Chapter II: System of All Principles of Pure Understanding (1)

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.