I.2.1. Analogies of Experience

The principle of the analogies is: Experience is possible only through the representation of a necessary connection of perceptions.

Experience is an empirical knowledge, that is, a knowledge which determines an object through perceptions. 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 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 200,000 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 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 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.

In all change of appearances substance is permanent; its quantum in nature is neither increased nor diminished.

All appearances are in time; and in it alone, as substrate (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 substrate which represents time in general; and all change or coexistence must, in being apprehended, be perceived in this substrate, and through relation of the appearances to it. But the substrate 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. And simultaneity and succession being the only relations in time, it follows that 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 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 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 (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.

All alterations take place in conformity with the law of the connection of cause and effect.

(The preceding 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. But imagination can connect these two states 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 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 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 merely subjective succession is altogether arbitrary, it does not by itself 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] 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, 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 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 clear, but in making the 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 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 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 hollow in the 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 existing text-books. But I must not leave unconsidered the empirical criterion of a substance, 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 sub stance 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 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, but its state. It is, therefore, only alteration, not a coming 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, the point of time of the second is distinct from that of the first, and follows upon it. Similarly, the second state as reality in the [field of] appearance differs from the first wherein it did not exist, as from zero. That is to say, even if the state 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 to another = 4. 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 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 o and a.

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 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.

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 reciprocally. 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 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 its position in time, and also reversewise B for A, because only on this condition can these substances be empirically represented as coexisting. Now that alone which can determine the position of anything else in time is its cause or the cause of its determinations. 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, 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. 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 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.