Each of the three categories of relation, i. e. those of substance and accident, of cause and effect, and of interaction between agent and patient involves, according to Kant, a special principle, and these special principles he calls 'analogies of experience'. They are stated thus:[1] (1) In all changes of phenomena the substance is permanent, and its quantity in nature is neither increased nor diminished. (2) All changes take place according to the law of the connexion of cause and effect. (3) All substances, so far as they can be perceived in space as coexistent, are in complete interaction. The justification of the term analogy of experience is as follows. In mathematics an analogy is a formula which asserts the equality of two quantitative relations, and is such that, if three of the terms are given, we can discover the fourth, e. g. if we know that a : b = c : d, and that a = 2, b = 4, c = 6 we can discover that d = 12. But in philosophy an analogy is the assertion of the equality of two qualitative relations and is such that, if three of the terms are given, we can discover, not the fourth, but only the relation of the third to the fourth, though at the same time we are furnished with a clue whereby to search for the fourth in experience. In this philosophical sense, the principles involved in the categories of relation are analogies. For instance, the principles of causality can be stated in the form 'Any known event X is to some other event Y, whatever it be, as effect to cause'; so stated, it clearly informs us not of the character of Y but only of the fact that there must be a Y, i. e. a necessary antecedent, though at the same time this knowledge enables us to search in experience for the special character of Y.

The principles to be established relate to the two kinds of temporal relation apprehended in the world of nature, viz. coexistence and succession. The method of proof, which is to be gathered from the proofs themselves rather than from Kant's general remarks[2] on the subject, is the same in each case. Kant expressly rejects any proof which is 'dogmatical' or 'from conceptions', e. g. any attempt to show that the very conception of change presupposes the thought of an identical subject of change.[3] The proof is transcendental in character, i. e. it argues that the principle to be established is a condition of the possibility of apprehending the temporal relation in question, e. g. that the existence of a permanent subject of change is presupposed in any apprehension of change. It assumes that we become aware of sequences and coexistences in the world of nature by a process which begins with a succession of mere perceptions, i. e. perceptions which are so far not the perceptions of a sequence or of a coexistence or indeed of anything;[4] and it seeks to show that this process involves an appeal to one of the principles in question—the particular principle involved depending on the temporal relation apprehended—and consequently, that since we do apprehend this temporal relation, which, as belonging to the world of nature, must be distinct from any temporal relation of our perceptions, the principle appealed to is valid.

The proof of the first analogy is given somewhat differently in the first edition, and in a passage added in the second. The earlier version, which is a better expression of the attitude underlying Kant's general remarks on the analogy, is as follows:

"Our apprehension of the manifold of a phenomenon is always successive, and is therefore always changing. By it alone, therefore, we can never determine whether this manifold, as an object of experience, is coexistent or successive, unless there lies at the base of it something that exists always, that is, something enduring and permanent, of which all succession and coexistence are nothing but so many ways (modi of time) in which the permanent exists. Only in the permanent, then, are time relations possible (for simultaneity and succession are the only relations in time); i. e. the permanent is the substratum of the empirical representation of time itself, in which alone all time-determination is possible. Permanence expresses in general time, as the persisting correlate of all existence of phenomena, of all change, and of all concomitance.... Only through the permanent does existence in different parts of the successive series of time gain a quantity which we call duration. For, in mere succession, existence is always vanishing and beginning, and never has the least quantity. Without this permanent, then, no time relation is possible. Now, time in itself cannot be perceived[5]; consequently this permanent in phenomena is the substratum of all time-determination, and therefore also the condition of the possibility of all synthetic unity of sense-perceptions, that is, of experience, and in this permanent all existence and all change in time can only be regarded as a mode of the existence of that which endures and is permanent. Therefore in all phenomena the permanent is the object itself, i. e. the substance (phenomenon); but all that changes or can change belongs only to the way in which this substance or substances exist, consequently to their determinations."[6] "Accordingly since substance cannot change in existence, its quantity in nature can neither be increased nor diminished."[7] The argument becomes plainer if it be realized that in the interval between the two editions, Kant came to think that the permanent in question was matter or bodies in space.[8] "We find that in order to give something permanent in perception corresponding to the conception of substance (and thereby to exhibit the objective reality of this conception), we need a perception in space (of matter), because space alone has permanent determinations, while time, and consequently everything which is in the internal sense, is continually flowing."[9]

Kant's thought appears to be as follows: 'Our apprehension of the manifold consists of a series of successive acts in which we apprehend its elements one by one and in isolation. This apprehension, therefore, does not enable us to determine that its elements are temporally related either as successive or as coexistent.[10] In order to determine this, we must apprehend the elements of the manifold as related to something permanent. For a succession proper, i. e. a change, is a succession of states or determinations of something permanent or unchanging. A mere succession which is not a succession of states of something which remains identical is an unconnected series of endings and beginnings, and with respect to it, 'duration', which has meaning with regard to changes, i. e. successions proper, has no meaning at all. Similarly, coexistence is a coexistence of states of two permanents. Hence, to apprehend elements of the manifold as successive or coexistent, we must apprehend them in relation to a permanent or permanents. Therefore, to apprehend a coexistence or a succession, we must perceive something permanent. But this permanent something cannot be time, for time cannot be perceived. It must therefore be a permanent in phenomena; and this must be the object itself or the substance of a phenomenon, i. e. the substratum of the changes which it undergoes, or that of which the elements of the manifold are states or modifications.[11] Consequently, there must be a permanent substance of a phenomenon, and the quantity of substances taken together must be constant.'

Now, if Kant's thought has been here represented fairly, it is open to the following comments. In the first place, even if his position be right in the main, Kant should not introduce the thought of the quantity of substance, and speak of the quantity as constant. For he thereby implies that in a plurality of substances—if such a plurality can in the end be admitted—there may be total extinction of, or partial loss in, some, if only there be a corresponding compensation in others; whereas such extinction and creation would be inconsistent with the nature of a substance.[12] Even Kant himself speaks of having established the impossibility of the origin and extinction of substance.[13]

In the second place, it is impossible to see how it can be legitimate for Kant to speak of a permanent substratum of change at all.[14] For phenomena or appearances neither are nor imply the substratum of which Kant is thinking. They might be held to imply ourselves as the identical substratum of which they are successive states, but this view would be irrelevant to, if not inconsistent with, Kant's doctrine. It is all very well to say that the substratum is to be found in matter, i. e. in bodies in space,[15] but the assertion is incompatible with the phenomenal character of the world; for the sensations or appearances produced in us by the thing in itself cannot be successive states of bodies in space. In the third place, in spite of Kant's protests against any proof which is 'dogmatical' or 'from conceptions', such a proof really forms the basis of his thought. For if the argument is to proceed not from the nature of change as such but from the possibility of perceiving change, it must not take into account any implications of the possibility of perceiving change which rest upon implications of the nature of change as such. Yet this is what the argument does. For the reason really given for the view that the apprehension of change involves the apprehension of the manifold as related to a permanent substratum is that a change, as such, implies a permanent substratum. It is only because change is held to imply a substratum that we are said to be able to apprehend a change only in relation to a substratum. Moreover, shortly afterwards, Kant, apparently without realizing what he is doing, actually uses what is, on the very face of it, the dogmatic method, and in accordance with it develops the implications of the perception of change. "Upon this permanence is based the justification of the conception of change. Coming into being and perishing are not changes of that which comes to be or perishes. Change is but a mode of existence, which follows on another mode of existence of the same object. Hence everything which changes endures and only its condition changes.... Change, therefore, can be perceived only in substances, and absolute coming to be or perishing, which does not concern merely a determination of the permanent, cannot be a possible perception."[16] Surely the fact that Kant is constrained in spite of himself to use the dogmatic method is some indication that it is the right method. It is in reality impossible to make any discoveries about change, or indeed about anything, except by consideration of the nature of the thing itself; no study of the conditions under which it can be apprehended can throw any light upon its nature.[17] Lastly, although the supposition is not so explicit as the corresponding supposition made in the case of the other analogies, Kant's argument really assumes, and assumes wrongly, the existence of a process by which, starting with the successive apprehension of elements of the manifold in isolation, we come to apprehend them as temporally related.

The deduction of the second and third analogies argues that the principles of causality and reciprocal action are involved respectively in the processes by which we become aware of successions and of coexistences in the world of nature. From this point of view it would seem that the first analogy is a presupposition of the others, and that the process which involves the first is presupposed by the process which involves the others. It would seem that it is only upon the conclusion of a process by which, beginning with the successive apprehension of elements of the manifold in isolation, we come to apprehend them as either successive or coexistent elements in the world of nature, that there can arise a process by which we come to decide whether the specific relation is that of succession or of coexistence. For if the latter process can take place independently of the former, i. e. if it can start from the successive apprehension of the manifold, the former process will be unnecessary, and in that case the vindication of the first analogy will be invalid. It is necessary, however, to distinguish between Kant's nominal and his actual procedure. Though he nominally regards the first analogy as the presupposition of the others,[18] he really does not. For he does not in fact treat the process which involves the validity of the first analogy as an antecedent condition of the processes which involve the validity of the others. On the contrary, the latter processes begin ab initio with the mere successive apprehension of the manifold, i. e. they begin at a stage where we are not aware of any relation in the physical world at all; and Kant, in his account of them, nowhere urges that they involve the first analogy.[19]

Moreover, just because Kant does not face the difficulties involved in the thought of a process which begins in this way until he comes to vindicate causality, it is only when we come to this vindication that we realize the real nature of his deduction of the analogies, and, in particular, of that of the first.

Kant, prompted no doubt by his desire to answer Hume, treats the principle of causality very fully. The length of the discussion, however, is due not so much to the complication of the argument as to Kant's desire to make his meaning unmistakable; his account consists mainly in a repetition of what is substantially the same argument no less than five times. Hence it will suffice to consider those passages which best express Kant's meaning. At the same time, the prominence of the principle of causality in Kant's theory, and in the history of philosophy generally, and also the way in which Kant's treatment of it reveals the true nature of his general position, makes it necessary to consider these passages in some detail.

Hume had denied that we are justified in asserting any causal connexion, i. e. any necessity of succession in the various events which we perceive, but even this denial presupposed that we do apprehend particular sequences in the world of nature, and therefore that we succeed in distinguishing between a sequence of events in nature and a mere sequence of perceptions, such as is also to be found when we apprehend a coexistence of bodies in space. Kant urges, in effect, that this denial renders it impossible to explain, as we should be able to do, the possibility of making the distinction in question, which even the denial itself presupposes that we make. Holding, with Hume, that in all cases of perception what we are directly aware of is a succession of perceptions, he contends that it is necessary to explain how in certain cases we succeed in passing from the knowledge of our successive perceptions to the knowledge of a succession in what we perceive. How is it that we know, when, as we say, we see a boat going down stream, that there is a succession in what we perceive, and not merely a succession in our perception of it, as is the case when, as we say, we see the parts of a house? Hume, according to Kant, cannot answer this question; he has only the right to say that in all cases we have a succession of perceptions; for in reality an answer to the question will show that the acquisition of this knowledge involves an appeal to the principle of causality. Since, then, we do in fact, as even Hume implicitly allowed, succeed in distinguishing between a succession in objects in nature and a succession in our apprehension of them, the law of causality must be true. "It is only under this presupposition (i. e. of causality) that even the experience of an event is possible."[20]

Kant begins[21] his proof as follows: "Our apprehension of the manifold of a phenomenon is always successive. The representations of the parts succeed one another. Whether they succeed one another in the object also is a second point for reflection which is not contained in the first."[22] But, before he can continue, the very nature of these opening sentences compels him to consider a general problem which they raise. The distinction referred to between a succession in our apprehensions or representations and a succession in the object implies an object distinct from the apprehensions or representations. What, then, can be meant by such an object? For prima facie, if we ignore the thing in itself as unknowable, there is no object; there are only representations. But, in that case, what can be meant by a succession in the object? Kant is therefore once more[23] forced to consider the question 'What is meant by object of representations?' although on this occasion with special reference to the meaning of a succession in the object; and the vindication of causality is bound up with the answer. The answer is stated thus:

"Now we may certainly give the name of object to everything, and even to every representation, so far as we are conscious thereof; but what this word may mean in the case of phenomena, not in so far as they (as representations) are objects, but in so far as they only indicate an object, is a question requiring deeper consideration. So far as they, as representations only, are at the same time objects of consciousness, they are not to be distinguished from apprehension, i. e. 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 infer from the succession of the representations of their manifold how this manifold is connected in the object. For after all 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 wholly outside the sphere of our knowledge. Now, although phenomena are not things in themselves, and are nevertheless the only thing which can be given to us as data for knowledge, it is my business to show what kind of connexion in time belongs to the manifold in phenomena themselves, while the representation of this manifold in apprehension is always successive. Thus, for example, the apprehension of the manifold in the phenomenon of a house which stands before me is successive. Now arises the question, whether the manifold of this house itself is in itself also successive, which of course no one will grant. But, so soon as I raise my conceptions of an object to the transcendental meaning thereof, the house is not a thing in itself, but only a phenomenon, i. e. a representation, the transcendental object of which is unknown. What, then, am I to understand by the question, 'How may the manifold be connected in the phenomenon itself (which is nevertheless nothing in itself)?' Here that which lies in the successive apprehension is regarded as representation, while the phenomenon which is given me, although 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, is to agree. It is soon seen that, since agreement of knowledge with the object is truth, we can ask here only for the formal conditions of empirical truth, and that the phenomenon, in opposition to the representations of apprehension, can only be represented as the object of the same, distinct therefrom, if it stands under a rule, which distinguishes it from every other apprehension, and which renders necessary a mode of conjunction of the manifold. That in the phenomenon which contains the condition of this necessary rule of apprehension is the object."[24]

This passage is only intelligible if we realize the impasse into which Kant has been led by his doctrine that objects, i. e. realities in the physical world, are only representations or ideas. As has already been pointed out,[25] an apprehension is essentially inseparable from a reality of which it is the apprehension. In other words, an apprehension is always the apprehension of a reality, and a reality apprehended, i. e. an object of apprehension, cannot be stated in terms of the apprehension of it. We never confuse an apprehension and its object; nor do we take the temporal relations which belong to the one for the temporal relations which belong to the other, for these relations involve different terms which are never confused, viz. apprehensions and the objects apprehended. Now Kant, by his doctrine of the unknowability of the thing in itself, has really deprived himself of an object of apprehension or, in his language, of an object of representations. For it is the thing in itself which is, properly speaking, the object of the representations of which he is thinking, i. e. representations of a reality in nature; and yet the thing in itself, being on his view inapprehensible, can never be for him an object in the proper sense, i. e. a reality apprehended. Hence he is only able to state the fact of knowledge in terms of mere apprehensions, or ideas, or representations—the particular name is a matter of indifference—and consequently his efforts to recover an object of apprehension are fruitless. As a matter of fact, these efforts only result in the assertion that the object of representations consists in the representations themselves related in a certain necessary way. But this view is open to two fatal objections. In the first place, a complex of representations is just not an object in the proper sense, i. e. a reality apprehended. It essentially falls on the subject side of the distinction between an apprehension and the reality apprehended. The complexity of a complex of representations in no way divests it of the character which it has as a complex of representations. In the second place, on this view the same terms have to enter at once into two incompatible relations. Representations have to be related successively as our representations or apprehensions—as in fact they are related—and, at the same time, successively or otherwise, as the case may be, as parts of the object apprehended, viz. a reality in nature. In other words, the same terms have to enter into both a subjective and an objective relation, i. e. both a relation concerning us, the knowing subjects, and a relation concerning the object which we know.[26] "A phenomenon in opposition to the representations of apprehension can only be represented as the object of the same, distinct therefrom, if it stands under a rule which distinguishes it from every other apprehension, and renders necessary a mode of conjunction of the manifold."[27] A representation, however, cannot be so related by a rule to another representation, for the rule meant relates to realities in nature, and, however much Kant may try to maintain the contrary, two representations, not being realities in nature, cannot be so related. Kant is in fact only driven to treat rules of nature as relating to representations, because there is nothing else to which he can regard them as relating. The result is that he is unable to justify the very distinction, the implications of which it is his aim to discover, and he is unable to do so for the very reason which would have rendered Hume unable to justify it. Like Hume, he is committed to a philosophical vocabulary which makes it meaningless to speak of relations of objects at all in distinction from relations of apprehensions. It has been said that for Kant the road to objectivity lay through necessity.[28] But whatever Kant may have thought, in point of fact there is no road to objectivity, and, in particular, no road through necessity. No necessity in the relation between two representations can render the relation objective, i. e. a relation between objects. No doubt the successive acts in which we come to apprehend the world are necessarily related; we certainly do not suppose their order to be fortuitous. Nevertheless, their relations are not in consequence a relation of realities apprehended.

Kant only renders his own view plausible by treating an apprehension or representation as if it consisted in a sensation or an appearance. A sensation or an appearance, so far from being the apprehension of anything, is in fact a reality which can be apprehended, of the kind called mental. Hence it can be treated as an object, i. e. something apprehended or presented, though not really as an object in nature. On the other hand, from the point of view of the thing in itself it can be treated as only an apprehension, even though it is an unsuccessful apprehension. Thus, for Kant, there is something which can with some plausibility be treated as an object as well as an apprehension, and therefore as capable of standing in both a subjective and an objective relation to other realities of the same kind.[29]

If we now turn to the passage under discussion, we find it easy to vindicate the justice of the criticism that Kant, inconsistently with the distinction which he desires to elucidate, treats the same thing as at once the representation of an object and the object represented. He is trying to give such an account of 'object of representations' as will explain what is meant by a succession in an object in nature, i. e. a phenomenon, in distinction from the succession in our apprehension of it. In order to state this distinction at all, he has to speak of what enters into the two successions as different. "It is my business to show what sort of connexion in time belongs to the manifold in phenomena themselves, while the representation of this manifold in apprehension is always successive."[30] Here an element of the manifold is distinguished from the representation of it. Yet Kant, though he thus distinguishes them, repeatedly identifies them; in other words, he identifies a representation with that of which it is a representation, viz. an element in or part of the object itself. "Our apprehension of the manifold of the phenomenon is always successive. The representations of the parts succeed one another. Whether they [i. e. the representations[31]] succeed one another in the object also, is a second point for reflection.... So far as they [i. e. phenomena], as representations only, are at the same time objects of consciousness, they are not to be distinguished from apprehension, i. e. 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 infer from the succession of the representations how this manifold is connected in the object.... The phenomenon, in opposition to the representations of apprehension, can only be represented as the object of the same, distinct therefrom, if it stands under a rule, which distinguishes it from every other representation and which renders necessary a mode of conjunction of the manifold."[32]

Since Kant in introducing his vindication of causality thus identifies elements in the object apprehended (i. e. the manifold of phenomena) with the apprehensions of them, we approach the vindication itself with the expectation that he will identify a causal rule, which consists in a necessity in the succession of objects, viz. of events in nature, with the necessity in the succession of our apprehensions of them. This expectation turns out justified. The following passage adequately expresses the vindication:

"Let us now proceed to our task. That something happens, i. e. that something or some state comes to be which before was not, cannot be empirically perceived, unless a phenomenon precedes, which does not contain in itself this state; for a reality which follows upon an empty time, and therefore a coming into existence preceded by no state of things, can just as little be apprehended as empty time itself. Every apprehension of an event is therefore a perception which follows upon another perception. But because this is the case with all synthesis of apprehension, as I have shown above[33] in the phenomenon of a house, the apprehension of an event is thereby not yet distinguished from other apprehensions. But I notice also, that if in a phenomenon which contains an event, I call the preceding state of my perception A, and the following state B, B can only follow A in apprehension, while the perception A cannot follow B but can only precede it. For example, I see a ship float down a stream. 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 apprehension is bound to this order. In the former example of a house, my perceptions in apprehension could begin at the roof and end at the foundation, or begin below and end above; in the same way they could apprehend the manifold of the empirical perception from left to right, or 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 to combine the manifold empirically. But this rule is always to be found in the perception of that which happens, and it makes the order of the successive perceptions (in the apprehension of this phenomenon) necessary."

"In the present case, therefore, I shall have to derive the subjective sequence of apprehension from the objective sequence of phenomena, for otherwise the former is wholly undetermined, and does not distinguish one phenomenon from another. The former alone proves nothing as to the connexion of the manifold in the object, for it is wholly arbitrary. The latter, therefore [i. e. the objective sequence of phenomena[34]], will consist in that order of the manifold of the phenomenon, according to which the apprehension of the one (that which happens) follows that of the other (that which precedes) according to a rule. In this way alone can I be justified in saying of the phenomenon itself, and not merely of my apprehension, that a sequence is to be found therein, which is the same as to say that I cannot arrange my apprehension otherwise than in just this sequence."

"In conformity with such a rule, therefore, there must exist in that which in general precedes an event the condition of a rule, according to which this event follows always and necessarily, but I cannot conversely go back from the event, and determine (by apprehension) that which precedes it. For no phenomenon goes back from the succeeding point of time to the preceding point, although it does certainly relate to some preceding point of time; on the other hand, the advance from a given time to the determinate succeeding time is necessary. Therefore, because there certainly is something which follows, I must relate it necessarily to something else in general, which precedes, and upon which it follows in conformity with a rule, that is necessarily, so that the event, as the conditioned, affords certain indication of some condition, while this condition determines the event."

"If we suppose that nothing precedes an event, upon which this event must follow in conformity with a rule, all sequence of perception would exist only in apprehension, i. e. would be merely subjective, but it would not thereby be objectively determined which of the perceptions must in fact be the preceding and which the succeeding one. We should in this manner have only a play of representations, which would not be related to any object, i. e. no phenomenon would be distinguished through our perception in respect of time relations from any other, because the succession in apprehension is always of the same kind, and so there is nothing in the phenomenon to determine the succession, so as to render a certain sequence objectively necessary. I could therefore not say that in the phenomenon two states follow each other, but only that one apprehension follows on another, a fact which is merely subjective and does not determine any object, and cannot therefore be considered as knowledge of an object (not even in the phenomenon)."

"If therefore we experience that something happens, we always thereby presuppose that something precedes, on which it follows according to a rule. For otherwise, I should not say of the object, that it follows, because the mere sequence in my apprehension, if it is not determined by a rule in relation to something preceding, does not justify the assumption of a sequence in the object. It is therefore always in reference to a rule, according to which phenomena are determined in their sequence (i. e. as they happen) by the preceding state, that I make my subjective synthesis (of apprehension) objective, and it is solely upon this presupposition that even the experience of something which happens is possible."[35]

The meaning of the first paragraph is plain. Kant is saying that when we reflect upon the process by which we come to apprehend the world of nature, we can lay down two propositions. The first is that the process is equally successive whether the object apprehended be a succession in nature or a coexistence of bodies in space, so that the knowledge that we have a succession of apprehensions would not by itself enable us to decide whether the object of the apprehensions is a sequence or not. The second proposition is that, nevertheless, there is this difference between the succession of our apprehensions where we apprehend a succession and where we apprehend a coexistence, that in the former case, and in that only, the succession of our apprehensions is irreversible or, in other words, is the expression of a rule of order which makes it a necessary succession. So far we find no mention of causality, i. e. of a necessity of succession in objects, but only a necessity of succession in our apprehension of them. So far, again, we find no contribution to the problem of explaining how we distinguish between successive perceptions which are the perceptions of an event and those which are not. For it is reasonable to object that it is only possible to say that the order of our perceptions is irreversible, if and because we already know that what we have been perceiving is an event, and that therefore any attempt to argue from the irreversibility of our perceptions to the existence of a sequence in the object must involve a [Greek: hysteron proteron]. And it is clear that, if irreversibility in our perceptions were the only irreversibility to which appeal could be made, even Kant would not have supposed that the apprehension of a succession was reached through belief in an irreversibility.

The next paragraph, of which the interpretation is difficult, appears to introduce a causal rule, i. e. an irreversibility in objects, by identifying it with the irreversibility in our perceptions of which Kant has been speaking. The first step to this identification is taken by the assertion: "In the present case, therefore, I shall have to derive the subjective sequence of perceptions from the objective sequence of phenomena.... The latter will consist in the order of the manifold of the phenomenon, according to which the apprehension of the one (that which happens) follows that of the other (that which precedes) according to a rule."[36] Here Kant definitely implies that an objective sequence, i. e. an order or sequence of the manifold of a phenomenon, consists in a sequence of perceptions or apprehensions of which the order is necessary or according to a rule; in other words, that a succession of perceptions in the special case where the succession is necessary is a succession of events perceived.[37] This implication enables us to understand the meaning of the assertion that 'we must therefore derive the subjective sequence of perceptions from the objective sequence of phenomena', and to see its connexion with the preceding paragraph. It means, 'in view of the fact that in all apprehensions of a succession, and in them alone, the sequence of perceptions is irreversible, we are justified in saying that a given sequence of perceptions is the apprehension of a succession, if we know that the sequence is irreversible; in that case we must be apprehending a real succession, for an irreversible sequence of perceptions is a sequence of events perceived.' Having thus implied that irreversibility of perceptions constitutes them events perceived, he is naturally enough able to go on to speak of the irreversibility of perceptions as if it were the same thing as an irreversibility of events perceived, and thus to bring in a causal rule. "In this way alone [i. e. only by deriving the subjective from the objective sequence] can I be justified in saying of the phenomenon itself, and not merely of my apprehension, that a sequence is to be found therein, which is the same as to say that I cannot arrange my apprehension otherwise than in just this sequence. In conformity with such a rule, therefore, there must exist in that which in general precedes an event the condition of a rule, according to which this event follows always and necessarily."[38] Here the use of the word 'arrange'[39] and the statement about the rule in the next sentence imply that Kant has now come to think of the rule of succession as a causal rule relating to the objective succession. Moreover, if any doubt remains as to whether Kant really confuses the two irreversibilities or necessities of succession, it is removed by the last paragraph of the passage quoted. "If therefore we experience that something happens, we always thereby presuppose that something precedes on which it follows according to a rule. For otherwise I should not say of the object that it follows; because the mere succession of my apprehension, if it is not determined by a rule in relation to something preceding, does not justify the assumption of a succession in the object. It is therefore always in reference to a rule, according to which phenomena are determined in their sequence (i. e. as they happen) by the preceding state, that I make my subjective sequence (of apprehension) objective."[40] The fact is simply that Kant must identify the two irreversibilities, because, as has been pointed out, he has only one set of terms to be related as irreversible, viz. the elements of the manifold, which have to be, from one point of view, elements of an object and, from another, representations or apprehensions of it.

As soon, therefore, as the real nature of Kant's vindication of causality has been laid bare, it is difficult to describe it as an argument at all. He is anxious to show that in apprehending A B as a real or objective succession we presuppose that they are elements in a causal order of succession. Yet in support of his contention he points only to the quite different fact that where we apprehend a succession A B, we think of the perception of A and the perception of B as elements in a necessary but subjective succession.

Before we attempt to consider the facts with which Kant is dealing, we must refer to a feature in Kant's account to which no allusion has been made. We should on the whole expect from the passage quoted that, in the case where we regard two perceptions A B as necessarily successive and therefore as constituting an objective succession, the necessity of succession consists in the fact that A is the cause of B. This, however, is apparently not Kant's view; on the contrary, he seems to hold that, in thinking of A B as an objective succession, we presuppose not that A causes B, but only that the state of affairs which precedes B, and which therefore includes A, contains a cause of B, the coexistence or identity of this cause with A rendering the particular succession A B necessary. "Thus [if I perceive that something happens] it arises that there comes to be an order among our representations in which the present (so far as it has taken place) points to some preceding state as a correlate, though a still undetermined correlate,[41] of this event which is given, and this correlate relates to the event by determining the event as its consequence, and connects the event with itself necessarily in the series of time."[42]

The fact is that Kant is in a difficulty which he feels obscurely himself. He seems driven to this view for two reasons. If he were to maintain that A was necessarily the cause of B, he would be maintaining that all observed sequences are causal, i. e. that in them the antecedent and consequent are always cause and effect, which is palpably contrary to fact. Again, his aim is to show that we become aware of a succession by presupposing the law of causality. This law, however, is quite general, and only asserts that something must precede an event upon which it follows always and necessarily. Hence by itself it palpably gives no means of determining whether this something is A rather than anything else.[43] Therefore if he were to maintain that the antecedent member of an apprehended objective succession must be thought of as its cause, the analogy would obviously provide no means of determining the antecedent member, and therefore the succession itself, for the succession must be the sequence of B upon some definite antecedent. On the other hand, the view that the cause of B need not be A only incurs the same difficulty in a rather less obvious form. For, even on this view, the argument implies that in order to apprehend two individual perceptions A B as an objective succession, we must know that A must precede B, and the presupposition that B implies a cause in the state of affairs preceding B in no way enables us to say either that A coexists with the cause, or that it is identical with it, and therefore that it must precede B.

Nevertheless, it cannot be regarded as certain that Kant did not think of A, the apprehended antecedent of B, as necessarily the cause of B, for his language is both ambiguous and inconsistent. When he considers the apprehension of a succession from the side of the successive perceptions, he at least tends to think of A B as cause and effect;[44] and it may well be that in discussing the problem from the side of the law of causality, he means the cause of B to be A, although the generality of the law compels him to refer to it as something upon which B follows according to a rule.

Further, it should be noticed that to allow as Kant, in effect, does elsewhere[45], that experience is needed to determine the cause of B is really to concede that the apprehension of objective successions is prior to, and presupposed by, any process which appeals to the principle of causality; for if the principle of causality does not by itself enable us to determine the cause of B, it cannot do more than enable us to pick out the cause of B among events known to precede B independently of the principle. Hence, from this point of view, there can be no process such as Kant is trying to describe, and therefore its precise nature is a matter of indifference.

We may now turn to the facts. There is, it seems, no such thing as a process by which, beginning with the knowledge of successive apprehensions or representations, of the object of which we are unaware, we come to be aware of their object. Still less is there a process—and it is really this which Kant is trying to describe—by which, so beginning, we come to apprehend these successive representations as objects, i. e. as parts of the physical world, through the thought of them as necessarily related. We may take Kant's instance of our apprehension of a boat going down stream. We do not first apprehend two perceptions of which the object is undetermined and then decide that their object is a succession rather than a coexistence. Still less do we first apprehend two perceptions or representations and then decide that they are related as successive events in the physical world. From the beginning we apprehend a real sequence, viz. the fact that the boat having left one place is arriving at another; there is no process to this apprehension. In other words, from the beginning we are aware of real elements, viz. of events in nature, and we are aware of them as really related, viz. as successive in nature. This must be so. For if we begin with the awareness of two mere perceptions, we could never thence reach the knowledge that their object was a succession, or even the knowledge that they had an object; nor, so beginning, could we become aware of the perceptions themselves as successive events in the physical world. For suppose, per impossibile, the existence of a process by which we come to be aware of two elements A and B as standing in a relation of sequence in the physical world. In the first place, A and B, with the awareness of which we begin, must be, and be known to be, real or objective, and not perceptions or apprehensions; otherwise we could never come to apprehend them as related in the physical world. In the second place, A and B must be, and be known to be, real with the reality of a physical event, otherwise we could never come to apprehend them as related by way of succession in the physical world. If A and B were bodies, as they are when we apprehend the parts of a house, they could never be apprehended as successive. In other words, the process by which, on Kant's view, A and B become, and become known to be, events presupposes that they already are, and are known to be, events. Again, even if it be granted that A and B are real events, it is clear that there can be no process by which we come to apprehend them as successive. For if we apprehended events A and B separately, we could never thence advance to the apprehension of their relation, or, in other words, we could never discover which came first. Kant himself saw clearly that the perception of A followed by the perception of B does not by itself yield the perception that B follows A. In fact it was this insight which formed the starting-point of his discussion.[46] Unfortunately, instead of concluding that the apprehension of a succession is ultimate and underivable from a more primitive apprehension, he tried to formulate the nature of the process by which, starting from such a succession of perceptions, we reach the apprehension of a succession. The truth is simply that there is and can be no process to the apprehension of a succession; in other words, that we do and must apprehend a real succession immediately or not at all. The same considerations can of course be supplied mutatis mutandis to the apprehension of the coexistence of bodies in space, e. g. of the parts of a house.

It may be objected that this denial of the existence of the process which Kant is trying to describe must at least be an overstatement. For the assertion that the apprehension of a succession or of a coexistence is immediate may seem to imply that the apprehension of the course of a boat or of the shape of a house involves no process at all; yet either apprehension clearly takes time and so must involve a process. But though a process is obviously involved, it is not a process from the apprehension of what is not a succession to the apprehension of a succession, but a process from the apprehension of one succession to that of another. It is the process by which we pass from the apprehension of one part of a succession which may have, and which it is known may have, other parts to the apprehension of what is, and what is known to be, another part of the same succession. Moreover, the assertion that the apprehension of a succession must be immediate does not imply that it may not be reached by a process. It is not inconsistent with the obvious fact that to apprehend that the boat is now turning a corner is really to apprehend that what before was going straight is now changing its course, and therefore presupposes a previous apprehension of the boat's course as straight. It only implies that the apprehension of a succession, if reached by a process at all, is not reached by a process of which the starting-point is not itself the apprehension of a succession.

Nevertheless, a plausible defence of Kant's treatment of causality can be found, which may be formulated thus: 'Time, just as much as space, is a sphere within which we have to distinguish between appearance and reality. For instance, when moving in a lift, we see, as we say, the walls moving, while the lift remains stationary. When sitting in a train which is beginning to move out of a station, we see, as we say, another train beginning to move, although it is in fact standing still. When looking at distant trees from a fast train, we see, as we say, the buildings in the intermediate space moving backwards. In these cases the events seen are not real, and we only succeed in determining what is really happening, by a process which presupposes the law of causality. Thus, in the last case we only believe that the intermediate buildings do not move, by realizing that, given the uniformity of nature, belief in their motion is incompatible with what we believe on the strength of experience of these buildings on other occasions and of the rest of the world. These cases prove the existence of a process which enables us, and is required to enable us, to decide whether a given change is objective or subjective, i. e. whether it lies in the reality apprehended or in our apprehension of it; and this process involves an appeal to causality. Kant's mistake lay in his choice of illustrations. His illustrations implied that the process which involves causality is one by which we distinguish a succession in the object apprehended from another relation in the object, viz. a coexistence of bodies. But he ought to have taken illustrations which implied that the process is one by which we distinguish a succession in the object from a succession in our perception of it. In other words, the illustrations should, like those just given, have illustrated the process by which we distinguish an objective from a subjective change, and not a process by which we distinguish an objective change from something else also objective. Consequently, Kant's conclusion and his general method of treatment are right, even if, misled by his instances, he supports his position by arguments which are wrong.'

This defence is, however, open to the following reply: 'At first sight the cases taken undoubtedly seem to illustrate a process in which we seek to discover whether a certain change belongs to objects or only to our apprehension of them, and in which we appeal to causality in arriving at a decision. But this is only because we ignore the relativity of motion. To take the third case: our first statement of the facts is that we saw the intermediate buildings moving, but that subsequent reflection on the results of other experience forced us to conclude that the change perceived was after all only in our apprehension and not in the things apprehended. The statement, however, that we saw the buildings moving really assumes that we, the observers, were stationary; and it states too much. What we really perceived was a relative changing of position between us, the near buildings, and the distant trees. This is a fact, and the apprehension of it, therefore, does not afterwards prove mistaken. It is equally compatible with motion on the part of the trees, or of the buildings, or of the observers, or of a combination of them; and that for which an appeal to causality is needed is the problem of deciding which of these alternatives is correct. Moreover, the perceived relative change of position is objective; it concerns the things apprehended. Hence, in this case too, it can be said that we perceive an objective succession from the beginning, and that the appeal to causality is only needed to determine something further about it. It is useless to urge that to be aware of an event is to be aware of it in all its definiteness, and that this awareness admittedly involves an appeal to causality; for it is easy to see that unless our awareness of the relative motion formed the starting-point of any subsequent process in which we appealed to the law of causality, we could never use the law to determine which body really moved.'

Two remarks may be made in conclusion. In the first place, the basis of Kant's account, viz. the view that in our apprehension of the world we advance from the apprehension of a succession of perceptions to the apprehension of objects perceived, involves a [Greek: hysteron proteron]. As Kant himself in effect urges in the Refutation of Idealism,[47] self-consciousness, in the sense of the consciousness of the successive process in which we apprehend the world, is plainly only attained by reflecting upon our apprehension of the world. We first apprehend the world and only by subsequent reflection become aware of our activity in apprehending it. Even if consciousness of the world must lead to, and so is in a sense inseparable from, self-consciousness, it is none the less its presupposition.

In the second place, it seems that the true vindication of causality, like that of the first analogy, lies in the dogmatic method which Kant rejects. It consists in insight into the fact that it is of the very nature of a physical event to be an element in a process of change undergone by a system of substances in space, this process being through and through necessary in the sense that any event (i. e. the attainment of any state by a substance) is the outcome of certain preceding events (i. e. the previous attainment of certain states by it and other substances), and is similarly the condition of certain subsequent events.[48] To attain this insight, we have only to reflect upon what we really mean by a 'physical event'. The vindication can also be expressed in the form that the very thought of a physical event presupposes the thought of it as an element in a necessary process of change—provided, however, that no distinction is implied between the nature of a thing and what we think its nature to be. But to vindicate causality in this way is to pursue the dogmatic method; it is to argue from the nature, or, to use Kant's phrase, from the conception, of a physical event. On the other hand, it seems that the method of arguing transcendentally, or from the possibility of perceiving events, must be doomed to failure in principle. For if, as has been argued to be the case,[49] apprehension is essentially the apprehension of a reality as it exists independently of the apprehension of it, only those characteristics can be attributed to it, as characteristics which it must have if it is to be apprehended, which belong to it in its own nature or in virtue of its being what it is. It can only be because we think that a thing has some characteristic in virtue of its own nature, and so think 'dogmatically', that we can think that in apprehending it we must apprehend it as having that characteristic.[50]

There remains to be considered Kant's proof of the third analogy, i. e. the principle that all substances, so far as they can be perceived in space as coexistent, are in thorough-going interaction. The account is extremely confused, and it is difficult to extract from it a consistent view. We shall consider here the version added in the second edition, as being the fuller and the less unintelligible.

"Things are coexistent, when in empirical intuition[51] the perception[52] of the one can follow upon the perception of the other, and vice versa (which cannot occur in the temporal succession of phenomena, as we have shown in the second principle). Thus I can direct my perception first to the moon and afterwards to the earth, or conversely, first to the earth and then to the moon, and because the perceptions of these objects can reciprocally follow each other, I say that they coexist. Now coexistence is the existence of the manifold in the same time. But we cannot perceive time itself, so as to conclude from the fact that things are placed in the same time that the perceptions of them can follow each other reciprocally. The synthesis of the imagination in apprehension, therefore, would only give us each of these perceptions as existing in the subject when the other is absent and vice versa; but it would not give us that the objects are coexistent, i. e. that, if the one exists, the other also exists in the same time, and that this is necessary in order that the perceptions can follow each other reciprocally. Hence there is needed a conception-of-the-understanding[53] of the reciprocal sequence of the determinations of these things coexisting externally to one another, in order to say that the reciprocal succession of perceptions is grounded in the object, and thereby 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 if, reciprocally, the former contains the ground of the determinations in the latter, it is the relation of community or interaction. Consequently, the coexistence of substances in space cannot be known in experience otherwise than under the presupposition of their interaction; this is therefore also the condition of the possibility of things themselves as objects of experience."[54]

The proof begins, as we should expect, in a way parallel to that of causality. Just as Kant had apparently argued that we learn that a succession of perceptions is the perception of a sequence when we find the order of the perceptions to be irreversible, so he now definitely asserts that we learn that certain perceptions are the perceptions of a coexistence of bodies in space when we find that the order of the perceptions is reversible, or, to use Kant's language, that there can be a reciprocal sequence of the perceptions. This beginning, if read by itself, seems as though it should also be the end. There seems nothing more which need be said. Just as we should have expected Kant to have completed his account of the apprehension of a succession when he pointed out that it is distinguished by the irreversibility of the perceptions, so here we should expect him to have said enough when he points out that the earth and the moon are said to be coexistent because our perceptions of them can follow one another reciprocally.

The analogy, however, has in some way to be brought in, and to this the rest of the proof is devoted. In order to consider how this is done, we must first consider the nature of the analogy itself. Kant speaks of 'a conception-of-the-understanding of the reciprocal sequence of the determinations of things which coexist externally to one another'; and he says that 'that relation of substances in which the one contains determinations, the ground of which is contained in the other substance, is the relation of influence'. His meaning can be illustrated thus. Suppose two bodies, A, a lump of ice, and B, a fire, close together, yet at such a distance that they can be observed in succession. Suppose that A passes through changes of temperature a₁ a₂ a₃ ... in certain times, the changes ending in states a₁ a₂ a₃ ..., and that B passes through changes of temperature b₁ b₂ b₃ ... in the same times, the changes ending in states _{1 2 3}. Suppose also, as we must, that A and B interact, i. e. that A in passing through its changes conditions the changes through which B passes, and therefore also the states in which B ends, and vice versa, so that a₂ and a₂ will be the outcome not of a₁ and a₁ alone, but of a₁ and a₁, and b₁ and ₁ jointly. Then we can say (1) that A and B are in the relation of influence, and also of interaction or reciprocal influence, in the sense that they mutually (not alternately) determine one another's states. Again, if we first perceive A in the state a_1 by a perception A₁, then B in the state ₂ by a perception B₂, then A in the state a₃ by a perception A₃ and so on, we can speak (2) of a reciprocal sequence of perceptions, in the sense of a sequence of perceptions in which alternately a perception of B follows a perception of A and a perception of A follows a perception of B; for first a perception of B, viz. B₂, follows a perception of A, viz. A₁, and then a perception of A, viz. A₃, follows a perception of B, viz. B₂. We can also speak (3) of a reciprocal sequence of the determinations of two things in the sense of a necessary succession of states which alternately are states of A and of B; for a₁, which is perceived first, can be said to contribute to determine ₂, which is perceived next, and ₂ can be said to contribute to determine a₃, which is perceived next, and so on; and this reciprocal sequence can be said to be involved in the very nature of interaction. Further, it can be said (4) that if we perceive A and B alternately, and so only in the states a₁ a₃ ... _{2 4} ... respectively, we can only fill in the blanks, i. e. discover the states a₂ a₄ ... _{1 3} ... coexistent with _{2 4} ... and a₁ a₃ ... respectively, if we presuppose the thought of interaction. For it is only possible to use the observed states as a clue to the unobserved states, if we presuppose that the observed states are members of a necessary succession of which the unobserved states are also members and therefore have partially determined and been determined by the observed states. Hence it may be said that the determination of the unobserved states coexistent with the observed states presupposes the thought of interaction.

How then does Kant advance from the assertion that the apprehension of a coexistence requires the knowledge that our perceptions can be reciprocally sequent to the assertion that it presupposes the thought that the determinations of phenomena are reciprocally sequent? The passage in which the transition is effected is obscure and confused, but it is capable of interpretation as soon as we see that it is intended to run parallel to the proof of the second analogy which is added in the second edition.[55] Kant apparently puts to himself the question, 'How are we to know when we have a reciprocal sequence of perceptions from which we can infer a coexistence in what we perceived?' and apparently answers it thus: 'Since we cannot perceive time, and therefore cannot perceive objects as dated in time with respect to one another, we cannot begin with the apprehension of the coexistence of two objects, and thence infer the possibility of reciprocal sequence in our perceptions. This being so, the synthesis of imagination in apprehension can indeed combine these perceptions [these now being really considered as determinations or states of an object perceived] in a reciprocal sequence, but there is so far no guarantee that the sequence produced by the synthesis is not an arbitrary product of the imagination, and therefore we cannot think of it as a reciprocal sequence in objects. In order to think of such a reciprocal sequence as not arbitrary but as constituting a real sequence in objects [ = 'as grounded in the object'], we must think of the states reciprocally sequent [as necessarily related and therefore] as successive states of two coexisting substances which interact or mutually determine one another's successive states. Only then shall we be able to think of the coexistence of objects involved in the reciprocal sequence as an objective fact, and not merely as an arbitrary product of the imagination.' But, if this fairly expresses Kant's meaning, his argument is clearly vitiated by two confusions. In the first place, it confuses a subjective sequence of perceptions which are alternately perceptions of A and of B, two bodies in space, with an objective sequence of perceived states of bodies, a_{1 2} a_{3 4}, which are alternately states of two bodies A and B, the same thing being regarded at once as a perception and as a state of a physical object. In the second place, mainly in consequence of the first confusion, it confuses the necessity that the perceptions of A and of B can follow one another alternately with the necessity of succession in the alternately perceived states of A and B as interacting. Moreover, there is really a change in the cases under consideration. The case with which he begins, i. e. when he is considering merely the reciprocal sequence of perceptions, is the successive perceptions of two bodies in space alternately, e. g. of the moon and the earth, the nature of their states at the time of perception not being in question. But the case with which he ends is the successive perception of the states of two bodies alternately, e. g. of the states of the fire and of the lump of ice. Moreover, it is only in the latter case that the objective relation apprehended is that of coexistence in the proper sense, and in the sense which Kant intends throughout, viz. that of being contemporaneous in distinction from being successive. For when we say that two bodies, e. g. the moon and the earth, coexist, we should only mean that both exist, and not, as Kant means, that they are contemporaneous. For to a substance, being as it is the substratum of changes, we can ascribe no temporal predicates. That which changes cannot be said either to begin, or to end, or to exist at a certain moment of time, or, therefore, to exist contemporaneously with, or after, or before anything else; it cannot even be said to persist through a portion of time or, to use the phrase of the first analogy, to be permanent. It will be objected that, though the cases are different, yet the transition from the one to the other is justified, for it is precisely Kant's point that the existence together of two substances in space can only be discovered by consideration of their successive states under the presupposition that they mutually determine one another's states. "Besides the mere fact of existence there must be something by which A determines the place in time for B, and conversely B the place for A, because only under this condition can these substances be empirically represented as coexistent."[56] The objection, however, should be met by two considerations, each of which is of some intrinsic importance. In the first place, the apprehension of a body in space in itself involves the apprehension that it exists together with all other bodies in space, for the apprehension of something as spatial involves the apprehension of it as spatially related to, and therefore as existing together with, everything else which is spatial. No process, therefore, such as Kant describes is required in order that we may learn that it exists along with some other body. In the second place, that for which the principle of interaction is really required is not, as Kant supposes, the determination of the coexistence of an unperceived body with a perceived body, but the determination of that unperceived state of a body already known to exist which is coexistent with a perceived state of a perceived body. As has been pointed out, if we perceive A and B alternately in the states a_{1 2} a_{3 4} ... we need the thought of interaction to determine the nature of ₁ a_{2 3} a₄ ... Thus it appears that Kant in his vindication of the third analogy omits altogether to notice the one process which really presupposes it.