Section II. Of the Supreme Principle of all Synthetical Judgements
The explanation of the possibility of synthetical judgements is a task with which general logic has nothing to do; indeed she needs not even be acquainted with its name. But in transcendental logic it is the most important matter to be dealt with—indeed the only one, if the question is of the possibility of synthetical judgements à priori, the conditions and extent of their validity. For when this question is fully decided, it can reach its aim with perfect ease, the determination, to wit, of the extent and limits of the pure understanding.
In an analytical judgement I do not go beyond the given conception, in order to arrive at some decision respecting it. If the judgement is affirmative, I predicate of the conception only that which was already cogitated in it; if negative, I merely exclude from the conception its contrary. But in synthetical judgements, I must go beyond the given conception, in order to cogitate, in relation with it, something quite different from that which was cogitated in it, a relation which is consequently never one either of identity or contradiction, and by means of which the truth or error of the judgement cannot be discerned merely from the judgement itself.
Granted, then, that we must go out beyond a given conception, in order to compare it synthetically with another, a third thing is necessary, in which alone the synthesis of two conceptions can originate. Now what is this tertium quid that is to be the medium of all synthetical judgements? It is only a complex in which all our representations are contained, the internal sense to wit, and its form à priori, time.
The synthesis of our representations rests upon the imagination; their synthetical unity (which is requisite to a judgement), upon the unity of apperception. In this, therefore, is to be sought the possibility of synthetical judgements, and as all three contain the sources of à priori representations, the possibility of pure synthetical judgements also; nay, they are necessary upon these grounds, if we are to possess a knowledge of objects, which rests solely upon the synthesis of representations.
If a cognition is to have objective reality, that is, to relate to an object, and possess sense and meaning in respect to it, it is necessary that the object be given in some way or another. Without this, our conceptions are empty, and we may indeed have thought by means of them, but by such thinking we have not, in fact, cognized anything, we have merely played with representation. To give an object, if this expression be understood in the sense of “to present” the object, not mediately but immediately in intuition, means nothing else than to apply the representation of it to experience, be that experience real or only possible. Space and time themselves, pure as these conceptions are from all that is empirical, and certain as it is that they are represented fully à priori in the mind, would be completely without objective validity, and without sense and significance, if their necessary use in the objects of experience were not shown. Nay, the representation of them is a mere schema, that always relates to the reproductive imagination, which calls up the objects of experience, without which they have no meaning. And so it is with all conceptions without distinction.
The possibility of experience is, then, that which gives objective reality to all our à priori cognitions. Now experience depends upon the synthetical unity of phenomena, that is, upon a synthesis according to conceptions of the object of phenomena in general, a synthesis without which experience never could become knowledge, but would be merely a rhapsody of perceptions, never fitting together into any connected text, according to rules of a thoroughly united (possible) consciousness, and therefore never subjected to the transcendental and necessary unity of apperception. Experience has therefore for a foundation, à priori principles of its form, that is to say, general rules of unity in the synthesis of phenomena, the objective reality of which rules, as necessary conditions even of the possibility of experience can which rules, as necessary conditions—even of the possibility of experience—can always be shown in experience. But apart from this relation, à priori synthetical propositions are absolutely impossible, because they have no third term, that is, no pure object, in which the synthetical unity can exhibit the objective reality of its conceptions.
Although, then, respecting space, or the forms which productive imagination describes therein, we do cognize much à priori in synthetical judgements, and are really in no need of experience for this purpose, such knowledge would nevertheless amount to nothing but a busy trifling with a mere chimera, were not space to be considered as the condition of the phenomena which constitute the material of external experience. Hence those pure synthetical judgements do relate, though but mediately, to possible experience, or rather to the possibility of experience, and upon that alone is founded the objective validity of their synthesis.
While then, on the one hand, experience, as empirical synthesis, is the only possible mode of cognition which gives reality to all other synthesis; on the other hand, this latter synthesis, as cognition à priori, possesses truth, that is, accordance with its object, only in so far as it contains nothing more than what is necessary to the synthetical unity of experience.
Accordingly, the supreme principle of all synthetical judgements is: “Every object is subject to the necessary conditions of the synthetical unity of the manifold of intuition in a possible experience.”
À priori synthetical judgements are possible when we apply the formal conditions of the à priori intuition, the synthesis of the imagination, and the necessary unity of that synthesis in a transcendental apperception, to a possible cognition of experience, and say: “The conditions of the possibility of experience in general are at the same time conditions of the possibility of the objects of experience, and have, for that reason, objective validity in an à priori synthetical judgement.”
Section III. Systematic Representation of all Synthetical Principles of the Pure Understanding
That principles exist at all is to be ascribed solely to the pure understanding, which is not only the faculty of rules in regard to that which happens, but is even the source of principles according to which everything that can be presented to us as an object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. Even the laws of nature, if they are contemplated as principles of the empirical use of the understanding, possess also a characteristic of necessity, and we may therefore at least expect them to be determined upon grounds which are valid à priori and antecedent to all experience. But all laws of nature, without distinction, are subject to higher principles of the understanding, inasmuch as the former are merely applications of the latter to particular cases of experience. These higher principles alone therefore give the conception, which contains the necessary condition, and, as it were, the exponent of a rule; experience, on the other hand, gives the case which comes under the rule.
There is no danger of our mistaking merely empirical principles for principles of the pure understanding, or conversely; for the character of necessity, according to conceptions which distinguish the latter, and the absence of this in every empirical proposition, how extensively valid soever it may be, is a perfect safeguard against confounding them. There are, however, pure principles à priori, which nevertheless I should not ascribe to the pure understanding—for this reason, that they are not derived from pure conceptions, but (although by the mediation of the understanding) from pure intuitions. But understanding is the faculty of conceptions. Such principles mathematical science possesses, but their application to experience, consequently their objective validity, nay the possibility of such à priori synthetical cognitions (the deduction thereof) rests entirely upon the pure understanding.
On this account, I shall not reckon among my principles those of mathematics; though I shall include those upon the possibility and objective validity à priori, of principles of the mathematical science, which, consequently, are to be looked upon as the principle of these, and which proceed from conceptions to intuition, and not from intuition to conceptions.
In the application of the pure conceptions of the understanding to possible experience, the employment of their synthesis is either mathematical or dynamical, for it is directed partly on the intuition alone, partly on the existence of a phenomenon. But the à priori conditions of intuition are in relation to a possible experience absolutely necessary, those of the existence of objects of a possible empirical intuition are in themselves contingent. Hence the principles of the mathematical use of the categories will possess a character of absolute necessity, that is, will be apodeictic; those, on the other hand, of the dynamical use, the character of an à priori necessity indeed, but only under the condition of empirical thought in an experience, therefore only mediately and indirectly. Consequently they will not possess that immediate evidence which is peculiar to the former, although their application to experience does not, for that reason, lose its truth and certitude. But of this point we shall be better able to judge at the conclusion of this system of principles.
The table of the categories is naturally our guide to the table of principles, because these are nothing else than rules for the objective employment of the former. Accordingly, all principles of the pure understanding are:
Axioms
of Intuition
2 3
Anticipations Analogies
of Perception of Experience
4
Postulates of
Empirical Thought
in general
These appellations I have chosen advisedly, in order that we might not lose sight of the distinctions in respect of the evidence and the employment of these principles. It will, however, soon appear that—a fact which concerns both the evidence of these principles, and the à priori determination of phenomena—according to the categories of quantity and quality (if we attend merely to the form of these), the principles of these categories are distinguishable from those of the two others, in as much as the former are possessed of an intuitive, but the latter of a merely discursive, though in both instances a complete, certitude. I shall therefore call the former mathematical, and the latter dynamical principles.[27] It must be observed, however, that by these terms I mean just as little in the one case the principles of mathematics as those of general (physical) dynamics in the other. I have here in view merely the principles of the pure understanding, in their application to the internal sense (without distinction of the representations given therein), by means of which the sciences of mathematics and dynamics become possible. Accordingly, I have named these principles rather with reference to their application than their content; and I shall now proceed to consider them in the order in which they stand in the table.
[27] All combination (conjunctio) is either composition (compositio) or connection (nexus). The former is the synthesis of a manifold, the parts of which do not necessarily belong to each other. For example, the two triangles into which a square is divided by a diagonal, do not necessarily belong to each other, and of this kind is the synthesis of the homogeneous in everything that can be mathematically considered. This synthesis can be divided into those of aggregation and coalition, the former of which is applied to extensive, the latter to intensive quantities. The second sort of combination (nexus) is the synthesis of a manifold, in so far as its parts do belong necessarily to each other; for example, the accident to a substance, or the effect to the cause. Consequently it is a synthesis of that which though heterogeneous, is represented as connected à priori. This combination—not an arbitrary one—I entitle dynamical because it concerns the connection of the existence of the manifold. This, again, may be divided into the physical synthesis, of the phenomena divided among each other, and the metaphysical synthesis, or the connection of phenomena à priori in the faculty of cognition.
1. AXIOMS OF INTUITION.
The principle of these is: All Intuitions are Extensive Quantities.
PROOF.
All phenomena contain, as regards their form, an intuition in space and time, which lies à priori at the foundation of all without exception. Phenomena, therefore, cannot be apprehended, that is, received into empirical consciousness otherwise than through the synthesis of a manifold, through which the representations of a determinate space or time are generated; that is to say, through the composition of the homogeneous and the consciousness of the synthetical unity of this manifold (homogeneous). Now the consciousness of a homogeneous manifold in intuition, in so far as thereby the representation of an object is rendered possible, is the conception of a quantity (quanti). Consequently, even the perception of an object as phenomenon is possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous manifold in the conception of a quantity is cogitated; that is to say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time they must be represented by means of the same synthesis through which space and time themselves are determined.
An extensive quantity I call that wherein the representation of the parts renders possible (and therefore necessarily antecedes) the representation of the whole. I cannot represent to myself any line, however small, without drawing it in thought, that is, without generating from a point all its parts one after another, and in this way alone producing this intuition. Precisely the same is the case with every, even the smallest, portion of time. I cogitate therein only the successive progress from one moment to another, and hence, by means of the different portions of time and the addition of them, a determinate quantity of time is produced. As the pure intuition in all phenomena is either time or space, so is every phenomenon in its character of intuition an extensive quantity, inasmuch as it can only be cognized in our apprehension by successive synthesis (from part to part). All phenomena are, accordingly, to be considered as aggregates, that is, as a collection of previously given parts; which is not the case with every sort of quantities, but only with those which are represented and apprehended by us as extensive.
On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition à priori, under which alone the schema of a pure conception of external intuition can exist; for example, “be tween two points only one straight line is possible,” “two straight lines cannot enclose a space,” etc. These are the axioms which properly relate only to quantities (quanta) as such.
But, as regards the quantity of a thing (quantitas), that is to say, the answer to the question: “How large is this or that object?” although, in respect to this question, we have various propositions synthetical and immediately certain (indemonstrabilia); we have, in the proper sense of the term, no axioms. For example, the propositions: “If equals be added to equals, the wholes are equal”; “If equals be taken from equals, the remainders are equal”; are analytical, because I am immediately conscious of the identity of the production of the one quantity with the production of the other; whereas axioms must be à priori synthetical propositions. On the other hand, the self-evident propositions as to the relation of numbers, are certainly synthetical but not universal, like those of geometry, and for this reason cannot be called axioms, but numerical formulae. That 7 + 5 = 12 is not an analytical proposition. For neither in the representation of seven, nor of five, nor of the composition of the two numbers, do I cogitate the number twelve. (Whether I cogitate the number in the addition of both, is not at present the question; for in the case of an analytical proposition, the only point is whether I really cogitate the predicate in the representation of the subject.) But although the proposition is synthetical, it is nevertheless only a singular proposition. In so far as regard is here had merely to the synthesis of the homogeneous (the units), it cannot take place except in one manner, although our use of these numbers is afterwards general. If I say: “A triangle can be constructed with three lines, any two of which taken together are greater than the third,” I exercise merely the pure function of the productive imagination, which may draw the lines longer or shorter and construct the angles at its pleasure. On the contrary, the number seven is possible only in one manner, and so is likewise the number twelve, which results from the synthesis of seven and five. Such propositions, then, cannot be termed axioms (for in that case we should have an infinity of these), but numerical formulae.
This transcendental principle of the mathematics of phenomena greatly enlarges our à priori cognition. For it is by this principle alone that pure mathematics is rendered applicable in all its precision to objects of experience, and without it the validity of this application would not be so self-evident; on the contrary, contradictions and confusions have often arisen on this very point. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition (of space and time); consequently, what geometry affirms of the latter, is indisputably valid of the former. All evasions, such as the statement that objects of sense do not conform to the rules of construction in space (for example, to the rule of the infinite divisibility of lines or angles), must fall to the ground. For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics can be applied to phenomena. The synthesis of spaces and times as the essential form of all intuition, is that which renders possible the apprehension of a phenomenon, and therefore every external experience, consequently all cognition of the objects of experience; and whatever mathematics in its pure use proves of the former, must necessarily hold good of the latter. All objections are but the chicaneries of an ill-instructed reason, which erroneously thinks to liberate the objects of sense from the formal conditions of our sensibility, and represents these, although mere phenomena, as things in themselves, presented as such to our understanding. But in this case, no à priori synthetical cognition of them could be possible, consequently not through pure conceptions of space and the science which determines these conceptions, that is to say, geometry, would itself be impossible.
2. ANTICIPATIONS OF PERCEPTION.
The principle of these is: In all phenomena the Real, that which is an object of sensation, has Intensive Quantity, that is, has a Degree.
PROOF.
Perception is empirical consciousness, that is to say, a consciousness which contains an element of sensation. Phenomena as objects of perception are not pure, that is, merely formal intuitions, like space and time, for they cannot be perceived in themselves.[28] They contain, then, over and above the intuition, the materials for an object (through which is represented something existing in space or time), that is to say, they contain the real of sensation, as a representation merely subjective, which gives us merely the consciousness that the subject is affected, and which we refer to some external object. Now, a gradual transition from empirical consciousness to pure consciousness is possible, inasmuch as the real in this consciousness entirely vanishes, and there remains a merely formal consciousness (à priori) of the manifold in time and space; consequently there is possible a synthesis also of the production of the quantity of a sensation from its commencement, that is, from the pure intuition = 0 onwards up to a certain quantity of the sensation. Now as sensation in itself is not an objective representation, and in it is to be found neither the intuition of space nor of time, it cannot possess any extensive quantity, and yet there does belong to it a quantity (and that by means of its apprehension, in which empirical consciousness can within a certain time rise from nothing = 0 up to its given amount), consequently an intensive quantity. And thus we must ascribe intensive quantity, that is, a degree of influence on sense to all objects of perception, in so far as this perception contains sensation.
[28] They can be perceived only as phenomena, and some part of them must always belong to the non-ego; whereas pure intuitions are entirely the products of the mind itself, and as such are cognized in themselves.—Tr
All cognition, by means of which I am enabled to cognize and determine à priori what belongs to empirical cognition, may be called an anticipation; and without doubt this is the sense in which Epicurus employed his expression prholepsis. But as there is in phenomena something which is never cognized à priori, which on this account constitutes the proper difference between pure and empirical cognition, that is to say, sensation (as the matter of perception), it follows, that sensation is just that element in cognition which cannot be at all anticipated. On the other hand, we might very well term the pure determinations in space and time, as well in regard to figure as to quantity, anticipations of phenomena, because they represent à priori that which may always be given à posteriori in experience. But suppose that in every sensation, as sensation in general, without any particular sensation being thought of, there existed something which could be cognized à priori, this would deserve to be called anticipation in a special sense—special, because it may seem surprising to forestall experience, in that which concerns the matter of experience, and which we can only derive from itself. Yet such really is the case here.
Apprehension[29], by means of sensation alone, fills only one moment, that is, if I do not take into consideration a succession of many sensations. As that in the phenomenon, the apprehension of which is not a successive synthesis advancing from parts to an entire representation, sensation has therefore no extensive quantity; the want of sensation in a moment of time would represent it as empty, consequently = 0. That which in the empirical intuition corresponds to sensation is reality (realitas phaenomenon); that which corresponds to the absence of it, negation = 0. Now every sensation is capable of a diminution, so that it can decrease, and thus gradually disappear. Therefore, between reality in a phenomenon and negation, there exists a continuous concatenation of many possible intermediate sensations, the difference of which from each other is always smaller than that between the given sensation and zero, or complete negation. That is to say, the real in a phenomenon has always a quantity, which however is not discoverable in apprehension, inasmuch as apprehension take place by means of mere sensation in one instant, and not by the successive synthesis of many sensations, and therefore does not progress from parts to the whole. Consequently, it has a quantity, but not an extensive quantity.
[29] Apprehension is the Kantian word for preception, in the largest sense in which we employ that term. It is the genus which includes under i, as species, perception proper and sensation proper—Tr
Now that quantity which is apprehended only as unity, and in which plurality can be represented only by approximation to negation = O, I term intensive quantity. Consequently, reality in a phenomenon has intensive quantity, that is, a degree. If we consider this reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change), we call the degree of reality in its character of cause a momentum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the apprehension of which is not successive, but instantaneous. This, however, I touch upon only in passing, for with causality I have at present nothing to do.
Accordingly, every sensation, consequently every reality in phenomena, however small it may be, has a degree, that is, an intensive quantity, which may always be lessened, and between reality and negation there exists a continuous connection of possible realities, and possible smaller perceptions. Every colour—for example, red—has a degree, which, be it ever so small, is never the smallest, and so is it always with heat, the momentum of weight, etc.
This property of quantities, according to which no part of them is the smallest possible (no part simple), is called their continuity. Space and time are quanta continua, because no part of them can be given, without enclosing it within boundaries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only boundaries, that is, the mere places or positions of their limitation. But places always presuppose intuitions which are to limit or determine them; and we cannot conceive either space or time composed of constituent parts which are given before space or time. Such quantities may also be called flowing, because synthesis (of the productive imagination) in the production of these quantities is a progression in time, the continuity of which we are accustomed to indicate by the expression flowing.
All phenomena, then, are continuous quantities, in respect both to intuition and mere perception (sensation, and with it reality). In the former case they are extensive quantities; in the latter, intensive. When the synthesis of the manifold of a phenomenon is interrupted, there results merely an aggregate of several phenomena, and not properly a phenomenon as a quantity, which is not produced by the mere continuation of the productive synthesis of a certain kind, but by the repetition of a synthesis always ceasing. For example, if I call thirteen dollars a sum or quantity of money, I employ the term quite correctly, inasmuch as I understand by thirteen dollars the value of a mark in standard silver, which is, to be sure, a continuous quantity, in which no part is the smallest, but every part might constitute a piece of money, which would contain material for still smaller pieces. If, however, by the words thirteen dollars I understand so many coins (be their value in silver what it may), it would be quite erroneous to use the expression a quantity of dollars; on the contrary, I must call them aggregate, that is, a number of coins. And as in every number we must have unity as the foundation, so a phenomenon taken as unity is a quantity, and as such always a continuous quantity (quantum continuum).
Now, seeing all phenomena, whether considered as extensive or intensive, are continuous quantities, the proposition: “All change (transition of a thing from one state into another) is continuous,” might be proved here easily, and with mathematical evidence, were it not that the causality of a change lies, entirely beyond the bounds of a transcendental philosophy, and presupposes empirical principles. For of the possibility of a cause which changes the condition of things, that is, which determines them to the contrary to a certain given state, the understanding gives us à priori no knowledge; not merely because it has no insight into the possibility of it (for such insight is absent in several à priori cognitions), but because the notion of change concerns only certain determinations of phenomena, which experience alone can acquaint us with, while their cause lies in the unchangeable. But seeing that we have nothing which we could here employ but the pure fundamental conceptions of all possible experience, among which of course nothing empirical can be admitted, we dare not, without injuring the unity of our system, anticipate general physical science, which is built upon certain fundamental experiences.
Nevertheless, we are in no want of proofs of the great influence which the principle above developed exercises in the anticipation of perceptions, and even in supplying the want of them, so far as to shield us against the false conclusions which otherwise we might rashly draw.
If all reality in perception has a degree, between which and negation there is an endless sequence of ever smaller degrees, and if, nevertheless, every sense must have a determinate degree of receptivity for sensations; no perception, and consequently no experience is possible, which can prove, either immediately or mediately, an entire absence of all reality in a phenomenon; in other words, it is impossible ever to draw from experience a proof of the existence of empty space or of empty time. For in the first place, an entire absence of reality in a sensuous intuition cannot of course be an object of perception; secondly, such absence cannot be deduced from the contemplation of any single phenomenon, and the difference of the degrees in its reality; nor ought it ever to be admitted in explanation of any phenomenon. For if even the complete intuition of a determinate space or time is thoroughly real, that is, if no part thereof is empty, yet because every reality has its degree, which, with the extensive quantity of the phenomenon unchanged, can diminish through endless gradations down to nothing (the void), there must be infinitely graduated degrees, with which space or time is filled, and the intensive quantity in different phenomena may be smaller or greater, although the extensive quantity of the intuition remains equal and unaltered.
We shall give an example of this. Almost all natural philosophers, remarking a great difference in the quantity of the matter of different kinds in bodies with the same volume (partly on account of the momentum of gravity or weight, partly on account of the momentum of resistance to other bodies in motion), conclude unanimously that this volume (extensive quantity of the phenomenon) must be void in all bodies, although in different proportion. But who would suspect that these for the most part mathematical and mechanical inquirers into nature should ground this conclusion solely on a metaphysical hypothesis—a sort of hypothesis which they profess to disparage and avoid? Yet this they do, in assuming that the real in space (I must not here call it impenetrability or weight, because these are empirical conceptions) is always identical, and can only be distinguished according to its extensive quantity, that is, multiplicity. Now to this presupposition, for which they can have no ground in experience, and which consequently is merely metaphysical, I oppose a transcendental demonstration, which it is true will not explain the difference in the filling up of spaces, but which nevertheless completely does away with the supposed necessity of the above-mentioned presupposition that we cannot explain the said difference otherwise than by the hypothesis of empty spaces. This demonstration, moreover, has the merit of setting the understanding at liberty to conceive this distinction in a different manner, if the explanation of the fact requires any such hypothesis. For we perceive that although two equal spaces may be completely filled by matters altogether different, so that in neither of them is there left a single point wherein matter is not present, nevertheless, every reality has its degree (of resistance or of weight), which, without diminution of the extensive quantity, can become less and less ad infinitum, before it passes into nothingness and disappears. Thus an expansion which fills a space—for example, caloric, or any other reality in the phenomenal world—can decrease in its degrees to infinity, yet without leaving the smallest part of the space empty; on the contrary, filling it with those lesser degrees as completely as another phenomenon could with greater. My intention here is by no means to maintain that this is really the case with the difference of matters, in regard to their specific gravity; I wish only to prove, from a principle of the pure understanding, that the nature of our perceptions makes such a mode of explanation possible, and that it is erroneous to regard the real in a phenomenon as equal quoad its degree, and different only quoad its aggregation and extensive quantity, and this, too, on the pretended authority of an à priori principle of the understanding.
Nevertheless, this principle of the anticipation of perception must somewhat startle an inquirer whom initiation into transcendental philosophy has rendered cautious. We must naturally entertain some doubt whether or not the understanding can enounce any such synthetical proposition as that respecting the degree of all reality in phenomena, and consequently the possibility of the internal difference of sensation itself—abstraction being made of its empirical quality. Thus it is a question not unworthy of solution: “How the understanding can pronounce synthetically and à priori respecting phenomena, and thus anticipate these, even in that which is peculiarly and merely empirical, that, namely, which concerns sensation itself?”
The quality of sensation is in all cases merely empirical, and cannot be represented à priori (for example, colours, taste, etc.). But the real—that which corresponds to sensation—in opposition to negation = 0, only represents something the conception of which in itself contains a being (ein seyn), and signifies nothing but the synthesis in an empirical consciousness. That is to say, the empirical consciousness in the internal sense can be raised from 0 to every higher degree, so that the very same extensive quantity of intuition, an illuminated surface, for example, excites as great a sensation as an aggregate of many other surfaces less illuminated. We can therefore make complete abstraction of the extensive quantity of a phenomenon, and represent to ourselves in the mere sensation in a certain momentum, a synthesis of homogeneous ascension from 0 up to the given empirical consciousness, All sensations therefore as such are given only à posteriori, but this property thereof, namely, that they have a degree, can be known à priori. It is worthy of remark, that in respect to quantities in general, we can cognize à priori only a single quality, namely, continuity; but in respect to all quality (the real in phenomena), we cannot cognize à priori anything more than the intensive quantity thereof, namely, that they have a degree. All else is left to experience.
3. ANALOGIES OF EXPERIENCE.
The principle of these is: Experience is possible only through the representation of a necessary connection of Perceptions.
PROOF.
Experience is an empirical cognition; that is to say, a cognition which determines an object by means of perceptions. It is therefore a synthesis of perceptions, a synthesis which is not itself contained in perception, but which contains the synthetical unity of the manifold of perception in a consciousness; and this unity constitutes the essential of our cognition of objects of the senses, that is, of experience (not merely of intuition or sensation). Now in experience our perceptions come together contingently, so that no character of necessity in their connection appears, or can appear from the perceptions themselves, because apprehension is only a placing together of the manifold of empirical intuition, and no representation of a necessity in the connected existence of the phenomena which apprehension brings together, is to be discovered therein. But as experience is a cognition of objects by means of perceptions, it follows that the relation of the existence of the existence of the manifold must be represented in experience not as it is put together in time, but as it is objectively in time. And as time itself cannot be perceived, the determination of the existence of objects in time can only take place by means of their connection in time in general, consequently only by means of à priori connecting conceptions. Now as these conceptions always possess the character of necessity, experience is possible only by means of a representation of the necessary connection of perception.
The three modi of time are permanence, succession, and coexistence. Accordingly, there are three rules of all relations of time in phenomena, according to which the existence of every phenomenon is determined in respect of the unity of all time, and these antecede all experience and render it possible.
The general principle of all three analogies rests on the necessary unity of apperception in relation to all possible empirical consciousness (perception) at every time, consequently, as this unity lies à priori at the foundation of all mental operations, the principle rests on the synthetical unity of all phenomena according to their relation in time. For the original apperception relates to our internal sense (the complex of all representations), and indeed relates à priori to its form, that is to say, the relation of the manifold empirical consciousness in time. Now this manifold must be combined in original apperception according to relations of time—a necessity imposed by the à priori transcendental unity of apperception, to which is subjected all that can belong to my (i.e., my own) cognition, and therefore all that can become an object for me. This synthetical and à priori determined unity in relation of perceptions in time is therefore the rule: “All empirical determinations of time must be subject to rules of the general determination of time”; and the analogies of experience, of which we are now about to treat, must be rules of this nature.
These principles have this peculiarity, that they do not concern phenomena, and the synthesis of the empirical intuition thereof, but merely the existence of phenomena and their relation to each other in regard to this existence. Now the mode in which we apprehend a thing in a phenomenon can be determined à priori in such a manner that the rule of its synthesis can give, that is to say, can produce this à priori intuition in every empirical example. But the existence of phenomena cannot be known à priori, and although we could arrive by this path at a conclusion of the fact of some existence, we could not cognize that existence determinately, that is to say, we should be incapable of anticipating in what respect the empirical intuition of it would be distinguishable from that of others.
The two principles above mentioned, which I called mathematical, in consideration of the fact of their authorizing the application of mathematic phenomena, relate to these phenomena only in regard to their possibility, and instruct us how phenomena, as far as regards their intuition or the real in their perception, can be generated according to the rules of a mathematical synthesis. Consequently, numerical quantities, and with them the determination of a phenomenon as a quantity, can be employed in the one case as well as in the other. Thus, for example, out of 200,000 illuminations by the moon, I might compose and give à priori, that is construct, the degree of our sensations of the sun-light.[30] We may therefore entitle these two principles constitutive.
[30] Kant’s meaning is: The two principles enunciated under the heads of “Axioms of Intuition,” and “Anticipations of Perception,” authorize the application to phenomena of determinations of size and number, that is of mathematic. For example, I may compute the light of the sun, and say that its quantity is a certain number of times greater than that of the moon. In the same way, heat is measured by the comparison of its different effects on water, &c., and on mercury in a thermometer.—Tr
The case is very different with those principles whose province it is to subject the existence of phenomena to rules à priori. For as existence does not admit of being constructed, it is clear that they must only concern the relations of existence and be merely regulative principles. In this case, therefore, neither axioms nor anticipations are to be thought of. Thus, if a perception is given us, in a certain relation of time to other (although undetermined) perceptions, we cannot then say à priori, what and how great (in quantity) the other perception necessarily connected with the former is, but only how it is connected, quoad its existence, in this given modus of time. Analogies in philosophy mean something very different from that which they represent in mathematics. In the latter they are formulae, which enounce the equality of two relations of quantity, and are always constitutive, so that if two terms of the proportion are given, the third is also given, that is, can be constructed by the aid of these formulae. But in philosophy, analogy is not the equality of two quantitative but of two qualitative relations. In this case, from three given terms, I can give à priori and cognize the relation to a fourth member, but not this fourth term itself, although I certainly possess a rule to guide me in the search for this fourth term in experience, and a mark to assist me in discovering it. An analogy of experience is therefore only a rule according to which unity of experience must arise out of perceptions in respect to objects (phenomena) not as a constitutive, but merely as a regulative principle. The same holds good also of the postulates of empirical thought in general, which relate to the synthesis of mere intuition (which concerns the form of phenomena), the synthesis of perception (which concerns the matter of phenomena), and the synthesis of experience (which concerns the relation of these perceptions). For they are only regulative principles, and clearly distinguishable from the mathematical, which are constitutive, not indeed in regard to the certainty which both possess à priori, but in the mode of evidence thereof, consequently also in the manner of demonstration.
But what has been observed of all synthetical propositions, and must be particularly remarked in this place, is this, that these analogies possess significance and validity, not as principles of the transcendental, but only as principles of the empirical use of the understanding, and their truth can therefore be proved only as such, and that consequently the phenomena must not be subjoined directly under the categories, but only under their schemata. For if the objects to which those principles must be applied were things in themselves, it would be quite impossible to cognize aught concerning them synthetically à priori. But they are nothing but phenomena; a complete knowledge of which—a knowledge to which all principles à priori must at last relate—is the only possible experience. It follows that these principles can have nothing else for their aim than the conditions of the empirical cognition in the unity of synthesis of phenomena. But this synthesis is cogitated only in the schema of the pure conception of the understanding, of whose unity, as that of a synthesis in general, the category contains the function unrestricted by any sensuous condition. These principles will therefore authorize us to connect phenomena according to an analogy, with the logical and universal unity of conceptions, and consequently to employ the categories in the principles themselves; but in the application of them to experience, we shall use only their schemata, as the key to their proper application, instead of the categories, or rather the latter as restricting conditions, under the title of “formulae” of the former.
A. FIRST ANALOGY.
Principle of the Permanence of Substance.
In all changes of phenomena, substance is permanent, and the quantum thereof in nature is neither increased nor diminished.
PROOF.
All phenomena exist in time, wherein alone as substratum, that is, as the permanent form of the internal intuition, coexistence and succession can be represented. Consequently time, in which all changes of phenomena must be cogitated, remains and changes not, because it is that in which succession and coexistence can be represented only as determinations thereof. Now, time in itself cannot be an object of perception. It follows that in objects of perception, that is, in phenomena, there must be found a substratum which represents time in general, and in which all change or coexistence can be perceived by means of the relation of phenomena to it. But the substratum of all reality, that is, of all that pertains to the existence of things, is substance; all that pertains to existence can be cogitated only as a determination of substance. Consequently, the permanent, in relation to which alone can all relations of time in phenomena be determined, is substance in the world of phenomena, that is, the real in phenomena, that which, as the substratum of all change, remains ever the same. Accordingly, as this cannot change in existence, its quantity in nature can neither be increased nor diminished.
Our apprehension of the manifold in a phenomenon is always successive, is Consequently always changing. By it alone we could, therefore, never determine whether this manifold, as an object of experience, is coexistent or successive, unless it had for a foundation something fixed and permanent, of the existence of which all succession and coexistence are nothing but so many modes (modi of time). Only in the permanent, then, are relations of time possible (for simultaneity and succession are the only relations in time); that is to say, the permanent is the substratum of our empirical representation of time itself, in which alone all determination of time is possible. Permanence is, in fact, just another expression for time, as the abiding correlate of all existence of phenomena, and of all change, and of all coexistence. For change does not affect time itself, but only the phenomena in time (just as coexistence cannot be regarded as a modus of time itself, seeing that in time no parts are coexistent, but all successive). If we were to attribute succession to time itself, we should be obliged to cogitate another time, in which this succession would be possible. It is only by means of the permanent that existence in different parts of the successive series of time receives a quantity, which we entitle duration. For in mere succession, existence is perpetually vanishing and recommencing, and therefore never has even the least quantity. Without the permanent, then, no relation in time is possible. Now, time in itself is not an object of perception; consequently the permanent in phenomena must be regarded as the substratum of all determination of time, and consequently also as the condition of the possibility of all synthetical unity of perceptions, that is, of experience; and all existence and all change in time can only be regarded as a mode in the existence of that which abides unchangeably. Therefore, in all phenomena, the permanent is the object in itself, that is, the substance (phenomenon); but all that changes or can change belongs only to the mode of the existence of this substance or substances, consequently to its determinations.
I find that in all ages not only the philosopher, but even the common understanding, has preposited this permanence as a substratum of all change in phenomena; indeed, I am compelled to believe that they will always accept this as an indubitable fact. Only the philosopher expresses himself in a more precise and definite manner, when he says: “In all changes in the world, the substance remains, and the accidents alone are changeable.” But of this decidedly synthetical proposition, I nowhere meet with even an attempt at proof; nay, it very rarely has the good fortune to stand, as it deserves to do, at the head of the pure and entirely à priori laws of nature. In truth, the statement that substance is permanent, is tautological. For this very permanence is the ground on which we apply the category of substance to the phenomenon; and we should have been obliged to prove that in all phenomena there is something permanent, of the existence of which the changeable is nothing but a determination. But because a proof of this nature cannot be dogmatical, that is, cannot be drawn from conceptions, inasmuch as it concerns a synthetical proposition à priori, and as philosophers never reflected that such propositions are valid only in relation to possible experience, and therefore cannot be proved except by means of a deduction of the possibility of experience, it is no wonder that while it has served as the foundation of all experience (for we feel the need of it in empirical cognition), it has never been supported by proof.
A philosopher was asked: “What is the weight of smoke?” He answered: “Subtract from the weight of the burnt wood the weight of the remaining ashes, and you will have the weight of the smoke.” Thus he presumed it to be incontrovertible that even in fire the matter (substance) does not perish, but that only the form of it undergoes a change. In like manner was the saying: “From nothing comes nothing,” only another inference from the principle or permanence, or rather of the ever-abiding existence of the true subject in phenomena. For if that in the phenomenon which we call substance is to be the proper substratum of all determination of time, it follows that all existence in past as well as in future time, must be determinable by means of it alone. Hence we are entitled to apply the term substance to a phenomenon, only because we suppose its existence in all time, a notion which the word permanence does not fully express, as it seems rather to be referable to future time. However, the internal necessity perpetually to be, is inseparably connected with the necessity always to have been, and so the expression may stand as it is. “Gigni de nihilo nihil; in nihilum nil posse reverti,”[31] are two propositions which the ancients never parted, and which people nowadays sometimes mistakenly disjoin, because they imagine that the propositions apply to objects as things in themselves, and that the former might be inimical to the dependence (even in respect of its substance also) of the world upon a supreme cause. But this apprehension is entirely needless, for the question in this case is only of phenomena in the sphere of experience, the unity of which never could be possible, if we admitted the possibility that new things (in respect of their substance) should arise. For in that case, we should lose altogether that which alone can represent the unity of time, to wit, the identity of the substratum, as that through which alone all change possesses complete and thorough unity. This permanence is, however, nothing but the manner in which we represent to ourselves the existence of things in the phenomenal world.
[31] Persius, Satirae, iii.83-84.
The determinations of a substance, which are only particular modes of its existence, are called accidents. They are always real, because they concern the existence of substance (negations are only determinations, which express the non-existence of something in the substance). Now, if to this real in the substance we ascribe a particular existence (for example, to motion as an accident of matter), this existence is called inherence, in contradistinction to the existence of substance, which we call subsistence. But hence arise many misconceptions, and it would be a more accurate and just mode of expression to designate the accident only as the mode in which the existence of a substance is positively determined. Meanwhile, by reason of the conditions of the logical exercise of our understanding, it is impossible to avoid separating, as it were, that which in the existence of a substance is subject to change, whilst the substance remains, and regarding it in relation to that which is properly permanent and radical. On this account, this category of substance stands under the title of relation, rather because it is the condition thereof than because it contains in itself any relation.
Now, upon this notion of permanence rests the proper notion of the conception change. Origin and extinction are not changes of that which originates or becomes extinct. Change is but a mode of existence, which follows on another mode of existence of the same object; hence all that changes is permanent, and only the condition thereof changes. Now since this mutation affects only determinations, which can have a beginning or an end, we may say, employing an expression which seems somewhat paradoxical: “Only the permanent (substance) is subject to change; the mutable suffers no change, but rather alternation, that is, when certain determinations cease, others begin.”
Change, when, cannot be perceived by us except in substances, and origin or extinction in an absolute sense, that does not concern merely a determination of the permanent, cannot be a possible perception, for it is this very notion of the permanent which renders possible the representation of a transition from one state into another, and from non-being to being, which, consequently, can be empirically cognized only as alternating determinations of that which is permanent. Grant that a thing absolutely begins to be; we must then have a point of time in which it was not. But how and by what can we fix and determine this point of time, unless by that which already exists? For a void time—preceding—is not an object of perception; but if we connect this beginning with objects which existed previously, and which continue to exist till the object in question in question begins to be, then the latter can only be a determination of the former as the permanent. The same holds good of the notion of extinction, for this presupposes the empirical representation of a time, in which a phenomenon no longer exists.
Substances (in the world of phenomena) are the substratum of all determinations of time. The beginning of some, and the ceasing to be of other substances, would utterly do away with the only condition of the empirical unity of time; and in that case phenomena would relate to two different times, in which, side by side, existence would pass; which is absurd. For there is only one time in which all different times must be placed, not as coexistent, but as successive.
Accordingly, permanence is a necessary condition under which alone phenomena, as things or objects, are determinable in a possible experience. But as regards the empirical criterion of this necessary permanence, and with it of the substantiality of phenomena, we shall find sufficient opportunity to speak in the sequel.
B. SECOND ANALOGY.
Principle of the Succession of Time According to the Law of Causality. All changes take place according to the law of the connection of Cause and Effect.
PROOF.
(That all phenomena in the succession of time are only changes, that is, a successive being and non-being of the determinations of substance, which is permanent; consequently that a being of substance itself which follows on the non-being thereof, or a non-being of substance which follows on the being thereof, in other words, that the origin or extinction of substance itself, is impossible—all this has been fully established in treating of the foregoing principle. This principle might have been expressed as follows: “All alteration (succession) of phenomena is merely change”; for the changes of substance are not origin or extinction, because the conception of change presupposes the same subject as existing with two opposite determinations, and consequently as permanent. After this premonition, we shall proceed to the proof.)
I perceive that phenomena succeed one another, that is to say, a state of things exists at one time, the opposite of which existed in a former state. In this case, then, I really connect together two perceptions in time. Now connection is not an operation of mere sense and intuition, but is the product of a synthetical faculty of imagination, which determines the internal sense in respect of a relation of time. But imagination can connect these two states in two ways, so that either the one or the other may antecede in time; for time in itself cannot be an object of perception, and what in an object precedes and what follows cannot be empirically determined in relation to it. I am only conscious, then, that my imagination places one state before and the other after; not that the one state antecedes the other in the object. In other words, the objective relation of the successive phenomena remains quite undetermined by means of mere perception. Now in order that this relation may be cognized as determined, the relation between the two states must be so cogitated that it is thereby determined as necessary, which of them must be placed before and which after, and not conversely. But the conception which carries with it a necessity of synthetical unity, can be none other than a pure conception of the understanding which does not lie in mere perception; and in this case it is the conception of “the relation of cause and effect,” the former of which determines the latter in time, as its necessary consequence, and not as something which might possibly antecede (or which might in some cases not be perceived to follow). It follows that it is only because we subject the sequence of phenomena, and consequently all change, to the law of causality, that experience itself, that is, empirical cognition of phenomena, becomes possible; and consequently, that phenomena themselves, as objects of experience, are possible only by virtue of this law.
Our apprehension of the manifold of phenomena is always successive. The representations of parts succeed one another. Whether they succeed one another in the object also, is a second point for reflection, which was not contained in the former. Now we may certainly give the name of object to everything, even to every representation, so far as we are conscious thereof; but what this word may mean in the case of phenomena, not merely in so far as they (as representations) are objects, but only in so far as they indicate an object, is a question requiring deeper consideration. In so far as they, regarded merely as representations, are at the same time objects of consciousness, they are not to be distinguished from apprehension, that is, reception into the synthesis of imagination, and we must therefore say: “The manifold of phenomena is always produced successively in the mind.” If phenomena were things in themselves, no man would be able to conjecture from the succession of our representations how this manifold is connected in the object; for we have to do only with our representations. How things may be in themselves, without regard to the representations through which they affect us, is utterly beyond the sphere of our cognition. Now although phenomena are not things in themselves, and are nevertheless the only thing given to us to be cognized, it is my duty to show what sort of connection in time belongs to the manifold in phenomena themselves, while the representation of this manifold in apprehension is always successive. For example, the apprehension of the manifold in the phenomenon of a house which stands before me, is successive. Now comes the question whether the manifold of this house is in itself successive—which no one will be at all willing to grant. But, so soon as I raise my conception of an object to the transcendental signification thereof, I find that the house is not a thing in itself, but only a phenomenon, that is, a representation, the transcendental object of which remains utterly unknown. What then am I to understand by the question: “How can the manifold be connected in the phenomenon itself—not considered as a thing in itself, but merely as a phenomenon?” Here that which lies in my successive apprehension is regarded as representation, whilst the phenomenon which is given me, notwithstanding that it is nothing more than a complex of these representations, is regarded as the object thereof, with which my conception, drawn from the representations of apprehension, must harmonize. It is very soon seen that, as accordance of the cognition with its object constitutes truth, the question now before us can only relate to the formal conditions of empirical truth; and that the phenomenon, in opposition to the representations of apprehension, can only be distinguished therefrom as the object of them, if it is subject to a rule which distinguishes it from every other apprehension, and which renders necessary a mode of connection of the manifold. That in the phenomenon which contains the condition of this necessary rule of apprehension, is the object.
Let us now proceed to our task. That something happens, that is to say, that something or some state exists which before was not, cannot be empirically perceived, unless a phenomenon precedes, which does not contain in itself this state. For a reality which should follow upon a void time, in other words, a beginning, which no state of things precedes, can just as little be apprehended as the void time itself. Every apprehension of an event is therefore a perception which follows upon another perception. But as this is the case with all synthesis of apprehension, as I have shown above in the example of a house, my apprehension of an event is not yet sufficiently distinguished from other apprehensions. But I remark also that if in a phenomenon which contains an occurrence, I call the antecedent state of my perception, A, and the following state, B, the perception B can only follow A in apprehension, and the perception A cannot follow B, but only precede it. For example, I see a ship float down the stream of a river. My perception of its place lower down follows upon my perception of its place higher up the course of the river, and it is impossible that, in the apprehension of this phenomenon, the vessel should be perceived first below and afterwards higher up the stream. Here, therefore, the order in the sequence of perceptions in apprehension is determined; and by this order apprehension is regulated. In the former example, my perceptions in the apprehension of a house might begin at the roof and end at the foundation, or vice versa; or I might apprehend the manifold in this empirical intuition, by going from left to right, and from right to left. Accordingly, in the series of these perceptions, there was no determined order, which necessitated my beginning at a certain point, in order empirically to connect the manifold. But this rule is always to be met with in the perception of that which happens, and it makes the order of the successive perceptions in the apprehension of such a phenomenon necessary.
I must, therefore, in the present case, deduce the subjective sequence of apprehension from the objective sequence of phenomena, for otherwise the former is quite undetermined, and one phenomenon is not distinguishable from another. The former alone proves nothing as to the connection of the manifold in an object, for it is quite arbitrary. The latter must consist in the order of the manifold in a phenomenon, according to which order the apprehension of one thing (that which happens) follows that of another thing (which precedes), in conformity with a rule. In this way alone can I be authorized to say of the phenomenon itself, and not merely of my own apprehension, that a certain order or sequence is to be found therein. That is, in other words, I cannot arrange my apprehension otherwise than in this order.
In conformity with this rule, then, it is necessary that in that which antecedes an event there be found the condition of a rule, according to which in this event follows always and necessarily; but I cannot reverse this and go back from the event, and determine (by apprehension) that which antecedes it. For no phenomenon goes back from the succeeding point of time to the preceding point, although it does certainly relate to a preceding point of time; from a given time, on the other hand, there is always a necessary progression to the determined succeeding time. Therefore, because there certainly is something that follows, I must of necessity connect it with something else, which antecedes, and upon which it follows, in conformity with a rule, that is necessarily, so that the event, as conditioned, affords certain indication of a condition, and this condition determines the event.
Let us suppose that nothing precedes an event, upon which this event must follow in conformity with a rule. All sequence of perception would then exist only in apprehension, that is to say, would be merely subjective, and it could not thereby be objectively determined what thing ought to precede, and what ought to follow in perception. In such a case, we should have nothing but a play of representations, which would possess no application to any object. That is to say, it would not be possible through perception to distinguish one phenomenon from another, as regards relations of time; because the succession in the act of apprehension would always be of the same sort, and therefore there would be nothing in the phenomenon to determine the succession, and to render a certain sequence objectively necessary. And, in this case, I cannot say that two states in a phenomenon follow one upon the other, but only that one apprehension follows upon another. But this is merely subjective, and does not determine an object, and consequently cannot be held to be cognition of an object—not even in the phenomenal world.
Accordingly, when we know in experience that something happens, we always presuppose that something precedes, whereupon it follows in conformity with a rule. For otherwise I could not say of the object that it follows; because the mere succession in my apprehension, if it be not determined by a rule in relation to something preceding, does not authorize succession in the object. Only, therefore, in reference to a rule, according to which phenomena are determined in their sequence, that is, as they happen, by the preceding state, can I make my subjective synthesis (of apprehension) objective, and it is only under this presupposition that even the experience of an event is possible.
No doubt it appears as if this were in thorough contradiction to all the notions which people have hitherto entertained in regard to the procedure of the human understanding. According to these opinions, it is by means of the perception and comparison of similar consequences following upon certain antecedent phenomena that the understanding is led to the discovery of a rule, according to which certain events always follow certain phenomena, and it is only by this process that we attain to the conception of cause. Upon such a basis, it is clear that this conception must be merely empirical, and the rule which it furnishes us with—“Everything that happens must have a cause”—would be just as contingent as experience itself. The universality and necessity of the rule or law would be perfectly spurious attributes of it. Indeed, it could not possess universal validity, inasmuch as it would not in this case be à priori, but founded on deduction. But the same is the case with this law as with other pure à priori representations (e.g., space and time), which we can draw in perfect clearness and completeness from experience, only because we had already placed them therein, and by that means, and by that alone, had rendered experience possible. Indeed, the logical clearness of this representation of a rule, determining the series of events, is possible only when we have made use thereof in experience. Nevertheless, the recognition of this rule, as a condition of the synthetical unity of phenomena in time, was the ground of experience itself and consequently preceded it à priori.
It is now our duty to show by an example that we never, even in experience, attribute to an object the notion of succession or effect (of an event—that is, the happening of something that did not exist before), and distinguish it from the subjective succession of apprehension, unless when a rule lies at the foundation, which compels us to observe this order of perception in preference to any other, and that, indeed, it is this necessity which first renders possible the representation of a succession in the object.
We have representations within us, of which also we can be conscious. But, however widely extended, however accurate and thoroughgoing this consciousness may be, these representations are still nothing more than representations, that is, internal determinations of the mind in this or that relation of time. Now how happens it that to these representations we should set an object, or that, in addition to their subjective reality, as modifications, we should still further attribute to them a certain unknown objective reality? It is clear that objective significancy cannot consist in a relation to another representation (of that which we desire to term object), for in that case the question again arises: “How does this other representation go out of itself, and obtain objective significancy over and above the subjective, which is proper to it, as a determination of a state of mind?” If we try to discover what sort of new property the relation to an object gives to our subjective representations, and what new importance they thereby receive, we shall find that this relation has no other effect than that of rendering necessary the connection of our representations in a certain manner, and of subjecting them to a rule; and that conversely, it is only because a certain order is necessary in the relations of time of our representations, that objective significancy is ascribed to them.
In the synthesis of phenomena, the manifold of our representations is always successive. Now hereby is not represented an object, for by means of this succession, which is common to all apprehension, no one thing is distinguished from another. But so soon as I perceive or assume that in this succession there is a relation to a state antecedent, from which the representation follows in accordance with a rule, so soon do I represent something as an event, or as a thing that happens; in other words, I cognize an object to which I must assign a certain determinate position in time, which cannot be altered, because of the preceding state in the object. When, therefore, I perceive that something happens, there is contained in this representation, in the first place, the fact, that something antecedes; because, it is only in relation to this that the phenomenon obtains its proper relation of time, in other words, exists after an antecedent time, in which it did not exist. But it can receive its determined place in time only by the presupposition that something existed in the foregoing state, upon which it follows inevitably and always, that is, in conformity with a rule. From all this it is evident that, in the first place, I cannot reverse the order of succession, and make that which happens precede that upon which it follows; and that, in the second place, if the antecedent state be posited, a certain determinate event inevitably and necessarily follows. Hence it follows that there exists a certain order in our representations, whereby the present gives a sure indication of some previously existing state, as a correlate, though still undetermined, of the existing event which is given—a correlate which itself relates to the event as its consequence, conditions it, and connects it necessarily with itself in the series of time.
If then it be admitted as a necessary law of sensibility, and consequently a formal condition of all perception, that the preceding necessarily determines the succeeding time (inasmuch as I cannot arrive at the succeeding except through the preceding), it must likewise be an indispensable law of empirical representation of the series of time that the phenomena of the past determine all phenomena in the succeeding time, and that the latter, as events, cannot take place, except in so far as the former determine their existence in time, that is to say, establish it according to a rule. For it is of course only in phenomena that we can empirically cognize this continuity in the connection of times.
For all experience and for the possibility of experience, understanding is indispensable, and the first step which it takes in this sphere is not to render the representation of objects clear, but to render the representation of an object in general, possible. It does this by applying the order of time to phenomena, and their existence. In other words, it assigns to each phenomenon, as a consequence, a place in relation to preceding phenomena, determined à priori in time, without which it could not harmonize with time itself, which determines a place à priori to all its parts. This determination of place cannot be derived from the relation of phenomena to absolute time (for it is not an object of perception); but, on the contrary, phenomena must reciprocally determine the places in time of one another, and render these necessary in the order of time. In other words, whatever follows or happens, must follow in conformity with a universal rule upon that which was contained in the foregoing state. Hence arises a series of phenomena, which, by means of the understanding, produces and renders necessary exactly the same order and continuous connection in the series of our possible perceptions, as is found à priori in the form of internal intuition (time), in which all our perceptions must have place.
That something happens, then, is a perception which belongs to a possible experience, which becomes real only because I look upon the phenomenon as determined in regard to its place in time, consequently as an object, which can always be found by means of a rule in the connected series of my perceptions. But this rule of the determination of a thing according to succession in time is as follows: “In what precedes may be found the condition, under which an event always (that is, necessarily) follows.” From all this it is obvious that the principle of cause and effect is the principle of possible experience, that is, of objective cognition of phenomena, in regard to their relations in the succession of time.