internal nature of things by comparing all objects with the understanding only and with the abstract formal concepts of his thought. Our table of reflective concepts gives us the unexpected advantage of being able to exhibit clearly the distinctive features of his system in all its parts, and at the same time the leading principle of this peculiar view which rested on a simple misunderstanding. He compared all things with each other by means of concepts only, and naturally found no other differences but those by which the understanding distinguishes its pure concepts from each other. The conditions of sensuous intuition, which carry their own differences, are not considered by him as original and independent; for sensibility was with him a confused mode of representation only, and not a separate source of representations. According to him a phenomenon was the representation of a thing by itself, though different, in its logical form, from knowledge by means of the [p. 271] understanding, because the phenomenon, in the ordinary absence of analysis, brings a certain admixture of collateral representations into the concept of a thing which the understanding is able to separate. In one word, Leibniz intellectualised phenomena, just as Locke, according to his system of Noogony (if I may use such an expression), sensualised all concepts of the understanding, that is, represented them as nothing but empirical, though abstract, reflective concepts. Instead of regarding the understanding and sensibility as two totally distinct sources of representations, which however can supply objectively valid judgments of things only in conjunction with each other, each of these great men recognised but one of them, which in their opinion applied immediately to things by themselves, while the other did nothing but to produce either disorder or order in the representations of the former.
Leibniz accordingly compared the objects of the senses with each other as things in general and in the understanding only. He did this,
First, so far as they are judged by the understanding to be either identical or different. As he considers their concepts only and not their place in intuition, in which alone objects can be given, and takes no account of the transcendental place of these concepts (whether the object is to be counted among phenomena or among things by themselves), it could not happen otherwise than [p. 272] that he should extend his principle of indiscernibility, which is valid with regard to concepts of things in general only, to objects of the senses also (mundus phaenomenon), and imagine that he thus added no inconsiderable extension to our knowledge of nature. No doubt, if I know a drop of water as a thing by itself in all its internal determinations, I cannot allow that one is different from the other, when their whole concepts are identical. But if the drop of water is a phenomenon in space, it has its place not only in the understanding (among concepts), but in the sensuous external intuition (in space), and in this case the physical place is quite indifferent with regard to the inner determinations of things, so that a place B can receive a thing which is perfectly similar or identical with another in place A, quite as well as if it were totally different from it in its internal determinations. Difference of place by itself and without any further conditions renders the plurality and distinction of objects as phenomena not only possible, but also necessary. That so-called law of Leibniz therefore is no law of nature, but only an analytical rule, or a comparison of things by means of concepts only.
Thirdly. The Leibnizian monadology has really no other foundation than that Leibniz represented the difference of the internal and the external in relation to the understanding only. Substances must have something internal, which is free from all external relations, and therefore from composition also. The simple, therefore, or uncompounded, is the foundation of the internal of things by themselves. This internal in the state of substances cannot consist in space, form, contact, or motion (all these determinations being external relations), and we cannot therefore ascribe to substances any other internal state but that which belongs to our own internal sense, namely, the state of representations. This is the history of the monads, which were to form the elements of the whole universe, and the energy of which consists in representations only, so that properly they can be active within themselves only.
For this reason, his principle of a possible community of substances could only be a pre-established harmony, and not a physical influence. For, as everything [p. 275] is actively occupied internally only, that is, with its own representations, the state of representations in one substance could not be in active connection with that of another; but it became necessary to admit a third cause, exercising its influence on all substances, and making their states to correspond with each other, not indeed by occasional assistance rendered in each particular case (systema assistentiae), but through the unity of the idea of a cause valid for all, and in which all together must receive their existence and permanence, and therefore also their reciprocal correspondence according to universal laws.
Fourthly. Leibniz’s celebrated doctrine of space and time, in which he intellectualised these forms of sensibility, arose entirely from the same delusion of transcendental reflection. If by means of the pure understanding alone I want to represent the external relations of things, I can do this only by means of the concept of their reciprocal action; and if I want to connect one state with another state of the same thing, this is possible only in the order of cause and effect. Thus it happened that Leibniz conceived space as a certain order in the community of substances, and time as the dynamical sequence of their states. That which space and time seem to possess as proper to themselves and independent [p. 276] of things, he ascribed to the confusion of these concepts. which made us mistake what is a mere form of dynamical relations for a peculiar and independent intuition, antecedent to things themselves. Thus space and time became with him the intelligible form of the connection of things (substances and their states) by themselves, and things were intelligible substances (substantiae noumena). Nevertheless he tried to make these concepts valid for phenomena, because he would not concede to sensibility any independent kind of intuition, but ascribed all, even the empirical representation of objects, to the understanding, leaving to the senses nothing but the contemptible work of confusing and mutilating the representations of the understanding.
But, even if we could predicate anything synthetically by means of the pure understanding of things by themselves (which however is simply impossible), this could never be referred to phenomena, because these do not represent things by themselves. We should therefore in such a case have to compare our concepts in a transcendental reflection under the conditions of sensibility only, and thus space and time would never be determinations of things by themselves, but of phenomena. What things may be by themselves we know not, nor need [p. 277] we care to know, because, after all, a thing can never come before me otherwise than as a phenomenon.
The remaining reflective conceptions have to be treated in the same manner. Matter is substantia phenomenon. What may belong to it internally, I seek for in all parts of space occupied by it, and in all effects produced by it, all of which, however, can be phenomena of the external senses only. I have therefore nothing that is absolutely, but only what is relatively internal, and this consists itself of external relations. Nay, what according to the pure understanding should be the absolutely internal of matter is a mere phantom, for matter is never an object of the pure understanding, while the transcendental object which may be the ground of the phenomenon which we call matter, is a mere something of which we could not even understand what it is, though somebody should tell us. We cannot understand anything except what carries with it in intuition something corresponding to our words. If the complaint ‘that we do not understand the internal of things,’ means that we do not comprehend by means of the pure understanding what the things which appear to us may be of themselves, it seems totally unjust and unreasonable; for it means that without senses we should be able to know and therefore to see things, that is, that we should possess a faculty of knowledge totally different from the human, not only in degree, but in kind [p. 278] and in intuition, in fact, that we should not be men, but beings of whom we ourselves could not say whether they are even possible, much less what they would be like. Observation and analysis of phenomena enter into the internal of nature, and no one can say how far this may go in time. Those transcendental questions, however, which go beyond nature, would nevertheless remain unanswerable, even if the whole of nature were revealed to us, for it is not given to us to observe even our own mind with any intuition but that of our internal sense. In it lies the mystery of the origin of our sensibility. Its relation to an object, and the transcendental ground of that unity, are no doubt far too deeply hidden for us, who can know even ourselves by means of the internal sense only, that is, as phenomena, and we shall never be able to use the same imperfect instrument of investigation in order to find anything but again and again phenomena, the non-sensuous, and non-phenomenal cause of which we are seeking in vain.
What renders this criticism of the conclusions by means of the acts of mere reflection extremely useful is, that it shows clearly the nullity of all conclusions with regard to objects compared with each other in the understanding only, and that it confirms at the same time what [p. 279] we have so strongly insisted on, namely, that phenomena, though they cannot be comprehended as things by themselves among the objects of the pure understanding, are nevertheless the only objects in which our knowledge can possess objective reality, i.e. where intuition corresponds to concepts.
When we reflect logically only, we only compare in our understanding concepts among themselves, trying to find out whether both have exactly the same contents, whether they contradict themselves or not, whether something belongs to a concept, or is added to it, and which of the two may be given, while the other may be a mode only of thinking the given concept. But if I refer these concepts to an object in general (in a transcendental sense), without determining whether it be an object of sensuous or intellectual intuition, certain limitations appear at once, warning us not to go beyond the concept, and upsetting all empirical use of it, thus proving that a representation of an object, as of a thing in general, is not only insufficient, but, if without sensuous determination, and independent of empirical conditions, self-contradictory. It is necessary therefore either to take no account at all of the object (as we do in logic) or, if not, then to think it under the conditions of sensuous intuition, because the intelligible would require a quite peculiar intuition which we do not possess, and, without it, would be nothing to us, while on the other side phenomena also could never [p. 280] be things by themselves. For if I represent to myself things in general only, the difference of external relations cannot, it is true, constitute a difference of the things themselves, but rather presupposes it; and, if the concept of one thing does not differ at all internally from that of another, I only have one and the same thing placed in different relations. Furthermore, by adding a mere affirmation (reality) to another, the positive in it is indeed augmented, and nothing is taken away or removed, so that we see that the real in things can never be in contradiction with itself, etc.
* * * * * * * *
A certain misunderstanding of these reflective concepts has, as we showed, exercised so great an influence on the use of the understanding, as to mislead even one of the most acute philosophers to the adoption of a so-called system of intellectual knowledge, which undertakes to determine objects without the intervention of the senses. For this reason the exposition of the cause of the misunderstanding, which lies in the amphiboly of these concepts, as the origin of false principles, is of great utility in determining and securing the true limits of the understanding.
It is no doubt true, that what can be affirmed or denied of a concept in general, can also be affirmed or denied of any part of it (dictum de omni et nullo); but it [p. 281] would be wrong so to change this logical proposition as to make it say that whatever is not contained in a general concept, is not contained either in the particular concepts comprehended under it; for these are particular concepts for the very reason that they contain more than is conceived in the general concept. Nevertheless the whole intellectual system of Leibniz is built up on this fallacy, and with it falls necessarily to the ground, together with all equivocation in the use of the understanding, that had its origin in it.
Leibniz’s principle of discernibility is really based on the supposition that, if a certain distinction is not to be found in the general concept of a thing, it could not be met with either in the things themselves, and that therefore all things were perfectly the same (numero eadem), which are not distinguished from each other in their concept also, as to quality or quantity. And because in the mere concept of a thing, no account has been taken of many a necessary condition of its intuition, it has rashly been concluded that that which, in forming an abstraction, has been intentionally left out of account, did really not exist anywhere, and nothing has been allowed to a thing except what is contained in its concept. [p. 282]
If by purely intelligible objects we understand things which, without all schemata of sensibility, are thought by mere categories, such objects are simply impossible. It is our sensuous intuition by which objects are given to us that forms the condition of the objective application of all the concepts of our understanding, and without that intuition the categories have no relation whatever to any object. Nay, even if we admitted a kind of intuition different from the sensuous, our functions of thought would have no meaning with regard to it. If we only mean objects of a non-sensuous intuition, to which our categories do not apply, and of which we can have no knowledge whatever (either intuitional or conceptual), there is no reason why noumena, in this merely negative meaning, should not be admitted, because in this case we mean no more than this, that our intuition does not embrace all things, but objects of our senses only; that, consequently, its objective validity is limited, and space left for some other kind of intuition, and consequently for things as objects of it. But in that sense the concept of a noumenon is problematical, that is, the representation of a thing of which we can neither say that it is possible or that it is impossible, because we have no conception of any kind of intuition but that of our senses, or of any kind of concepts but of our categories, [p. 287] neither of them being applicable to any extra-sensuous object. We cannot therefore extend in a positive sense the field of the objects of our thought beyond the conditions of our sensibility, or admit, besides phenomena, objects of pure thought, that is, noumena, simply because they do not possess any positive meaning that could be pointed out. For it must be admitted that the categories by themselves are not sufficient for a knowledge of things, and that, without the data of sensibility, they would be nothing but subjective forms of unity of the understanding, and without an object. We do not say that thought is a mere product of the senses, and therefore limited by them, but it does not follow that therefore thought, without sensibility, has its own pure use, because it would really be without an object. Nor would it be right to call the noumenon such an object of the pure understanding, for the noumenon means the problematical concept of an object, intended for an intuition and understanding totally different from our own, and therefore themselves mere problems. The concept of the noumenon is not therefore the concept of an object, but only a problem, inseparable from the limitation of our sensibility, whether there may not be objects independent of its intuition. This is a question that [p. 288] can only be answered in an uncertain way, by saying that as sensuous intuition does not embrace all things without exception, there remains a place for other objects, that cannot therefore be absolutely denied, but cannot be asserted either as objects of our understanding, because there is no definite concept for them (our categories being unfit for that purpose).
The understanding therefore limits the sensibility without enlarging thereby its own field, and by warning the latter that it can never apply to things by themselves, but to phenomena only, it forms the thought of an object by itself, but as transcendental only, which is the cause of phenomena, and therefore never itself a phenomenon: which cannot be thought as quantity, nor as reality, nor as substance (because these concepts require sensuous forms in which to determine an object), and of which therefore it must always remain unknown, whether it is to be found within us only, or also without us; and whether, if sensibility were removed, it would vanish or remain. If we like to call this object noumenon, because the representation of it is not sensuous, we are at liberty to do so. But as we cannot apply to it any of the concepts of our understanding, such a representation remains to us empty, serving no purpose but that of indicating the limits of our sensuous knowledge, and leaving at the same time an [p. 289] empty space which we cannot fill either by possible experience, or by the pure understanding.
The critique of the pure understanding does not therefore allow us to create a new sphere of objects beyond those which can come before it as phenomena, or to stray into intelligible worlds, or even into the concept of such. The mistake which leads to this in the most plausible manner, and which, though excusable, can never be justified, consists in making the use of the understanding, contrary to its very intention, transcendental, so that objects, that is, possible intuitions, are made to conform to concepts, not concepts to possible intuitions, on which alone their objective validity can rest. The cause of this is again, that apperception, and with it thought, precedes every possible determinate arrangement of representations. We are thinking something in general, and determine it on one side sensuously, but distinguish at the same time the general object, represented in abstraction, from this particular mode of sensuous intuition. Thus there remains to us a mode of determining the object by thought only, which, though it is a mere logical form without any contents, seems to us nevertheless a mode in which the object by itself exists (noumenon), without regard to the intuition which is restricted to our senses. [p. 290]
* * * * * * * *
Before leaving this transcendental Analytic, we have to add something which, though in itself of no particular importance, may yet seem to be requisite for the completeness of the system. The highest concept of which all transcendental philosophy generally begins, is the division into the possible and the impossible. But, as all division presupposes a divisible concept, a higher concept is required, and this is the concept of an object in general, taken as problematical, it being left uncertain whether it be something or nothing. As the categories are the only concepts which apply to objects in general, the distinction whether an object is something or nothing must proceed according to the order and direction of the categories.
I. Opposed to the concepts of all, many, and one, is the concept which annihilates everything, that is, none; and thus the object of a concept, to which no intuition can be found to correspond, is = 0, that is, a concept without an object, like the noumena, which cannot be counted as possibilities, though not as impossibilities either (ens nationis); or like certain fundamental forces, [p. 291] which have been newly invented, and have been conceived without contradiction, but at the same time without any example from experience, and must not therefore be counted among possibilities.
II. Reality is something, negation is nothing; that is, it is the concept of the absence of an object, as shadow or cold (nihil privativum).
III. The mere form of intuition (without substance) is in itself no object, but the merely formal condition of it (as a phenomenon), as pure space and pure time (ens imaginarium), which, though they are something, as forms of intuition, are not themselves objects of intuition.
IV. The object of a concept which contradicts itself, is nothing, because the concept is nothing; it is simply the impossible, as a figure composed of two straight lines (nihil negativum).
A table showing this division of the concept of nothing (the corresponding division of the concept of something follows by itself) would have to be arranged as follows.
We see that the ens rationis (No. 1) differs from the ens negativum (No. 4), because the former cannot be counted among the possibilities, being the result of fancy, though not self-contradictory, while the latter is opposed to possibility, the concept annihilating itself. Both, however, are empty concepts. The nihil privativum (No. 2) and the ens imaginarium (No. 3) are, on the contrary, empty data for concepts. It would be impossible to represent to ourselves darkness, unless light had been given to the senses, or space, unless extended beings had been perceived. The negation, as well as the pure form of intuition are, without something real, no objects.
Transcendental Dialectic in two books, with their chapters and sections [p. 293]
[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.
[1 ]Here follows, in the later Editions, Supplement XVI.
[1 ]Here follows in the Second Edition, Supplement XVI b.
[1 ]Kant wrote, etwas — etwas Auffallendes, the second etwas being the adverb. Rosenkranz has left out one etwas, without necessity. It seems necessary, however, to add Überlegung after transcendentalen, as done by Erdmann.
[2 ]Anticipiren könne must certainly be added, as suggested by Schopenhauer.
[1 ]The first and later editions have a priori. The correction is first made in the Seventh Edition, 1828.
[2 ]See Supplement XVII.
[1 ]The First and Second Editions read ‘When two terms of a proposition are given, the third also.’
[1 ]Read den Erscheinungen.
[1 ]I read deren, and afterwards der ersteren, though even then the whole passage is very involved. Professor Noiré thinks that dessen may be referred to Gebrauch, and des ersteren to Grundsatz.
[1 ]See Supplement XVIII.
[1 ]Read das man.
[1 ]See Supplement XIX.
[1 ]Read anzunehmamen berechtigt.
[1 ]The reading of the First Edition is Ursache; Ursachen is a conjecture made by Rosenkranz and approved by others.
[1 ]It should be remarked that I am not speaking here of the change of certain relations, but of the change of a state. Therefore when a body moves in a uniform way, it does not change its state of movement, but it does so when its motion increases or decreases.
[1 ]See Supplement XX.
[1 ]The unity of the universe, in which all phenomena are supposed to be connected, is evidently a mere deduction of the quietly adopted principle of the communion of all substances as coexistent; for if they were isolated, they would not form parts of a whole, and if their connection (the reciprocity of the manifold) were not necessary for the sake of their coexistence, it would be impossible to use the latter, which is a purely ideal relation, as a proof of the former, which is real. We have shown, however, that communion is really the ground of the possibility of an empirical knowledge of coexistence, and that really we can only conclude from this the existence of the former, as its condition.
[1 ]Here the same as transcendent.
[1 ]I have adopted Erdmann’s conjecture, als solche Begriffe instead of aus solchen Begriffen.
[1 ]See Supplement XXI.
[2 ]Insert man before gleichwohl, and leave out können at the end of the sentence.
[1 ]Read seine Ursache instead of ihre.
[1 ]No doubt by reality I assert more than by possibility, but not in the thing itself, which can never contain more in its reality than what is contained in its complete possibility. While possibility is only the positing of a thing in reference to the understanding (in its empirical use), reality is, at the same time, a connection of it with perception.
[1 ]See Supplement XXII.
[1 ]Additions of the Second Edition.
[1 ]I am treating here of the real definition, which not only puts in place of the name of a thing other and more intelligible words, but that which contains a clear mark by which the object (definitum) can at all times be safely recognised, and by which the defined concept becomes fit for practical use. A real definition (Realarklärung) must therefore render clear the concept itself, and its objective reality also. Of this kind are the mathematical explanations which represent an object in intuition, according to its concept.
[2 ]Read nimmt instead of nehmen, and können instead of könne.
[1 ]The passage from ‘It seems to be’ to ‘objective concepts’ is left out in the Second Edition, and replaced by a short note, see Supplement XXIII.
[1 ]The passage from ‘Appearances’ to ‘given to me in intuition’ is left out in the Second Edition, and replaced by Supplement XXIV.
[1 ]Read welches instead of welcher.
[1 ]Addition of the Second Edition.
[1 ]An additional note in the Second Edition is given in Supplement XXV.