P 188 TRANSCENDENTAL DOCTRINE OF JUDGMENT (OR ANALYTIC OF PRINCIPLES) CHAPTER II SYSTEM OF ALL PRINCIPLES OF PURE UNDERSTANDING In the preceding chapter we have considered transcendental judgment with reference merely to the universal conditions under which it is alone justified in employing pure concepts of understanding for synthetic judgments. Our task now is to exhibit, in systematic connection, the judgments which understanding, under this critical provision, actually achieves a priori. There can be no question that in this enquiry our table of categories is the natural and the safe guide. For since it is through the relation of the categories to possible experience that all pure a priori knowledge of understanding has to be constituted, their relation to sensibility in general will exhibit completely and systematically all the transcendental principles of the use of the understanding. Principles a priori are so named not merely because they contain in themselves grounds of other judgements, but also because they are not themselves grounded in higher and more universal modes of knowledge. But this characteristic does not remove them beyond the sphere of proof. This proof cannot, indeed, be carried out in any objective fashion, since such principles [do not rest on objective considerations but] lie at the foundation of all knowledge of objects. This does not, however, prevent our attempting a proof, from the subjective sources of the possibility of knowledge of an object in general. Such proof is, indeed, indispensable, if the propositions are not to incur the suspicion of being merely surreptitious assertions. P 189 Secondly, we shall limit ourselves merely to those principles which stand in relation to the categories. The principles of the Transcendental Aesthetic, according to which space and time are the conditions of the possibility of all things as appearances, and likewise the restriction of these principles, namely, that they cannot be applied to things in themselves, are matters which do not come within the range of our present enquiry. For similar reasons mathematical principles form no part of this system. They are derived solely from intuition, not from the pure concept of understanding. Nevertheless, since they too are synthetic a priori judgments, their possibility must receive recognition in this chapter. For though their correctness and apodeictic certainty do not indeed require to be established, their possibility, as cases of evident a priori knowledge, has to be rendered conceivable, and to be deduced. We shall also have to treat of the principle of analytic judgments, in so far as it stands in contrast with that of synthetic judgments with which alone strictly we have to deal. For by thus contrasting them we free the theory of synthetic judgments from all misunderstanding, and have them in their own peculiar nature clear before us. THE SYSTEM OF THE PRINCIPLES OF PURE UNDERSTANDING Section 1 THE HIGHEST PRINCIPLE OF ALL ANALYTIC JUDGMENTS The universal, though merely negative, condition of all our judgments in general, whatever be the content of our knowledge, and however it may relate to the object, is that they be not self-contradictory; for if self-contradictory, these judgments are in themselves, even without reference to the object, null and void. But even if our judgment contains no contradiction, it may connect concepts in a manner not borne out by the object, or else in a manner for which no ground is given, either a priori or a posteriori, sufficient to justify such judgment, and so may P 190 still, in spite of being free from all inner contradiction, be either false or groundless. The proposition that no predicate contradictory of a thing can belong to it, is entitled the principle of contradiction, and is a universal, though merely negative, criterion of all truth. For this reason it belongs only to logic. It holds of knowledge, merely as knowledge in general, irrespective of content; and asserts that the contradiction completely cancels and invalidates it. But it also allows of a positive employment, not merely, that is, to dispel falsehood and error (so far as they rest on contradiction), but also for the knowing of truth. For, if the judgment is analytic, whether negative or affirmative, its truth can always be adequately known in accordance with the principle of contradiction. The reverse of that which as concept is contained and is thought in the knowledge of the object, is always rightly denied. But since the opposite of the concept would contradict the object, the concept itself must necessarily be affirmed of it. The principle of contradiction must therefore be recognised as being the universal and completely sufficient principle of all analytic knowledge; but beyond the sphere of analytic knowledge it has, as a sufficient criterion of truth, no authority and no field of application. The fact that no knowledge can be contrary to it without self-nullification, makes this principle a conditio sine qua non, but not a determining ground, of the truth of our [non-analytic] knowledge. Now in our critical enquiry it is only with the synthetic portion of our knowledge that we are concerned; and in regard to the truth of this kind of knowledge we can never look to the above principle for any positive information, though, of course, since it is inviolable, we must always be careful to conform to it. Although this famous principle is thus without content and merely formal, it has sometimes been carelessly formulated in a manner which involves the quite unnecessary admixture of a synthetic element. The formula runs: It is impossible that something should at one and the same time both be and not be. Apart from the fact that the apodeictic certainty, expressed through the word 'impossible', is superfluously added -- since P 191 it is evident of itself from the [very nature of the] proposition -- the proposition is modified by the condition of time. It then, as it were, asserts: A thing = A, which is something = B, cannot at the same time be not-B, but may very well in succession be both B and not-B. For instance, a man who is young cannot at the same time be old, but may very well at one time be young and at another time not-young, that is, old. The principle of contradiction, however, as a merely logical principle, must not in any way limit its assertions to time-relations. The above formula is therefore completely contrary to the intention of the principle. The misunderstanding results from our first of all separating a predicate of a thing from the concept of that thing, and afterwards connecting this predicate with its opposite -- a procedure which never occasions a contradiction with the subject but only with the predicate which has been synthetically connected with that subject, and even then only when both predicates are affirmed at one and the same time. If I say that a man who is unlearned is not learned, the condition, at one and the same time, must be added; for he who is at one time unlearned can very well at another be learned. But if I say, no unlearned man is learned, the proposition is analytic, since the property, unlearnedness, now goes to make up the concept of the subject, and the truth of the negative judgment then becomes evident as an immediate consequence of the principle of contradiction, without requiring the supplementary condition, at one and the same time. This, then, is the reason why I have altered its formulation, namely, in order that the nature of an analytic proposition be clearly expressed through it. THE SYSTEM OF THE PRINCIPLES OF PURE UNDERSTANDING Section 2 THE HIGHEST PRINCIPLE OF ALL SYNTHETIC JUDGMENTS The explanation of the possibility of synthetic judgments is a problem with which general logic has nothing to do. It need not even so much as know the problem by name. But in P 192 transcendental logic it is the most important of all questions; and indeed, if in treating of the possibility of synthetic a priori judgments we also take account of the conditions and scope of their validity, it is the only question with which it is concerned. For upon completion of this enquiry, transcendental logic is in a position completely to fulfil its ultimate purpose, that of determining the scope and limits of pure understanding. In the analytic judgment we keep to the given concept, and seek to extract something from it. If it is to be affirmative, I ascribe to it only what is already thought in it. If it is to be negative, I exclude from it only its opposite. But in synthetic judgments I have to advance beyond the given concept, viewing as in relation with the concept something altogether different from what was thought in it. This relation is consequently never a relation either of identity or of contradiction; and from the judgment, taken in and by itself, the truth or falsity of the relation can never be discovered. Granted, then, that we must advance beyond a given concept in order to compare it synthetically with another, a third something is necessary, as that wherein alone the synthesis of two concepts can be achieved. What, now, is this third something that is to be the medium of all synthetic judgments? There is only one whole in which all our representations are contained, namely, inner sense and its a priori form, time. The synthesis of representations rests on imagination; and their synthetic unity, which is required for judgment, on the unity of apperception. In these, therefore, [in inner sense, imagination, and apperception], we must look for the possibility of synthetic judgments; and since all three contain the sources of a priori representations, they must also account for the possibility of pure synthetic judgments. For these reasons they are, indeed, indispensably necessary for any knowledge of objects, which rests entirely on the synthesis of representations. If knowledge is to have objective reality, that is, to relate to an object, and is to acquire meaning and significance in respect to it, the object must be capable of being in some P 193 manner given. Otherwise the concepts are empty; through them we have indeed thought, but in this thinking we have really known nothing; we have merely played with representations. That an object be given (if this expression be taken, not as referring to some merely mediate process, but as signifying immediate presentation in intuition), means simply that the representation through which the object is thought relates to actual or possible experience. Even space and time, however free their concepts are from everything empirical, and however certain it is that they are represented in the mind completely a priori, would yet be without objective validity, senseless and meaningless, if their necessary application to the objects of experience were not established. Their representation is a mere schema which always stands in relation to the reproductive imagination that calls up and assembles the objects of experience. Apart from these objects of experience, they would be devoid of meaning. And so it is with concepts of every kind. The possibility of experience is, then, what gives objective reality to all our a priori modes of knowledge. Experience, however, rests on the synthetic unity of appearances, that is, on a synthesis according to concepts of an object of appearances in general. Apart from such synthesis it would not be knowledge, but a rhapsody of perceptions that would not fit into any context according to rules of a completely interconnected (possible) consciousness, and so would not conform to the transcendental and necessary unity of apperception. Experience depends, therefore, upon a priori principles of its form, that is, upon universal rules of unity in the synthesis of appearances. Their objective reality, as necessary conditions of experience, and indeed of its very possibility, can always be shown in experience. Apart from this relation synthetic a priori principles are completely impossible. For they have then no third something, that is, no object, in which the synthetic unity can exhibit the objective reality of its concepts. Although we know a priori in synthetic judgments a great deal regarding space in general and the figures which productive P 194 imagination describes in it, and can obtain such judgments without actually requiring any experience, yet even this knowledge would be nothing but a playing with a mere figment of the brain, were it not that space has to be regarded as a condition of the appearances which constitute the material for outer experience. Those pure synthetic judgments therefore relate, though only mediately, to possible experience, or rather to the possibility of experience; and upon that alone is founded the objective validity of their synthesis. Accordingly, since experience, as empirical synthesis, is, in so far as such experience is possible, the one species of knowledge which is capable of imparting reality to any non- empirical synthesis, this latter [type of synthesis], as knowledge a priori, can possess truth, that is, agreement with the object, only in so far as it contains nothing save what is necessary to synthetic unity of experience in general. The highest principle of all synthetic judgments is therefore this: every object stands under the necessary conditions of synthetic unity of the manifold of intuition in a possible experience. Synthetic a priori judgements are thus possible when we relate the formal conditions of a priori intuition, the synthesis of imagination and the necessary unity of this synthesis in a transcendental apperception, to a possible empirical knowledge in general. We then assert that the conditions of the possibility of experience in general are likewise conditions of the possibility of the objects of experience, and that for this reason they have objective validity in a synthetic a priori judgment. THE SYSTEM OF THE PRINCIPLES OF PURE UNDERSTANDING Section 3 SYSTEMATIC REPRESENTATION OF ALL THE SYNTHETIC PRINCIPLES OF PURE UNDERSTANDING That there should be principles at all is entirely due to the pure understanding. Not only is it the faculty of rules in respect P 195 of that which happens, but is itself the source of principles according to which everything that can be presented to us as an object must conform to rules. For without such rules appearances would never yield knowledge of an object corresponding to them. Even natural laws, viewed as principles of the empirical employment of understanding, carry with them an expression of necessity, and so contain at least the suggestion of a determination from grounds which are valid a priori and antecedently to all experience. The laws of nature, indeed, one and all, without exception, stand under higher principles of understanding. They simply apply the latter to special cases [in the field] of appearance. These principles alone supply the concept which contains the condition, and as it were the exponent, of a rule in general. What experience gives is the instance which stands under the rule. There can be no real danger of our regarding merely empirical principles as principles of pure understanding, or conversely. For the necessity according to concepts which distinguishes the principles of pure understanding, and the lack of which is evident in every empirical proposition, however general its application, suffices to make this confusion easily preventable. But there are pure a priori principles that we may not properly ascribe to the pure understanding, which is the faculty of concepts. For though they are mediated by the understanding, they are not derived from pure concepts but from pure intuitions. We find such principles in mathematics. The question, however, of their application to experience, that is, of their objective validity, nay, even the deduction of the possibility of such synthetic a priori knowledge, must always carry us back to the pure understanding. While, therefore, I leave aside the principles of mathematics, I shall none the less include those [more fundamental] principles upon which the possibility and a priori objective validity of mathematics are grounded. These latter must be regarded as the foundation of all mathematical principles. They proceed from concepts to intuition, not from intuition to concepts. In the application of pure concepts of understanding to P 196 possible experience, the employment of their synthesis is either mathematical or dynamical; for it is concerned partly with the mere intuition of an appearance in general, partly with its existence. The a priori conditions of intuition are absolutely necessary conditions of any possible experience; those of the existence of the objects of a possible empirical intuition are in themselves only accidental. The principles of mathematical employment will therefore be unconditionally necessary, that is, apodeictic. Those of dynamical employment will also indeed possess the character of a priori necessity, but only under the condition of empirical thought in some experience, therefore only mediately and indirectly. Notwithstanding their undoubted certainty throughout experience, they will not contain that immediate evidence which is peculiar to the former. But of this we shall be better able to judge at the conclusion of this system of principles. The table of categories is quite naturally our guide in the construction of the table of principles. For the latter are simply rules for the objective employment of the former. All principles of pure understanding are therefore -- 1 Axioms of intuition. 2 Anticipations of perception. P 196 3 Analogies of experience. 4 Postulates of empirical thought in general. P 196 These titles I have intentionally chosen in order to give prominence to differences in the evidence and in the application of the principles. It will soon become clear that the principles involved in the a priori determination of appearances according to the categories of quantity and of quality (only the formal aspect of quantity and quality being considered) allow of intuitive certainty, alike as regards their evidential force and as regards their a priori application to P 197 appearances. They are thereby distinguished from those of the other two groups, which are capable only of a merely discursive certainty. This distinction holds even while we recognise that the certainty is in both cases complete. I shall therefore entitle the former principles mathematical, and the latter dynamical. But it should be noted that we are as little concerned in the one case with the principles of mathematics as in the other with the principles of general physical dynamics. We treat only of the principles of pure understanding in their relation to inner sense (all differences among the given representations being ignored). It is through these principles of pure understanding that the special principles of mathematics and of dynamics become possible. I have named them, therefore, on account rather of their application than of their content. I now proceed to discuss them in the order in which they are given in the above table. 1 AXIOMS OF INTUITION Their principle is: All intuitions are extensive magnitudes. Proof ++ The Axioms of intuition. Principle of the pure understanding: All appearances are, in their intuition, extensive magnitudes. ++ All combination (conjunctio) is either composition (compositio) or connection (nexus). The former is the synthesis of the manifold where its constituents do not necessarily belong to one another. For example, the two triangles into which a square is divided by its diagonal do not necessarily belong to one another. Such also is the synthesis of the homogeneous in everything which can be mathematically treated. This synthesis can itself be divided into that of aggregation and that of coalition, the former P 198n applying to extensive and the latter to intensive quantities. P 197 Appearances, in their formal aspect, contain an intuition in space and time, which conditions them, one and all, P 198 a priori. They cannot be apprehended, that is, taken up into empirical consciousness, save through that synthesis of the manifold whereby the representations of a determinate space or time are generated, that is, through combination of the homogeneous manifold and consciousness of its synthetic unity. Consciousness of the synthetic unity of the manifold [and] homogeneous in intuition in general, in so far as the representation of an object first becomes possible by means of it, is, however, the concept of a magnitude (quantum). Thus even the perception of an object, as appearance, is only possible through the same synthetic unity of the manifold of the given sensible intuition as that whereby the unity of the combination of the manifold [and] homogeneous is thought in the concept of a magnitude. In other words, appearances are all without exception magnitudes, indeed extensive magnitudes. As intuitions in space or time, they must be represented through the same synthesis whereby space and time in general are determined. I entitle a magnitude extensive when the representation of the parts makes possible, and therefore necessarily precedes, the representation of the whole. I cannot represent to myself a line, however small, without drawing it in thought, that is, generating from a point all its parts one after another. Only in this way can the intuition be obtained. Similarly with all times, however small. In these I think to myself only that successive advance from one moment to another, whereby through the parts of time and their addition a determinate time-magnitude is generated. ++The second mode of combination (nexus) is the synthesis of the manifold so far as its constituents necessarily belong to one another, as, for example, the accident to some substance, or the effect to the cause. It is therefore synthesis of that which, though heterogeneous, is yet represented as combined a priori. This combination, as not being arbitrary and as concerning the connection of the existence of the manifold, I entitle dynamical. Such connection can itself, in turn, be divided into the physical connection of the appearances with one another, and their metaphysical connection in the a priori faculty of knowledge. P 198 As the [element of] P 199 pure intuition in all appearances is either space or time, every appearance is as intuition an extensive magnitude; only through successive synthesis of part to part in [the process of] its apprehension can it come to be known. All appearances are consequently intuited as aggregates, as complexes of previously given parts. This is not the case with magnitudes of every kind, but only with those magnitudes which are represented and apprehended by us in this extensive fashion. The mathematics of space (geometry) is based upon this successive synthesis of the productive imagination in the generation of figures. This is the basis of the axioms which formulate the conditions of sensible a priori intuition under which alone the schema of a pure concept of outer appearance can arise -- for instance, that between two points only one straight line is possible, or that two straight lines cannot enclose a space, etc. These are the axioms which, strictly, relate only to magnitudes (quanta) as such. As regards magnitude (quantitas), that is, as regards the answer to be given to the question, 'What is the magnitude of a thing? ' there are no axioms in the strict meaning of the term, although there are a number of propositions which are synthetic and immediately certain (indemonstrabilia). The propositions, that if equals be added to equals the wholes are equal, and if equals be taken from equals the remainders are equal, are analytic propositions; for I am immediately conscious of the identity of the production of the one magnitude with the production of the other. [Consequently, they are not] axioms, [for these] have to be a priori synthetic propositions. On the other hand, the evident propositions of numerical relation are indeed synthetic, but are not general like those of geometry, and cannot, therefore, be called axioms but only numerical formulas. The assertion that 7 & 5 is equal to 12 is not an analytic proposition. For neither in the representation of 7, nor in that of 5, nor in the representation of the combination of both, do I think the number 12. (That I must do so in the addition of the two numbers is not to the point, since in the analytic proposition the question is only whether I actually think the predicate in the representation of the subject. ) But although the proposition is synthetic, it is also P 200 only singular. So far as we are here attending merely to the synthesis of the homogeneous (of units), that synthesis can take place only in one way, although the employment of these numbers is general. If I assert that through three lines, two of which taken together are greater than the third, a triangle can be described, I have expressed merely the function of productive imagination whereby the lines can be drawn greater or smaller, and so can be made to meet at any and every possible angle. The number 7, on the other hand, is possible only in one way. So also is the number 12, as thus generated through the synthesis of 7 with 5. Such propositions must not, therefore, be called axioms (that would involve recognition of an infinite number of axioms), but numerical formulas. This transcendental principle of the mathematics of appearances greatly enlarges our a priori knowledge. For it alone can make pure mathematics, in its complete precision, applicable to objects of experience. Without this principle, such application would not be thus self-evident; and there has indeed been much confusion of thought in regard to it. Appearances are not things in themselves. Empirical intuition is possible only by means of the pure intuition of space and of time. What geometry asserts of pure intuition is therefore undeniably valid of empirical intuition. The idle objections, that objects of the senses may not conform to such rules of construction in space as that of the infinite divisibility of lines or angles, must be given up. For if these objections hold good, we deny the objective validity of space, and consequently of all mathematics, and no longer know why and how far mathematics can be applicable to appearances. The synthesis of spaces and times, being a synthesis of the essential forms of all intuition, is what makes possible the apprehension of appearance, and consequently every outer experience and all knowledge of the objects of such experience. Whatever pure mathematics establishes in regard to the synthesis of the form of apprehension is also necessarily valid of the objects apprehended. All objections are only the chicanery of a falsely P 201 instructed reason, which, erroneously professing to isolate the objects of the senses from the formal condition of our sensibility, represents them, in spite of the fact that they are mere appearances, as objects in themselves, given to the understanding. Certainly, on that assumption, no synthetic knowledge of any kind could be obtained of them a priori, and nothing therefore could be known of them synthetically through pure concepts of space. Indeed, the science which determines these concepts, namely geometry, would not itself be possible. 2 ANTICIPATIONS OF PERCEPTION In all appearances, the real that is an object of sensation has intensive magnitude, that is, a degree. Proof Perception is empirical consciousness, that is, a consciousness in which sensation is to be found. Appearances, as objects of perception, are not pure, merely formal, intuitions, like space and time. For in and by themselves these latter cannot be perceived. Appearances contain in addition to intuition the matter for some object in general (whereby something existing in space or time is represented); they contain, that is to say, the real of sensation as merely subjective representation, which gives us only the consciousness that the subject is affected, and which we relate to an object in general. Now from empirical consciousness to pure consciousness a graduated transition is possible, the real in the former completely vanishing and a merely formal a priori consciousness of the manifold in space and time remaining. ++ The Anticipations of Perception The principle which anticipates all perceptions, as such, is as follows: In all appearances sensation, and the real which corresponds to it in the object (realitas phaenomenon), has an intensive magnitude, that is, a degree. P 201 Consequently there is also possible a P 202 synthesis in the process of generating the magnitude of a sensation from its beginning in pure intuition = 0, up to any required magnitude. Since, however, sensation is not in itself an objective representation, and since neither the intuition of space nor that of time is to be met with in it, its magnitude is not extensive but intensive. This magnitude is generated in the act of apprehension whereby the empirical consciousness of it can in a certain time increase from nothing = 0 to the given measure. Corresponding to this intensity of sensation, an intensive magnitude, that is, a degree of influence on the sense [i.e. on the special sense involved], must be ascribed to all objects of perception, in so far as the perception contains sensation. All knowledge by means of which I am enabled to know and determine a priori what belongs to empirical knowledge may be entitled an anticipation; and this is undoubtedly the sense in which Epicurus employed the term prolepsis. But as there is an element in the appearances (namely, sensation, the matter of perception) which can never be known a priori, and which therefore constitutes the distinctive difference between empirical and a priori knowledge, it follows that sensation is just that element which cannot be anticipated. On the other hand, we might very well entitle the pure determinations in space and time, in respect of shape as well as of magnitude, anticipations of appearances, since they represent a priori that which may always be given a posteriori in experience. If, however, there is in every sensation, as sensation in general (that is, without a particular sensation having to be given), something that can be known a priori, this will, in a quite especial sense, deserve to be named anticipation. For it does indeed seem surprising that we should forestall experience, precisely in that which concerns what is only to be obtained through it, namely, its matter. Yet, none the less, such is actually the case. Apprehension by means merely of sensation occupies only an instant, if, that is, I do not take into account the succession of different sensations. As sensation is that element in P 203 the [field of] appearance the apprehension of which does not involve a successive synthesis proceeding from parts to the whole representation, it has no extensive magnitude. The absence of sensation at that instant would involve the representation of the instant as empty, therefore as = 0. Now what corresponds in empirical intuition to sensation is reality (realitas phaenomenon); what corresponds to its absence is negation = 0. Every sensation, however, is capable of diminution, so that it can decrease and gradually vanish. Between reality in the [field of] appearance and negation there is therefore a continuity of many possible intermediate sensations, the difference between any two of which is always smaller than the difference between the given sensation and zero or complete negation. In other words, the real in the [field of] appearance has always a magnitude. But since its apprehension by means of mere sensation takes place in an instant and not through successive synthesis of different sensations, and therefore does not proceed from the parts to the whole, the magnitude is to be met with only in the apprehension. The real has therefore magnitude, but not extensive magnitude. A magnitude which is apprehended only as unity, and in which multiplicity can be represented only through approximation to negation = 0, I entitle an intensive magnitude. Every reality in the [field of] appearance has therefore intensive magnitude or degree. If this reality is viewed as cause, either of sensation or of some other reality in the [field of] appearance, such as change, the degree of the reality as cause is then entitled a moment, the moment of gravity. It is so named for the reason that degree signifies only that magnitude the apprehension of which is not successive, but instantaneous. This, however, I touch on only in passing; for with causality I am not at present dealing. Every sensation, therefore, and likewise every reality in the [field of] appearance, however small it may be, has a degree, that is, an intensive magnitude which can always be diminished. Between reality and negation there is a continuity of possible realities and of possible smaller perceptions. P 204 Every colour, as for instance red, has a degree which, however small it may be, is never the smallest; and so with heat, the moment of gravity, etc. The property of magnitudes by which no part of them is the smallest possible, that is, by which no part is simple, is called their continuity. Space and time are quanta continua, because no part of them can be given save as enclosed between limits (points or instants), and therefore only in such fashion that this part is itself again a space or a time. Space therefore consists solely of spaces, time solely of times. Points and instants are only limits, that is, mere positions which limit space and time. But positions always presuppose the intuitions which they limit or are intended to limit; and out of mere positions, viewed as constituents capable of being given prior to space or time, neither space nor time can be constructed. Such magnitudes may also be called flowing, since the synthesis of productive imagination involved in their production is a progression in time, and the continuity of time is ordinarily designated by the term flowing or flowing away. All appearances, then, are continuous magnitudes, alike in their intuition, as extensive, and in their mere perception (sensation, and with it reality) as intensive. If the synthesis of the manifold of appearance is interrupted, we have an aggregate of different appearances, and not appearance as a genuine quantum. Such an aggregate is not generated by continuing without break productive synthesis of a certain kind, but through repetition of an ever-ceasing synthesis. If I called thirteen thalers a quantum of money, I should be correct, provided my intention is to state the value of a mark of fine silver. For this is a continuous magnitude in which no part is the smallest, and in which every part can constitute a piece of coin that always contains material for still smaller pieces. But if I understand by the phrase thirteen round thalers, so many coins, quite apart from the question of what their silver standard may be, I then use the phrase, quantum of thalers, inappropriately. It ought to be entitled an aggregate, that is, a number of pieces of money. But as unity must be presupposed in all number, appearance as unity is a quantum, and as a quantum is always a continum. P 205 Since all appearances, alike in their extensive and in their intensive aspect, are thus continuous magnitudes, it might seem to be an easy matter to prove with mathematical conclusiveness the proposition that all alteration (transition of a thing from one state to another), is continuous. But the causality of an alteration in general, presupposing, as it does, empirical principles, lies altogether outside the limits of a transcendental philosophy. For upon the question as to whether a cause capable of altering the state of a thing, that is, of determining it to the opposite of a certain given state, may be possible, the a priori understanding casts no light; and this not merely because it has no insight into its possibility (such insight is lacking to us in many other cases of a priori knowledge), but because alterableness is to be met with only in certain determinations of appearances, and because, whereas [in fact] the cause of these determinations lies in the unalterable, experience alone can teach what they are. Since in our present enquiry we have no data of which we can make use save only the pure fundamental concepts of all possible experience, in which there must be absolutely nothing that is empirical, we cannot, without destroying the unity of our system, anticipate general natural science, which is based on certain primary experiences. At the same time, there is no lack of proofs of the great value of our principle in enabling us to anticipate perceptions, and even to some extent to make good their absence, by placing a check upon all false inferences which might be drawn from their absence. If all reality in perception has a degree, between which and negation there exists an infinite gradation of ever smaller degrees, and if every sense must likewise possess some particular degree of receptivity of sensations, no perception, and consequently no experience, is possible that could prove, either immediately or mediately (no matter how far-ranging the reasoning may be), a complete absence of all reality in the [field of] appearance. In other words, the proof of an empty space or of an empty time can never be derived from experience. For, in the first place, the complete absence of reality P 206 from a sensible intuition can never be itself perceived; and, secondly, there is no appearance whatsoever and no difference in the degree of reality of any appearance from which it can be inferred. It is not even legitimate to postulate it in order to explain any difference. For even if the whole intuition of a certain determinate space or time is real through and through, that is, though no part of it is empty, none the less, since every reality has its degree, which can diminish to nothing (the void) through infinite gradations without in any way altering the extensive magnitude of the appearance, there must be infinite different degrees in which space and time may be filled. Intensive magnitude can in different appearances be smaller or greater, although the extensive magnitude of the intuition remains one and the same. Let us give an example. Almost all natural philosophers, observing -- partly by means of the moment of gravity or weight, partly by means of the moment of opposition to other matter in motion -- a great difference in the quantity of various kinds of matter in bodies that have the same volume, unanimously conclude that this volume, which constitutes the extensive magnitude of the appearance, must in all material bodies be empty in varying degrees. Who would ever have dreamt of believing that these students of nature, most of whom are occupied with problems in mathematics and mechanics, would base such an inference solely on a metaphysical presupposition -- the sort of assumption they so stoutly profess to avoid? They assume that the real in space (I may not here name it impenetrability or weight, since these are empirical concepts) is everywhere uniform and varies only in extensive magnitude, that is, in amount. Now to this presupposition, for which they could find no support in experience, and which is therefore purely metaphysical, I oppose a transcendental proof, which does not indeed explain the difference in the filling of spaces, but completely destroys the supposed necessity of the above presupposition, that the difference is only to be explained on the assumption of empty space. My proof has the merit at least of freeing the understanding, so that it is at liberty to think this difference in some other manner, should it be found that some other hypothesis is required for the explanation of the natural P 207 appearances. For we then recognise that although two equal spaces can be completely filled with different kinds of matter, so that there is no point in either where matter is not present, nevertheless every reality has, while keeping its quality unchanged, some specific degree (of resistance or weight) which can, without diminution of its extensive magnitude or amount, become smaller and smaller in infinitum, before it passes into the void and [so] vanishes [out of existence]. Thus a radiation which fills a space, as for instance heat, and similarly every other reality in the [field of] appearance, can diminish in its degree in infinitum, without leaving the smallest part of this space in the least empty. It may fill the space just as completely with these smaller degrees as another appearance does with greater degrees. I do not at all intend to assert that this is what actually occurs when material bodies differ in specific gravity, but only to establish from a principle of pure understanding that the nature of our perceptions allows of such a mode of explanation, that we are not justified in assuming the real in appearances to be uniform in degree, differing only in aggregation and extensive magnitude, and that we are especially in error when we claim that such interpretation can be based on an a priori principle of the understanding. This anticipation of perception must always, however appear somewhat strange to anyone trained in transcendental reflection, and to any student of nature who by such teaching has been trained to circumspection. The assertion that the understanding anticipates such a synthetic principle, ascribing a degree to all that is real in the appearances, and so asserting the possibility of an internal distinction in sensation itself (abstraction being made of its empirical quality), awakens doubts and difficulties. It is therefore a question not unworthy of solution, how the understanding can thus in a priori fashion pronounce synthetically upon appearances, and can indeed anticipate in that which in itself is merely empirical and concerns only sensation. The quality of sensation, as for instance in colours, taste, etc. , is always merely empirical, and cannot be represented P 208 a priori. But the real, which corresponds to sensations in general, as opposed to negation = 0, represents only that something the very concept of which includes being, and signifies nothing but the synthesis in an empirical consciousness in general. Empirical consciousness can in inner sense be raised from 0 to any higher degree, so that a certain extensive magnitude of intuition, as for instance of illuminated surface, may excite as great a sensation as the combined aggregate of many such surfaces has illuminated. [Since the extensive magnitude of the appearance thus varies independently], we can completely abstract from it, and still represent in the mere sensation in any one of its moments a synthesis that advances uniformly from 0 to the given empirical consciousness. Consequently, though all sensations as such are given only a posteriori, their property of possessing a degree can be known a priori. It is remarkable that of magnitudes in general we can know a priori only a single quality, namely, that of continuity, and that in all quality (the real in appearances) we can know a priori nothing save [in regard to] their intensive quantity, namely that they have degree. Everything else has to be left to experience. 3 ANALOGIES OF EXPERIENCE The principle of the analogies is: Experience is possible only through the representation of a necessary connection of perceptions. Proof Experience is an empirical knowledge, that is, a knowledge which determines an object through perceptions. ++ The Analogies of Experience The general principle of the analogies is: All appearances are, as regards their existence, subject a priori to rules determining their relation to one another in one time. P 209 It is a synthesis of perceptions, not contained in perception but itself containing in one consciousness the synthetic unity of the manifold of perceptions. This synthetic unity constitutes the essential in any knowledge of objects of the senses, that is, in experience as distinguished from mere intuition or sensation of the senses. In experience, however, perceptions come together only in accidental order, so that no necessity determining their connection is or can be revealed in the perceptions themselves. For apprehension is only a placing together of the manifold of empirical intuition; and we can find in it no representation of any necessity which determines the appearances thus combined to have connected existence in space and time. But since experience is a knowledge of objects through perceptions, the relation [involved] in the existence of the manifold has to be represented in experience, not as it comes to be constructed in time but as it exists objectively in time. Since time, however, cannot itself be perceived, the determination of the existence of objects in time can take place only through their relation in time in general, and therefore only through concepts that connect them a priori. Since these always carry necessity with them, it follows that experience is only possible through a representation of necessary connection of perceptions. The three modes of time are duration, succession, and coexistence. There will, therefore, be three rules of all relations of appearances in time, and these rules will be prior to all experience, and indeed make it possible. By means of these rules the existence of every appearance can be determined in respect of the unity of all time. The general principle of the three analogies rests on the necessary unity of apperception, in respect of all possible empirical consciousness, that is, of all perception, at every [instant of] time. And since this unity lies a priori at the foundation of empirical consciousness, it follows that the above principle rests on the synthetic unity of all appearances as regards their relation in time. For the original apperception stands in relation to inner sense (the sum of all representations), and indeed a priori to its form, that is, to the time-order of the manifold empirical consciousness. All this manifold must, as regards its time-relations, be united in the original apperception. This P 210 is demanded by the a priori transcendental unity of apperception, to which everything that is to belong to my knowledge (that is, to my unified knowledge), and so can be an object for me, has to conform. This synthetic unity in the time-relations of all perceptions, as thus determined a priori, is the law, that all empirical time-determinations must stand under rules of universal time-determination. The analogies of experience, with which we are now to deal, must be rules of this description. These principles have this peculiarity, that they are not concerned with appearances and the synthesis of their empirical intuition, but only with the existence of such appearances and their relation to one another in respect of their existence. The manner in which something is apprehended in appearance can be so determined a priori that the rule of its synthesis can at once give, that is to say, can bring into being, this [element of] a priori intuition in every example that comes before us empirically. The existence of appearances cannot, however, be thus known a priori; and even granting that we could in any such manner contrive to infer that something exists, we could not know it determinately, could not, that is, anticipate the features through which its empirical intuition is distinguished from other intuitions. The two previous principles, which, as justifying the application of mathematics to appearances, I entitled the mathematical, referred to the possibility of appearances, and taught how, alike as regards their intuition and the real in their perception, they can be generated according to rules of a mathematical synthesis. Both principles justify us in employing numerical magnitudes, and so enable us to determine appearance as magnitude. For instance, I can determine a priori, that is, can construct, the degree of sensations of sunlight by combining some 20,000 illuminations of the moon. These first principles may therefore be called constitutive. It stands quite otherwise with those principles which seek to bring the existence of appearances under rules a priori. For since existence cannot be constructed, the principles can apply only to the relations of existence, and can yield only regulative principles. We cannot, therefore, expect either axioms P 211 or anticipations. If, however, a perception is given in a time- relation to some other perception, then even although this latter is indeterminate, and we consequently cannot decide what it is, or what its magnitude may be, we may none the less assert that in its existence it is necessarily connected with the former in this mode of time. In philosophy analogies signify something very different from what they represent in mathematics. In the latter they are formulas which express the equality of two quantitative relations, and are always constitutive; so that if three members of the proportion are given, the fourth is likewise given, that is, can be constructed. But in philosophy the analogy is not the equality of two quantitative but of two qualitative relations; and from three given members we can obtain a priori knowledge only of the relation to a fourth, not of the fourth member itself. The relation yields, however, a rule for seeking the fourth member in experience, and a mark whereby it can be detected. An analogy of experience is, therefore, only a rule according to which a unity of experience may arise from perception. It does not tell us how mere perception or empirical intuition in general itself comes about. It is not a principle constitutive of the objects, that is, of the appearances, but only regulative. The same can be asserted of the postulates of empirical thought in general, which concern the synthesis of mere intuition (that is, of the form of appearance), of perception (that is, of the matter of perception), and of experience (that is, of the relation of these perceptions). They are merely regulative principles, and are distinguished from the mathematical, which are constitutive, not indeed in certainty -- both have certainty a priori -- but in the nature of their evidence, that is, as regards the character of the intuitive (and consequently of the demonstrative) factors peculiar to the latter. In this connection what has been said of all principles that are synthetic must be specially emphasised, namely, that these analogies have significance and validity only as principles of the empirical, not of the transcendental, employment of understanding; that only as such can they be established; and that appearances have therefore to be subsumed, not simply under P 212 the categories, but under their schemata. For if the objects to which these principles are to be related were things in themselves, it would be altogether impossible to know anything of them synthetically a priori. They are, however, nothing but appearances; and complete knowledge of them, in the furtherance of which the sole function of a priori principles must ultimately consist, is simply our possible experience of them. The principles can therefore have no other purpose save that of being the conditions of the unity of empirical knowledge in the synthesis of appearances. But such unity can be thought only in the schema of the pure concept of understanding. The category expresses a function which is restricted by no sensible condition, and contains the unity of this schema, [in so far only] as [it is the schema] of a synthesis in general. By these principles, then, we are justified in combining appearances only according to what is no more than an analogy with the logical and universal unity of concepts. In the principle itself we do indeed make use of the category, but in applying it to appearances we substitute for it its schema as the key to its employment, or rather set it alongside the category, as its restricting condition, and as being what may be called its formula. A FIRST ANALOGY Principle of Permanence of Substance In all change of appearances substance is permanent; its quantum in nature is neither increased nor diminished. ++ All appearances contain the permanent (substance) as the object itself, and the transitory as its mere determination that is, as a way in which the object exists. P 213 Proof All appearances are in time; and in it alone, as substratum (as permanent form of inner intuition), can either coexistence or succession be represented. Thus the time in which all change of appearances has to be thought, remains and does not change. For it is that in which, and as determinations of which, succession or coexistence can alone be represented. Now time cannot by itself be perceived. Consequently there must be found in the objects of perception, that is, in the appearances, the substratum which represents time in general; and all change or coexistence must, in being apprehended, be perceived in this substratum, and through relation of the appearances to it. But the substratum of all that is real, that is, of all that belongs to the existence of things, is substance; and all that belongs to existence can be thought only as a determination of substance. Consequently the permanent, in relation to which alone all time-relations of appearances can be determined, is substance in the [field of] appearance, that is, the real in appearance, and as the substrate of all change remains ever the same. And as it is thus unchangeable in its existence, its quantity in nature can be neither increased nor diminished. Our apprehension of the manifold of appearance is always successive, and is therefore always changing. Through it alone we can never determine whether this manifold, as object of experience, is coexistent or successive. For such determination we require an underlying ground which exists at all times, that is, something abiding and permanent, of which all change and coexistence are only so many ways (modes of time) in which the permanent exists. ++ Proof of this first Analogy All appearances are in time. Time can determine them as existing in a twofold manner, either as in succession to one another or as coexisting. Time, in respect of the former, is viewed as time-series, in respect of the latter as time-volume. P 214 And simultaneity and succession being the only relations in time, it follows tha t only in the permanent are relations of time possible. In other words, the permanent is the substratum of the empirical representation of time itself; in it alone is any determination of time possible. Permanence, as the abiding correlate of all existence of appearances, of all change and of all concomitance, expresses time in general. For change does not affect time itself, but only appearances in time. (Coexistence is not a mode of time itself; for none of the parts of time coexist; they are all in succession to one another. ) If we ascribe succession to time itself, we must think yet another time, in which the sequence would be possible. Only through the permanent does existence in different parts of the time-series acquire a magnitude which can be entitled duration. For in bare succession existence is always vanishing and recommencing, and never has the least magnitude. Without the permanent there is therefore no time- relation. Now time cannot be perceived in itself; the permanent in the appearances is therefore the substratum of all determination of time, and, as likewise follows, is also the condition of the possibility of all synthetic unity of perceptions, that is, of experience. All existence and all change in time have thus to be viewed as simply a mode of the existence of that which remains and persists. In all appearances the permanent is the object itself, that is, substance as phenomenon; everything, on the other hand, which changes or can change belongs only to the way in which substance or substances exist, and therefore to their determinations. I find that in all ages, not only philosophers, but even the common understanding, has recognised this permanence as a substratum of all change of appearances, and always assume it to be indubitable. The only difference in this matter between the common understanding and the philosopher is that the latter expresses himself somewhat more definitely, asserting that throughout all changes in the world substance remains, and that only the accidents change. But I nowhere find even the attempt at a proof of this obviously synthetic proposition. Indeed, it is very seldom placed, where it truly belongs, at the head of those laws of nature which are pure and completely a priori. Certainly the proposition, that substance is permanent, is tautological. For this permanence is P 215 our sole ground for applying the category of substance to appearance; and we ought first to have proved that in all appearances there is something permanent, and that the transitory is nothing but determination of its existence. But such a proof cannot be developed dogmatically, that is, from concepts, since it concerns a synthetic a priori proposition. Yet as it never occurred to anyone that such propositions are valid only in relation to possible experience, and can therefore be proved only through a deduction of the possibility of experience, we need not be surprised that though the above principle is always postulated as lying at the basis of experience (for in empirical knowledge the need of it is felt), it has never itself been proved. A philosopher, on being asked how much smoke weighs, made reply: "Subtract from the weight of the wood burnt the weight of the ashes which are left over, and you have the weight of the smoke". He thus presupposed as undeniable that even in fire the matter (substance) does not vanish, but only suffers an alteration of form. The proposition, that nothing arises out of nothing, is still another consequence of the principle of permanence, or rather of the ever-abiding existence, in the appearances, of the subject proper. For if that in the [field of] appearance which we name substance is to be the substratum proper of all time-determination, it must follow that all existence, whether in past or in future time, can be determined solely in and by it. We can therefore give an appearance the title 'substance' just for the reason that we presuppose its existence throughout all time, and that this is not adequately expressed by the word permanence, a term which applies chiefly to future time. But since the inner necessity of persisting is inseparably bound up with the necessity of always having existed, the expression [principle of permanence] may be allowed to stand. Gigni de nihilo nihil, in nihilum nil posse reverti, were two propositions which the ancients always connected together, but which are now sometimes mistakenly separated owing to the belief that they apply to things in themselves, and that the first would run counter to the dependence of the world -- even in respect of its substance -- upon a supreme cause. But such apprehension is unnecessary. For we have here to deal only with appearances in the P 216 field of experience; and the unity of experience would never be possible if we were willing to allow that new things, that is, new substances, could come into existence. For we should then lose that which alone can represent the unity of time, namely, the identity of the substratum, wherein alone all change has thoroughgoing unity. This permanence is, however, simply the mode in which we represent to ourselves the existence of things in the [field of] appearance. The determinations of a substance, which are nothing but special ways in which it exists, are called accidents. They are always real, because they concern the existence of substance. (Negations are only determinations which assert the non- existence of something in substance. ) If we ascribe a special [kind of] existence to this real in substance (for instance, to motion, as an accident of matter), this existence is entitled inherence, in distinction from the existence of substance which is entitled subsistence. But this occasions many misunderstandings; it is more exact and more correct to describe an accident as being simply the way in which the existence of a substance is positively determined. But since it is unavoidable, owing to the conditions of the logical employment of our understanding, to separate off, as it were, that which in the existence of a substance can change while the substance still remains, and to view this variable element in relation to the truly permanent and radical, this category has to be assigned a place among the categories of relation, but rather as the condition of relations than as itself containing a relation. The correct understanding of the concept of alteration is also grounded upon [recognition of] this permanence. Coming to be and ceasing to be are not alterations of that which comes to be or ceases to be. Alteration is a way of existing which follows upon another way of existing of the same object. All that alters persists, and only its state changes. Since this change thus concerns only the determinations, which can cease to be or begin to be, we can say, using what may seem a somewhat paradoxical expression, that only the permanent P 217 (substance) is altered, and that the transitory suffers no alteration but only a change, inasmuch as certain determinations cease to be and others begin to be. Alteration can therefore be perceived only in substances. A coming to be or ceasing to be that is not simply a determination of the permanent but is absolute, can never be a possible perception. For this permanent is what alone makes possible the representation of the transition from one state to another, and from not-being to being. These transitions can be empirically known only as changing determinations of that which is permanent. If we assume that something absolutely begins to be, we must have a point of time in which it was not. But to what are we to attach this point, if not to that which already exists? For a preceding empty time is not an object of perception. But if we connect the coming to be with things which previously existed, and which persist in existence up to the moment of this coming to be, this latter must be simply a determination of what is permanent in that which precedes it. Similarly also with ceasing to be; it presupposes the empirical representation of a time in which an appearance no longer exists. Substances, in the [field of] appearance, are the substrata of all determinations of time. If some of these substances could come into being and others cease to be, the one condition of the empirical unity of time would be removed. The appearances would then relate to two different times, and existence would flow in two parallel streams -- which is absurd. There is only one time in which all different times must be located not as coexistent but as in succession to one another. Permanence is thus a necessary condition under which alone appearances are determinable as things or objects in a possible experience. We shall have occasion in what follows to make such observations as may seem necessary in regard to the empirical criterion of this necessary permanence -- the criterion, consequently, of the substantiality of appearances. P 218 B SECOND ANALOGY Principle of Succession in Time, in accordance with the Law of Causality All alterations take place in conformity with the law of the connection of cause and effect. Proof (The preceeding principle has shown that all appearances of succession in time are one and all only alterations, that is a successive being and not-being of the determinations of substance which abides; and therefore that the being of substance as following on its not-being, or its not-being as following upon its being cannot be admitted -- in other words, that there is no coming into being or passing away of substance itself. Still otherwise expressed the principle is, that all change (succession) of appearances is merely alteration. Coming into being and passing away of substance are not alterations of it, since the concept of alteration presupposes one and the same subject as existing with two opposite determinations, and therefore as abiding. With this preliminary reminder, we pass to the proof. ) I perceive that appearances follow one another, that is, that there is a state of things at one time the opposite of which was in the preceding time. Thus I am really connecting two perceptions in time. Now connection is not the work of mere sense and intuition, but is here the product of a synthetic faculty of imagination, which determines inner sense in respect of the time-relation. ++ Principle of Production Everything that happens, that is, begins to be, presupposes something upon which it follows according to a rule. P 218 But imagination can connect these two states P 219 in two ways, so that either the one or the other precedes in time. For time cannot be perceived in itself, and what precedes and what follows cannot, therefore, by relation to it, be empirically determined in the object. I am conscious only that my imagination sets the one state before and the other after, not that the one state precedes the other in the object. In other words, the objective relation of appearances that follow upon one another is not to be determined through mere perception. In order that this relation be known as determined, the relation between the two states must be so thought that it is thereby determined as necessary which of them must be placed before, and which of them after, and that they cannot be placed in the reverse relation. But the concept which carries with it a necessity of synthetic unity can only be a pure concept that lies in the understanding, not in perception; and in this case it is the concept of the relation of cause and effect, the former of which determines the latter in time, as its consequence -- not as in a sequence that may occur solely in the imagination (or that may not be perceived at all). Experience itself -- in other words, empirical knowledge of appearances -- is thus possible only in so far as we subject the succession of appearances, and therefore all alteration, to the law of causality; and, as likewise follows, the appearances, as objects of experience, are themselves possible only in conformity with the law. The apprehension of the manifold of appearance is always successive. The representations of the parts follow upon one another. Whether they also follow one another in the object is a point which calls for further reflection, and which is not decided by the above statement. Everything, every representation even, in so far as we are conscious of it, may be entitled object. But it is a question for deeper enquiry what the word 'object' ought to signify in respect of appearances when these are viewed not in so far as they are (as representations) objects, but only in so far as they stand for an object. The appearances, in so far as they are objects of consciousness simply in virtue of being representations, are not in any way distinct from their apprehension, that is, from their reception in the synthesis of imagination; and we must therefore P 220 agree that the manifold of appearances is always generated in the mind successively. Now if appearances were things in themselves, then since we have to deal solely with our representations, we could never determine from the succession of the representations how their manifold may be connected in the object. How things may be in themselves, apart from the representations through which they affect us, is entirely outside our sphere of knowledge. In spite, however, of the fact that the appearances are not things in themselves, and yet are what alone can be given to us to know, in spite also of the fact that their representation in apprehension is always successive, I have to show what sort of a connection in time belongs to the manifold in the appearances themselves. For instance, the apprehension of the manifold in the appearance of a house which stands before me is successive. The question then arises, whether the manifold of the house is also in itself successive. This, however, is what no one will grant. Now immediately I unfold the transcendental meaning of my concepts of an object, I realise that the house is not a thing in itself, but only an appearance, that is, a representation, the transcendental object of which is unknown. What, then, am I to understand by the question: how the manifold may be connected in the appearance itself, which yet is nothing in itself? That which lies in the successive apprehension is here viewed as representation, while the appearance which is given to me, notwithstanding that it is nothing but the sum of these representations, is viewed as their object; and my concept, which I derive from the representations of apprehension, has to agree with it. Since truth consists in the agreement of knowledge with the object, it will at once be seen that we can here enquire only regarding the formal conditions of empirical truth, and that appearance, in contradistinction to the representations of apprehension, can be represented as an object distinct from them only if it stands under a rule which distinguishes it from every other apprehension and necessitates some one particular mode of connection of the manifold. The object is that in the appearance which contains the condition of this necessary rule of apprehension. Let us now proceed to our problem. That something happens, i.e. that something, or some state which did not P 221 previously exist, comes to be, cannot be perceived unless it is preceded by an appearance which does not contain in itself this state. For an event which should follow upon an empty time, that is, a coming to be preceded by no state of things, is as little capable of being apprehended as empty time itself. Every apprehension of an event is therefore a perception that follows upon another perception. But since, as I have above illustrated by reference to the appearance of a house, this likewise happens in all synthesis of apprehension, the apprehension of an event is not yet thereby distinguished from other apprehensions. But, as I also note, in an appearance which contains a happening (the preceding state of the perception we may entitle A, and the succeeding B) B can be apprehended only as following upon A; the perception A cannot follow upon B but only precede it. For instance, I see a ship move down stream. My perception of its lower position follows upon the perception of its position higher up in the stream, and it is impossible that in the apprehension of this appearance the ship should first be perceived lower down in the stream and afterwards higher up. The order in which the perceptions succeed one another in apprehension is in this instance determined, and to this order apprehension is bound down. In the previous example of a house my perceptions could begin with the apprehension of the roof and end with the basement, or could begin from below and end above; and I could similarly apprehend the manifold of the empirical intuition either from right to left or from left to right. In the series of these perceptions there was thus no determinate order specifying at what point I must begin in order to connect the manifold empirically. But in the perception of an event there is always a rule that makes the order in which the perceptions (in the apprehension of this appearance) follow upon one another a necessary order. In this case, therefore, we must derive the subjective succession of apprehension from the objective succession of appearances. Otherwise the order of apprehension is entirely undetermined, and does not distinguish one appearance from another. Since the subjective succession by itself is altogether P 222 arbitrary, it does not prove anything as to the manner in which the manifold is connected in the object. The objective succession will therefore consist in that order of the manifold of appearance according to which, in conformity with a rule, the apprehension of that which happens follows upon the apprehension of that which precedes. Thus only can I be justified in asserting, not merely of my apprehension, but of appearance itself, that a succession is to be met with in it. This is only another way of saying that I cannot arrange the apprehension otherwise than in this very succession. In conformity with such a rule there must lie in that which precedes an event the condition of a rule according to which this event invariably and necessarily follows. I cannot reverse this order, proceeding back from the event to determine through apprehension that which precedes. For appearance never goes back from the succeeding to the preceding point of time, though it does indeed stand in relation to some preceding point of time. The advance, on the other hand, from a given time to the determinate time that follows is a necessary advance. Therefore, since there certainly is something that follows [i.e. that is apprehended as following], I must refer it necessarily to something else which precedes it and upon which it follows in conformity with a rule, that is, of necessity. The event, as the conditioned, thus affords reliable evidence of some condition, and this condition is what determines the event. Let us suppose that there is nothing antecedent to an event, upon which it must follow according to rule. All succession of perception would then be only in the apprehension, that is, would be merely subjective, and would never enable us to determine objectively which perceptions are those that really precede and which are those that follow. We should then have only a play of representations, relating to no object; that is to say, it would not be possible through our perception to distinguish one appearance from another as regards relations of time. For the succession in our apprehension would always be one and the same, and there would be nothing in the appearance which so determines it that a certain sequence is rendered objectively necessary. I could not then assert that two states follow upon one another in the [field of] P 223 appearance, but only that one apprehension follows upon the other. That is something merely subjective, determining no object; and may not, therefore, be regarded as knowledge of any object, not even of an object in the [field of] appearance. If, then, we experience that something happens, we in so doing always presuppose that something precedes it, on which it follows according to a rule. Otherwise I should not say of the object that it follows. For mere succession in my apprehension, if there be no rule determining the succession in relation to something that precedes, does not justify me in assuming any succession in the object. I render my subjective synthesis of apprehension objective only by reference to a rule in accordance with which the appearances in their succession, that is, as they happen, are determined by the preceding state. The experience of an event [i.e. of anything as happening] is itself possible only on this assumption. This may seem to contradict all that has hitherto been taught in regard to the procedure of our understanding. The accepted view is that only through the perception and comparison of events repeatedly following in a uniform manner upon preceding appearances are we enabled to discover a rule according to which certain events always follow upon certain appearances, and that this is the way in which we are first led to construct for ourselves the concept of cause. Now the concept, if thus formed, would be merely empirical, and the rule which it supplies, that everything which happens has a cause, would be as contingent as the experience upon which it is based. Since the universality and necessity of the rule would not be grounded a priori, but only on induction, they would be merely fictitious and without genuinely universal validity. It is with these, as with other pure a priori representations -- for instance, space and time. We can extract clear concepts of them from experience, only because we have put them into experience, and because experience is thus itself brought about only by their means. Certainly, the logical clearness of this representation of a rule determining the series of events is possible only after we have employed it in experience. Nevertheless, P 224 recognition of the rule, as a condition of the synthetic unity of appearances in time, has been the ground of experience itself, and has therefore preceded it a priori. We have, then, to show, in the case under consideration, that we never, even in experience, ascribe succession (that is, the happening of some event which previously did not exist) to the object, and so distinguish it from subjective sequence in our apprehension, except when there is an underlying rule which compels us to observe this order of perceptions rather than any other; nay, that this compulsion is really what first makes possible the representation of a succession in the object. We have representations in us, and can become conscious of them. But however far this consciousness may extend, and however careful and accurate it may be, they still remain mere representations, that is, inner determinations of our mind in this or that relation of time. How, then, does it come about that we posit an object for these representations, and so, in addition to their subjective reality, as modifications, ascribe to them some mysterious kind of objective reality. Objective meaning cannot consist in the relation to another representation (of that which we desire to entitle object), for in that case the question again arises, how this latter representation goes out beyond itself, acquiring objective meaning in addition to the subjective meaning which belongs to it as determination of the mental state. If we enquire what new character relation to an object confers upon our representations, what dignity they thereby acquire, we find that it results only in subjecting the representations to a rule, and so in necessitating us to connect them in some one specific manner; and conversely, that only in so far as our representations are necessitated in a certain order as regards their time-relations do they acquire objective meaning. In the synthesis of appearances the manifold of representations is always successive. Now no object is hereby represented, since through this succession, which is common to all apprehensions, nothing is distinguished from anything else. But immediately I perceive or assume that in this succession there is a relation to the preceding state, from which the representation P 225 follows in conformity with a rule, I represent something as an event, as something that happens; that is to say, I apprehend an object to which I must ascribe a certain determinate position in time -- a position which, in view of the preceding state, cannot be otherwise assigned. When, therefore, I perceive that something happens, this representation first of all contains [the consciousness] that there is something preceding, because only by reference to what precedes does the appearance acquire its time-relation, namely, that of existing after a preceding time in which it itself was not. But it can acquire this determinate position in this relation of time only in so far as something is presupposed in the preceding state upon which it follows invariably, that is, in accordance with a rule. From this there results a twofold consequence. In the first place, I cannot reverse the series, placing that which happens prior to that upon which it follows. And secondly, if the state which precedes is posited, this determinate event follows inevitably and necessarily. The situation, then, is this: there is an order in our representations in which the present, so far as it has come to be, refers us to some preceding state as a correlate of the event which is given; and though this correlate is, indeed, indeterminate, it none the less stands in a determining relation to the event as its consequence, connecting the event in necessary relation with itself in the time-series. If, then, it is a necessary law of our sensibility, and therefore a formal condition of all perceptions, that the preceding time necessarily determines the succeeding (since I cannot advance to the succeeding time save through the preceding), it is also an indispensable law of empirical representation of the time-series that the appearances of past time determine all existences in the succeeding time, and that these latter, as events, can take place only in so far as the appearances of past time determine their existence in time, that is, determine them according to a rule. For only in appearances can we empirically apprehend this continuity in the connection of times. Understanding is required for all experience and for its possibility. Its primary contribution does not consist in making the representation of objects distinct, but in making the P 226 representation of an object possible at all. This it does by carrying the time-order over into the appearances and their existence. For to each of them, [viewed] as [a] consequent, it assigns, through relation to the preceding appearances, a position determined a priori in time. Otherwise, they would not accord with time itself, which [in] a priori [fashion] determines the position of all its parts. Now since absolute time is not an object of perception, this determination of position cannot be derived from the relation of appearances to it. On the contrary, the appearances must determine for one another their position in time, and make their time-order a necessary order. In other words, that which follows or happens must follow in conformity with a universal rule upon that which was contained in the preceding state. A series of appearances thus arises which, with the aid of the understanding, produces and makes necessary the same order and continuous connection in the series of possible perceptions as is met with a priori in time -- the form of inner intuition wherein all perceptions must have a position. That something happens is, therefore, a perception which belongs to a possible experience. This experience becomes actual when I regard the appearance as determined in its position in time, and therefore as an object that can always be found in the connection of perceptions in accordance with a rule. This rule, by which we determine something according to succession of time, is, that the condition under which an event invariably and necessarily follows is to be found in what precedes the event. The principle of sufficient reason is thus the ground of possible experience, that is, of objective knowledge of appearances in respect of their relation in the succession of time. The proof of this principle rests on the following considerations. All empirical knowledge involves the synthesis of the manifold by the imagination. This synthesis is always successive, that is, the representations in it are always sequent upon one another. In the imagination this sequence is not in any way determined in its order, as to what must precede and what must follow, and the series of sequent representations P 227 can indifferently be taken either in backward or in forward order. But if this synthesis is a synthesis of apprehension of the manifold of a given appearance, the order is determined in the object, or, to speak more correctly, is an order of successive synthesis that determines an object. In accordance with this order something must necessarily precede, and when this antecedent is posited, something else must necessarily follow. If, then, my perception is to contain knowledge of an event, of something as actually happening, it must be an empirical judgment in which we think the sequence as determined; that is, it presupposes another appearance in time, upon which it follows necessarily, according to a rule. Were it not so, were I to posit the antecedent and the event were not to follow necessarily thereupon, I should have to regard the succession as a merely subjective play of my fancy; and if I still represented it to myself as something objective, I should have to call it a mere dream. Thus the relation of appearances (as possible perceptions) according to which the subsequent event, that which happens, is, as to its existence, necessarily determined in time by something preceding in conformity with a rule -- in other words, the relation of cause to effect -- is the condition of the objective validity of our empirical judgments, in respect of the series of perceptions, and so of their empirical truth; that is to say, it is the condition of experience. The principle of the causal relation in the sequence of appearances is therefore also valid of all objects of experience ([in so far as they are] under the conditions of succession), as being itself the ground of the possibility of such experience. At this point a difficulty arises with which we must at once deal. The principle of the causal connection among appearances is limited in our formula to their serial succession, whereas it applies also to their coexistence, when cause and effect are simultaneous. For instance, a room is warm while the outer air is cool. I look around for the cause, and find a heated stove. Now the stove, as cause, is simultaneous with its effect, the heat of the room. Here there is no serial succession in time between cause and effect. They are simultaneous, and P 228 yet the law is valid. The great majority of efficient natural causes are simultaneous with their effects, and the sequence in time of the latter is due only to the fact that the cause cannot achieve its complete effect in one moment. But in the moment in which the effect first comes to be, it is invariably simultaneous with the causality of its cause. If the cause should have ceased to exist a moment before, the effect would never have come to be. Now we must not fail to note that it is the order of time, not the lapse of time, with which we have to reckon; the relation remains even if no time has elapsed. The time between the causality of the cause and its immediate effect may be [a] vanishing [quantity], and they may thus be simultaneous; but the relation of the one to the other will always still remain determinable in time. If I view as a cause a ball which impresses a hollow as it lies on a stuffed cushion, the cause is simultaneous with the effect. But I still distinguish the two through the time-relation of their dynamical connection. For if I lay the ball on the cushion, a hollow follows upon the previous flat smooth shape; but if (for any reason) there previously exists a cushion, a leaden ball does not follow upon it. The sequence in time is thus the sole empirical criterion of an effect in its relation to the causality of the cause which precedes it. A glass [filled with water] is the cause of the rising of the water above its horizontal surface, although both appearances are simultaneous. For immediately I draw off water from a larger vessel into the glass, something follows, namely the alteration from the horizontal position which the water then had to the concave form which it assumes in the glass. Causality leads to the concept of action, this in turn to the concept of force, and thereby to the concept of substance. As my critical scheme, which is concerned solely with the sources of synthetic a priori knowledge, must not be complicated through the introduction of analyses which aim only at the clarification, not at the extension, of concepts, I leave detailed exposition of my concepts to a future system of pure reason. Such an analysis has already, indeed, been developed in considerable detail in the text-books. But I must not leave unconsidered the empirical criterion of a substance, P 229 in so far as substance appears to manifest itself not through permanence of appearance, but more adequately and easily through action. Wherever there is action -- and therefore activity and force -- there is also substance, and it is in substance alone that the seat of this fruitful source of appearances must be sought. This is, so far, well said; but when we seek to explain what is to be understood by substance, and in so doing are careful to avoid the fallacy of reasoning in a circle, the discovery of an answer is no easy task. How are we to conclude directly from the action to the permanence of that which acts? For that is an essential and quite peculiar characteristic of substance (as phenomenon). But while according to the usual procedure, which deals with concepts in purely analytic fashion, this question would be completely insoluble, it presents no such difficulty from the standpoint which we have been formulating. Action signifies the relation of the subject of causality to its effect. Since, now, every effect consists in that which happens, and so in the transitory, which signifies time in its character of succession, its ultimate subject, as the substratum of everything that changes, is the permanent, that is, substance. For according to the principle of causality actions are always the first ground of all change of appearances, and cannot therefore be found in a subject which itself changes, because in that case other actions and another subject would be required to determine this change. For this reason action is a sufficient empirical criterion to establish the substantiality of a subject, without my requiring first to go in quest of its permanence through the comparison of perceptions. Besides, by such method (of comparison) we could not achieve the completeness required for the magnitude and strict universality of the concept. That the first subject of the causality of all coming to be and ceasing to be cannot itself, in the field of appearances, come to be and cease to be, is an assured conclusion which leads to [the concept of] empirical necessity and permanence in existence, and so to the concept of a substance as appearance. When something happens, the mere coming to be, apart from all question of what it is that has come to be, is already in P 230 itself a matter for enquiry. The transition from the not-being of a state to this state, even supposing that this state [as it occurs] in the [field of] appearance exhibited no quality, of itself demands investigation. This coming to be, as was shown above in the First Analogy, does not concern substance, which does not come to be out of nothing. For if coming to be out of nothing is regarded as effect of a foreign cause, it has to be entitled creation, and that cannot be admitted as an event among appearances since its mere possibility would destroy the unity of experience. On the other hand, when I view all things not as phenomena but as things in themselves, and as objects of the mere understanding, then despite their being substances they can be regarded, in respect of their existence, as depending upon a foreign cause. But our terms would then carry with them quite other meanings, and would not apply to appearances as possible objects of experience. How anything can be altered, and how it should be possible that upon one state in a given moment an opposite state may follow in the next moment -- of this we have not, a priori, the least conception. For that we require knowledge of actual forces, which can only be given empirically, as, for instance, of the moving forces, or what amounts to the same thing, of certain successive appearances, as motions, which indicate [the presence of] such forces. But apart from all question of what the content of the alteration, that is, what the state which is altered, may be, the form of every alteration, the condition under which, as a coming to be of another state, it can alone take place, and so the succession of the states themselves (the happening), can still be considered a priori according to the law of causality and the conditions of time. If a substance passes from one state, a, to another, b, the point of time of the second is distinct from that of the first, and follows upon it. ++ It should be carefully noted that I speak not of the alteration of certain relations in general, but of alteration of state. Thus, when a body moves uniformly, it does not in any way alter its state (of motion); that occurs only when its motion increases or diminishes. P 231 Similarly, the second state as reality in the [field of] appearance differs from the first wherein it did not exist, as b from zero. That is to say, even if the state b differed from the state a only in magnitude, the alteration would be a coming to be of b - a, which did not exist in the previous state, and in respect of which it = 0. The question therefore arises how a thing passes from one state = a to another = b. Between two instants there is always a time, and between any two states in the two instants there is always a difference which has magnitude. For all parts of appearances are always themselves magnitudes. All transition from one state to another therefore occurs in a time which is contained between two instants, of which the first determines the state from which the thing arises, and the second that into which it passes. Both instants, then, are limits of the time of a change, and so of the intermediate state between the two states, and therefore as such form part of the total alteration. Now every alteration has a cause which evinces its causality in the whole time in which the alteration takes place. This cause, therefore, does not engender the alteration suddenly, that is, at once or in one instant, but in a time; so that, as the time increases from the initial instant a to its completion in b, the magnitude of the reality (b - a) is in like manner generated through all smaller degrees which are contained between the first and the last. All alteration is thus only possible through a continuous action of the causality which, so far as it is uniform, is entitled a moment. The alteration does not consist of these moments, but is generated by them as their effect. That is the law of the continuity of all alteration. Its ground is this: that neither time nor appearance in time consists of parts which are the smallest [possible], and that, nevertheless, the state of a thing passes in its alteration through all these parts, as elements, to its second state. In the [field of] appearance there is no difference of the real that is the smallest, just as in the magnitude of times there is no time that is the smallest; and the new state of reality accordingly proceeds from the first wherein this reality was not, through all the infinite degrees, the differences of which from one another are all smaller than that between 0 and a. P 232 While we are not concerned to enquire what utility this principle may have in the investigation of nature, what does imperatively call for investigation is the question how such a principle, which seems to extend our knowledge of nature, can be possible completely a priori. Such an enquiry cannot be dispensed with, even though direct inspection may show the principle to be true and [empirically] real, and though the question, how it should be possible, may therefore be considered superfluous. For there are so many ungrounded claims to the extension of our knowledge through pure reason, that we must take it as a universal principle that any such pretension is of itself a ground for being always mistrustful, and that, in the absence of evidence afforded by a thoroughgoing deduction, we may not believe and assume the justice of such claims, no matter how clear the dogmatic proof of them may appear to be. All increase in empirical knowledge, and every advance of perception, no matter what the objects may be, whether appearances or pure intuitions, is nothing but an extension of the determination of inner sense, that is, an advance in time. This advance in time determines everything, and is not in itself determined through anything further. That is to say, its parts are given only in time, and only through the synthesis of time; they are not given antecedently to the synthesis. For this reason every transition in perception to something which follows in time is a determination of time through the generation of this perception, and since time is always and in all its parts a magnitude, is likewise the generation of a perception as a magnitude through all degrees of which no one is the smallest, from zero up to its determinate degree. This reveals the possibility of knowing a priori a law of alterations, in respect of their form. We are merely anticipating our own apprehension, the formal condition of which, since it dwells in us prior to all appearance that is given, must certainly be capable of being known a priori. In the same manner, therefore, in which time contains the sensible a priori condition of the possibility of a continuous advance of the existing to what follows, the understanding, by virtue of the unity of apperception, is the a priori condition of the possibility of a continuous determination of all positions for the appearances in this time, through the series of P 233 causes and effects, the former of which inevitably lead to the existence of the latter, and so render the empirical knowledge of the time-relations valid universally for all time, and therefore objectively valid. C THIRD ANALOGY Principle of Coexistence, in accordance with the Law of Reciprocity or Community All substances, in so far as they can be perceived to coexist in space, are in thoroughgoing reciprocity. Proof Things are coexistent when in empirical intuition the perceptions of them can follow upon one another reciprocally, which, as has been shown in the proof of the second principle, cannot occur in the succession of appearances. Thus I can direct my perception first to the moon and then to the earth, or, conversely, first to the earth and then to the moon; and because the perceptions of these objects can follow each other reciprocally, I say that they are coexistent. Now coexistence is the existence of the manifold in one and the same time. But time itself cannot be perceived, and we are not, therefore, in a position to gather, simply from things being set in the same time, that their perceptions can follow each other reciprocally. The synthesis of imagination in apprehension would only reveal that the one perception is in the subject when the other is not there, and vice versa, but not that the objects are coexistent, that is, that if the one exists the other exists at the same time, and that it is only because they thus coexist that the perceptions are able to follow one another re ciprocally. ++ Principle of Community All substances, so far as they coexist, stand in thoroughgoing community, that is, in mutual interaction. P 234 Consequently, in the case of things which coexist externally to one another, a pure concept of the reciprocal sequence of their determinations is required, if we are to be able to say that the reciprocal sequence of the perceptions is grounded in the object, and so to represent the coexistence as objective. But the relation of substances in which the one contains determinations the ground of which is contained in the other is the relation of influence; and when each substance reciprocally contains the ground of the determinations in the other, the relation is that of community or reciprocity. Thus the coexistence of substances in space cannot be known in experience save on the assumption of their reciprocal interaction. This is therefore the condition of the possibility of the things themselves as objects of experience. Things are coexistent so far as they exist in one and the same time. But how do we know that they are in one and the same time? We do so when the order in the synthesis of apprehension of the manifold is a matter of indifference, that is, whether it be from A through B, C, D to E, or reversewise from E to A. For if they were in succession to one another in time, in the order, say, which begins with A and ends in E, it is impossible that we should begin the apprehension in the perception of E and proceed backwards to A, since A belongs to past time and can no longer be an object of apprehension. Now assuming that in a manifold of substances as appearances each of them is completely isolated, that is, that no one acts on any other and receives reciprocal influences in return, I maintain that their coexistence would not be an object of a possible perception and that the existence of one could not lead by any path of empirical synthesis to the existence of another. For if we bear in mind that they would be separated by a completely empty space, the perception which advances from one to another in time would indeed, by means of a succeeding perception, determine the existence of the latter, but would not be able to distinguish whether it follows P 235 objectively upon the first or whether it is not rather coexistent with it. There must, therefore, besides the mere existence of A and B, be something through which A determines for B, and also reversewise B determines for A, its position in time, because only on this condition can these substances be empirically represented as coexisting. Now only that which is the cause of another, or of its determinations, determines the position of the other in time. Each substance (inasmuch as only in respect of its determinations can it be an effect) must therefore contain in itself the causality of certain determinations in the other substance, and at the same time the effects of the causality of that other; that is, the substances must stand, immediately or mediately, in dynamical community, if their coexistence is to be known in any possible experience. Now, in respect to the objects of experience, everything without which the experience of these objects would not itself be possible is necessary. It is therefore necessary that all substances in the [field of] appearance, so far as they coexist, should stand in thoroughgoing community of mutual interaction. The word community is in the German language ambiguous. It may mean either communio or commercium. We here employ it in the latter sense, as signifying a dynamical community, without which even local community (communio spatii) could never be empirically known. We may easily recognise from our experiences that only the continuous influences in all parts of space can lead our senses from one object to another. The light, which plays between our eye and the celestial bodies, produces a mediate community between us and them, and thereby shows us that they coexist. We cannot empirically change our position, and perceive the change, unless matter in all parts of space makes perception of our position possible to us. For only thus by means of their reciprocal influence can the parts of matter establish their simultaneous existence, and thereby, though only mediately, their coexistence, even to the most remote objects. Without community each perception of an appearance in space is broken off from every other, and the chain of empirical representations, that is, experience, P 236 would have to begin entirely anew with each new object, without the least connection with the preceding representation, and without standing to it in any relation of time. I do not by this argument at all profess to disprove void space, for it may exist where perceptions cannot reach, and where there is, therefore, no empirical knowledge of coexistence. But such a space is not for us an object of any possible experience. The following remarks may be helpful in [further] elucidation [of my argument]. In our mind, all appearances, since they are contained in a possible experience, must stand in community (communio) of apperception, and in so far as the objects are to be represented as coexisting in connection with each other, they must mutually determine their position in one time, and thereby constitute a whole. If this subjective community is to rest on an objective ground, or is to hold of appearances as substances, the perception of the one must as ground make possible the perception of the other, and reversewise -- in order that the succession which is always found in the perceptions, as apprehensions, may not be ascribed to the objects, and in order that, on the contrary, these objects may be represented as coexisting. But this is a reciprocal influence, that is, a real community (commercium) of substances; without it the empirical relation of coexistence could not be met with in experience. Through this commercium the appearances, so far as they stand outside one another and yet in connection, constitute a composite (compositum reale), and such composites are possible in many different ways. The three dynamical relations, from which all others spring, are therefore inherence, consequence, and composition. *** These, then, are the three analogies of experience. They are simply principles of the determination of the existence of appearances in time, according to all its three modes, viz. the relation to time itself as a magnitude (the magnitude of existence, that is, duration), the relation in time as a successive series, and finally the relation in time as a sum of all simultaneous existence. This unity of time-determination is altogether dynamical. P 237 For time is not viewed as that wherein experience immediately determines position for every existence. Such determination is impossible, inasmuch as absolute time is not an object of perception with which appearances could be confronted. What determines for each appearance its position in time is the rule of the understanding through which alone the existence of appearances can acquire synthetic unity as regards relations of time; and that rule consequently determines the position [in a manner that is] a priori and valid for each and every time. By nature, in the empirical sense, we understand the connection of appearances as regards their existence according to necessary rules, that is, according to laws. There are certain laws which first make a nature possible, and these laws are a priori. Empirical laws can exist and be discovered only through experience, and indeed in consequence of those original laws through which experience itself first becomes possible. Our analogies therefore really portray the unity of nature in the connection of all appearances under certain exponents which express nothing save the relation of time (in so far as time comprehends all existence) to the unity of apperception -- such unity being possible only in synthesis according to rules. Taken together, the analogies thus declare that all appearances lie, and must lie, in one nature, because without this a priori unity no unity of experience, and therefore no determination of objects in it, would be possible. As to the mode of proof of which we have made use in these transcendental laws of nature, and as to their peculiar character, an observation has to be made which must likewise be of very great importance as supplying a rule to be followed in every other attempt to prove a priori propositions that are intellectual and at the same time synthetic. Had we attempted to prove these analogies dogmatically; had we, that is to say, attempted to show from concepts that everything which exists is to be met with only in that which is permanent, that every event presupposes something in the preceding state upon which it follows in conformity with a rule; and finally, that in the manifold which is coexistent the states coexist in relation to one another in conformity with a rule and so stand in P 238 community, all our labour would have been wasted. For through mere concepts of these things, analyse them as we may, we can never advance from one object and its existence to the existence of another or to its mode of existence. But there is an alternative method, namely, to investigate the possibility of experience as a knowledge wherein all objects -- if their representation is to have objective reality for us -- must finally be capable of being given to us. In this third [medium], the essential form of which consists in the synthetic unity of the apperception of all appearances, we have found a priori conditions of complete and necessary determination of time for all existence in the [field of] appearance, without which even empirical determination of time would be impossible. In it we have also found rules of synthetic unity a priori, by means of which we can anticipate experience. For lack of this method, and owing to the erroneous assumption that synthetic propositions, which the empirical employment of the understanding recommends as being its principles, may be proved dogmatically, the attempt has, time and again, been made, though always vainly, to obtain a proof of the principle of sufficient reason. And since the guiding-thread of the categories, which alone can reveal and make noticeable every gap in the understanding, alike in regard to concepts and to principles, has hitherto been lacking, no one has so much as thought of the other two analogies, although use has always tacitly been made of them. ++ The unity of the world-whole, in which all appearances have to be connected, is evidently a mere consequence of the tacitly assumed principle of the community of all substances which are coexistent. For if they were isolated, they would not as parts constitute a whole. And if their connection (the reciprocal action of the manifold) were not already necessary because of their coexistence, we could not argue from this latter, which is a merely ideal relation to the former, which is a real relation. We have, however, in the proper context, shown that community is really the ground of the possibility of an empirical knowledge of coexistence, and that the inference, rightly regarded, is simply from this empirical knowledge to community as its condition. P 239 4 THE POSTULATES OF EMPIRICAL THOUGHT IN GENERAL 1. That which agrees with the formal conditions of experience, that is, with the conditions of intuition and of concepts, is possible. 2. That which is bound up with the material conditions of experience, that is, with sensation, is actual. 3. That which in its connection with the actual is determined in accordance with universal conditions of experience, is (that is, exists as) necessary. Explanation The categories of modality have the peculiarity that, in determining an object, they do not in the least enlarge the concept to which they are attached as predicates. They only express the relation of the concept to the faculty of knowledge. Even when the concept of a thing is quite complete, I can still enquire whether this object is merely possible or is also actual, or if actual, whether it is not also necessary. No additional determinations are thereby thought in the object itself; the question is only how the object, together with all its determinations, is related to understanding and its empirical employment, to empirical judgment, and to reason in its application to experience. Just on this account also the principles of modality are nothing but explanations of the concepts of possibility, actuality, and necessity, in their empirical employment; at the same time they restrict all categories to their merely empirical employment, and do not approve or allow their transcendental employment. For if they are not to have a purely logical significance, analytically expressing the form of thought, but are to refer to the possibility, actuality, or necessity of things, they must concern possible experience and its synthetic unity, in which alone objects of knowledge can be given. The postulate of the possibility of things requires that the concept of the things should agree with the formal conditions of an experience in general. But this, the objective form of experience in general, contains all synthesis that is P 240 required for knowledge of objects. A concept which contains a synthesis is to be regarded as empty and as not related to any object, if this synthesis does not belong to experience either as being derived from it, in which case it is an empirical concept, or as being an a priori condition upon which experience in general in its formal aspect rests, in which case it is a pure concept. In the latter case it still belongs to experience, inasmuch as its object is to be met with only in experience. For whence shall we derive the character of the possibility of an object which is thought through a synthetic a priori concept, if not from the synthesis which constitutes the form of the empirical knowledge of objects? It is, indeed, a necessary logical condition that a concept of the possible must not contain any contradiction; but this is not by any means sufficient to determine the objective reality of the concept, that is, the possibility of such an object as is thought through the concept. Thus there is no contradiction in the concept of a figure which is enclosed within two straight lines, since the concepts of two straight lines and of their coming together contain no negation of a figure. The impossibility arises not from the concept in itself, but in connection with its construction in space, that is, from the conditions of space and of its determination. And since these contain a priori in themselves the form of experience in general, they have objective reality, that is, they apply to possible things. We shall now proceed to show the far-reaching utility and influence of this postulate of possibility. If I represent to myself a thing which is permanent, so that everything in it which changes belongs only to its state, I can never know from such a concept that a thing of this kind is possible. Or if I represent to myself something which is so constituted that if it is posited something else invariably and inevitably follows from it, this may certainly be so thought without contradiction; but this thought affords no means of judging whether this property (causality) is to be met with in any possible thing. Lastly, I can represent to myself diverse things (substances), which are so constituted that the state of the one carries with it some consequence in the state of the other, and this reciprocally; but I can never determine from these concepts, which contain a merely arbitrary synthesis, whether a relation of this kind P 241 can belong to any [possible] things. Only through the fact that these concepts express a priori the relations of perceptions in every experience, do we know their objective reality, that is their transcendental truth, and this, indeed, independently of experience, though not independently of all relation to the form of an experience in general, and to the synthetic unity in which alone objects can be empirically known. But if we should seek to frame quite new concepts of substances, forces, reciprocal actions, from the material which perception presents to us, without experience itself yielding the example of their connection, we should be occupying ourselves with mere fancies, of whose possibility there is absolutely no criterion since we have neither borrowed these concepts [directly] from experience, nor have taken experience as our instructress in their formation. Such fictitious concepts, unlike the categories, can acquire the character of possibility not in a priori fashion, as conditions upon which all experience depends, but only a posteriori as being concepts which are given through experience itself. And, consequently, their possibility must either be known a posteriori and empirically, or it cannot be known at all. A substance which would be permanently present in space, but without filling it (like that mode of existence intermediate between matter and thinking being which some would seek to introduce), or a special ultimate mental power of intuitively anticipating the future (and not merely inferring it), or lastly a power of standing in community of thought with other men, however distant they may be -- are concepts the possibility of which is altogether groundless, as they cannot be based on experience and its known laws; and without such confirmation they are arbitrary combinations of thoughts, which, although indeed free from contradiction, can make no claim to objective reality, and none, therefore, as to the possibility of an object such as we here profess to think. As regards reality, we obviously cannot think it in concreto, without calling experience to our aid. For reality is bound up with sensation, the matter of experience, not with that form of relation in regard to which we can, if we so choose, resort to a playful inventiveness. But I leave aside everything the possibility of which can P 242 be derived only from its actuality in experience, and have here in view only the possibility of things through a priori concepts; and I maintain the thesis that their possibility can never be established from such concepts taken in and by themselves, but only when the concepts are viewed as formal and objective conditions of experience in general. It does, indeed, seem as if the possibility of a triangle could be known from its concept in and by itself (the concept is certainly independent of experience), for we can, as a matter of fact, give it an object completely a priori, that is, can construct it. But since this is only the form of an object, it would remain a mere product of imagination, and the possibility of its object would still be doubtful. To determine its possibility, something more is required, namely, that such a figure be thought under no conditions save those upon which all objects of experience rest. That space is a formal a priori condition of outer experiences, that the formative synthesis through which we construct a triangle in imagination is precisely the same as that which we exercise in the apprehension of an appearance, in making for ourselves an empirical concept of it -- these are the considerations that alone enable us to connect the representation of the possibility of such a thing with the concept of it. Similarly, since the concepts of continuous magnitudes, indeed of magnitudes in general, are one and all synthetic, the possibility of such magnitudes is never clear from the concepts themselves, but only when they are viewed as formal conditions of the determination of objects in experience in general. And where, indeed, should we seek for objects corresponding to these concepts if not in experience, through which alone objects are given to us? We can, indeed, prior to experience itself, know and characterise the possibility of things, merely by reference to the formal conditions under which in experience anything whatsoever is determined as object, and therefore can do so completely a priori. But, even so, this is possible only in relation to experience and within its limits. The postulate bearing on the knowledge of things as actual does not, indeed, demand immediate perception (and, therefore, sensation of which we are conscious) of the object whose existence is to be known. What we do, however, P 243 require is the connection of the object with some actual perception, in accordance with the analogies of experience, which define all real connection in an experience in general. In the mere concept of a thing no mark of its existence is to be found. For though it may be so complete that nothing which is required for thinking the thing with all its inner determinations is lacking to it, yet existence has nothing to do with all this, but only with the question whether such a thing be so given us that the perception of it can, if need be, precede the concept. For that the concept precedes the perception signifies the concept's mere possibility; the perception which supplies the content to the concept is the sole mark of actuality. We can also, however, know the existence of the thing prior to its perception and, consequently, comparatively speaking, in an a priori manner, if only it be bound up with certain perceptions, in accordance with the principles of their empirical connection (the analogies). For the existence of the thing being thus bound up with our perceptions in a possible experience, we are able in the series of possible perceptions and under the guidance of the analogies to make the transition from our actual perception to the thing in question. Thus from the perception of the attracted iron filings we know of the existence of a magnetic matter pervading all bodies, although the constitution of our organs cuts us off from all immediate perception of this medium. For in accordance with the laws of sensibility and the context of our perceptions, we should, were our senses more refined, come also in an experience upon the immediate empirical intuition of it. The grossness of our senses does not in any way decide the form of possible experience in general. Our knowledge of the existence of things reaches, then, only so far as perception and its advance according to empirical laws can extend. If we do not start from experience, or do not proceed accordance with laws of the P 244 empirical connection of appearances, our guessing or enquiring into the existence of anything will only be an idle pretence. Idealism raises, however, what is a serious objection to these rules for proving existence mediately; and this is the proper place for its refutation. *** Refutation of Idealism Idealism -- meaning thereby material idealism -- is the theory which declares the existence of objects in space outside us either to be merely doubtful and indemonstrable or to be false and impossible. The former is the problematic idealism of Descartes, which holds that there is only one empirical assertion that is indubitably certain, namely, that 'I am'. The latter is the dogmatic idealism of Berkeley. He maintains that space, with all the things of which it is the inseparable condition, is something which is in itself impossible; and he therefore regards the things in space as merely imaginary entities. Dogmatic idealism is unavoidable, if space be interpreted as a property that must belong to things in themselves. For in that case space, and everything to which it serves as condition, is a non-entity. The ground on which this idealism rests has already been undermined by us in the Transcendental Aesthetic. Problematic idealism, which makes no such assertion, but merely pleads incapacity to prove, through immediate experience, any existence except our own, is, in so far as it allows of no decisive judgment until sufficient proof has been found, reasonable and in accordance with a thorough and philosophical mode of thought. The required proof must, therefore, show that we have experience, and not merely imagination of outer things; and this, it would seem, cannot be achieved save by proof that even our inner experience, which for Descartes is indubitable, is possible only on the assumption of outer experience. P 245 THESIS The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me. Proof I am conscious of my own existence as determined in time. All determination of time presupposes something permanent in perception. This permanent cannot, however, be something in me, since it is only through this permanent that my existence in time can itself be determined. Thus perception of this permanent is possible only through a thing outside me and not through the mere representation of a thing outside me; and consequently the determination of my existence in time is possible only through the existence of actual things which I perceive outside me. Now consciousness [of my existence] in time is necessarily bound up with consciousness of the [condition of the] possibility of this time-determination; and it is therefore necessarily bound up with the existence of things outside me, as the condition of the time-determination. In other words, the consciousness of my existence is at the same time an immediate consciousness of the existence of other things outside me. Note 1. It will be observed that in the foregoing proof the game played by idealism has been turned against itself, and with greater justice. Idealism assumed that the only immediate experience is inner experience, and that from it we can only infer outer things -- and this, moreover, only in an untrustworthy manner, as in all cases where we are inferring from given effects to determinate causes. In this particular case, the cause of the representations, which we ascribe, perhaps falsely, to outer things, may lie in ourselves. But in the above proof it has been shown that outer experience is really P 246 immediate, and that only by means of it is inner experience -- not indeed the consciousness of my own existence, but the determination of it in time -- possible. Certainly, the representation 'I am', which expresses the consciousness that can accompany all thought, immediately includes in itself the existence of a subject; but it does not so include any knowledge of that subject, and therefore also no empirical knowledge, that is, no experience of it. For this we require, in addition to the thought of something existing, also intuition, and in this case inner intuition, in respect of which, that is, of time, the subject must be determined. But in order so to determine it, outer objects are quite indispensable; and it therefore follows that inner experience is itself possible only mediately, and only through outer experience. Note 2. With this thesis all employment of our cognitive faculty in experience, in the determination of time, entirely agrees. Not only are we unable to perceive any determination of time save through change in outer relations (motion) relatively to the permanent in space (for instance, the motion of the sun relatively to objects on the earth), we have nothing permanent on which, as intuition, we can base the concept of a substance, save only matter; and even this permanence is not obtained from outer experience, but is presupposed a priori as a necessary condition of determination of time, and therefore also as a determination of inner sense in respect of [the determination of] our own existence through the existence of outer things. ++ The immediate consciousness of the existence of outer things is, in the preceding thesis, not presupposed, but proved, be the possibility of this consciousness understood by us or not. The question as to its possibility would be this: whether we have an inner sense only, and no outer sense, but merely an outer imagination. It is clear, however, that in order even only to imagine something as outer, that is, to present it to sense in intuition, we must already have an outer sense, and must thereby immediately distinguish the mere receptivity of an outer intuition from the spontaneity which characterises every act of imagination. For should we merely be imagining an outer sense, the faculty of intuition, which is to be determined by the faculty of imagination, would itself be annulled. P 246 The consciousness of myself in the representation 'I' is not an intuition, but a P 247 merely intellectual representation of the spontaneity of a thinking subject. This 'I' has not, therefore, the least predicate of intuition, which, as permanent, might serve as correlate for the determination of time in inner sense -- in the manner in which, for instance, impenetrability serves in our empirical intuition of matter. Note 3. From the fact that the existence of outer things is required for the possibility of a determinate consciousness of the self, it does not follow that every intuitive representation of outer things involves the existence of these things, for their representation can very well be the product merely of the imagination (as in dreams and delusions). Such representation is merely the reproduction of previous outer perceptions, which, as has been shown, are possible only through the reality of outer objects. All that we have here sought to prove is that inner experience in general is possible only through outer experience in general. Whether this or that supposed experience be not purely imaginary, must be ascertained from its special determinations, and through its congruence with the criteria of all real experience. *** Lastly, as regards the third postulate, it concerns material necessity in existence, and not merely formal and logical necessity in the connection of concepts. Since the existence of any object of the senses cannot be known completely a priori, but only comparatively a priori, relatively to some other previously given existence; and since, even so, we can then arrive only at such an existence as must somewhere be contained in the context of the experience, of which the given perception is a part, the necessity of existence can never be known from concepts, but always only from connection with that which is perceived, in accordance with universal laws of experience. Now there is no existence that can be known as necessary under the condition of other given appearances, save the existence of effects from given causes, P 248 in accordance with laws of causality. It is not, therefore, the existence of things (substances) that we can know to be necessary, but only the existence of their state; and this necessity of the existence of their state we can know only from other states, which are given in perception, in accordance with empirical laws of causality. It therefore follows that the criterion of necessity lies solely in the law of possible experience, the law that everything which happens is determined a priori through its cause in the [field of] appearance. We thus know the necessity only of those effects in nature the causes of which are given to us, and the character of necessity in existence extends no further than the field of possible experience, and even in this field is not applicable to the existence of things as substances, since substances can never be viewed as empirical effects -- that is, as happening and coming to be. Necessity concerns only the relations of appearances in conformity with the dynamical law of causality and the possibility grounded upon it of inferring a priori from a given existence (a cause) to another existence (the effect). That everything which happens is hypothetically necessary is a principle which subordinates alteration in the world to a law, that is, to a rule of necessary existence, without which there would be nothing that could be entitled nature. The proposition that nothing happens through blind chance (in mundo non datur casus) is therefore an a - priori law of nature. So also is the proposition that no necessity in nature is blind, but always a conditioned and therefore intelligible necessity (non datur fatum). Both are laws through which the play of alterations is rendered subject to a nature of things (that is, of things as appearances), or what amounts to the same thing, to the unity of understanding, in which alone they can belong to one experience, that is, to the synthetic unity of appearances. Both belong to the class of dynamical principles. The first is really a consequence of the principle of causality, and so belongs to the analogies of experience. The second is a principle of modality; but this modality, while adding the concept of necessity to causal determination, itself stands under a rule of understanding. The principle of continuity forbids any leap in the series of appearances, that is, of alterations (in mundo non datur saltus); P 249 it also forbids, in respect of the sum of all empirical intuitions in space, any gaps or cleft between two appearances (non datur hiatus); for so we may express the proposition, that nothing which proves a vacuum, or which even admits it as a part of empirical synthesis, can enter into experience. As regards a void which may be conceived to lie beyond the field of possible experience, that is, outside the world, such a question does not come within the jurisdiction of the mere understanding -- which decides only upon questions that concern the use to be made of given appearances for the obtaining of empirical knowledge. It is a problem for that ideal reason which goes out beyond the sphere of a possible experience and seeks to judge of that which surrounds and limits it; and is a problem which will therefore have to be considered in the Transcendental Dialectic. These four propositions (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum), like all principles of transcendental origin, we can easily exhibit in their order, that is, in accordance with the order of the categories, and so assign to each its proper place. But the reader has now had sufficient practice to allow of his doing this for himself, or of easily discovering the guiding principle for so doing. They are all entirely at one in this, that they allow of nothing in the empirical synthesis which may do violence or detriment to the understanding and to the continuous connection of all appearances -- that is, to the unity of the concepts of the understanding. For in the understanding alone is possible the unity of experience, in which all perceptions must have their place. To enquire whether the field of possibility is larger than the field which contains all actuality, and this latter, again, larger than the sum of that which is necessary, is to raise somewhat subtle questions which demand a synthetic solution and yet come under the jurisdiction of reason alone. For they are tantamount to the enquiry whether things as appearances one and all belong to the sum and context of a single experience, of which every given perception is a part, a part which therefore cannot be connected with any other [series of] appearances, or whether my perceptions can belong, in their general connection, to more than one possible experience. The P 250 understanding, in accordance with the subjective and formal conditions of sensibility as well as of apperception, prescribes a priori to experience in general the rules which alone make experience possible. Other forms of intuition than space and time, other forms of understanding than the discursive forms of thought, or of knowledge through concepts, even if they should be possible, we cannot render in any way conceivable and comprehensible to ourselves; and even assuming that we could do so, they still would not belong to experience -- the only kind of knowledge in which objects are given to us. Whether other perceptions than those belonging to our whole possible experience, and therefore a quite different field of matter, may exist, the understanding is not in a position to decide. It can deal only with the synthesis of that which is given. Moreover, the poverty of the customary inferences through which we throw open a great realm of possibility, of which all that is actual (the objects of experience) is only a small part, is patently obvious. Everything actual is possible; from this proposition there naturally follows, in accordance with the logical rules of conversion, the merely particular proposition, that some possible is actual; and this would seem to mean that much is possible which is not actual. It does indeed seem as if we were justified in extending the number of possible things beyond that of the actual, on the ground that something must be added to the possible to constitute the actual. But this [alleged] process of adding to the possible I refuse to allow. For that which would have to be added to the possible, over and above the possible, would be impossible. What can be added is only a relation to my understanding, namely that in addition to agreement with the formal conditions of experience there should be connecttion with some perception. But whatever is connected with perception in accordance with empirical laws is actual, even although it is not immediately perceived. That yet another series of appearances in thoroughgoing connection with that which is given in perception, and consequently that more than one all-embracing experience is possible, cannot be inferred from what is given; and still less can any such inference be drawn independently of anything being given -- since P 251 without material nothing whatsoever can be thought. What is possible only under conditions which themselves are merely possible is not in all respects possible. But such [absolute] possibility is in question when it is asked whether the possibility of things extends further than experience can reach. I have made mention of these questions only in order to omit nothing which is ordinarily reckoned among the concepts of understanding. But as a matter of fact absolute possibility, that which is in all respects valid, is no mere concept of understanding, and can never be employed empirically. It belongs exclusively to reason, which transcends all possible empirical employment of the understanding. We have therefore had to content ourselves with some merely critical remarks; the matter must otherwise be left in obscurity until we come to the proper occasion for its further treatment. Before concluding this fourth section, and therewith the system of all principles of pure understanding, I must explain why I have entitled the principles of modality postulates. I interpret this expression not in the sense which some recent philosophical writers, wresting it from its proper mathematical significance, have given to it, namely, that to postulate should mean to treat a proposition as immediately certain, without justification or proof. For if, in dealing with synthetic propositions, we are to recognise them as possessing unconditioned validity, independently of deduction, on the evidence [merely] of their own claims, then no matter how evident they may be, all critique of understanding is given up. And since there is no lack of audacious pretensions, and these are supported by common belief (though that is no credential of their truth), the understanding lies open to every fancy, and is in no position to withhold approval of those assertions which, though illegitimate, yet press upon us, in the same confident tone, their claims to be accepted as actual axioms. Whenever, therefore, an a priori determination is synthetically added to the concept of a thing, it is indispensable that, if not a proof, at least a deduction of the legitimacy of such an assertion should be supplied. The principles of modality are not, however, objectively synthetic. For the predicates of possibility, actuality, and P 252 necessity do not in the least enlarge the concept of which they are affirmed, adding something to the representation of the object. But since they are none the less synthetic, they are so subjectively only, that is, they add to the concept of a thing (of something real), of which otherwise they say nothing, the cognitive faculty from which it springs and in which it has its seat. Thus if it is in connection only with the formal conditions of experience, and so merely in the understanding, its object is called possible. If it stands in connection with perception, that is, with sensation as material supplied by the senses, and through perception is determined by means of the understanding, the object is actual. If it is determined through the connection of perceptions according to concepts, the object is entitled necessary. The principles of modality thus predicate of a concept nothing but the action of the faculty of knowledge through which it is generated. Now in mathematics a postulate means the practical proposition which contains nothing save the synthesis through which we first give ourselves an object and generate its concept -- for instance, with a given line, to describe a circle on a plane from a given point. Such a proposition cannot be proved, since the procedure which it demands is exactly that through which we first generate the concept of such a figure. With exactly the same right we may postulate the principles of modality, since they do not increase our concept of things, but only show the manner in which it is connected with the faculty of knowledge. General Note on the System of the Principles That the possibility of a thing cannot be determined from the category alone, and that in order to exhibit the objective reality of the pure concept of understanding we must always have an intuition, is a very noteworthy fact. ++ Through the actuality of a thing I certainly posit more than the possibility of it, but not in the thing. For it can never contain more in its actuality than is contained in its complete possibility. But while possibility is merely a positing of the thing in relation to the understanding (in its empirical employment), actuality is at the same time a connection of it with perception. P 253 Take, for instance, the categories of relation. We cannot determine from mere concepts how (1) something can exist as subject only, and not as a mere determination of other things, that is, how a thing can be substance, or (2) how, because something is, something else must be, and how, therefore, a thing can be a cause, or (3) when several things exist, how because one of them is there, something follows in regard to the others and vice versa, and how in this way there can be a community of substances. This likewise applies to the other categories; for example, how a thing can be equal to a number of things taken together, that is, can be a quantity. So long as intuition is lacking, we do not know whether through the categories we are thinking an object, and whether indeed there can anywhere be an object suited to them. In all these ways, then, we obtain confirmation that the categories are not in themselves knowledge, but are merely forms of thought for the making of knowledge from given intuitions. For the same reason it follows that no synthetic proposition can be made from mere categories. For instance, we are not in a position to say that in all existence there is substance, that is, something which can exist only as subject and not as mere predicate; or that everything is a quantum, etc. For if intuition be lacking, there is nothing which can enable us to go out beyond a given concept, and to connect another with it. No one, therefore, has ever yet succeeded in proving a synthetic proposition merely from pure concepts of the understanding -- as, for instance, that everything which exists contingently has a cause. We can never get further than proving, that without this relation we are unable to comprehend the existence of the contingent, that is, are unable a priori through the understanding to know the existence of such a thing -- from which it does not, however, follow that this is also a condition of the possibility of the things themselves. If the reader will go back to our proof of the principle of causality -- that everything which happens, that is, every event, presupposes a cause -- he will observe that we were able to prove it only of objects of possible experience; and even so, not from pure concepts, but only as a principle of the possibility of experience, and therefore of the knowledge of an object given in empirical P 254 intuition. We cannot, indeed, deny that the proposition, that everything contingent must have a cause, is patent to everyone from mere concepts. But the concept of the contingent is then being apprehended as containing, not the category of modality (as something the not-being of which can be thought), but that of relation (as something which can exist only as consequence of something else); and it is then, of course, an identical proposition -- that which can exist only as consequence has a cause. As a matter of fact, when we are required to cite examples of contingent existence, we invariably have recourse to alterations, and not merely to the possibility of entertaining the opposite in thought. Now alteration is an event which, as such, is possible only through a cause, and the not-being of which is therefore in itself possible. In other words, we recognise contingency in and through the fact that something can exist only as the effect of a cause; and if, therefore, a thing is assumed to be contingent, it is an analytic proposition to say that it has a cause. But it is an even more noteworthy fact, that in order to understand the possibility of things in conformity with the categories, and so to demonstrate the objective reality of the latter, we need, not merely intuitions, but intuitions that are in all cases outer intuitions. When, for instance, we take the pure concepts of relation, we find, firstly, that in order to obtain something permanent in intuition corresponding to the concept of substance, and so to demonstrate the objective reality of this concept, we require an intuition in space (of matter). ++ We can easily think the non-existence of matter. From this the ancients did not, however, infer its contingency. Even the change from being to not-being of a given state of a thing, in which all alteration consists, does not prove the contingency of this state, on the ground of the reality of its opposite. For instance, that a body should come to rest after having been in motion does not prove the contingency of the motion as being the opposite of the state of rest. For this opposite is opposed to the other only logically, not realiter. To prove the contingency of its motion, we should have to prove that instead of the motion at the preceding moment, it was possible for the body to have been then at rest, not that it is afterwards at rest; for in the latter case the opposites are quite consistent with each other. P 255 For space alone is determined as permanent, while time, and therefore everything that is in inner sense, is in constant flux. Secondly, in order to exhibit alteration as the intuition corresponding to the concept of causality, we must take as our example motion, that is, alteration in space. Only in this way can we obtain the intuition of alterations, the possibility of which can never be comprehended through any pure understanding. For alteration is combination of contradictorily opposed determinations in the existence of one and the same thing. Now how it is possible that from a given state of a thing an opposite state should follow, not only cannot be conceived by reason without an example, but is actually incomprehensible to reason without intuition. The intuition required is the intuition of the movement of a point in space. The presence of the point in different locations (as a sequence of opposite determinations) is what alone first yields to us an intuition of alteration. For in order that we may afterwards make inner alterations likewise thinkable, we must represent time (the form of inner sense) figuratively as a line, and the inner alteration through the drawing of this line (motion), and so in this manner by means of outer intuition make comprehensible the successive existence of ourselves in different states. The reason of this is that all alteration, if it is to be perceived as alteration, presupposes something permanent in intuition, and that in inner sense no permanent intuition is to be met with. Lastly, the possibility of the category of community cannot be comprehended through mere reason alone; and consequently its objective reality is only to be determined through intuition, and indeed through outer intuition in space. For how are we to think it to be possible, when several substances exist, that, from the existence of one, something (as effect) can follow in regard to the existence of the others, and vice versa; in other words, that because there is something in the one there must also in the others be something which is not to be understood solely from the existence of these others? For this is what is required in order that there be community; community is not conceivable as holding between things each of which, through its subsistence, stands in complete isolation. Leibniz, in attributing to the substances of the P 256 world, as thought through the understanding alone, a community, had therefore to resort to the mediating intervention of a Deity. For, as he justly recognised, a community of substances is utterly inconceivable as arising simply from their existence. We can, however, render the possibility of community -- of substances as appearances -- perfectly comprehensible, if we represent them to ourselves in space, that is, in outer intuition. For this already contains in itself a priori formal outer relations as conditions of the possibility of the real relations of action and reaction, and therefore of the possibility of community. Similarly, it can easily be shown that the possibility of things as quantities, and therefore the objective reality of quantity, can be exhibited only in outer intuition, and that only through the mediation of outer intuition can it be applied also to inner sense. But, to avoid prolixity, I must leave the reader to supply his own examples of this. These remarks are of great importance, not only in confirmation of our previous refutation of idealism, but even more, when we come to treat of self-knowledge by mere inner consciousness, that is, by determination of our nature without the aid of outer empirical intuitions -- as showing us the limits of the possibility of this kind of knowledge. The final outcome of this whole section is therefore this: all principles of the pure understanding are nothing more than principles a priori of the possibility of experience, and to experience alone do all a priori synthetic propositions relate -- indeed, their possibility itself rests entirely on this relation.