Part 2 / Book 2 — CHAPTER II SYSTEM OF ALL PRINCIPLES OF PURE UNDERSTANDING

The introductory remarks to this important chapter are again dictated by Kant’s architectonic, and set its actual contents in an extremely false light. Kant would seem to imply that as the Analytic of Concepts has determined all the various conceptual elements constitutive of experience, and has proved that they serve as predicates of possible judgments, it now remains to show in an Analytic of Principles what a priori synthetic judgments, or in other words what principles, can actually be based upon them. Though this is a quite misleading account of the relation holding between the two books of the Analytic, it has been accepted by many commentators.[1128] For several reasons it must be rejected. The pure forms of understanding are not predicates for possible judgments. They underlie judgment as a whole, expressing the relation through which its total contents are organised. Thus in the proposition “cinnabar is heavy” the category of substance and attribute is not in any sense the predicate; it articulates the entire judgment, interpreting the experienced contents in terms of the dual relation of substance and attribute. Judgment, its nature and conditions, is the real problem of the misnamed Analytic of Concepts. As already indicated,[1129] the two main divisions of the Analytic deal with one and the same problem. But while doing so, they differ in two respects. In the first place, as above noted, the Analytic of Concepts supplies no proof of the validity of particular categories, but only a quite general demonstration that forms of unity, such as are involved in all judgment, are demanded for the possibility of apperception. The proofs of the indispensableness of specific categories are first given in the Analytic of Principles. Secondly, in the Analytic of Concepts the temporal aspect of experience falls somewhat into the background, whereas in the Analytic of Principles it is emphasised.

From these two fundamental points of difference there arises a third distinguishing feature. When the categories, or rather schemata, are explicitly defined, and receive individual proof, they are found to be just those principles that are demanded for the possibility of the positive sciences. This is, from Kant’s point of view, no mere coincidence. Scientific knowledge is possible only in so far as experience is grounded on a priori conditions; and the conditions of sense-experience are also the conditions of its conceptual interpretation. But while the Analytic of Concepts deals almost exclusively with ordinary experience, in the Analytic of Principles the physical sciences receive their due share of consideration.

First and Second Sections. The Highest Principles of Analytic and Synthetic Judgments.—These two sections contain nothing not already developed earlier in the Critique. Though the principle of non-contradiction is a merely negative test of truth, it can serve as a universal and completely adequate criterion in the case of all judgments that are analytic of given concepts. The principle of synthetic judgments, on the other hand, is the principle whereby we are enabled to advance beyond a given concept so as to attach a predicate which does not stand to it in the relation either of identity or of contradiction. This principle is the principle of the possibility of experience. Though a priori synthetic judgments cannot be logically demonstrated as following from higher and more universal propositions,[1130] they are capable of a transcendental proof, that is, as being conditions of sense-experience.

“The possibility of experience is what gives objective reality to all our a priori knowledge.”[1131] “Although we know a priori in synthetic judgments a great deal regarding space in general and the figures which productive imagination describes in it, and can obtain such judgments without actually requiring any experience; yet even this knowledge would be nothing but a playing with a mere figment of the brain, were it not that space has to be regarded as a condition of the appearances which constitute the material for outer experience....”[1132]

In the first part of the last sentence, as in the page which precedes it, Kant would seem to be inculcating his doctrine of a pure a priori manifold, but the latter part of the statement would not be affected by the admission that space is not an independent intuition but only the form of outer sense.

Third Section. Systematic Representation of all the Synthetic Principles of Understanding.—Kant is not concerned in this section with the fundamental propositions of mathematical science, since, on his view, they rest upon the evidence of intuition. He claims, however, that their objective validity depends upon two principles, which, though not themselves mathematical in the strict sense, may conveniently be so described from the transcendental standpoint—the principle of the “axioms of intuition,” and the principle of the “anticipations of experience.” The physicist, who takes the legitimacy of applied mathematics for granted, has no occasion to formulate these principles. That he none the less presupposes them is shown, however, by his unquestioning assumption that nature conforms to the strict requirements of pure mathematics. And since the principles involve pure concepts, the one embodying the schema of number, and the other the schema of quality, they fall outside the scope of the Transcendental Aesthetic, and call for a deduction similar to that of the other categories.

As already indicated, Kant’s procedure is extremely arbitrary, and is due to the perverting influence of his architectonic. Proof of the validity of applied mathematics has already been given in the Aesthetic[1133] of the first edition—a proof which is further developed in the Prolegomena,[1134] and recast in the second edition so as to constitute a separate “transcendental exposition.”[1135] As Kant teaches in these passages, the objective validity of applied mathematics rests upon proof that space and time are the a priori forms of outer and inner sense. The new deductions of the schemata of number and quality, which he now proceeds to formulate, are quite unnecessary, and also are by no means conclusive in the manner of their proof. This, however, is more than compensated by the extremely valuable proofs of the schematised categories of relation which he gives in the section on the Analogies of Experience. The section on the Postulates of Empirical Experience, which deals with the principles of modality, also contains matter of very real importance.

The principles with which this chapter has to deal can thus be arranged according to the fourfold division of the table of categories: (1) Axioms of Intuition, (2) Anticipations of Perception, (3) Analogies of Experience, (4) Postulates of Empirical Thought. And following the distinction already drawn in the Analytic of Concepts,[1136] Kant distinguishes between the Axioms and Anticipations on the one hand, and the Analogies and Postulates on the other. The former determine the conditions of intuition in space and time, and may therefore be called mathematical and constitutive. They express what is necessarily involved in every intuition as such. The latter are dynamical. They are principles according to which we must think the existence of an object as determined in its relation to others. While, therefore, the first set of principles can be intuitively verified, the second set have only an indirect relation to the objects experienced. Whereas a relation of causality can never be intuited as holding between two events, but only thought into them, spatial and temporal relations are direct objects of the mind. Similarly, the relation of substance and attribute cannot be intuited; it can only be thought into what is intuited. The mathematical principles thus acquire an immediate (though, be it remembered, merely de facto) evidence; the a priori certainty, equally complete, of the dynamical principles can be verified only through the circuitous channel of transcendental proof.

The composite constitution of these sections finds striking illustration in the duplicated account of this distinction which precedes and follows the table of principles. The two accounts can hardly have been written in immediate succession to one another. The earlier in location[1137] is probably the later in date. It would seem to rest upon some such uncritical distinction as that drawn in the Prolegomena between judgments of perception and judgments of experience.[1138] The second and briefer account[1139] is not open to this objection.

In A 178-80 = B 220-3 Kant develops a further point of difference between the mathematical and the dynamical principles, or rather explains what he means by his all too brief and consequently ambiguous reference in the first of the above accounts to “existence” (Dasein). The mathematical principles are constitutive; the dynamical are regulative. That is to say, the mathematical principles lay down the conditions for the generation or construction of appearances. The dynamical only specify rules whereby we can define the relation in which existences contingently given are connected. As existence can never be constructed a priori, we are limited to the determination of the interrelations between existences all of which must be given. Thus the principle of causality enables us to predict a priori that for every event there must exist some antecedent cause; but only through empirical investigation can we determine which of the particular given antecedents may be so described. That is to say, the principle defines conditions to which experience must conform, but does not enable us to construct it in advance. This distinction is inspired by the contrast between mathematical and physical science, and is valuable as defining the empirically regulative function of the a priori dynamical principles; but its somewhat forced character[1140] becomes apparent when we bear in mind Kant’s previous distinction between the principles of pure mathematical science and the transcendental principles which justify their application to experience. Those latter principles concern existence as apprehended through schematised categories, and are consequently, as regards certainty and method of proof, in exactly the same position as the dynamical principles. This is sufficiently evident from his own illustration of sunlight.[1141] There is as little possibility of “constructing” its intensity as of determining a priori the cause of an effect.

I. THE AXIOMS OF INTUITION

All appearances are in their intuition extensive magnitudes. Or as in the second edition: All intuitions are extensive magnitudes.

‘Extensive’ is here used in a very wide sense to include temporal as well as spatial magnitude. Kant bases this principle upon the schema of number, and the proof which he propounds in its support is therefore designed to show that apprehension of an object of perception, whether spatial or temporal, is only possible in so far as we bring that schema into play. But though this is the professed purpose of the argument, number is itself never even mentioned; and the reason for the omission is doubtless Kant’s consciousness of the obvious objections to any such position. That aspect of the argument is therefore, no doubt without explicit intention, kept in the background. But even as thus given, the argument must have left Kant with some feeling of dissatisfaction. Loyalty to his architectonic scheme prevents such doubt and disquietude from finding further expression.

The argument, in its first-edition statement, starts from the formulation of a view of space and time directly opposed to that of the Aesthetic:[1142]

“I entitle a magnitude extensive when the representation of the parts makes possible, and therefore necessarily precedes, the representation of the whole. I cannot represent to myself a line, however small, without drawing it in thought, i.e. generating from a point all its parts one after another, and thus for the first time recording this intuition.”

Similarly with even the smallest time. And as all appearances are intuited in space or time, every appearance, so far as intuited, is an extensive magnitude, that is to say, can be apprehended only through successive generation of its parts. All appearances are “aggregates, i.e. manifolds of antecedently given parts.”

This definition of extensive magnitude involves an assumption which Kant also employs elsewhere in the Critique,[1143] but which he nowhere attempts to establish by argument; namely, that it is impossible to apprehend a manifold save in succession. This assumption is, of course, entirely false (at least as applied to our empirical consciousness), as has since been amply demonstrated by experimental investigation. Kant adopted it in the earlier subjectivist stage of his teaching, before he had come to recognise that consciousness of space is involved in consciousness of time. But even after he had done so, the earlier view still tended to gain the upper hand whenever the doctrines of inner sense and of productive imagination were under consideration. For in regard to the transcendental activities of productive imagination, which are essentially synthetic, Kant continued to treat time as more fundamental than space. But, as already noted,[1144] a directly opposite view of the interrelations of space and time is expounded in passages added in the second edition.

The two central paragraphs are very externally connected with the main argument, and are probably later interpolations.[1145] In the first of these two paragraphs Kant ascribes the synthetic activity involved in the “generation of figures” to the productive imagination, and maintains that geometry is rendered possible by this faculty. In the other paragraph Kant deals with arithmetic, but makes no reference to the productive imagination. Its argument is limited to the contention that propositions expressive of numerical relation, though synthetic, are not universal. They are not axioms, but numerical formulae. This distinction has no very obvious bearing on the present argument, and serves only to indicate Kant’s recognition that no rigid parallelism can be established between geometry and arithmetic. There are, it would seem, no arithmetical axioms corresponding to the axioms of Euclid.[1146]

The concluding paragraph is a restatement of the argument of the Aesthetic and of § 13, Note i. of the Prolegomena. Appearances are not things in themselves. They are conditioned by the pure intuitional forms, and are therefore subject to pure mathematics “in all its precision.” Were we compelled to regard the objects of the senses as things in themselves, an applied science of geometry (again taken, in Kant’s habitual manner, as typically representing the mathematical disciplines) would not be possible. The only new element in the argument is the reference to synthesis as presupposed in all apprehension.

The additional proof with which in the second edition Kant prefaces the entire argument calls for no special comment. It may, however, be noted that though in the argument of the first edition the need of synthesis in all apprehension is clearly taught, the term synthesis is not itself employed except in the central and final paragraphs. In the proof given in the second edition both the term and what it stands for are allowed due prominence.

2. THE ANTICIPATIONS OF PERCEPTION

In all appearances sensation and the real which corresponds to it in the object (realitas phaenomenon) has an intensive magnitude or degree. Or as in the second edition: In all appearances the real, which is an object of sensation, has intensive magnitude or degree.

We may first analyse the total section. The first paragraph[1147] explains the term anticipation. The second and third paragraphs give a first proof of the principle. Paragraphs four to ten treat of continuity in space, time and change, and of the impossibility of empty space, and also afford Kant the opportunity to develop his dynamical theory of matter, and so to indicate the contribution which transcendental philosophy is able to make towards a more adequate understanding of the principles of physical science. The eleventh and twelfth paragraphs, evidently later interpolations, give a second proof of the principle which in one important respect varies from the first proof. In the second edition a third proof akin to this second proof, but carrying it a stage further, is added in the form of a new first paragraph.

Kant’s reason for changing the formulation of the principle in the second edition is evidently the unsatisfactoriness of the phrase “sensation and the real.”[1148] The principle, properly interpreted, applies not, as the first edition title and also the second proof would lead us to expect, to sensation itself, but to its object, realitas phaenomenon. It is phenomenalist in its teaching. The emphatic term “anticipation” is adopted by Kant to mark that in this principle we are able in a priori fashion to determine something in regard to what in itself is purely empirical. Sensation as such, being the matter of experience, can never be known a priori. Its quality, as being a colour or a taste, depends upon factors which are for us, owing to the limitations of our knowledge, wholly contingent. None the less in one particular respect we can predetermine the object of all sensation, and so can anticipate experience, even in its material aspect.

The first proof is as follows. Apprehension, so far as it takes place through a sensation, occupies only a single moment; it does not involve any successive synthesis proceeding from parts to the complete representation. That which is apprehended cannot, therefore, possess extensive magnitude. But, as already stated in the chapter on Schematism, reality is that in appearance which corresponds to a sensation. It is realitas phaenomenon. The absence of it is negation = 0. Now every sensation is capable of diminution; between reality in the appearance and negation there is a continuous series of many possible intermediate sensations, the difference between any two of which is always smaller than the difference between the given sensation and zero. That is to say, the real in appearance has intensive magnitude or degree. The argument is from capability of variation in the intensity of sensation to existence of degree in its object or cause. For the most part this reality is spoken of as that which is apprehended in sensation, but Kant adds that if it be

“...viewed as cause either of sensation or of other reality in appearance, such as change, the degree of its reality ... is then entitled a moment, as for instance the moment of gravity.”

The obscurity of what in itself is a very simple and direct argument would seem to be traceable to the lack of clearness in Kant’s own mind as to what is to be signified by reality. The implied distinction between sensation and its object has not been clearly formulated. Definitions have, indeed, been given of reality in the chapter on Schematism;[1149] but they are extremely difficult to decipher. Kant never varies from the assertion that reality is “that which corresponds to sensation in general.” Our difficulty is with the additional qualifications. This reality, he further declares, is

“...that, the concept of which in itself points to an existence [Sein] in time.”[1150]

The words ‘in time’ would seem to show that what is referred to is reality in the realm of appearance, the realitas phaenomenon of the Anticipations. But immediately below we find the following sentence:

“As time is only the form of intuition, and consequently of objects as appearances, what corresponds in them to sensation is the transcendental matter of all objects as things in themselves, thinghood [Sachheit], reality.”[1151]

The teaching of the first sentence is phenomenalist; that of the other is subjectivist.

Now in the section on Anticipations of Perception the phenomenalist tendencies of Kant’s thought are decidedly the more prominent. The implied distinction is threefold, between sensation as subjective state possessing intensive magnitude, spatial realities that possess both intensive and extensive magnitude, and the thing in itself. Objects as appearances are regarded as causes of sensation and as producing changes in one another.

The explanation of the phenomenalist character of this section is not far to seek. Kant’s chief purpose in it, as we shall find, is to develop the dynamical theory of matter to which he had long held, and which, as he was convinced, would ultimately be substituted for the mechanistic view to which almost all physicists then adhered. We can easily understand how in this endeavour the realist tendencies of his thinking should at once come to the surface, and why he should have been constrained to develop a position more precise and less ambiguous than that expressed in the definitions of reality and degree given in the chapter on Schematism. With these preliminary explanations we may pass to Kant’s second proof of his principle.

A link of connection between the two proofs may be found in the reason which Kant in the first proof gives for his assertion that sensation cannot possess extensive magnitude—the reason, namely, that as its apprehension takes place in a single moment, it involves no element of synthesis. In his second proof Kant modifies this contention, and maintains that we can abstract from the extensive magnitude of the appearance, and yet can recognise a synthesis as being involved.

“The real which corresponds to sensations in general, as opposed to negation = 0, represents only something the very conception of which contains an existence [ein Sein], and signifies nothing but the synthesis in an empirical consciousness in general.”[1152]

Kant adds that in a single moment we can represent to ourselves as involved in the bare sensation

“...a synthesis of the uniform progression from zero to the given empirical consciousness.”

These statements are far from clear; but it is hardly necessary to criticise them in detail. Since Kant is endeavouring to prove that a schema, that of reality or limitation, is involved in the apprehension of sensation, he is bound in consistency to maintain, in accordance with the teaching of his deduction of the categories, that the application of the schema demands some species of synthesis.

The third proof, added in the second edition,[1153] is somewhat more explicit, and represents a further and last stage in Kant’s vain endeavour to harmonise the teaching of this section with his general principles. In the empirical consciousness of sensation there is

“...a synthesis of the different quantities involved in the generation of a sensation from its beginning in pure intuition = 0 to its particular required magnitude.”

Or again, apprehension of magnitude is apprehension

“...in which the empirical consciousness can in a certain time increase from zero up to its given measure.”

Here, again, what Kant asserts as occurring in our awareness of sensation calls for much more rigorous demonstration. Like the argument of the second proof, it is not independently established; it is a mere corollary to the general principles of his deduction of the categories.

Thus Kant’s thesis, that the apprehension of sense qualities as intensive magnitudes presupposes a synthesis according to an a priori schema, is both obscure in statement, and unconvincing in argument; and some of the assertions made, especially in reference to the occurrence of synthesis, would seem to be hardly less arbitrary than the connection which Kant professes to trace between logical “quality,” as affirmation or negation, and the dynamical intensity of sensuous qualities. For, as already indicated,[1154] logical “quality” and intensive magnitude have nothing in common save the name.

Kant next proceeds to a discussion of the general problem of continuity. The connection is somewhat forced. But if we overlook the artificial ordering of the argument and are content to regard what is given as in the nature of parenthetical comment, we find in the middle paragraph of this section an excellent statement of his view of the nature of continuity and a very clear statement of his dynamical theory of matter.

Kant develops the conception of continuity (a) in reference to space and time, and (b) in its application to the intensity of sensations and of their causes.

(a) Kant’s own words require no comment:

“Space and time are quanta continua because no part of them can be given, save as enclosed between limits (points or moments), and therefore as being itself a space or a time. Space therefore consists only of spaces, time only of times. Points and moments are only limits, i.e. mere positions that limit space and time. But positions always presuppose the intuitions which they limit or are intended to limit; and out of mere positions, viewed as constituents capable of being given prior to space and time, neither space nor time can be constructed. Such magnitudes may also be called flowing, since the synthesis of productive imagination involved in their production is a progression in time, and the continuity of time is ordinarily denoted by the expression flowing.”[1155]

(b) When Kant proceeds to apply the principle of continuity to intensive magnitude, his conclusion rests upon a somewhat different basis. He argues that appearances must be continuous owing to the fact that they are apprehended in space and time.[1156] So far as they are extended in space and enduring in time that may perhaps be true; but Kant’s assertion has a wider sweep. It implies that sensations and the physical conditions of sensation, as for instance the sensation of red or the force of gravity, are capable of existing in every possible degree between zero and any given intensity. This affords the key to his method of formulating his second and third proofs of the principle of Anticipations of Perception, which, in the form in which he interprets it, contains this further implication of continuity. These proofs are inspired by the desire to make all apprehension, even that of simple sensation, a temporal process, and by that indirect means to establish for sensuous intensity and its objective conditions a continuity similar to that of space and time. The proof is, however, as we have seen, inconclusive. This application of continuity must be regarded as more in the nature of a mere hypothesis than Kant is willing to recognise. As regards sensations, it would seem to have been positively disproved by the results of experimental psychology.

From his supposed proof of the continuity of all intensive magnitudes Kant draws two further conclusions: first, that experience can never be made to yield proof of the void in either space or time. For if all reality can exist in innumerable degrees, and if each sense has a determinate degree of receptivity, the complete absence of reality can never be itself experienced. Inference to such absence is also impossible for a second reason, namely, that one and the same extensive magnitude may be completely occupied by an infinite number of different intensive degrees, indefinitely approximating to, and yet also indefinitely differing from, zero. Kant is here referring to the dynamical theory of matter which he had long held,[1157] and which he expounds in opposition to the current mechanistic view.[1158] The mechanistic theory rests, he contends, upon an assumption purely metaphysical and therefore wholly dogmatic, that the real in space has no internal differences, but is uniform like the empty space in which it exists.[1159] In accordance with this assumption physicists infer that all qualitative differences in our sensations must be due to merely quantitative differences in their material causes, and ultimately to differences in the number and distribution of the constituent parts of material bodies. If two bodies of the same volume differ in weight or in inertia, the variation must be traced to differences in the amount of matter, or, otherwise stated, to differences in the amount of unoccupied space, in the two bodies. To this view Kant opposes his own hypothesis—for it is in this more modest form that it is presented in these paragraphs—namely, that matter occupies space by intensity and not by mere bulk, and that it may therefore be diminished indefinitely in degree without for that reason ceasing completely to fill the same extensive area. Thus an expanded force such as heat, filling space without leaving the smallest part of it empty, may be indefinitely diminished in degree, and yet may still with these lesser degrees continue to occupy that space as completely as before. This may not, Kant admits, be the true explanation of physical differences, but it at least has the merit of freeing the understanding from metaphysical preconceptions, and of demonstrating the possibility of an alternative to the current view. If matter has intensity as well as extensity, and so can vary in quality as well as in quantity, physical science may perhaps be fruitfully developed on dynamical lines.

3. THE ANALOGIES OF EXPERIENCE

The principle of the Analogies is: Experience is possible only through the representation of a necessary connection of perceptions.[1160]

Kant introduces the three analogies with the statement of an underlying principle, which corresponds to the central thesis of the transcendental deduction. In the second edition this general principle is reformulated, and a new proof is added. These alterations do not seem, however, to be of any special significance. The two proofs repeat the main argument of the transcendental deduction, but with special emphasis upon the temporal aspect of experience. The categories of relation, as schematised, yield the Analogies, which acquire objective validity in so far as they render experience possible. The first proof (given in the second paragraph of the first edition) maintains that they are indispensable for apperception, and the second proof (that of the second edition) that they are indispensable for knowledge of objects. The references to time in the second proof are too condensed to be intelligible save in the light of the more explicit arguments given in support of the three Analogies.

The first paragraph in the first edition must be a later interpolation, as its assertion that simultaneity is a mode of time conflicts with the proof given of the first Analogy, but agrees with what must be regarded as a later interpolated passage introductory to that proof.[1161] This paragraph is also peculiar in another respect. Hitherto Kant has traced the existence of the three analogies to the three categories of relation, each of which conditions a separate schema. But in this paragraph he bases their threefold form on the fact that time has three modes, duration, sequence,[1162] and coexistence, and that there is therefore a threefold problem: first, what is involved in consciousness of duration; secondly, what is involved in consciousness of succession; and thirdly, what is involved in consciousness of coexistence. This is not, however, a satisfactory mode of stating the matter, for it might seem to imply that the three aspects of time can be separately apprehended, and that each has its own independent conditions. What Kant really proves is that all three involve one another. We can only be conscious of duration in contrast to succession, and of succession in contrast to the permanent, while both involve consciousness of coexistence. The three analogies thus treat of three aspects of the same problem, the first connecting with the category of substance, the second with that of causality, and the third with that of reciprocity.

The only point that calls for further comment[1163] concerns Kant’s adoption of the term Analogy as a title for the three principles of “relation.” The term is employed in contra-distinction to constitutive principle or axiom; and Kant points out that this usage of the term must be carefully distinguished from the other or mathematical. “In philosophy analogy is not the likeness of two quantitative but of two qualitative relations.” In mathematical analogy a fourth term can be discovered from three given terms; but in an ‘analogy of experience’ we possess a rule that suffices only for the determination of the relation to a term not given, never for knowledge of this term itself. Thus if we are informed that 15 is to x as 5 is to 10, the value of x can be determined as 30. But if it be stated that a given event stands to an antecedent event as effect to cause, only the relation holding between the events can be specified, not the actual cause itself. The principle of causality thus serves only as a regulative principle, directing us to search for the cause of an event among its antecedents.

Riehl has suggested a very different explanation of the term, namely, as signifying that the categories of relation are employed only on the analogy of the corresponding, pure logical forms.

“In so far as I know matter in terms of its empirical properties as the substance of outer experiences, I do not gain knowledge of the nature of matter but only of its relation to my thinking. In all judgments upon outer things I employ matter as the subject. That knowledge is therefore nothing but an analogy to the conceptual relation of a subject to its predicates. Matter is related to its properties and effects in the realm of appearance as the subject of a categorical judgment is related to its predicates. In so far as an antecedent is entitled the cause of an event, we do not gain knowledge of its nature but only of the analogy of the relation of cause and effect with that of antecedent and consequent in a hypothetical proposition; the connection of the changes is analogous to the conceptual relation of ground and consequence; the principle of the sufficient ground of changes is an analogy of experience.”[1164]

This explanation may at first sight seem to be supported by Kant’s own statement in the concluding paragraph of the section before us.

“Through these principles we are justified in combining appearances only according to an analogy with the logical and general unity of concepts ...”[1165]

This assertion is, however, incidental to Kant’s explanation that the analogies are not principles of “transcendental” (i.e. transcendent), but only of empirical application—an explanation itself in turn occasioned by his desire to connect his present argument with the chapter on Schematism. This interpretation of the term analogy is probably, therefore, of the nature of an afterthought. Having adopted the term on the grounds above stated in A 179-80 = B 222, he finds in it an opportunity to reinforce his previous assertion of the restricting character of the time condition through which categories are transformed into schemata. The entire paragraph is probably, as Adickes remarks, a later interpolation. But there are further reasons why we cannot accept this passage as representing the real origin of the term analogy. It would involve adoption of the subjectivist standpoint from which Riehl, despite his otherwise realistic reading of Kant, interprets Kant’s phenomenalist doctrines. For it implies that it is only in the noumenal, and not also in the phenomenal sphere, that substantial existences and genuinely dynamical activities are to be found.[1166] It would also seem to imply, what is by no means Kant’s invariable position, the absolute validity of the logical forms. And lastly, it would involve the priority of the logical to the real use of the categories, a violation of Critical principles of which Kant is himself occasionally guilty, but never, as it would seem, in this exaggerated form.

A. First Analogy.—All appearances contain the permanent (substance) as the object itself, and the changeable as its mere determination, i.e. as a mode in which the object exists. Or as in the second edition: In all change of appearances substance is permanent; its quantum in Nature neither increases nor diminishes.

The second paragraph[1167] is of composite character. Its first part (consisting of the first three sentences) and its second part give separate proofs, involving assertions directly contradictory of one another. The one asserts change and simultaneity to be modes of time; the other denies this. They cannot, therefore, be of the same date. The first would seem to be the later; it connects with the first paragraph of the preceding section.

In the first edition the principle is defined as expressing the schema of the dual category of substance and attribute. In the second edition it is reformulated in much less satisfactory form, as being the scientific principle of the conservation (i.e. indestructibility) of matter. This second formulation emphasises the weaker side of the argument of the first edition, and is largely due to the perverting influence of Kant’s method of distinguishing between the Analytic of Concepts and the Analytic of Judgments. It reveals Kant’s growing tendency to contrast the two divisions of the Analytic, as dealing, the one with ordinary experience, and the other with its scientific reorganisation.[1168]

The first proof in the first edition gives explicit expression to a presupposition underlying this entire section, namely, that all apprehension is necessarily successive, or in other words that it is impossible to apprehend a manifold save in succession.[1169] From this assumption it follows that if such succession is not only to occur but is to be apprehended as occurring, and if we are to be able to distinguish between the successive order of all our apprehensions and the order of coexisting independent existences, a permanent must be thought into the succession, that is to say, the successive experiences must be interpreted into an objective order in terms of the category of abiding substance and changing attributes. Kant neither here nor elsewhere makes any attempt to explain how this position is to be reconciled with his doctrine that space can be intuited as well as time; and there is equal difficulty in reconciling it with the doctrine developed in his second proof (in the second division of this same paragraph) that time itself does not change but only the appearances in it.

As above shown,[1170] there are two tendencies in Kant’s treatment of time, each of which carries with it its own set of connected consequences. There is the view that consciousness of time as a whole preconditions consciousness of any part of it. This tends to recognition of simultaneity as a mode of time and of the simultaneous as apprehended in a single non-successive act of apprehension. On the other hand, there is the counter-view that consciousness of time is only possible through the successive combination of its parts. This leads to the assertion that simultaneity is not a mode of time, and that time itself cannot be apprehended save as the result of synthesis in accordance with unifying categories. Through the categories there arises consciousness of objectivity, and so for the first time consciousness of a distinction between the subjective which exists invariably and exclusively in succession, and the objective which may exist either as successive or as permanent, and in whose existence both elements are, indeed, inseparably involved.

To turn now to Kant’s second[1171] proof of the principle;[1172] it is as follows. All our perceptions are in time, and in time are represented as either coexistent or successive. Time itself cannot change,[1173] for only as in it can change be represented. Time, however, cannot by itself be apprehended. As such, it is the mere empty form of our perceptions. There must be found in the objects of perception some abiding substrate or substance which will represent the permanence of time in consciousness, and through relation to which coexistence and succession of events may be perceived. And since only in relation to this substrate can time relations be apprehended, it must be altogether unchangeable, and may therefore[1174] be called substance. And being unchangeable it can neither increase nor diminish in quantity. Kant, without further argument, at once identifies this substance with matter.

This proof may be restated in briefer fashion.[1175] The consciousness of events in time involves the dating of them in time. But that is only possible in so far as we have a representation of the time in which they are to be dated. Time, however, not being by itself experienced, must be represented in consciousness by an abiding substrate in which all change takes place, and since, as the substrate of all change, it will necessarily be unchangeable, it may be called substance.

The argument, in both proofs, is needlessly abstract, and as already remarked,[1176] the reason of this abstractness is that Kant here, as in the chapter on Schematism, unduly ignores space, limiting his analysis to inner sense. He defines the schema of substance as the permanence of the real in time, i.e. as the representation of the real which persists while all else changes. As the second edition of the Critique shows,[1177] Kant himself came to recognise the inadequacy of this definition, and therefore of the proof of the first Analogy. Consciousness is only possible through the representation of objects in space. Only in outer sense is a permanent given in contrast to which change may be perceived. The proof ought therefore to have proceeded in the following manner. Time can be conceived only as motion, and motion is perceivable only against a permanent background in space. Consciousness of time therefore involves consciousness of a permanent in space. He might have added that consciousness of relative time involves consciousness of change in relation to something relatively permanent, and that the scientific conception of all changes as taking place in a single absolute time involves the determining of change through relation to something absolutely permanent, this ultimate standard being found in the heavenly bodies. By the permanent is not meant the immovable, but only that which is uniform and unchanging in its motions. The uniform motions of the heavenly bodies constitute our ultimate standard of time. The degree of their uniformity is the measure of our approximation to an absolute standard. A marginal note upon this Analogy in Kant’s private copy of the Critique reveals Kant’s late awakened recognition of the necessity of this mode of restating the argument.

“Here the proof must be so developed as to apply only to substances as phenomena of outer sense, and must therefore be drawn from space, which with its determinations exists at all times. In space all change is motion....”[1178]

That the new argument of the second edition still proceeds on the same lines as the second argument of the first edition is probably due, as Erdmann remarks,[1179] to Kant’s unwillingness to make the extensive alterations which would have been called for in the chapter on Schematism as well as in the statement of this Analogy.

A second serious objection to Kant’s treatment of the first Analogy follows at once from the above. Kant identifies the permanent which represents time in consciousness with matter, and seeks to prove by means of this identification the principle of the conservation of matter.[1180] That principle is not really capable of transcendental proof. It is not a presupposition of possible experience, but merely a generalisation empirically grounded. Kant is here confounding a particular theory as to the manner in which the element of permanence, necessary to possible experience, is realised, with the much more general conclusion which alone can be established by transcendental methods. His argument also conflicts with his own repeated assertion that the notion of change, in so far as it is distinct from that of temporal succession or of motion in space, is empirical, and consequently falls outside the scope of transcendental enquiry. By the conservation of matter we mean the constancy of the weight of matter throughout all changes. But the only permanent which can be postulated as necessary to render our actual consciousness of time possible, consists of spatial objects sufficiently constant to act as a standard by comparison with which motions may be measured against one another. And as this first Analogy, properly understood, thus deals solely with spatial changes of bodies, the principle of the conservation of matter has no real connection with it.

Then thirdly, and lastly, Kant takes this first Analogy as showing the indispensable function performed in experience by the category of substance and attribute. Substance, he argues, corresponds to the time in which events happen, and its attributes correspond to the changing events. Just as all events are only to be conceived as happening in time, so too all changes are only to be conceived as changes in an abiding substance. These, he would seem to hold, are simply two ways of making one and the same assertion. Now Kant may perhaps be right in insisting that all change is change in, and not of, time. Unity of consciousness would seem to demand consciousness of a single time in which all events happen. But this relation of time to its events does not justify the same assertion being made of substance. Substance may be what corresponds to time in general, and may represent it in consciousness, but we cannot for that reason say that changes are also only in and not of it. To regard the changes in this way as attributes inhering in substance directly contradicts the view developed in the second Analogy. For the notion of substance is there treated as an implication of the principle of causality. Substance, Kant there insists, is not a bare static existence in which changes take place, but a dynamic energy which from its very nature is in perpetual necessitated change. Change is not change in, but change of, substance.

Even in the passage in which Kant identifies the notion of the permanent in change with that of substance and attribute, he shows consciousness of this difficulty. We must not, he says, separate the substance from its accidents, treating it as a separate existence. The accidents are merely the special forms of its existence. But all the same, he adds, withdrawing the words which he has just uttered, such a separation of the changing accidents from the abiding substance is “unavoidable, owing to the conditions of the logical employment of our understanding.”[1181] Kant is here so hard pressed to account for the use of the category of substance and attribute in experience, and to explain the contradictions to which it gives rise, that the only way he sees out of the difficulty is to refer the contradictions involved in the category to the constitution of our understanding in its logical employment. Yet as such employment of understanding is, according to his own showing, secondary to, and dependent upon, its “real” employment, the category of substance and attribute can hardly have originated in this way.

We must, then, conclude that Kant offers no sufficient deduction or explanation of the category of substance and attribute, and as he does so nowhere else, we are driven to the further conclusion that he is unable to account for its use in experience, or at least to reconcile it in any adequate fashion with the principle of causality.

B. Second Analogy.—Everything that happens, i.e. begins to be, presupposes something on which it follows according to a rule. Or as in the second edition: All changes take place in conformity with the law of the connection of cause and effect.

This section, as Kant very rightly felt, contains one of the most important and fundamental arguments of the entire Critique; and this would seem to be the reason why he has so multiplied the proofs which he gives of the Analogy. Within the limits of the section no less than five distinct proofs are to be found, and still another was added in the second edition. As Adickes[1182] argues, it is extremely unlikely that Kant should have written five very similar proofs in immediate succession. The probability is that they are of independent origin and were later combined to constitute this section; or, if we hold with Adickes that Kant first composed a “brief outline,” we may conclude that he combined the one or more proofs, which that outline contained, with others of earlier or of later origin. The first to the fourth paragraphs of the first edition contain a first proof; the fifth to the seventh a second proof (a repetition of the first proof but in indirect form); the eighth to the tenth a third proof (almost identical with the first); the eleventh to the thirteenth a fourth proof (different in character from all the others); the fourteenth a fifth proof (probably the latest in time of writing; an anticipation of the argument in the second edition). The paragraph added in the second edition (the second paragraph in the text of the second edition) gives a sixth and last proof.

We may first state the central argument, deferring treatment of such additional points as arise in connection with Kant’s varying formulations of it in his successive proofs. The second Analogy, though crabbedly, diffusely, and even confusedly stated, is one of the finest and most far-reaching pieces of argument in the whole Critique. It is of special historical importance as being Kant’s answer to Hume’s denial of the validity of the causal principle. Hume had maintained that we can never be conscious of anything but mere succession. Kant in reply seeks to prove that consciousness of succession is only possible through consciousness of a necessity that determines the order of the successive events.

Kant, we must bear in mind, accepts much of Hume’s criticism of the category of causality. The general principle that every event must have an antecedent cause is, Kant recognises, neither intuitively certain nor demonstrable by general reasoning from more ultimate truths. It is not to be accounted for by analytic thought, but like all synthetic judgments a priori can only be proved by reference to the contingent fact of actual experience. Secondly, Kant makes no attempt, either in this Analogy or elsewhere in the Critique, to explain the nature and possibility of causal connection, that is, to show how one event, the cause, is able to give rise to another and different event, the effect. We can never by analysis of an effect discover any reason why it must necessarily be preceded by a cause.[1183] Thirdly, the principle of causality, as deduced by Kant and shown to be necessarily involved in all consciousness of time, is the quite general principle that every event must have some cause in what immediately precedes it. What in each special case the cause may be, can only be empirically discovered; and that any selected event is really the cause can never be absolutely certain. The particular causal laws are discovered from experience, not by means of the general principle but only in accordance with it, and are therefore neither purely empirical nor wholly a priori. As even J. S. Mill teaches, the general principle is assumed in every inference to a causal law, and save by thus assuming the general principle the particular inference to causal connection cannot be proved. But at the same time, since the proof of causal connection depends upon satisfaction of those empirical tests which Mill formulates in his inductive methods, such special causal laws can be gathered only from experience.

The starting-point of Kant’s analysis is our consciousness of an objective order in time. This is for Kant a legitimate starting-point since he has proved in the Transcendental Deduction that only through consciousness of the objective is consciousness of the subjective in any form possible. The independent argument by which it is here supported is merely a particular application of the general principle of that deduction. When we apprehend any very large object, such as a house, though we do so by successively perceiving the different parts of it, we never think of regarding these successive perceptions as representing anything successive in the house. On the other hand, when we apprehend successive events in time, such as the successive positions of a ship sailing down stream, we do regard the succession of our experiences as representing objective succession in what is apprehended. Kant therefore feels justified in taking as fact, that we have the power of distinguishing between subjective and objective succession, i.e. between sequences which are determined by the order of our attentive experience and sequences which are given as such. It is this fact which affords Kant a precise method of formulating the problem of the second Analogy, viz. how consciousness of objective change, as distinguished from subjective succession, is possible?

Schopenhauer, owing to the prominence in his system of the principle of sufficient reason, has commented upon this second Analogy in considerable detail;[1184] and we may here employ one of his chief criticisms to define more precisely the general intention of Kant’s argument. The succession in our experiences of the parts of a house and of the positions of a ship is, Schopenhauer maintains, in both cases of genuinely objective character. In both instances the changes are due to the position of two bodies relatively to one another. In the first example one of these bodies is the body of the observer, or rather one of his bodily organs, namely the eye, and the other is the house, in relation to the parts of which the position of the eye is successively altered. In the second example the ship changes its position relatively to the stream. The motion of the eye from roof to cellar is one event; its motion from cellar to roof is a second event; and both are events of the same nature as the sailing of the ship. Had we the same power of dragging the ship upstream that we have of moving the eye in a direction opposite to that of its first movement, the positions of the ship could be reversed in a manner exactly analogous to our reversal of the perceptions of the house.

This criticism is a typical illustration of Schopenhauer’s entire failure to comprehend the central thesis of Kant’s Critical idealism.[1185] The Analytic, so far as the main argument of its objective deduction is concerned, was to him a closed book; and as this second analogy is little else than a special application of the results of the deduction, he was equally at a loss in its interpretation. Kant was himself, of course, in large part responsible for the misunderstanding. The distinction which would seem to be implied by Kant’s language between sequence that is objective and sequence that is merely subjective is completely inconsistent with Critical principles,[1186] and is as thoroughly misleading as that other distinction which he so frequently employs between the a priori and the merely empirical. Schopenhauer, however, regarded these distinctions as valid, and accordingly applies them in the interpretation of Kant’s method of argument. If inner and outer experience are to be contrasted as two kinds of experience, there is, as Schopenhauer rightly insists, no sufficient ground for regarding changes due to movements of the eye as being subjective and those that are due to movements of a ship as being objective. That is not, however, Kant’s intention in the employment of these illustrations. He uses them only to make clear the fairly obvious fact that while in certain cases the order of our perceptions is subjectively initiated, in other cases we apprehend the subjective order of our experiences as corresponding to, and explicable only through, the objective sequence of events. In holding to this distinction Kant is not concerned to deny that even in the order which is determined by the subject’s purposes or caprice objective factors are likewise involved. The fact that the foundations of a house support its roof, and will therefore determine what it is that we shall apprehend when we turn the eye upwards, does not render the order of our apprehensions any the less subjective in character. But that this order is purely subjective, Kant could never have asserted. His Critical principles definitely commit him to the view that even sensations and desires are integral parts of the unitary system of natural law. Kant, as we shall find, is maintaining that some such distinction between subjective and objective sequence as is illustrated in the above contrasted instances must be present from the very start of our experience—must, indeed, be constitutive of experience as such. Out of a consciousness of the purely subjective the notion of the objective can never arise.[1187] Or otherwise stated, consciousness of a time order, even though subjective, must ultimately involve the application of some non-subjective standard.

“I shall be obliged ... to derive the subjective sequence of apprehension from the objective sequence of appearances, because otherwise the former is entirely undetermined, and does not distinguish any one appearance from any other.”[1188]

We interpret the subjective order in terms of an objective system; consciousness of the latter is the necessary presupposition of all awareness. It is as necessary to the interpretation of what is apprehended through the rotating eyeballs as to the apprehension of a moving ship. So far from refusing to recognise that the subjective order of our experiences is objectively conditioned, Kant is prepared to advance to the further assertion that it is only apprehensible when so conceived.

In the third Analogy Kant proceeds to the connected problem, how we can apprehend the parts of a house as simultaneous notwithstanding the sequent relation of our perceptions of them, and what justification we have for thus interpreting the subjectively sequent experiences as representing objective coexistence. Just as Kant in this second Analogy does not argue that irreversibility is by itself proof of causal relation, but only that the consciousness of such irreversibility demands the employment of the conception of causality, so in the third Analogy he does not attempt to reduce the consciousness of coexistence to the consciousness of reversibility, but to prove that only through the application of the conception of reciprocity can the reversibility be properly interpreted. In each case the category conditions the empirical consciousness; the latter is an apprehension of determinate order only in so far as it presupposes the category. Though Kant’s treatment of the third Analogy has less historical importance, and perhaps less intrinsic interest, than the proof of the second Analogy, it is even more significant of the kind of position which he is endeavouring to establish, and I may therefore forewarn the reader that he must not spare himself the labour of mastering its difficult, and somewhat illusive, argument. The doctrines which it expounds at once reinforce and extend the results of the second Analogy, while the further difficulties which it brings to view, but which it is not itself capable of meeting, indicate that the problems of the Analytic call for reconsideration in the light of certain wider issues first broached in the Dialectic.

We may now return to Kant’s main argument. His problem, as we have found, is how consciousness of objective change, as distinguished from subjective succession, is possible. The problem, being formulated in this particular way, demands, Kant felt, careful definition of what is meant by the term ‘objective,’ upon which so much depends. To apply the illustration above used, the house as apprehended is not a thing in itself but only an appearance to the mind. What, then, do we mean by the house, as distinguished from our subjective representations of it, when that house is nothing but a complex (Inbegriff) of representations?[1189] The question and Kant’s answer to it are stated in subjectivist fashion, in terms of his earlier doctrine of the transcendental object. To contrast an object with the representations through which we apprehend it, is only possible if these representations stand under a rule which renders necessary their combination in some one particular way, and so distinguishes this one particular mode of representation as the only true mode from all others. The origin, therefore, of our distinction between the subjectively successive and the succession which is also objective must be due in the one case to the presence of a rule compelling us to combine the events in some particular successive order, and in the other to the absence of such a rule. Our apprehension of the house, for instance, may proceed in any order, from the roof downwards or vice versa, and as the order may always be reversed there is no compulsion upon the mind to regard the order of its apprehension as representing objective sequence. But since in our apprehension of an event B in time, the apprehension of B follows upon the apprehension of a previous event A, and we cannot reverse the order, the mind is compelled to view the order of succession, in terms of the category of causality, as necessitated, and therefore as objective. The order is a necessary order not in the sense that A must always precede B, that A is the cause of B, but that the order, if we are to apprehend it correctly, must in this particular case be conceived as necessary. The succession, that is, need not be conceived as a causal one, but in order to be conceived as objective succession it must be conceived as rendered necessary by connections that are causal.

Having, in this general fashion, shown the bearing of his previous analysis of objective experience upon the problem in hand, Kant proceeds to develop from it his proof of the special principle of causality. The schema of causality is necessary succession in time, and it is through this, its time aspect, that Kant approaches the principle. It has to do with the special case of change. To be conscious of change we must be conscious of an event, that is, of something as happening at a particular point in time. The change, in other words, requires to be dated, and as we are not conscious of time in general, it must be dated by reference to other events, and obviously in this case in relation to the preceding events, in contrast to which it is apprehended as change. But according to the results of our analysis of what constitutes objective experience, it can be fixed in its position in objective time only if it be conceived as related to the preceding events according to a necessary law; and the law of necessary connection in time is the law of causality. In order, then, that something which has taken place may be apprehended as having occurred, that is, as being an objective change, it must be apprehended as necessarily following upon that which immediately precedes it in time, i.e. as causally necessary.

The principle of causality thus conditions consciousness of objective succession, and Hume, in asserting that we are conscious of the succession of events, therefore admits all that need be assumed in order to prove the principle. The reason why Hume failed to recognise this, is that he ignored the distinction between consciousness of the subjective order of our apprehensions and consciousness of the objective sequence of events. Yet that is a distinction upon which his own position rested. For he teaches that determination of causal laws, sufficiently certain to serve the purposes alike of practical life and of natural science, can be obtained through observation of those sequences which remain constant. Such is also the position of all empiricists. They hold that causal relation is discovered by comparison of given sequences. Kant’s contention is that the apprehension of change as change, and therefore ultimately the apprehension even of an arbitrarily determined order of subjective succession,[1190] presupposes, and is only possible through, an application of the category of causality. The primary function of the understanding does not consist in the clarification of our representation of an event, but in making such representation possible at all.[1191] The primary field of exercise for the understanding lies not in the realm of reflective comparison, but in the more fundamental sphere of creative synthesis.[1192] In determining the nature of the given it predetermines the principles to which all reflection upon the given must conform. The discursive activities of scientific reflection are secondary to, and conditioned by, the transcendental processes which generate the experience of ordinary consciousness. Only an experience which conforms to the causal principle can serve as foundation either for the empirical judgments of sense experience, or for that ever-increasing body of scientific knowledge into which their content is progressively translated. The principle of causality is applicable to everything experienced, for the sufficient reason that experience is itself possible only in terms of it. This conclusion finds its most emphatic and adequate statement in the Methodology.

“...through concepts of understanding pure reason establishes secure principles, not however directly from concepts, but always only indirectly through relation of these concepts to something altogether contingent, namely, possible experience. For when such experience (i.e. something as object of possible experience) is presupposed, the principles are apodictically certain, though by themselves (directly) a priori they cannot even be recognised at all. Thus no one can acquire insight into the proposition that everything which happens has its cause, merely from the concepts involved. It is not, therefore, a dogma, although from another point of view, namely, from that of the sole field of its possible employment, i.e. experience, it can be proved with complete apodictic certainty. But though it needs proof, it should be entitled a principle, not a theorem, because it has the peculiar character that it makes possible the very experience which is its own ground of proof, and in this experience must always itself be presupposed.”[1193]

Before making further comment upon Kant’s central argument, it is advisable to consider the varying statements which Kant has given of it. We may take his successive proofs in the order in which they occur in the first edition.

First Proof.[1194]—The argument is developed in terms of Kant’s early doctrine of the transcendental object. The only points specially characteristic of the statement here given of that doctrine consist (a) in the emphasis with which it is asserted that representations can be experienced only in succession to one another, and that they can never stand in the relation of coexistence,[1195] and (b) in the almost complete ignoring of the transcendental object as source or ground of the rule in terms of which the successive representations are organised. (a) This is a point common to the arguments of all three Analogies. In the first and third the problem is how, from representations merely successive, permanence and coexistence can be determined. In the second Analogy the problem is how from representations invariably successive a distinction can be drawn between the subjectively determined order of our apprehensions and the objective sequence of events. Or in other words: how under such conditions we can recognise an order as given, and so as prescribing the order in which it must be apprehended. Or to state the same point in still another manner: how we can distinguish between an arbitrary or reversible order and an imposed or fixed order, and so come to apprehend the subjective order of our apprehensions as in certain cases controlled by, and explicable only through, the objective sequence of events.[1196]

(b) The reason why the transcendental object, as source of the determinate and prescribed order of the given events, falls into the background in this passage is that Kant is concerned only with the general principle or category by means of which the order is apprehended as necessary. That principle has a subjective origin even though the particular sequences of concrete events have by means of that concept to be conceived as inexorably determined by their noumenal conditions.[1197] The principle accounts for the comprehension of the order as objective, and that is the only point with which Kant is here immediately concerned. That the assertion of the subjective origin of the category is not inconsistent with recognition of the imposed order of the given has already been shown above.[1198] Kant’s own illustration, in this section, of the ship sailing down stream shows that he was prepared to assume without question that they are compatible. His argument is, however, obscure, owing to his failure to distinguish between the two senses in which the term ‘rule’ may be employed. The term may signify either the universal and merely formal principle that every event must have a cause, or it may be used to denote the fixed order in which concrete events are presented to sense-perception. The latter order need not represent a series the members of which are causally connected with one another, but only one that is due to causal necessities. Thus the successive positions of a ship sailing down stream are not interrelated as cause and effect, and yet in order to be apprehended as objectively successive must be conceived as causally conditioned. The term ‘rule’ has very different meanings in the two cases. ‘Rule’ in the first sense is of subjective origin. It is formal, and can never be given. It is read into the given. ‘Rule’ in the second sense is given merely, and being due to noumenal conditions constitutes the material element in natural science, the empirical content of some particular causal law. Owing to Kant’s failure explicitly to distinguish between these two very different connotations of the term, such a sentence as the following is ambiguous: “That in appearance which contains the condition of this necessary rule of apprehension is the object.” Kant may mean that the prescribed order of the concrete events is due to the transcendental object; but in that case it is not given as necessary. Necessity, as he constantly insists, is the one thing that can never be given. The sentence is also misleading through its use of the term ‘appearance.’ That term has no legitimate place in a passage inspired by the doctrine of the transcendental object; there can be no such middle term between subjective representations and the thing in itself. As Kant himself states,[1199] appearance defined in terms of that doctrine is “nothing save a complex of representations.”

There is a very essential difference in the view which Kant takes of the causal relation according as he is proceeding upon subjectivist or upon phenomenalist lines. From the one point of view appearances are representations merely, and accordingly are entirely devoid of causal efficacy. They are not causes and effects of one another. They have not the independence or self-persistence necessary for the exercise of dynamical energy or even for the reception of modifications. Being “states of the identical self,” all causal relation, dynamically conceived, must lie solely in their noumenal conditions. Causality reduces to the thought of necessitated (not necessitating) sequence. It is, as Kant has suggested in A 181 = B 224, a mere ‘analogy’ in terms of which we apply the logical relation of ground and consequence[1200] to the interpretation of our subjective representations, and so view them as grounded not in one another but exclusively in the thing in itself. Causality in the strict sense, i.e. dynamical agency, can be looked for only in the noumenal sphere.

Caird, while adopting this explanation of the term ‘analogy,’[1201] is, as might be expected from his Hegelian standpoint, extremely indefinite and non-committal as to whether or not empirical objects can be genuine causes. Riehl, notwithstanding his professedly realistic interpretation of Kant, adopts the above subjectivist view of natural causation. So also do Benno Erdmann and Paulsen. The latter[1202] speaks with no uncertain voice.

“Causality in the phenomenal world signifies for Kant, as for Hume, nothing but regularity in the sequence of phenomena. Real causal efficiency cannot of course occur here, for phenomena are ideational products. As such they can no more produce an effect than concepts can.”

The corresponding phenomenalist view of the causal relation receives no quite definite formulation either in this section or elsewhere in the Critique, but may be gathered from the general trend of Kant’s phenomenalist teaching.[1203] It is somewhat as follows. The term ‘analogy’ is viewed as having a meaning very different from that above suggested. The causal relation is not a mere analogy from the logical relation of ground and consequence; it is the representation of genuinely dynamical activities in the objects apprehended. Those objects are not mere states of the self, subjective representations. They are part of an independent order which in the form known to us is a phenomenalist transcript of a deeper reality. If the causal relation is the analogy of anything distinguishable from itself, it is an analogon or interpretation of dynamical powers exercised by things in themselves,[1204] not of the merely logical relation between premisses and conclusion. The objects of representation may exercise powers which representations as such can never be conceived as possessing. Between the individual’s subjective states and things in themselves stands the phenomenal world of the natural sciences. Its function, whether as directly experienced through sense-perception or as conceptually reconstructed through scientific hypothesis, is to stand as the representative in human consciousness of that noumenal realm in which all existence is ultimately rooted. The causal interactions of material bodies in space are as essentially constitutive of those bodies as are any of their quantitative properties. Causal relation, even in the phenomenal sphere, must not be identified with mere conformity to law. The true and complete purpose of the natural sciences is not to be found in the Berkeleian or sceptical ideal of simplification, but in the older and sounder conception of causal explanation. That, at least, is the view which Kant invariably defends whenever he has occasion to discuss the principles of physical science.

Second Proof.[1205]—The argument of the first proof is here developed in indirect fashion. In the absence of any rule prescribing necessary sequence, no distinction can be made between subjective and objective succession. The justification for such a rule lies therefore, not in an inductive inference from repeated experience, but in its necessity for the possibility of experience. It is an expression of the synthetic unity in which experience consists.

Third Proof.[1206]—This is for the most part merely a restatement of the first proof. It differs from it in making rather more explicit that the objective reference involved in the notion of the transcendental object is one that carries the mind beyond all representations to the thought of something which determines their order according to a rule. Otherwise the ambiguities of the terms employed are identical with those of the first proof. Its concluding paragraph, however, is a much clearer statement of the difficult argument of A 192-3 = B 238-9.

Fourth Proof.[1207]—This proof differs from all the others. It argues from the characteristics of pure time to the properties necessary to the empirical representation of the time-series. As time cannot be experienced in and by itself, all its essential characteristics must be capable of being represented in terms of appearance. “Only in appearances can we empirically recognise continuity in the connection of times.” The primary function of the understanding is to make such recognition possible, and it does so by “transferring the time order to the appearances and their existence.” It is a necessary law of time that we can only advance to the succeeding through the preceding. Each moment of time is the indispensable condition of the existence of that which follows it. We can pass to the year 1915 only by way of the preceding year 1914. And since, as just noted, time is not cognisable by itself but only as the form of our perceptions, this law must be applicable to them. We can only be conscious of all times as successively conditioning one another in one single time, and that means in one single objective time, if we are conscious of all the phenomena perceived as conditioning one another in their order in time.

It is somewhat difficult to understand how Kant came to formulate the argument in this form. The explanation may perhaps be found in his preoccupation[1208] with the doctrine of a transcendental activity of the productive imagination and with the connected doctrine of a pure a priori manifold. For this proof would seem to rest upon the assumption that the characteristics of time are known purely a priori and therefore with complete certainty, independently of sense experience. The unusual and somewhat scholastic character of the proof also appears in Kant’s substitution of the principle of sufficient reason for the principle of causality. But despite the artificial character of the standpoint, the argument serves to bring prominently forward Kant’s central thesis, viz. that the principle of causality is presupposed in all consciousness of time, even of the subjectively successive. Also, by emphasising that time in and by itself can never be “an object of perception,” and that the relating of appearances to “absolute time” is possible only through the determining of them in their relations to one another, it supplies the data for correction of its own starting-point.

Fifth Proof.[1209]—This proof is probably later than the preceding proofs. Though its essential content coincides with that of the opening proof, its formulation would seem to be a first attempt at statement of the sixth proof, i.e. of the argument which Kant added in the second edition. Adickes considers this proof to be earlier in date than the first four proofs, but the reason which he assigns for so regarding it, viz. that Kant here postulates a synthesis of the imagination independent of the categories as preceding a synthesis of apprehension in terms of the categories, seems to be based upon a much too literal reading of Kant’s loose mode of statement. The argument rather appears to be, as in the sixth proof, that synthesis of the imagination may be either subjective or objective; and the term “apprehension” would seem to be used as signifying that the manifold synthesised is given to the imagination through actual sense experience, and that as thus given it has a determinate order of its own. The argument concludes with the statement (more definite than any to be found in the preceding arguments), that the proof of the principle of causality consists in its indispensableness as a condition of all empirical judgments, and so of experience as such. As a ground of the possibility of experience it must be valid of all the objects of experience.

Sixth Proof.[1210]—The argument of the fifth proof is here more clearly stated. All synthesis is due to “the faculty of imagination which determines inner sense in respect of the time relation.” Such synthesis may, however, yield the consciousness either of subjective succession or of succession “in the object.” In the latter form it presupposes the employment of a pure concept of the understanding, that of the relation of cause and effect. And the conclusion reached is again that only so is empirical knowledge possible. This mode of stating the argument is far from satisfactory. It tends to obscure Kant’s central thesis, that only through consciousness of an objective order is consciousness of subjective sequence possible, and that the principle of causality is therefore a conditioning factor of all consciousness. The misleading distinction drawn in the Prolegomena between judgments of perception and judgments of experience also crops out in Kant’s use of the phrase “mere perception.”[1211]

We may again return to Kant’s central argument. For we have still to consider certain objections to which it may seem to lie open, and also to comment upon Kant’s further explanations in the remaining paragraphs of the section.[1212] Kant’s imperfect statement of his position has suggested to Hutchison Stirling and others a problem which is largely artificial, namely, how the mind is enabled to recognise the proper occasions upon which to apply the category of causality. On the one hand sequence as such cannot be the criterion, since many sequences are not causal, and on the other hand the absence of sequence does not appear to debar its application, since cause and effect would frequently seem to be co-existent. This difficulty arises from failure to appreciate the central thesis upon which Kant’s proof of the principle of causality ultimately rests. Kant’s diffuse and varying mode of statement may conceal but never conflicts with that thesis, which consists in the contention that the category of causality is a necessary and invariable factor in all consciousness. Nothing can be apprehended save in terms of it.[1213] It prescribes an interpretation which the mind has no option save to apply in the consciousness of each and every event, of the coexistent no less than of the sequent. Whether two changes are coexistent or are successive, each must be conceived as possessing an antecedent cause. The only difference is that in the case of sequent events one of them (i.e. the antecedent change) may, upon empirical investigation, be found to be itself the cause of the second and subsequent event, whereas with coexistent events this can never be possible. As the principle of causality is that every event must have an antecedent cause, it follows that where there is no sequence there can be no causation. But when Kant states that sequence is “the sole empirical criterion”[1214] of the causal relation, he does less than justice to the position he is defending. The empirical criteria are manifold in number, and are such as John Stuart Mill has attempted to formulate in his inductive methods.

Schopenhauer has objected[1215] that Kant’s argument proves too much, since it would involve that all objective sequences, such as that of night and day or of the notes in a piece of music, are themselves causal sequences. This criticism has been replied to by Stadler[1216] in the following terms:

“When Schopenhauer adduces the sequence of musical notes or of day and night, as objective sequences which can be known without the causal law, we need only meet him with the question, Where in these cases is the substance that changes? So soon as he is forced to put his objection into the form required to bring it into relation to the question of the possibility of knowledge, his error becomes obvious. His instances must then be expressed thus:—The instrument passes from one state of sound into another; the earth changes from the measure of enlightenment which makes day, to that which makes night. Of such changes no one will say that they are not referred to a cause. And we may quote in this reference the appropriate saying of Kant himself, ‘Days are, as it were, the children of Time, since the following day with that which it contains is the product of the previous day.’”

Night and day, in so far as they are sequent events, must be conceived in terms of causality, not in the sense that night causes day, but as being determined by causes that account not only for each separately, but also for the alternating sequence of the one upon the other. Such causes are found by the astronomer to lie in the changing positions of the earth relatively to the sun.

Schopenhauer adds a further objection of a more subtle nature, which has again been excellently stated and answered by Stadler:

“Schopenhauer points out that what we call chance is just a sequence of events which do not stand in causal connexion. ‘I come out of the house and a tile falls from the roof which strikes me; in such a case there is no causal connexion between the falling of the tile and my coming out of the house, yet the succession of these two events is objectively determined in my apprehension of them.’ How have we to criticise this case from the transcendental point of view? We know that successions become necessary, i.e. objective, for our consciousness, when we regard them as changes of a substance which are determined by a cause. But it is shown here that there are successions in which the single members are changes of different substances. If substance S changes its state A into B on account of the cause X, and substance S´ changes its state A´ into B´ on account of the cause X´, and if I call the first change V and the second V´, the question arises how the objectivity of the succession V V´ is related to the law of causality. Sequences such as V V´ are very frequent, and our consciousness of the objectivity is certain. Do we owe this consciousness to the same rule as holds good in other cases? Certainly. The distinction is not qualitative, but rests only on the greater complication of the change in question. The sequence V V´ can become objective only if I think it as a necessary connexion. It must be so determined that V can only follow V´ in ‘consciousness in general’; there must be a U, the introduction of which is the cause that V´ follows V. To be convinced of this, I do not need actually to know U. I know that on every occasion U causes the succession V V´. Of course, this presupposes that all data of the states considered, A and A´, remain identical. But whether these data are very simple or endlessly complex, whether they are likely to combine to the given result frequently or seldom, is indifferent for the objectifying of the event; it is not the perception of U, but the presupposition of it, which makes the change necessary and so objective for us.”[1217]

To turn now to the other difficulty which Kant himself raises in A 202-3 = B 247-8, viz. that cause and effect would frequently seem to be coexistent, and the “sole empirical criterion” to be therefore absent. It may from this point of view be maintained that the great majority of causes occur simultaneously with their effects, and that such time sequence as occurs is due solely to the fact that the cause cannot execute itself in one single instant. Kant has little difficulty in disposing of this objection. Causality concerns only the order, not the lapse, of time; and the sequence relation must remain even though there is no interval between the two events. If a leaden ball lies upon a cushion it makes a depression in it. The ball and the depression are coexistent. None the less, when viewed in their dynamical relation, the latter must be regarded as sequent upon the former. If the leaden ball is placed upon a smooth cushion a hollow is at once made, but if a hollow exists in a cushion a ball need not appear. In other words, the criteria for the determination of specific causal relations are neither the presence nor the absence of sequence, but are empirical considerations verifiable only upon special investigation.[1218] The observer is called upon to disentangle the complicated web of given appearances under the guidance of the quite general and formal principle that every event is due to some antecedent cause. He must do so as best he can through the application of his acquired insight, and, when necessary, by means of the requisite experimental variation of conditions.

In the two following paragraphs (A 204-5 = B 249-51) Kant raises points which he later discussed more fully in the Metaphysical First Principles of Natural Science.[1219] As adequate explanation of the argument would be a very lengthy matter, and not of any very real importance for the understanding of the general Critical position, we may omit all treatment of it. In the sections of the Metaphysical First Principles just cited, the reader will find the necessary comment and explanation. Such bearing as these two paragraphs have upon Kant’s view of the nature of the causal relation has been noted above.[1220]

In the section on Anticipations of Perception[1221] Kant has stated that the principle of the continuity of change involves empirical factors, and therefore falls outside the limits of transcendental philosophy. To this more correct attitude Kant, unfortunately, did not hold. In A 207-11 = B 252-6 he professes to establish the principle in a priori transcendental fashion as a necessary consequence of the nature of time. This proof is indeed thrice repeated with unessential variations, thereby clearly showing that these paragraphs also are of composite origin. The argument in all three cases consists in inferring from the continuity of time the continuity of all changes in time. As the parts of time are themselves times, of which no one is the smallest, so in all generation in time, the cause must in its action pass through all the degrees of quantity from zero to that of the final effect.

“Every change has a cause which evinces its causality in the whole time in which the change takes place. This cause, therefore, does not engender the change suddenly (at once or in one moment), but in a time, so that, as the time increases from its initial moment a to its completion in b, the quantity of the reality (b-a) is in like manner generated through all lesser degrees which are contained between the first and the last.”[1222]

This argument is inconclusive. As Kant himself recognises in regard to space,[1223] we may not without special proof assume that what is true of time must be true of the contents of time. If time, change, and causation can be equated, what is true of one will be true of all three. But the assumption upon which the argument thus rests has not itself been substantiated.

In the third proof[1224] the argument is stated in extreme subjectivist terms which involve the further assumption that what is true of apprehension is ipso facto true of everything apprehended. The possibility of establishing the law of dynamical continuity follows, Kant declares, as a consequence of its being a law of our subjective apprehension.

“We anticipate only our own apprehension, the formal condition of which, inasmuch as it inheres in the mind prior to all given appearances, must certainly be capable of being known a priori.”[1225]

Kant’s attitude towards the physical principle of continuity underwent considerable change. In his New Doctrine of Motion and Rest (1758)[1226] he maintains that it cannot be proved, and that physicists may rightly refuse to recognise it even as an hypothesis. It is in the Essay on Negative Quantity (1763)[1227] that Kant first adopts the attitude of the Critique, and rejects the “speculative” objections raised against the mathematical conception of the infinitely small. In the Metaphysical First Principles of Natural Science[1228] the principle of continuity is defended and developed, but only in its application to material existence, not in its relation to the causal process.

C. Third Analogy.—All substances, in so far as they are coexistent, stand in thoroughgoing communion,[1229] i.e. in reciprocity with one another. Or, as in the second edition: All substances, so far as they can be perceived to coexist in space, are in thoroughgoing reciprocity.

This section contains four separate proofs. The first three paragraphs in the text of the first edition contain the first proof. The fourth paragraph supplies a second proof, and the fifth paragraph a third. In the second edition Kant adds a fourth proof (the first paragraph of the text of the second edition).

We may lead up to these proofs by first formulating (a) the fundamental assumption upon which they proceed, and (b) the thesis which they profess to establish. (a) The argument involves the same initial assumption as the preceding Analogies, viz. that representations exist exclusively in succession, or stated in phenomenalist terms, that the objectively coexistent can be apprehended only in and through representations that are sequent to one another in time.[1230] Upon this assumption the problem of the third Analogy is to explain how from representations all of which are in succession we can determine the objectively coexistent. (b) In the Dissertation[1231] Kant had maintained that though the possibility of dynamical communion of substances is not necessarily involved in their mere existence, such interaction may be assumed as a consequence of their common origin in, and dependence upon, a Divine Being. In the Critique no such metaphysical speculations are any longer in order, and Kant recognises that as regards things in themselves it is not possible to decide whether dynamical interaction is, or is not, necessarily involved in coexistence. The problem of this third Analogy concerns only appearances, which as such must be subject to the conditions of unitary experience; and one such condition is that they be apprehended as belonging to a single objective order of nature, and therefore as standing in reciprocal relations of interaction. The apprehension of substances as reciprocally determining one another is, Kant contends, an indispensable condition of their being known even as coexistent. Such is Kant’s thesis. The proof may first be stated in what may be called its typical or generic form. Kant’s four successive proofs can then be related to it as to a common standard.

Two things, A and B, can be apprehended as coexistent only in so far as we can experience them in either order, i.e. when the order of our perceptions of them is reversible. If they existed in succession, this could never be possible. The earlier member of a time series is past when the succeeding member is present, and what belongs to the past can never be an object of perception. The fact that the order in which things can be perceived is reversible would thus seem to prove that they do not exist successively to one another in time.[1232] That, however, is not the case. By itself such experience does not really suffice to yield consciousness of coexistence. It can yield only consciousness of an alternating succession.[1233] A further factor, namely, interpretation of the reversibility of our perceptions as due to their being conditioned by objects which stand in the relation of reciprocal determination, must first be postulated. If these objects mutually determine one another to be what they are, no one of them can be antecedent to or subsequent upon the others; and by their mutual reference each will date the others as simultaneous with itself. In other words, the perception of the coexistence of objects involves the conception of them as mutually determining one another. The principle of communion or reciprocity conditions the experience of coexistence, and is therefore valid for objects apprehended in that manner.

Kant also maintains, more by implication than by explicit statement, that as A and B need not stand in any direct relation, the apprehension of them as coexistent involves the conception of an all-embracing order of nature within which they fall and which determines them to be what they are. If any one of them, even the most minute and insignificant, were conceived as altered, corresponding simultaneous variations would have to be postulated for all the others. The unity of the phenomenal world is the counterpart of the unity of apperception. Unity of experience involves principles which prescribe a corresponding unity in the natural realm. Dynamical communion is the sufficient and necessary fulfilment of this demand. It carries to completion the unity demanded by the preceding Analogies of substance and causality. Kant sums up his position in a note to A 218 = B 265.

“The unity of the world-whole, in which all appearances have to be connected, is evidently a mere consequence of the tacitly assumed principle of the communion of all substances which are coexistent. For if they were isolated, they would not as parts constitute a whole. And if their coexistence alone did not necessitate their connection (the reciprocal action of the manifold) we could not argue from the former, which is a merely ideal relation, to the latter, which is a real relation. We have, however, in the proper context, shown that communion is really the ground of the possibility of an empirical knowledge of coexistence, and that therefore the actual inference is merely from this empirical knowledge to communion as its condition.”

To turn now to Kant’s successive proofs. The first[1234] calls for no special comment. It coincides with the above. The second[1235] proof is an incompletely stated argument, which differs from the first only in its more concrete statement of the main thesis and in its limitation of the argument to spatial existences. Dynamical community is the indispensable condition of our apprehension of any merely spatial side-by-sideness. Kant now adds that it is the dynamical continuity of the spatial world which enables us to apprehend the coexistence of its constituents. The important bearing of this argument we shall consider in its connection with the proof which Kant added in the second edition.

The third[1236] proof is probably the earliest in date of writing. It draws a misleading distinction between subjective and objective coexistence, and seems to argue that only the latter form of coexistence need presuppose the employment of the category of reciprocity. That runs directly counter to the central thesis of the other proofs, that only in terms of dynamical relation is coexistence at all apprehensible. That the above distinction indicates an early date of writing would seem to be confirmed by the obscure phrase “community of apperception” which is reminiscent of the prominence given to apperception in Kant’s earlier views, and by the concluding sentence in which Kant employs terms—inherence, consequence, and composition—that are also characteristic of the earlier stages of his Critical enquiries.[1237]