I. THE TRANSCENDENTAL AESTHETIC…

I. THE TRANSCENDENTAL AESTHETIC

The Aesthetic opens with a series of definitions. =Intuition= (Anschauung) is knowledge (Erkenntnis) which is in immediate relation to objects (sich auf Gegenstände unmittelbar bezieht). Each term in this definition calls for comment. Anschauung etymologically applies only to visual sensation. Kant extends it to cover sensations of all the senses. The current term was Empfindung. Kant’s reason for introducing the term intuition in place of sensation was evidently the fact that the latter could not be made to cover space and time. We can speak of pure intuitions, but not of pure sensations. Knowledge is used in a very wide sense, not strictly consistent with A 50-1 = B 74-5.[345] The phrase sich bezieht is quite indefinite and ambiguous. Its meaning will depend upon the interpretation of its context. Object is used in its widest and most indefinite meaning. It may be taken as signifying content (Inhalt, a term which does not occur in this passage, but which Kant elsewhere employs[346]). That, at least, is the meaning which best fits the context. For when Kant adds that intuition relates itself to objects immediately, it becomes clear that he has in mind its distinction from conception (Begriff) which as expressing the universal is related to objects only indirectly, representing some one or more attributes of the given objects. Ultimately the whole content of conception must be given.[347] The phrase “relates itself to objects” may, therefore, be paraphrased “has some content, such as red or cold, as its immediate object.” Through the content of intuition the whole material of thought is supplied. Intuition in itself is blind, but not empty. “Thoughts without content are empty; intuitions without concepts are blind.”[348]

But the phrase “is in relation to objects” has also for Kant a second meaning, implied in the above, but supplementary to it. As he states in the very next sentence, intuition can have an object, meaning thereby a content, only in so far as that content is given. The material of thought must be supplied; it cannot be invented.[349] The only mode, however, in which it can be supplied, at least to the human mind, is through the affecting of the mind by “the object.” This is an excellent instance of Kant’s careless mode of expressing himself. In the first part of the sentence object means object of intuition. In the latter part it signifies the cause of intuition. And on Kant’s view the two cannot coincide. The object which affects the mind is independently real; the immediate object of the intuition is a sense-content, which Kant, following the universally accepted view of his time, regards as purely subjective. The term object is thus used in two quite distinct meanings within one and the same sentence.

Kant’s definition of intuition, when stated quite explicitly, and cleared of all ambiguity, is therefore as follows. Intuition is the immediate apprehension of a content which as given is due to the action of an independently real object upon the mind. This definition is obviously not meant to be a description of intuition as it presents itself to introspection, but to be a reflective statement of its indispensable conditions. Also it has in view only empirical intuitions. It does not cover the pure intuitions space and time.[350] Though space and time are given, and though each possesses an intrinsic content, these contents are not due to the action of objects upon the sensibility.

“An intuition is such a representation as immediately depends upon the presence of the object. Hence it seems impossible originally to intuit a priori because intuition would in that event take place without either a former or a present object to refer to, and by consequence could not be intuition.”[351]

This interpretation is borne out by Kant’s answer to Beck when the latter objected that only through subsumption under the categories can a representation become objective. Kant replies in a marginal note, the meaning of which, though difficult to decipher, admits of a fairly definite interpretation.

“The determining of a concept through intuition so as to yield knowledge of the object falls within the province of the faculty of judgment, but not the relation of the intuition to an object in general [i.e. the view of it as having a content which is given and which is therefore due to some object], for that is merely the logical use of the representation, whereby it is thought as falling within the province of knowledge. On the other hand, if this single representation is related only to the subject, the use is aesthetic (feeling), and the representation cannot be an act of knowledge.”[352]

=Mind= (Gemüt) is a neutral term without metaphysical implications.[353] It is practically equivalent to the term which is substituted for it in the next paragraph, power of representation (Vorstellungsfähigkeit). =Representation= (Vorstellung) Kant employs in the widest possible meaning. It covers any and every cognitive state. The definition here given of =sensibility=--“the capacity (receptivity) to obtain representations through the mode in which we are affected by objects”--is taken directly over from the Dissertation.[354] In this definition, as in that of intuition, Kant, without argument or question, postulates the existence of independently existing objects. The existence of given sensations presupposes the existence of things in themselves. Sensibility is spoken of as the source both of objects and of intuitions. This is legitimate since object and intuition mutually imply one another; the latter is the apprehension of the former. By “objects” is obviously meant what in the third paragraph is called the matter of appearances, i.e. sensations in their objective aspect, as qualities or contents. The term “object” is similarly employed in the last line of this first paragraph.

=Understanding= (Verstand) is defined only in its logical or discursive employment. Kant wisely defers all reference to its more fundamental synthetic activities. In us (bei uns) is an indirect reference to the possibility of intellectual (non-sensuous) intuition which is further developed in other parts of the Aesthetic.[355] Sensuous intuition is due to affection by an object. In intellectual intuition the mind must produce the object in the act of apprehending it.[356]

Kant’s definition of intuition applies, as already noted, only to empirical intuition. He proceeds[357] to define the relation in which =sensation= (Empfindung) stands to empirical intuition. What he here says amounts to the assertion that through sensation intuition acquires its object, i.e. that sensation is the content of intuition. And that being so, it is also through sensation that empirical intuition acquires its relation to the object (= thing in itself) which causes it. (That would seem to be the meaning of the ambiguous second sentence; but it still remains uncertain whether the opposition intended is to pure or to intellectual intuition.) If this interpretation of the paragraph be correct, sensation is counted as belonging exclusively to the content side of subjective apprehension. But Kant views sensation in an even more definite manner than he here indicates. Though sensation is given, it likewise involves a reaction of the mind.

“Whatever is sensuous in knowledge depends upon the subject’s peculiar nature, in so far as it is capable of this or that modification upon the presence of the object.”[358]

Thus for Kant sensation is a modification or state of the subject, produced by affection through an object. The affection produces a modification or state of the subject, and this subjective modification is the sensation.

“Sensation is a perception [Perception] which relates itself solely to the subject as the modification of its state.”[359]

This view of sensation, as subjective, was universally held in Kant’s day. He accepts it without argument or question. That it could possibly be challenged never seems to have occurred to him. He is equally convinced that it establishes the existence of an actually present object.

“Sensation argues the presence of something, but depends as to its quality upon the nature of the subject.”[360] “Sensation presupposes the actual presence of the object.”[361]

Kant’s view of sensation, as developed in the Aesthetic,[362] thus involves three points: (1) It must be counted as belonging to the content side of mental apprehension. (2) Though a quality or content, it is purely subjective, depending upon the nature of our sensibility. (3) It is due to the action of some object upon the sensibility.

Kant distinguishes between =sensation= (Empfindung) and =feeling= (Gefühl).[363] It had been usual to employ them as synonyms.

“We understand by the word sensation an objective representation of the senses; and in order to preclude the danger of being misunderstood, we shall denote that which must always remain merely subjective and can constitute absolutely no representation of an object by the ordinary (sonst üblichen) term feeling.”[364]

=Appearance= (Erscheinung) is here defined as the undetermined object of an intuition. By undetermined object is meant, as we have seen, the object in so far as it consists of the given sense contents. When these contents are interpreted through the categories they become phenomena.

“Appearances so far as they are thought as objects according to the unity of the categories are called phenomena.”[365]

But this distinction between appearance and phenomenon is not held to by Kant. He more usually speaks of the categorised objects as appearances. The term phenomenon is of comparatively rare occurrence in the Critique. This has been concealed from English readers, as both Meiklejohn and Max Müller almost invariably translate Erscheinung phenomenon. The statement that appearance is the object of an empirical intuition raises a very fundamental and difficult question, namely, as to the relation in which representation stands to the represented.[366] Frequently Kant’s argument implies this distinction, yet constantly he speaks and argues as if it were non-existent. We have to recognise two tendencies in Kant, subjectivist and phenomenalist.[367] When the former tendency is in the ascendent, he regards all appearances, all phenomena, all empirical objects, as representations, modifications of the sensibility, merely subjective. When, on the other hand, his thinking is dominated by the latter tendency, appearances gain an existence independent of the individual mind. They are known through subjective representations, but must not be directly equated with them. They have a genuine objectivity. To this distinction, and its consequences, we shall have frequent occasion to return.

The phenomenalist standpoint is dominant in these first two paragraphs of the Aesthetic, and it finds still more pronounced expression in the opening of the third paragraph. “That in the appearances which corresponds (correspondirt) to sensation, I call its matter.” This sentence, through the use of the term corresponds, clearly implies a distinction between sensation and the real object apprehended in and through it. That, in turn, involves a threefold distinction, between sensation as subjective content (= appearance in the strict sense), the real enduring object in space (= phenomenon, the categorised object, appearance in its wider and more usual sense), and the thing in itself.[368] Yet in the immediately following sentence Kant says that “the matter of all appearance is given a posteriori.” By “matter of appearance” Kant must there mean sensations, for they alone are given a posteriori.[369] On this view the phenomena or empirical objects reduce to, and consist of, sensations. The intermediate term of the above threefold distinction is eliminated. The matter of appearance does not correspond to, but itself is, sensation. Thus in these successive sentences the two conflicting tendencies of Kant’s teaching find verbal expression. They intervene even in the preliminary definition of his terms. This fundamental conflict cannot, however, be profitably discussed at this stage.

The =manifold of appearance= (das Mannichfaltige der Erscheinung). The meaning to be assigned to this phrase must depend upon the settlement of the above question.[370] But in this passage it allows only of a subjectivist interpretation, whereby sensations are appearance. The given sensations as such constitute a manifold; as objects in space they are already ordered. Kant’s more usual phrase is “the manifold of intuition.” His adoption of the term “manifold” (the varia of the Dissertation) expresses his conviction that synthesis is indispensable for all knowledge, and also his correlative view that nothing absolutely simple can be apprehended in sense-experience. By the manifold Kant does not mean, however, as some of his commentators would seem to imply, the chaotic or disordered. The emphasis is on manifoldness or plurality, as calling for reduction to unity and system. The unity has to be found in it, not introduced into it forcibly from the outside. The manifold has to be interpreted, even though the principles of interpretation may originate independently of it. Though, for instance, the manifold as given is not in space and time, the specific space and time relations assigned by us are determined for us by the inherent nature of the manifold itself.[371]

The form of appearance is defined--if the definition given in the first edition be translated literally--as “that which causes (dasjenige, welches macht dass) the manifold of appearance to be intuited as ordered in certain relations.” This phrase is employed by Kant in other connections, and, as Vaihinger points out,[372] need not necessarily indicate activity. “Sensation is that in our knowledge which causes it to be called a posteriori knowledge.”[373] In the second edition Kant altered the text from “geordnet angeschaut wird” to “geordnet werden kann.” The reason probably was that the first edition’s wording might seem to imply that the form is (as the Dissertation taught) capable in and by itself of ordering the manifold. Throughout the second edition Kant makes more prominent the part which understanding plays in the apprehension of space.[374]

This distinction between matter and form is central in Kant’s system.[375] As he himself says:

“These are two conceptions which underlie all other reflection, so inseparably are they bound up with all employment of the understanding. The one [matter] signifies the determinable in general, the other [form] its determination.”[376]

On the side of matter falls the manifold, given, empirical, contingent material of sense; on the side of form fall the unifying, a priori, synthetic, relational instruments of sensibility and thought. For Kant these latter are no mere abstractions, capable of being distinguished by the mind; they differ from the matter of experience in nature, in function, and in origin. Upon this dualistic mode of conceiving the two factors depends the strength as well as the weakness of his position. To its perverting influence most of the unsatisfactory features of his doctrine of space and time can be directly traced. But to it is also due his appreciation of the new Critical problems, with their revolutionary consequences, as developed in the Analytic.

Kant proceeds to argue: (a) that the distinction is between two elements of fundamentally different nature and origin. The matter is given a posteriori in sensation; the form, as distinct from all sensation, must lie ready a priori in the mind. (b) Kant also argues that form, because of its separate origin, is capable of being contemplated apart from all sensation. The above statements rest upon the unexpressed assumption that sensations have no spatial attributes of any kind.[377] In themselves they have only intensive, not extensive, magnitude.[378] Kant assumes this without question, and without the least attempt at proof.[379] The assumption appears in Kant’s writings as early as 1768 as a self-evident principle;[380] and throughout the Critique is treated as a premiss for argument, never as a statement calling for proof. The only kind of supporting argument which is even indirectly suggested by Kant is that space cannot by itself act upon the senses.[381] This would seem to be his meaning when he declares[382] that it is no object, but only an ens imaginarium. “Space is no object of the senses.”[383] Such argument, however, presupposes that space can be conceived apart from objects. It is no proof that an extended object may not yield extended sensations. Kant completely ignores the possibility that formal relations may be given in and with the sensations. If our sensibility, in consequence of the action of objects upon it, is able to generate qualitative sensations, why, as Vaihinger very pertinently enquires,[384] should it be denied the power of also producing, in consequence of these same causes, impressions of quantitative formal nature? Sensations, on Kant’s view, are the product of mind much more than of objects. Why, then, may not space itself be sensational?[385] From the point of view of empirical science there is no such radical difference between cause and effect in the latter case as exists in the former. As Herbert Spencer has remarked,[386] Kant makes the enormous assumption

“...that no differences among our sensations are determined by any differences in the non-ego (for to say that they are so determined is to say that the form under which the non-ego exists produces an effect upon the ego); and as it similarly follows that the order of coexistence and sequence among these sensations is not determined by any order in the non-ego; we are compelled to conclude that all these differences and changes in the ego are self-determined.”

Kant’s argument in the Dissertation is exactly of this nature.

“Objects do not strike the senses by their form. In order, therefore, that the various impressions from the object acting on the sense may coalesce into some whole of representation, there is required an inner principle of the mind through which in accordance with stable and innate laws that manifold may take on some form.”[387]

In the paragraph before us Kant may, at first sight, seem to offer an argument. He is really only restating his premiss. “That wherein alone sensations can be arranged (sich ordnen[388]) and placed in a certain form cannot itself again be sensation.” Now, of course, if the term sensation is to be limited to the sense qualities, i.e. to content or matter, conceived as existing apart from all formal relations, the formal elements cannot possibly be sensational. The legitimacy of that limitation is, however, the question at issue. It cannot be thus decided by an arbitrary verbal distinction.

“Were the contention that the relations of sensations are not themselves sensed correct, the inference to the pure apriority of the form of our perception would be inevitable. For sensation is the sole form of interaction between consciousness and reality.... But that contention is false. The relations of sensations, their determined coexistence and sequence, impress consciousness, just as do the sensations. We feel this impression in the compulsion which the determinateness of the empirical manifolds lays upon the perceiving consciousness. The mere affection of consciousness by these relations does not, indeed, by itself suffice for their apprehension; but neither does it suffice for the apprehension of the sensation itself. Thus there is in these respects no difference between the matter and the form of appearance.”[389]

In this way, then, by means of his definition of sensation, Kant surreptitiously introduces his fundamental assumption. That assumption reappears as the conclusion that since the form of appearance cannot be sensation, it does not arise through the action of the object, and consequently must be a priori. Though the paragraph seems to offer an argument in support of the apriority of space and time, it is found on examination merely to unfold a position adopted without the slightest attempt at proof.[390]

=The form of appearance must lie ready in the mind.=[391]--Comment upon this, in order to be adequate, had best take the form of a systematic discussion of Kant’s views, here and elsewhere, of space as an a priori form of intuition. As already stated, the definition which Kant gives of intuition--as knowledge which stands in immediate relation to objects--applies only to empirical intuition. Though by the term object Kant, in so far as he is definite, means content, that content is such as can arise only through the action of some independent object upon the sensibility. In other words, the content apprehended must be sensuous. Now such a view of intuition obviously does not apply to pure intuition. As the concluding line of the paragraph before us states, pure intuition “can be contemplated in separation from all sensation;” and as the next paragraph adds, it exists in the mind “without any actual object of the senses.” Yet Kant does not mean to imply that it is without content of any kind. “This pure form of sensibility may also itself be called pure intuition.”[392] “It can be known before all actual perception, and for that reason is called pure intuition.”[393] Though, therefore, pure intuition has an intrinsic content, and is the immediate apprehension of that content, it stands in no relation to any actual independent object. The content as well as the form is a priori. That, however, raises wider questions, and these we must now discuss.

Here, as in most of his fundamental positions, Kant entertains divergent and mutually contradictory doctrines. Only in his later utterances does he in any degree commit himself to one consistent view. The position to which he finally inclines must not, however, be allowed to dominate the interpretation of his earlier statements. The Aesthetic calls for its own separate exegesis, quite as if it formed by itself an independent work. Its problems are discussed from a standpoint more or less peculiar to itself. The commentator has the twofold task of stating its argumentation both in its conflict with, and in its relation to, the other parts of the Critique.

One essential difference between Kant’s earlier and later treatments of space is that in his earlier utterances it is viewed almost exclusively as a psychological a priori. The logical aspect of the problem first receives anything like adequate recognition in the Analytic. If we keep this important fact in mind, two distinct and contradictory views of the psychological nature of space intuition can be traced throughout the Aesthetic. On one view, it antedates experience as an actual, completed, conscious intuition. On the other view, it precedes experience only as a potential disposition. We rule ourselves out from understanding Kant’s most explicit utterances if we refuse to recognise the existence of both views. Kant’s commentators have too frequently shut their eyes to the first view, and have then blamed Kant for using misleading expressions. It is always safer to take Kant quite literally. He nearly always means exactly what he says at the time when he says it. Frequently he holds views which run completely counter to present-day psychology, and on several occasions he flatly contradicts what he has with equal emphasis maintained in other contexts. The aspects of Kant’s problems are so complex and various, and he is so preoccupied in doing complete justice to each in turn, that the question of the mutual consistency of his results is much less considered than is ideally desirable.

The two views can be more explicitly formulated. The first view alone is straightforward and unambiguous. Space lies ready (liegt bereit) in the mind, i.e. it does not arise. Prior even to sense-experience it exists as a conscious intuition. For this reason it can be contemplated apart from all sensation. It still remains when all sense content is thought away, and yet is not a mere form. In independence of the sensuous manifold it possesses a pure manifold of its own. The ground thesis of the second view--that space, prior to sense-experience, exists only as a permanent endowment of the mind--is likewise unambiguous. But in its development Kant throws consistency to the winds. The possible ways in which, on the second view, consciousness of space may be gained, can be tabulated as follows:

(a) By reflection upon the activity of the mind in the construction of experience, yielding the intuition of a pure manifold; or (b) by reflection upon the space-endowed products of experience.[394] The latter mode of reflection may reveal:

(α) A pure manifold distinct from the manifold of sense; or

(β) Space as a form of the sensuous manifold.

There are thus three different ways (a, α, β) in which the second view can be developed: (a) represents the view of the Dissertation (1770), of the reply to Eberhard (1790), and of those parts of the first edition’s deduction of the categories which are of very early origin; (α) represents the final standpoint of the Analytic; (β), the prevailing view of the present day, is nowhere accepted by Kant.[395]

Kant’s utterances in the Aesthetic are all of them coloured by the first main view. We can best approach them by way of the contrasted teaching of the Dissertation of 1770. The teaching there formulated practically coincides, as above stated, with (a) of the second main view. Space, he maintains, is neither innate nor acquired from sense-experience.

“Certainly both conceptions [of time and of space] are undoubtedly acquired, not indeed by abstraction from our sensations of objects (for sensation gives the matter, not the form of human cognition), but from the mind’s own action in co-ordinating its sensations in accordance with unchanging laws. Each represents, as it were, an immutable type, and so can be known intuitively. Sensations excite this act of mind but do not contribute to the intuition. There is here nothing innate except this law of the mind according to which it conjoins in a certain manner the sensations derived from the presence of some object.”[396]

How this view is to be reconciled with the contention, no less explicitly maintained,[397] that space is not only a form of intuition but itself a pure intuition, Kant does not make clear. Reflection upon an activity of the mind may yield the representation of space as a form; it is difficult to comprehend how it should also yield an a priori content.

Kant nowhere in the Critique directly discusses the question whether the representation of space is innate or acquired. Such suggestions as occur refer (with the solitary exceptions of A 196 = B 241 and B 166 ff.)[398] only to the categories,[399] or as in the Prolegomena[400] to the Ideas of reason. But in 1790 Kant in his reply to Eberhard[401] again formulates the view of the Dissertation. The Critique allows, he there says, of no innate representations. All, without exception, are acquired. But of certain representations there is an original acquisition (ursprüngliche Erwerbung). Their ground (Grund) is inborn. In the case of space this ground is the mind’s peculiar capacity for acquiring sensations in accordance with its subjective constitution.[402]

“This first formal ground is alone inborn, not the space representation itself. For it always requires impressions to determine the faculty of knowledge to the representation of an object (which in every case is its own action). Thus arises the formal intuition, which we name space, as an originally acquired representation (the form of outer objects in general), the ground of which (as mere receptivity) is likewise inborn, and the acquisition of which long antedates the determinate conception of things which are in accordance with this form.”[403]

That last remark is confusing. Kant cannot mean that the representation of space is acquired prior to sense-experience, but only that since the mind gains it by reflection upon its own activity, it is among the first things to be apprehended--an extremely questionable assertion, could the premisses be granted. If “the determinate conception of things” comes late, still later must come the determinate conception of anything so abstract as pure space. The above passage thus repeats without essential modification the teaching of the Dissertation, and is open to the same objections. This teaching coincides with that of Leibniz in his Nouveaux Essais; and in formulating it in the Dissertation Kant was very probably influenced by Leibniz. Though it is an improvement upon the more extreme forms of the Cartesian doctrine of innate ideas, it does not go sufficiently far.

Now while Kant thus in 1770 and in 1790 so emphatically teaches that the representation of space is not innate, he none the less, in the intermediate period represented by the Aesthetic, would seem to maintain the reactionary view. Space is no mere potential disposition. As a conscious representation it lies ready in the mind. What, then, were the causes which constrained Kant to go back upon his own better views and to adopt so retrograde a position? The answer must be conjectural, but may perhaps be found in the other main point in which the teaching of the Aesthetic is distinguished from that of the Dissertation. Throughout the Critique Kant insists that space is a form of receptivity. It is given to the mind. It has nothing to do with spontaneity or understanding, and therefore cannot be acquired by reflection upon any activity of the mind. But neither can it, as a priori, be acquired from without. Consequently it cannot be acquired at all. But if given, and yet not acquired, it must as a representation lie ready in the mind from the very birth of consciousness. Constrained by such reasoning, Kant views it as given in all its completeness just as truly as is a sensation of colour or sound. This conclusion may not be satisfactory. Kant’s candid recognition of it is, however, greatly preferable to the blurring of the issue by most of his commentators.

Kant came, no doubt, to the more consistent position of the Aesthetic chiefly through further reflection upon the arguments of the Dissertation,[404] and especially by recognition of the fact that though reflection upon an activity of the mind may be regarded as yielding a form of intuition, it can hardly be capable of yielding a pure manifold which can be substituted for, and take the place of, the manifold of sense. There are for Kant only two ways of escape from this unhappy quandary: (a) Either he must return to the Dissertation position, and admit that the mind is active in the construction of space. This he does in the 1790 reply to Eberhard, but only by misrepresenting his own teaching in the Critique. In order consistently to maintain that space is acquired by reflection upon an activity of the mind, he would have to recast the entire Aesthetic, as well as much of the Analytic, and to do so in ways which cannot genuinely harmonise with the main tendencies of his teaching.[405] (b) No such obstacle lay in the way of an alternative modification of his position. Kant might very easily have given up the contention that space is a pure intuition. If he had been willing to recognise that the sole possible manifold of intuition is sensuous, he could then have maintained that though space is innate as a potential form of receptivity, it is acquired only through reflection upon the space-endowed products of sensibility. So obvious are the advantages of this position, so completely does it harmonise with the facts of experience and with the teaching of modern psychology, and so obscure are the various passages in which Kant touches on this central issue, that many of his most competent commentators are prepared to regard it as being the actual teaching of the Critique. The evidence[406] seems to me, however, to refute this interpretation of Kant’s position. The traditional, Cartesian, semi-mystical worship of mathematical truth, as altogether independent of the contingencies of sense-experience, and as a body of knowledge absolutely distinct in origin from the merely empirical sciences, influences Kant’s thinking even at the very moment when he is maintaining, in opposition to the Cartesians, that its subject matter is a merely subjective intuition. Kant, as it would seem, still maintains that there is a pure manifold of intuition distinct from the manifold of sense; and so by the inevitable logic of his thought is constrained to view space as innate in conscious form. This is not, of course, a conclusion which he could permanently stand by, but its elimination would have involved a more radical revision of his whole view of pure intuition and of mathematical science than he was willing to undertake. Though in the Analytic he has come to recognise[407] that it is acquired by reflection upon objects, to the end he would seem to persist in the difficult contention that such reflection yields a pure manifold distinct from the manifold of sense.[408] His belief that mathematical science is based upon pure intuition prevented him from recognising that though space may be a pure form of intuition, it can never by itself constitute a complete intuition. Its sole possible content is the manifold of sense. But even apart from the fact that our apprehension of space is always empirically conditioned, Kant’s view of mathematical propositions as grounded in intuition is, as already observed, not itself tenable. For though intuitions may perhaps be the ultimate subject matter of geometry, concepts are its sole possible instruments. Intuitions yield scientific insight in exact proportion to our powers of restating their complex content in the terms of abstract thought. Until the evidence which they supply has been thus intellectually tested and defined, they cannot be accepted as justifying even the simplest proposition.[409]

The complicated ambiguities of Kant’s treatment of space may be illustrated and further clarified by discussion of another difficulty. Is space a totum analyticum or a totum syntheticum? Does the whole precondition the parts, or does it arise through combination of the parts? Or to ask another but connected question, do we intuit infinitude, or is it conceptually apprehended only as the presupposition of our limited intuitions? To these questions diametrically opposite answers can be cited from the Critique. As we have above noted, Kant teaches in the Aesthetic that space is given as a whole, and that the parts arise only by limitation of it. But in A 162 = B 203 we find him also teaching that a magnitude is to be entitled 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.”[410]

He adds in the second edition[411] that extensive magnitude cannot be apprehended save through a “synthesis of the manifold,” a “combination of the homogeneous.”

The note which Kant appends to B 136 is a very strange combination of both views. It first of all reaffirms the doctrine of the Aesthetic that space and time are not concepts, but intuitions within which as in a unity a multitude of representations are contained; and then proceeds to argue that space and time, as thus composite, must presuppose an antecedent synthesis. In A 505 = B 533 we find a similar attempt to combine both assertions.

“The parts of a given appearance are first given through and in the regress of decomposing synthesis (decomponirenden Synthesis).”

The clash of conflicting tenets which Kant is striving to reconcile could hardly find more fitting expression than in this assertion of an analytic synthesis. The same conflict appears, though in a less violent form, in A 438 = B 466.

“Space should properly be called not compositum but totum, since its parts are possible only in the whole, not the whole through the parts. It might, indeed, be said to be a compositum that is ideale, but not reale. That, however, is a mere subtlety.”[412]

The arguments by which Kant proves space to be an a priori intuition rest upon the view that space is given as infinite, and that its parts arise through limitation of this prior-existent whole. But a principle absolutely fundamental to the entire Critique is the counter principle, that all analysis rests upon and presupposes a previously exercised synthesis. Synthesis or totality as such can never be given. Only in so far as a whole is synthetically constructed can it be apprehended by the mind. Representation of the parts precedes and renders possible representation of the whole.

The solution of the dilemma arising out of these diverse views demands the drawing of two distinctions. First, between a synthesised totality and a principle of synthesis; the former may involve a prior synthesis; the latter does not depend upon synthesis, but expresses the predetermined nature of some special form of synthesis. Secondly, it demands a distinction between the a priori manifolds of space and time and the empirical manifold which is apprehended in and through them. This, as we have already noted, is a distinction difficult to take quite seriously, and is entirely unsupported by psychological evidence. But it would seem to be insisted upon by Kant, and to have been a determining factor in the formulation of several of his main doctrines.

In terms of the first distinction we are compelled to recognise that the view of space which underlies the Aesthetic is out of harmony with the teaching of the Analytic. In the Aesthetic Kant interprets space not merely as a form of intuition but also as a formal intuition, which is given complete in its totality, and which is capable of being apprehended independently of its empirical contents, and even prior to them. That would seem to be the view of space which is presupposed in Kant’s explanation of pure mathematical science. The passages from the Analytic, quoted above, are, however, its express recantation. Space, as the intuition of a manifold, is a totum syntheticum, not a totum analyticum. It is constructed, not given. The divergence of views between the Aesthetic and the Analytic springs out of the difficulty of meeting at once the logical demands of a world which Kant conceives objectively, and the psychological demands which arise when this same world is conceived as subjectively conditioned. In principle, the whole precedes the parts; in the process of being brought into existence as an intuition, the parts precede the whole. The principle which determines our apprehension of any space, however small or however large, is that it exists in and through universal space. This is the principle which underlies both the synthetic construction of space and also its apprehension once it is constructed. In principle, therefore, i.e. in the order of logical thought, the whole precedes the parts.[413] The process, however, which this principle governs and directs, cannot start with space as a whole, but must advance to it through synthesis of smaller parts.

But Kant does not himself recognise any conflict between this teaching and the doctrine of the Aesthetic. He seems to himself merely to be making more definite a position which he has consistently held all along; and this was possible owing to his retention and more efficient formulation of the second of the two distinctions mentioned above, viz. that between the manifold of sense and the manifold of intuition. This distinction enables him to graft the new view upon the old, and so in the very act of insisting upon the indispensableness of the conceptual syntheses of understanding, none the less to maintain his view of geometry as an intuitive science.[414]

“Space and time contain a manifold of pure a priori intuition, but at the same time are conditions of the receptivity of our mind--conditions under which alone it can receive representations of objects, and which therefore must also affect the concept of them. But if this manifold is to be known, the spontaneity of our thinking requires that it be gone through in a certain way, taken up, and connected. This action I name synthesis.... Such a synthesis is pure, if the manifold is not empirical, but is given a priori, as is that of space and of time.”[415]

Thus Kant recognises that space, as apprehended by us, is constructed, not given, and so by implication that the infinitude of space is a principle of apprehension, not a given intuition. But he also holds to the view that it contains a pure, and presumably infinite, manifold, given as such.[416] In what this pure manifold consists, and how the description of it as a manifold, demanding synthesis for its apprehension, is to be reconciled with its continuity, Kant nowhere even attempts to explain. Nor does he show what the simple elements are from which the synthesis of apprehension and reproduction in pure intuition might start. The unity and multiplicity of space are, indeed, as he himself recognises,[417] inseparably involved in one another; and recognition of this fact must render it extremely difficult to assign them to separate faculties. For the same reason it is impossible to distinguish temporally, as Kant so frequently does, the processes of synthesis and of analysis, making the former in all cases precede the latter in time. The very nature of space and time, and, as he came to recognise, the very nature of all Ideas of reason, in so far as they involve the notion of the unconditioned, conflict with such a view.

Even when Kant is dealing with space as a principle of synthesis, he speaks with no very certain voice. In the Analytic it is ascribed to the co-operation of sensibility and understanding. In the Dialectic it is, by implication, ascribed to Reason; and in the Metaphysical First Principles it is explicitly so ascribed.

“Absolute space cannot be object of experience; for space without matter is no object of perception, and yet it is a necessary conception of Reason, and therefore nothing but a mere Idea.”[418] “Absolute space is not necessary as a conception of an actual object, but as an Idea which can serve as rule....”[419]

Kant’s teaching in the Critique of Judgment is a further development of this position.

“The mind listens to the voice of Reason which, for every given magnitude--even for those that can never be entirely apprehended, although (in sensible representation) they are judged as entirely given--requires totality.... It does not even except the infinite (space and past time) from this requirement; on the contrary, it renders it unavoidable to think the infinite (in the judgment of common reason) as entirely given (in its totality). But the infinite is absolutely (not merely comparatively) great. Compared with it everything else (of the same kind of magnitudes) is small. But what is most important is that the mere ability to think it as a whole indicates a faculty of mind which surpasses every standard of sense.... The bare capability of thinking the given infinite without contradiction requires in the human mind a faculty itself supersensible. For it is only by means of this faculty and its Idea of a noumenon ... that the infinite of the world of sense, in the pure intellectual estimation of magnitude, can be completely comprehended under one concept.... Nature is, therefore, sublime in those of its phenomena, whose intuition brings with it the Idea of its infinity.... For just as imagination and understanding, in judging of the beautiful, generate a subjective purposiveness of the mental powers by means of their harmony, so imagination and Reason do so by means of their conflict.”[420]

Kant has here departed very far indeed from the position of the Aesthetic.[421]

THE TRANSCENDENTAL AESTHETIC

SECTION I

SPACE

METAPHYSICAL EXPOSITION OF THE CONCEPTION OF SPACE[422]

=Space: First Argument.=--“Space is not an empirical concept (Begriff) which has been abstracted from outer experiences. For in order that certain sensations be related to something outside me (i.e. to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside [and alongside][423] one another, and accordingly as not only [qualitatively] different but as in different places, the representation of space must be presupposed (muss schon zum Grunde liegen). The representation of space cannot, therefore, be empirically obtained at second-hand from the relations of outer appearance. This outer experience is itself possible at all only through that representation.”[424]

The first sentence states the thesis of the argument: space is not an empirical concept abstracted from outer experiences. The use of the term Begriff in the title of the section, and also in this sentence, is an instance of the looseness with which Kant employs his terms. It is here synonymous with the term representation (Vorstellung), which covers intuitions as well as general or discursive concepts. Consequently, the contradiction is only verbal, not real, when Kant proceeds to prove that the concept of space is an intuition, not a concept. But this double employment of the term is none the less misleading. When Kant employs it in a strict sense, it signifies solely the general class concept.[425] All true concepts are for Kant of that single type. He has not re-defined the term concept in any manner which would render it applicable to the relational categories. For unfortunately, and very strangely, he never seems to have raised the question whether categories are not also concepts. The application to the forms of understanding of the separate title categories seems to have contented him. Much that is obscure and even contradictory in his teaching might have been prevented had he recognised that the term concept is a generic title which includes, as its sub-species, both general notions and relational categories.

Kant’s limitation of the term concept to the merely generic,[426] and his consequent equating of the categorical proposition with the assertion of the substance-attribute relation,[427] would seem in large part to be traceable to his desire to preserve for himself, in the pioneer labours of his Critical enquiries, the guiding clues of the distinctions drawn in the traditional logic. Kant insists on holding to them, at least in outward appearance, at whatever sacrifice of strict consistency. Critical doctrine is made to conform to the exigencies of an artificial framework, with which its own tenets are only in very imperfect harmony. Appreciation of the ramifying influence, and, as regards the detail of exposition, of the far-reaching consequences, of this desire to conform to the time-honoured rubrics, is indeed an indispensable preliminary to any adequate estimate whether of the strength or of the defects of the Critical doctrines. As a separate and ever-present influence in the determining of Kant’s teaching, this factor may conveniently and compendiously be entitled Kant’s logical architectonic.[428] We shall have frequent occasion to observe its effects.[429]

The second sentence gives expression to the fact through which Kant proves his thesis. Certain sensations, those of the special senses as distinguished from the organic sensations,[430] are related to something which stands in a different region of space from the embodied self, and consequently are apprehended as differing from one another not only in quality but also in spatial position. As is proved later in the Analytic, thought plays an indispensable part in constituting this reference of sensations to objects. Kant here, however, makes no mention of this further complication. He postulates, as he may legitimately do at this stage, the fact that our sensations are thus objectively interpreted, and limits his enquiry to the spatial factor. Now the argument, as Vaihinger justly points out,[431] hinges upon the assumption which Kant has already embodied[432] in his definition of the “form” of sense, viz. that sensations are non-spatial, purely qualitative. Though this is an assumption of which Kant nowhere attempts to give proof, it serves none the less as an unquestioned premiss from which he draws all-important conclusions. This first argument on space derives its force entirely from it.

The proof that the representation of space is non-empirical may therefore be explicitly stated as follows. As sensations are non-spatial and differ only qualitatively, the representation of space must have been added to them. And not being supplied by the given sensations, it must, as the only alternative, have been contributed by the mind. The representation of space, so far from being derived from external experience, is what first renders it possible. As a subjective form that lies ready in the mind, it precedes experience and co-operates in generating it. This proof of the apriority of space is thus proof of the priority of the representation of space to every empirical perception.

In thus interpreting Kant’s argument as proving more than the thesis of the first sentence claims, we are certainly reading into the proof more than Kant has himself given full expression to. But, as is clearly shown by the argument of the next section, we are only stating what Kant actually takes the argument as having proved, namely, that the representation of space is not only non-empirical but is likewise of subjective origin and precedes experience in temporal fashion.

The point of view which underlies and inspires the argument can be defined even more precisely. Kant’s conclusion may be interpreted in either of two ways. The form of space may precede experience only as a potentiality. Existing as a power of co-ordination,[433] it will come to consciousness only indirectly through the addition which it makes to the given sensations. Though subjective in origin, it will be revealed to the mind only in and through experience. This view may indeed be reconciled with the terms of the proof. But a strictly literal interpretation of its actual wording is more in keeping with what, as we shall find, is the general trend of the Aesthetic as a whole. We are then confronted by a very different and extremely paradoxical view, which may well seem too naive to be accepted by the modern reader, but which we seem forced,[434] none the less, to regard as the view actually presented in the text before us. Kant here asserts, in the most explicit manner, that the mind, in order to construe sensations in spatial terms, must already be in possession of a representation of space, and that it is in the light of this representation that it apprehends sensations. The conscious representation of space precedes in time external experience. Such, then, would seem to be Kant’s first argument on space. It seeks to establish a negative conclusion, viz. that space is not derived from experience. But, in so doing, it also yields a positive psychological explanation of its origin.

Those commentators[435] who refuse to recognise that Kant’s problem is in any degree psychological, or that Kant himself so regards it, and who consequently seek to interpret the Aesthetic from the point of view of certain portions of the Analytic, give a very different statement of this first argument. They state it in purely logical terms.[436] Its problem, they claim, is not that of determining the origin of our representation of space, but only its logical relation to our specific sense-experiences. The notion of space in general precedes, as an indispensable logical presupposition, all particular specification of the space relation. Consciousness of space as a whole is not constructed from consciousness of partial spaces; on the contrary, the latter is only possible in and through the former.

Such an argument does of course represent a valuable truth; and it alone harmonises with much in Kant’s maturer teaching;[437] but we must not therefore conclude that it is also the teaching of the Aesthetic. The Critique contains too great a variety of tendencies, too rich a complexity of issues, to allow of such simplification. It loses more than it gains by such rigorous pruning of the luxuriant secondary tendencies of its exposition and thought. And above all, this procedure involves the adoption by the commentator of impossible responsibilities, those of deciding what is essential and valuable in Kant’s thought and what is irrelevant. The value and suggestiveness of Kant’s philosophy largely consist in his sincere appreciation of conflicting tendencies, and in his persistent attempt to reduce them to unity with the least possible sacrifice. But in any case the logical interpretation misrepresents this particular argument. Kant is not here distinguishing between space in general and its specific modifications. He is maintaining that no space relation can be revealed in sensation. It is not only that the apprehension of any limited space presupposes the representation of space as a whole. Both partial and infinite space are of mental origin; sensation, as such, is non-spatial, purely subjective. And lastly, the fact that Kant means to assert that space is not only logically presupposed but is subjectively generated, is sufficiently borne out by his frequent employment elsewhere in the Aesthetic of such phrases as “the subjective condition of sensibility,” “lying ready in our minds,” and “necessarily preceding [as the form of the subject’s receptivity] all intuitions of objects.”

=Second Argument.=--Having proved by the first argument that the representation of space is not of empirical origin, Kant in the second argument proceeds to establish the positive conclusion that it is a priori.[438] The proof, when all its assumptions are rendered explicit, runs as follows. Thesis: Space is a necessary representation, and consequently is a priori. Proof: It is impossible to imagine the absence of space, though it is possible to imagine it as existing without objects to fill it. A representation which it is impossible for the mind to be without is a necessary representation. But necessity is one of the two criteria of the a priori. The proof of the necessary character of space is therefore also a proof of its being a priori.

The argument, more freely stated, is that what is empirically given from without can be thought away, and that since space cannot be thus eliminated, it must be grounded in our subjective organisation, i.e. must be psychologically a priori. The argument, as stated by Kant, emphasises the apriority, not the subjectivity, of space, but none the less the asserted apriority is psychological, not logical in character. For the criterion employed is not the impossibility of thinking otherwise, but our incapacity to represent this specific element as absent. The ground upon which the whole argument is made to rest is the merely brute fact (asserted by Kant) of our incapacity to think except in terms of space.

The argument is, however, complicated by the drawing of a further consequence, which follows as a corollary from the main conclusion. From the subjective necessity of space follows its objective necessity. Space being necessary a priori, objects can only be apprehended in and through it. Consequently it is not dependent upon the objects apprehended, but itself underlies outer appearances as the condition of their possibility. This corollary is closely akin to the first argument on space, and differs from it only in orientation. The first argument has a psychological purpose. It maintains that the representation of space precedes external experience, causally conditioning it. The corollary has a more objective aim. It concludes that space is a necessary constituent of the external experience thus generated. The one proves that space is a necessary subjective antecedent; the other that it is a necessary objective ingredient.[439]

To consider the proof in detail. The exact words which Kant employs in stating the nervus probandi of the argument are that we can never represent (eine Vorstellung davon machen) space as non-existent, though we can very well think (denken) it as being empty of objects. The terms Vorstellung and denken are vague and misleading. Kant himself recognises that it is possible to conceive that there are beings who intuit objects in some other manner than in space. He cannot therefore mean that we are unable to think or conceive space as non-existent. He must mean that we cannot in imagination intuit it as absent. It is the necessary form of all our intuitions, and therefore also of imagination, which is intuitive in character. Our consciousness is dependent upon given intuitions for its whole content, and to that extent space is a form with which the mind can never by any possibility dispense. Pure thought enables it to realise this de facto limitation, but not to break free from it. Even in admitting the possibility of other beings who are not thus constituted, the mind still recognises its own ineluctable limitations.

Kant offers no proof of his assertion that space can be intuited in image as empty of all sensible content; and as a matter of fact the assertion is false. Doubtless the use of the vague term Vorstellung is in great part responsible for Kant’s mistaken position. So long as imagination and thought are not clearly distinguished, the assertion is correspondingly indefinite. Pure space may possibly be conceived, but it can also be conceived as altogether non-existent. If, on the other hand, our imaginative power is alone in question, the asserted fact must be categorically denied. With the elimination of all sensible content space itself ceases to be a possible image. Kant’s proof thus rests upon a misstatement of fact.

In a second respect Kant’s proof is open to criticism. He takes the impossibility of imagining space as absent as proof that it originates from within. The argument is valid only if no other psychological explanation can be given of this necessity, as for instance through indissoluble association or through its being an invariable element in the given sensations. Kant’s ignoring of these possibilities is due to his unquestioning belief that sensations are non-spatial, purely qualitative. That is a presupposition whose truth is necessary to the cogency of the argument.

=Third Argument.=--This argument, which was omitted in the second edition, will be considered in its connection with the transcendental exposition into which it was then merged.

=Fourth (in second edition, Third) Argument.=--The next two arguments seek to show that space is not a discursive or general concept but an intuition. The first proof falls into two parts, (a) We can represent only a single space. For though we speak of many spaces, we mean only parts of one and the same single space. Space must therefore be an intuition. For only intuition is thus directly related to a single individual. A concept always refers indirectly, per notas communes, to a plurality of individuals. (b) The parts of space cannot precede the one all-comprehensive space. They can be thought only in and through it. They arise through limitation of it. Now the parts (i.e. the attributes) which compose a concept precede it in thought. Through combination of them the concept is formed. Space cannot, therefore, be a concept. Consequently it must, as the only remaining alternative, be an intuition. Only in an intuition does the whole precede the parts. In a concept the parts always precede the whole. Intuition stands for multiplicity in unity, conception for unity in multiplicity.

The first part of the argument refers to the extension, the second part to the intension of the space representation. In both aspects it appears as intuitional.[440]

Kant, in repeating his thesis as a conclusion from the above grounds, confuses the reader by an addition which is not strictly relevant to the argument, viz. by the statement that this intuition must be non-empirical and a priori. This is simply a recapitulation of what has been established in the preceding proofs. It is not, as might at first sight appear, part of the conclusion established by the argument under consideration. The reader is the more apt to be misled owing to the fact that very obviously arguments for the non-empirical and for the a priori character of space can be derived from proof (b). That space is non-empirical would follow from the fact that representation of space as a whole is necessary for the apprehension of any part of it. Empirical intuition can only yield the apprehension of a limited space. The apprehension of the comprehensive space within which it falls must therefore be non-empirical.

“As we intuitively apprehend (anschauend erkennen) not only the space of the object which affects our senses, but the whole space, space cannot arise out of the actual affection of the senses, but must precede it in time (vor ihr vorhergehen).”[441]

But in spite of its forcibleness this argument is nowhere presented in the Critique.

Similarly, in so far as particular spaces can be conceived only in and through space as a whole, and in so far as the former are limitations of the one antecedent space, the intuition which underlies all external perception must be a priori. This is in essentials a stronger and more cogent mode of formulating the second argument on space. But again, and very strangely, it is nowhere employed by Kant in this form.

The concluding sentence, ambiguously introduced by the words so werden auch, is tacked on to the preceding argument. Interpreted in the light of § 15 C of the Dissertation,[442] and of the corresponding fourth[443] argument[444] on time, it may be taken as offering further proof that space is an intuition. The concepts of line and triangle, however attentively contemplated, will never reveal the proposition that in every triangle two sides taken together are greater than the third. An a priori intuition will alone account for such apodictic knowledge. This concluding sentence thus really belongs to the transcendental exposition; and as such ought, like the third argument, to have been omitted in the second edition.

Kant’s proof rests on the assumption that there are only two kinds of representation, intuitions and concepts, and also in equal degree upon the further assumption that all concepts are of one and the same type.[445] Intuition is, for Kant, the apprehension of an individual. Conception is always the representation of a class or genus. Intuition is immediately related to the individual. Conception is reflective or discursive; it apprehends a plurality of objects indirectly through the representation of those marks which are common to them all.[446] Intuition and conception having been defined in this manner, the proof that space is single or individual, and that in it the whole precedes the parts, is proof conclusive that it is an intuition, not a conception. Owing, however, to the narrowness of the field assigned to conception, the realm occupied by intuition is proportionately wide, and the conclusion is not as definite and as important as might at first sight appear. By itself, it amounts merely to the statement, which no one need challenge, that space is not a generic class concept. Incidentally certain unique characteristics of space are, indeed, forcibly illustrated; but the implied conclusion that space on account of these characteristics must belong to receptivity, not to understanding, does not by any means follow. It has not, for instance, been proved that space and time are radically distinct from the categories, i.e. from the relational forms of understanding.

In 1770, while Kant still held to the metaphysical validity of the pure forms of thought, the many difficulties which result from the ascription of independent reality to space and time were, doubtless, a sufficient reason for regarding the latter as subjective and sensuous. But upon adoption of the Critical standpoint such argument is no longer valid. If all our forms of thought may be subjective, the existence of antinomies has no real bearing upon the question whether space and time do or do not have a different constitution and a different mental origin from the categories. The antinomies, that is to say, may perhaps suffice to prove that space and time are subjective; they certainly do not establish their sensuous character.

But though persistence of the older, un-Critical opposition between the intellectual and the sensuous was partly responsible for Kant’s readiness to regard as radical the very obvious differences between a category such as that of substance and attribute and the visual or tactual extendedness with which objects are endowed, it can hardly be viewed as the really decisive influence. That would rather seem to be traceable to Kant’s conviction that mathematical knowledge is unique both in fruitfulness and in certainty, and to his further belief that it owes this distinction to the content character of the a priori forms upon which it rests. For though the categories of the physical sciences are likewise a priori, they are exclusively relational,[447] and serve only to organise a material that is empirically given. To account for the superiority of mathematical knowledge Kant accordingly felt constrained to regard space and time as not merely forms in terms of which we interpret the matter of sense, but as also themselves intuited objects, and as therefore possessing a character altogether different from anything which can be ascribed to the pure understanding. The opposition between forms of sense and categories of the understanding, in the strict Kantian mode of envisaging that opposition, is thus inseparably bound up with Kant’s doctrine of space and time as being not only forms of intuition, but as also in their purity and independence themselves intuitions. Even the sensuous subject matter of pure mathematics--so Kant would seem to contend--is a priori in nature. If this latter view be questioned--and to the modern reader it is indeed a stone of stumbling--much of the teaching of the Aesthetic will have to be modified or at least restated.

=Fifth (in second edition, Fourth) Argument.=--This argument is quite differently stated in the two editions of the Critique, though the purpose of the argument is again in both cases to prove that space is an intuition, not a general concept. In the first edition this is proved by reference to the fact that space is given as an infinite magnitude. This characteristic of our space representation cannot be accounted for so long as it is regarded as a concept. A general conception of space which would abstract out those properties and relations which are common to all spaces, to a foot as well as to an ell, could not possibly determine anything in regard to magnitude. For since spaces differ in magnitude, any one magnitude cannot be a common quality. Space is, however, given us as determined in magnitude, namely, as being of infinite magnitude; and if a general conception of space relations cannot determine magnitude, still less can it determine infinite magnitude. Such infinity must be derived from limitlessness in the progression of intuition. Our conceptual representations of infinite magnitude must be derivative products, acquired from this intuitive source.

In the argument of the second edition the thesis is again established by reference to the infinity of space. But in all other respects the argument differs from that of the first edition. A general conception, which abstracts out common qualities from a plurality of particulars, contains an infinite number of possible different representations under it; but it cannot be thought as containing an infinite number of representations in it. Space must, however, be thought in this latter manner, for it contains an infinite number of coexisting parts.[448] Since, then, space cannot be a concept, it must be an intuition.

The definiteness of this conclusion is somewhat obscured by the further characterisation of the intuition of space as a priori, and by the statement that it is the original (ursprüngliche) representation which is of this intuitive nature. The first addition must here, again, just as in the fourth argument, be regarded as merely a recapitulation of what has already been established, not a conclusion from the present argument. The introduction of the word ‘original’ seems to be part of Kant’s reply to the objections which had already been made to his admission in the first edition that there is a conception as well as an intuition of space. It is the original given intuition of space which renders such reflective conception possible.

The chief difficulty of these proofs arises out of the assertion which they seem to involve that space is given as actually infinite. There are apparently, on this point, two views in Kant, which were retained up to the very last, and which are closely connected with his two representations of space, on the one hand as a formal intuition given in its purity and in its completeness, and on the other hand as the form of intuition, which exists only so far as it is constructed, and which is dependent for its content upon given matter.

=Third Argument, and Transcendental Exposition of Space.=--The distinction between the metaphysical and the transcendental expositions, introduced in the second edition of the Critique,[449] is one which Kant seems to have first made clear to himself in the process of writing the Prolegomena.[450] It is a genuine improvement, marking an important distinction. It separates out two comparatively independent lines of argument. The terms in which the distinction is stated are not, however, felicitous. Kant’s reason for adopting the title metaphysical is indicated in the Prolegomena:[451]

“As concerns the sources of metaphysical cognition, its very concept implies that they cannot be empirical.... For it must not be physical but metaphysical knowledge, i.e. knowledge lying beyond experience.... It is therefore a priori knowledge, coming from pure understanding and pure Reason.”

The metaphysical exposition, it would therefore seem, is so entitled because it professes to prove that space is a priori, not empirical, and to do so by analysis of its concept.[452] Now by Kant’s own definition of the term transcendental, as the theory of the a priori, this exposition might equally well have been named the transcendental exposition. In any case it is an essential and chief part of the Transcendental Aesthetic. Such division of the Transcendental Aesthetic into a metaphysical and a transcendental part involves a twofold use, wider and narrower, of one and the same term. Only as descriptive of the whole Aesthetic is transcendental employed in the sense defined.

Exposition (Erörterung, Lat. expositio) is Kant’s substitute for the more ordinary term definition. Definition is the term which we should naturally have expected; but as Kant holds that no =given= concept, whether a priori or empirical, can be defined in the strict sense,[453] the substitutes the term exposition, using it to signify such definition of the nature of space as is possible to us. To complete the parallelism Kant speaks of the transcendental enquiry as also an exposition. It is, however, in no sense a definition. Kant’s terms here, as so often elsewhere, are employed in a more or less arbitrary and extremely inexact manner.

The distinction between the two expositions is taken by Kant as follows. The metaphysical exposition determines the nature of the concept of space, and shows it to be a given a priori intuition. The transcendental exposition shows how space, when viewed in this manner, renders comprehensible the possibility of synthetic a priori knowledge.

The omission of the third argument on space from the second edition, and its incorporation into the new transcendental exposition, is certainly an improvement. In its location in the first edition, it breaks in upon the continuity of Kant’s argument without in any way contributing to the further definition of the concept of space. Also, in emphasising that mathematical knowledge depends upon the construction of concepts,[454] Kant presupposes that space is intuitional; and that has not yet been established.

The argument follows the strict, rigorous, synthetic method. From the already demonstrated a priori character of space, Kant deduces the apodictic certainty of all geometrical principles. But though the paragraph thus expounds a consequence that follows from the a priori character of space, not an argument in support of it, something in the nature of an argument is none the less implied. The fact that this view of the representation of space alone renders mathematical science possible can be taken as confirming this interpretation of its nature. Such an argument, though circular, is none the less cogent. Consideration of Kant’s further statements, that were space known in a merely empirical manner we could not be sure that in all cases only one straight line is possible between two points, or that space will always be found to have three dimensions, must meantime be deferred.[455]

In the new transcendental exposition Kant adopts the analytic method of the Prolegomena, and accordingly presents his argument in independence of the results already established. He starts from the assumption of the admitted validity of geometry, as being a body of synthetic a priori knowledge. Yet this, as we have already noted, does not invalidate the argument; in both the first and the last paragraphs it is implied that the a priori and intuitive characteristics of space have already been proved. From the synthetic character of geometrical propositions Kant argues[456] that space must be an intuition. Through pure concepts no synthetic knowledge is possible. Then from the apodictic character of geometry he infers that space exists in us as pure and a priori;[457] no experience can ever reveal necessity. But geometry also exists as an applied science; and to account for our power of anticipating experience, we must view space as existing only in the perceiving subject as the form of its sensibility. If it precedes objects as the necessary subjective condition of their apprehension, we can to that extent predetermine the conditions of their existence.

In the concluding paragraph Kant says that this is the only explanation which can be given of the possibility of geometry. He does not distinguish between pure and applied geometry, though the proof which he has given of each differs in a fundamental respect. Pure geometry presupposes only that space is an a priori intuition; applied geometry demands that space be conceived as the a priori form of external sense. Only in reference to applied geometry does the Critical problem arise:--viz. how we can form synthetic judgments a priori which yet are valid of objects; or, in other words, how judgments based upon a subjective form can be objectively valid. But any attempt, at this point, to define the nature and possibility of applied geometry must anticipate a result which is first established in Conclusion b.[458] Though, therefore, the substitution of this transcendental exposition for the third space argument is a decided improvement, Kant, in extending it so as to cover applied as well as pure mathematics, overlooks the real sequence of his argument in the first edition. The employment of the analytic method, breaking in, as it does, upon the synthetic development of Kant’s original argument, is a further irregularity.[459]

It may be noted that in the third paragraph Kant takes the fact that geometry can be applied to objects as proof of the subjectivity of space.[460] He refuses to recognise the possibility that space may be subjective as a form of receptivity, and yet also be a mode in which things in themselves exist. This, as regards its conclusion, though not as regards its argument, is therefore an anticipation of Conclusion a. In the last paragraph Kant is probably referring to the views both of Leibniz and of Berkeley.

CONCLUSIONS FROM THE ABOVE CONCEPTS[461]

=Conclusion a.=--Thesis: Space is not a property of things in themselves,[462] nor a relation of them to one another. Proof: The properties of things in themselves can never be intuited prior to their existence, i.e. a priori. Space, as already proved, is intuited in this manner. In other words, the apriority of space is by itself sufficient proof of its subjectivity.

This argument has been the subject of a prolonged controversy between Trendelenburg and Kuno Fischer.[463] Trendelenburg was able to prove his main point, namely, that the above argument is quite inconclusive. Kant recognises only two alternatives, either space as objective is known a posteriori, or being an a priori representation it is subjective in origin. There exists a third alternative, namely, that though our intuition of space is subjective in origin, space is itself an inherent property of things in themselves. The central thesis of the rationalist philosophy of the Enlightenment was, indeed, that the independently real can be known by a priori thinking. Even granting the validity of Kant’s later conclusion, first drawn in the next paragraph, that space is the subjective form of all external intuition, that would only prove that it does not belong to appearances, prior to our apprehension of them; nothing is thereby proved in regard to the character of things in themselves. We anticipate by a priori reasoning only the nature of appearances, never the constitution of things in themselves. Therefore space, even though a priori, may belong to the independently real. The above argument cannot prove the given thesis.

Vaihinger contends[464] that the reason why Kant does not even attempt to argue in support of the principle, that the a priori must be purely subjective, is that he accepts it as self-evident. This explanation does not, however, seem satisfactory. But Vaihinger supplies the data for modification of his own assertion. It was, it would seem, the existence of the antinomies which first and chiefly led Kant to assert the subjectivity of space and time.[465] For as he then believed that a satisfactory solution of the antinomies is possible only on the assumption of the subjectivity of space and time, he regarded their subjectivity as being conclusively established, and accordingly failed to examine with sufficient care the validity of his additional proof from their apriority. This would seem to be confirmed by the fact that when later,[466] in reply to criticisms of the arguments of the first edition, he so far modified his position as to offer reasons in support of the above general principle, even then he nowhere discussed the principle in reference to the forms of sense. All his discussions concern only the possible independent reality of the forms of thought.[467] To the very last Kant would seem to have regarded the above argument as an independent, and by itself a sufficient, proof of the subjectivity of space.

The refutation of Trendelenburg’s argument which is offered by Caird[468] is inconclusive. Caird assumes the chief point at issue, first by ignoring the possibility that space may be known a priori in reference to appearances and yet at the same time be transcendently real; and secondly by ignoring the fact that to deny spatial properties to things in themselves is as great a violation of Critical principles as to assert them. One point, however, in Caird’s reply to Trendelenburg calls for special consideration, viz. Caird’s contention that Kant did actually take account of the third alternative, rejecting it as involving the “absurd” hypothesis of a pre-established harmony.[469] Undoubtedly Kant did so. But the contention has no relevancy to the point before us. The doctrine of pre-established harmony is a metaphysical theory which presupposes the possibility of gaining knowledge of things in themselves. For that reason alone Kant was bound to reject it. A metaphysical proof of the validity of metaphysical judgments is, from the Critical point of view, a contradiction in terms. As the validity of all speculations is in doubt, a proof which is speculative cannot meet our difficulties. And also, as Kant himself further points out, the pre-established harmony, even if granted, can afford no solution of the Critical problem how a priori judgments can be passed upon the independently real. The judgments, thus guaranteed, could only possess de facto validity; we could never be assured of their necessity.[470] It is chiefly in these two inabilities that Kant locates the “absurdity” of a theory of pre-established harmony. The refutation of that theory does not, therefore, amount to a disproof of the possibility which we are here considering.

=Conclusion b.=--The next paragraph maintains two theses: (a) that space is the form of all outer intuition; (b) that this fact explains what is otherwise entirely inexplicable and paradoxical, namely, that we can make a priori judgments which yet apply to the objects experienced. The first thesis, that the pure intuition of space is only conceivable as the form of appearances of outer sense, is propounded in the opening sentence without argument and even without citation of grounds. The statement thus suddenly made is not anticipated save by the opening sentences of the section on space.[471] It is an essentially new doctrine. Hitherto Kant has spoken of space only as an a priori intuition. The further assertion that as such it must necessarily be conceived as the form of outer sense (i.e. not only as a formal intuition but also as a form of intuition), calls for the most definite and explicit proof. None, however, is given. It is really a conclusion from points all too briefly cited by Kant in the general Introduction, namely, from his distinction between the matter and the form of sense. The assertions there made, in a somewhat casual manner, are here, without notification to the reader, employed as premisses to ground the above assertion. His thesis is not, therefore, as by its face value it would seem to profess to be, an inference from the points established in the preceding expositions. It interprets these conclusions in the light of points considered in the Introduction; and thereby arrives at a new and all-important interpretation of the nature of the a priori intuition of space.

The second thesis employs the first to explain how prior to all experience we can determine the relations of objects. Since (a) space is merely the form of outer sense, and (b) accordingly exists in the mind prior to all empirical intuition, all appearances must exist in space, and we can predetermine them from the pure intuition of space that is given to us a priori. Space, when thus viewed as the a priori form of outer sense, renders comprehensible the validity of applied mathematics.

As we have already noted,[472] Kant in the second edition obscures the sequence of his argument by offering in the new transcendental exposition a justification of applied as well as of pure geometry. In so doing he anticipates the conclusion which is first drawn in this later paragraph. This would have been avoided had Kant given two separate transcendental expositions. First, an exposition of pure mathematics, placed immediately after the metaphysical exposition; for pure mathematics is exclusively based upon the results of the metaphysical exposition. And secondly, an exposition of applied mathematics, introduced after Conclusion b. The explanation of applied geometry is really the more essential and central of the two, as it alone involves the truly Critical problem, how judgments formed a priori can yet apply to objects. Conclusion b constitutes, as Vaihinger rightly insists,[473] the very heart of the Aesthetic. The arrangement of Kant’s argument diverts the reader’s attention from where it ought properly to centre.

The use which Kant makes of the Prolegomena in his statement of the new transcendental exposition is one cause of the confusion. The exposition is a brief summary of the corresponding Prolegomena[474] sections. In introducing this summary into the Critique Kant overlooked the fact that in referring to applied mathematics he is anticipating a point first established in Conclusion b. The real cause, however, of the trouble is common to both editions, namely Kant’s failure clearly to appreciate the fundamental distinction between the view that space is an a priori intuition and the view that it is the a priori form of all external intuition, i.e. of outer sense. He does not seem to have fully realised how very different are those two views. In consequence of this he fails to distinguish between the transcendental expositions of pure and applied geometry.[475]

=Third paragraph.=--Kant proceeds to develop the subjectivist conclusions which follow from a and b.

“We may say that space contains all things which can appear to us externally, but not all things in themselves, whether intuited or not, nor again all things intuited by any and every subject.”[476]

This sentence makes two assertions: (a) space does not belong to things in and by themselves; (b) space is not a necessary form of intuition for all subjects whatsoever.

The grounds for the former assertion are not here considered, and that is doubtless the reason why the oder nicht is excised in Kant’s private copy of the Critique. As we have seen, Kant does not anywhere in the Aesthetic even attempt to offer argument in support of this assertion. In defence of (a) Kant propounds for the first time the view of sensibility as a limitation. Space is a limiting condition to which human intuition is subject. Whether the intuitions of other thinking beings are subject to the same limitation, we have no means of deciding. But for all human beings, Kant implies, the same conditions must hold universally.[477]

In the phrase “transcendental ideality of space”[478] Kant, it may be noted, takes the term ideality as signifying subjectivity, and the term transcendental as equivalent to transcendent. He is stating that judged from a transcendent point of view, i.e. from the point of view of the thing in itself, space has a merely subjective or “empirical” reality. This is an instance of Kant’s careless use of the term transcendental. Space is empirically real, but taken transcendently, is merely ideal.[479]

KANT’S ATTITUDE TO THE PROBLEMS OF MODERN GEOMETRY

This is an appropriate point at which to consider the consistency of Kant’s teaching with modern developments in geometry. Kant’s attitude has very frequently been misrepresented. As he here states, he is willing to recognise that the forms of intuition possessed by other races of finite beings may not coincide with those of the human species. But in so doing he does not mean to assert the possibility of other spatial forms, i.e. of spaces that are non-Euclidean. In his pre-Critical period Kant had indeed attempted to deduce the three-dimensional character of space as a consequence of the law of gravitation; and recognising that that law is in itself arbitrary, he concluded that God might, by establishing different relations of gravitation, have given rise to spaces of different properties and dimensions.

“A science of all these possible kinds of space would undoubtedly be the highest enterprise which a finite understanding could undertake in the field of geometry.”[480]

But from the time of Kant’s adoption, in 1770, of the Critical view of space as being the universal form of our outer sense, he seems to have definitely rejected all such possibilities. Space, to be space at all, must be Euclidean; the uniformity of space is a presupposition of the a priori certainty of geometrical science.[481] One of the criticisms which in the Dissertation[482] he passes upon the empirical view of mathematical science is that it would leave open the possibility that “a space may some time be discovered endowed with other fundamental properties, or even perhaps that we may happen upon a two-sided rectilinear figure.” This is the argument which reappears in the third argument on space in the first edition of the Critique.[483] The same examples are employed with a somewhat different wording.

“It would not even be necessary that there should be only one straight line between two points, though experience invariably shows this to be so. What is derived from experience has only comparative universality, namely, that which is obtained through induction. We should therefore only be able to say that, so far as hitherto observed, no space has been found which has more than three dimensions.”

But that Kant should have failed to recognise the possibility of other spaces does not by itself point to any serious defect in his position. There is no essential difficulty in reconciling the recognition of such spaces with his fundamental teaching. He admits that other races of finite beings may perhaps intuit through non-spatial forms of sensibility; he might quite well have recognised that those other forms of intuition, though not Euclidean, are still spatial. It is in another and more vital respect that Kant’s teaching lies open to criticism. Kant is convinced that space is given to us in intuition as being definitely and irrevocably Euclidean in character. Both our intuition and our thinking, when we reflect upon space, are, he implies, bound down to, and limited by, the conditions of Euclidean space. And it is in this positive assumption, and not merely in his ignoring of the possibility of other spaces, that he comes into conflict with the teaching of modern geometry. For in making the above assumption Kant is asserting that we definitely know physical space to be three-dimensional, and that by no elaboration of concepts can we so remodel it in thought that the axiom of parallels will cease to hold. Euclidean space, Kant implies, is given to us as an unyielding form that rigidly resists all attempts at conceptual reconstruction. Being quite independent of thought and being given as complete, it has no inchoate plasticity of which thought might take advantage. The modern geometer is not, however, prepared to admit that intuitional space has any definiteness or preciseness of nature apart from the concepts through which it is apprehended; and he therefore allows, as at least possible, that upon clarification of our concepts space may be discovered to be radically different from what it at first sight appears to be. In any case, the perfecting of the concepts must have some effect upon their object. But even--as the modern geometer further maintains--should our space be definitely proved, upon analytic and empirical investigation, to be Euclidean in character, other possibilities will still remain open for speculative thought. For though the nature of our intuitional data may constrain us to interpret them through one set of concepts rather than through another, the competing sets of alternative concepts will represent genuine possibilities beyond what the actual is found to embody.

Thus the defect of Kant’s teaching, in regard to space, as judged in the light of the later teaching of geometrical science, is closely bound up with his untenable isolation of the a priori of sensibility from the a priori of understanding.[484] Space, being thus viewed as independent of thought, has to be regarded as limiting and restricting thought by the unalterable nature of its initial presentation. And unfortunately this is a position which Kant continued to hold, despite his increasing recognition of the part which concepts must play in the various mathematical sciences. In the deduction of the first edition we find him stating that synthesis of apprehension is necessary to all representation of space and time.[485] He further recognises that all arithmetical processes are syntheses according to concepts.[486] And in the Prolegomena[487] there occurs the following significant passage.

“Do these laws of nature lie in space, and does the understanding learn them by merely endeavouring to find out the fruitful meaning that lies in space; or do they inhere in the understanding and in the way in which it determines space according to the conditions of the synthetical unity towards which its concepts are all directed? Space is something so uniform and as to all particular properties so indeterminate, that we should certainly not seek a store of laws of nature in it. That which determines space to the form of a circle or to the figures of a cone or a sphere, is, on the contrary, the understanding, so far as it contains the ground of the unity of these constructions. The mere universal form of intuition, called space, must therefore be the substratum of all intuitions determinable to particular objects, and in it, of course, the condition of the possibility and of the variety of these intuitions lies. But the unity of the objects is solely determined by the understanding, and indeed in accordance with conditions which are proper to the nature of the understanding....”

Obviously Kant is being driven by the spontaneous development of his own thinking towards a position much more consistent with present-day teaching, and completely at variance with the hard and fast severance between sensibility and understanding which he had formulated in the Dissertation and has retained in the Aesthetic. In the above Prolegomena passage a plasticity is being allowed to space, sufficient to permit of essential modification in the conceptual processes through which it is articulated. But, as I have just stated, that did not lead Kant to disavow the conclusions which he had drawn from his previous teaching.

This defect in Kant’s doctrine of space, as expounded in the Aesthetic, indicates a further imperfection in his argument. He asserts that the form of space cannot vary from one human being to another, and that for this reason the judgments which express it are universally valid. Now, in so far as Kant’s initial datum is consciousness of time,[488] he is entirely justified in assuming that everything which can be shown to be a necessary condition of such consciousness must be uniform for all human minds. But as his argument is not that consciousness of Euclidean space is necessary to consciousness of time, but only that consciousness of the permanent in space is a required condition, he has not succeeded in showing the necessary uniformity of the human mind as regards the specific mode in which it intuits space. The permanent might still be apprehended as permanent, and therefore as yielding a possible basis for consciousness of sequence, even if it were apprehended in some four-dimensional form.

* * * * *

=Fourth Paragraph.=--The next paragraph raises one of the central problems of the Critique, namely, the question as to the kind of reality possessed by appearances. Are they subjective, like taste or colour? Or have they a reality at least relatively independent of the individual percipient? In other words, is Kant’s position subjectivism or phenomenalism? Kant here alternates between these positions. This fourth paragraph is coloured by his phenomenalism, whereas in the immediately following fifth paragraph his subjectivism gains the upper hand. The taste of wine, he there states, is purely subjective, because dependent upon the particular constitution of the gustatory organ on which the wine acts. Similarly, colours are not properties of the objects which cause them.

“They are only modifications of the sense of sight which is affected in a certain manner by the light.... They are connected with the appearances only as effects accidentally added by the particular constitution of the sense organs.”[489]

Space, on the other hand, is a necessary constituent of the outer objects. In contrast to the subjective sensations of taste and colour, it possesses objectivity. This mode of distinguishing between space and the matter of sense implies that extended objects are not mere ideas, but are sufficiently independent to be capable of acting upon the sense organs, and of thereby generating the sensations of the secondary qualities.

Kant, it must be observed, refers only to taste and colour. He says nothing in regard to weight, impenetrability, and the like. These are revealed through sensation, and therefore on his view ought to be in exactly the same position as taste or colour. But if so, the relative independence of the extended object can hardly be maintained. Kant’s distinction between space and the sense qualities cannot, indeed, be made to coincide with the Cartesian distinction between primary and secondary qualities.

A second difference, from Kant’s point of view, between space and the sense qualities is that the former can be represented a priori, in complete separation from everything empirical, whereas the latter can only be known a posteriori. This, as we have seen, is a very questionable assertion. The further statement that all determinations of space can be represented in the same a priori fashion is even more questionable. At most the difference is only between a homogeneous subjective form yielded by outer sense and the endlessly varied and consequently unpredictable contents revealed by the special senses. The contention that the former can be known apart from the latter implies the existence of a pure manifold additional to the manifold of sense.

=Fifth Paragraph.=--In the next paragraph Kant emphasises the distinction between the empirical and the transcendental meanings of the term appearance. A rose, viewed empirically, as a thing with an intrinsic independent nature, may appear of different colour to different observers.

“The transcendental conception of appearances in space, on the other hand, is a Critical reminder that nothing intuited in space is a thing in itself, that space is not a form inhering in things in themselves ... and that what we call outer objects are nothing but mere representations of our sensibility, the form of which is space.”

In other words, the distinction drawn in the preceding paragraph between colour as a subjective effect and space as an objective existence is no longer maintained. Kant, when thus developing his position on subjectivist lines, allows no kind of independent existence to anything in the known world. Objects as known are mere Ideas (blosse Vorstellungen unserer Sinnlichkeit), the sole correlate of which is the unknowable thing in itself. But even in this paragraph both tendencies find expression. “Colour, taste, etc., must not rightly be regarded as properties of things, but only as changes in the subject.” This implies a threefold distinction between subjective sensations, empirical objects in space, and the thing in itself. The material world, investigated by science, is recognised as possessing a relatively independent mode of existence.

=Substituted Fourth Paragraph of second edition.=--In preparing the second edition Kant himself evidently felt the awkwardness of this abrupt juxtaposition of the two very different points of view; and he accordingly adopts a non-committal attitude, substituting a logical distinction for the ontological. Space yields synthetic judgments a priori; the sense qualities do not. Only in the concluding sentence does there emerge any definite phenomenalist implication. The sense qualities, “as they are mere sensations and not intuitions, in themselves reveal no object, least of all [an object] a priori.”[490] The assertion that the secondary qualities have no ideality implies a new and stricter use of the term ideal than we find anywhere in the first edition--a use which runs counter to Kant’s own constant employment of the term. On this interpretation it is made to signify what though subjective is also a priori. Here, as in many of the alterations of the second edition, Kant is influenced by the desire to emphasise the points which distinguish his idealism from that of Berkeley.

THE TRANSCENDENTAL AESTHETIC

SECTION II

TIME

METAPHYSICAL EXPOSITION OF THE CONCEPTION OF TIME

=Time: First Argument.=--This argument is in all respects the same as the first argument on space. The thesis is that the representation[491] of time is not of empirical origin. The proof is based on the fact that this representation must be previously given in order that the perception of coexistence or succession be possible. It also runs on all fours with the first argument in the Dissertation.

“The idea of time does not originate in, but is presupposed by the senses. When a number of things act upon the senses, it is only by means of the idea of time that they can be represented whether as simultaneous or as successive. Nor does succession generate the conception of time; but stimulates us to form it. Thus the notion of time, even if acquired through experience, is very badly defined as being a series of actual things existing one after another. For I can understand what the word after signifies only if I already know what time means. For those things are after one another which exist at different times, as those are simultaneous which exist at one and the same time.”[492]

=Second Argument.=--Kant again applies to time the argument already employed by him in dealing with space. The thesis is that time is given a priori. Proof is found in the fact that it cannot be thought away, i.e. in the fact of its subjective necessity. From this subjective necessity follows its objective necessity, so far as all appearances are concerned. In the second edition Kant added a phrase--“as the general condition of their possibility”--which is seriously misleading. The concluding sentence is thereby made to read as if Kant were arguing from the objective necessity of time, i.e. from its necessity as a constituent in the appearances apprehended, to its apriority. It is indeed possible that Kant himself regarded this objective necessity of time as contributing to the proof of its apriority. But no such argument can be accepted. Time may be necessary to appearances, once appearances are granted. This does not, however, prove that it must therefore precede them a priori. This alteration in the second edition is an excellent, though unfortunate, example of Kant’s invincible carelessness in the exposition of his thought. It has contributed to a misreading by Herbart and others of this and of the corresponding argument on space.

“Let us not talk of an absolute space as the presupposition of all our constructed figures. Possibility is nothing but thought, and it arises only when it is thought. Space is nothing but possibility, for it contains nothing save images of the existent; and absolute space is nothing save the abstracted general possibility of such constructions, abstracted from it after completion of the construction. The necessity of the representation of space ought never to have played any rôle in philosophy. To think away space is to think away the possibility of that which has been previously posited as actual. Obviously that is impossible, and the opposite is necessary.”[493]

Were Kant really arguing here and in the second argument on space solely from the objective necessity of time and space, this criticism would be unanswerable. But even taking the argument in its first edition form, as an argument from the psychological necessity of time, it lies open to the same objection as the argument on space. It rests upon a false statement of fact. We cannot retain time in the absence of all appearances of outer and inner sense. With the removal of the given manifold, time itself must vanish.

=Fourth Argument.=[494]--This argument differs only slightly, and mainly through omissions,[495] from the fourth[496] of the arguments in regard to space; but a few minor points call for notice. (a) In the first sentence, instead of intuition, which alone is under consideration in its contrast to conception, Kant employs the phrase “pure form of intuition.” (b) In the third sentence Kant uses the quite untenable phrase “given through a single object (Gegenstand).” Time is not given from without, nor is it due to an object. (c) The concluding sentences properly belong to the transcendental exposition. They are here introduced, not in the ambiguous manner of the fourth[1] argument on space, but explicitly as a further argument in proof of the intuitive character of time. The synthetic proposition which Kant cites is taken neither from the science of motion nor from arithmetic. It expresses the nature of time itself, and for that reason is immediately contained in the intuition of time.

=Fifth Argument.=--This argument differs fundamentally from the corresponding argument on space, whether of the first or of the second edition, and must therefore be independently analysed. The thesis is again that time is an intuition. Proof is derived from the fact that time is a representation in which the parts arise only through limitation, and in which, therefore, the whole must precede the parts. The original (ursprüngliche) time-representation, i.e. the fundamental representation through limitation of which the parts arise as secondary products, must be an intuition.

To this argument Kant makes two explanatory additions. (a) As particular times arise through limitation of one single time, time must in its original intuition be given as infinite, i.e. as unlimited. The infinitude of time is not, therefore, as might seem to be implied by the prominence given to it, and by analogy with the final arguments of both the first and the second edition, a part of the proof that it is an intuition, but only a consequence of the feature by which its intuitive character is independently established. The unwary reader, having in mind the corresponding argument on space, is almost inevitably misled. All reference to infinitude could, so far as this argument is concerned, have been omitted. The mode in which the argument opens seems indeed to indicate that Kant was not himself altogether clear as to the cross-relations between the arguments on space and time respectively. The real parallel to this argument is to be found in the second part of the fourth[1] argument on space. That part was omitted by Kant in his fourth argument on time, and is here developed into a separate argument. This is, of course, a further cause of confusion to the reader, who is not prepared for such arbitrary rearrangement. Indeed it is not surprising to find that when Kant became the reader of his own work, in preparing it for the second edition, he was himself misled by the intricate perversity of his exposition. In re-reading the argument he seems to have forgotten that it represents the second part of the fourth[497] argument on space. Interpreting it in the light of the fifth[498] argument on space which he had been recasting for the second edition, it seemed to him possible, by a slight alteration, to bring this argument on time into line with that new proof.[499] This unfortunately results in the perverting of the entire paragraph. The argument demands an opposition between intuition in which the whole precedes the parts, and conception in which the parts precede the whole. In order to bring the opposition into line with the new argument on space, according to which a conception contains an infinite number of parts, not in it, but only under it, Kant substitutes for the previous parenthesis the statement that “concepts contain only partial representations,” meaning, apparently, that their constituent elements are merely abstracted attributes, not real concrete parts, or in other words, not strictly parts at all, but only partial representations. But this does not at all agree with the context. The point at issue is thereby obscured.

(b) The main argument rests upon and presupposes a very definite view as to the manner in which alone, according to Kant, concepts are formed. Only if this view be granted as true of all concepts without exception is the argument cogent. This doctrine[500] of the concept is accordingly stated by Kant in the words of the parenthesis. The partial representations, i.e. the different properties which go to constitute the object or content conceived, precede the representation of the whole. “The aggregation of co-ordinate attributes (Merkmale) constitutes the totality of the concept.”[501] Upon the use which Kant thus makes of the traditional doctrine of the concept, and upon its lack of consistency with his recognition of relational categories, we have already dwelt.[502]

=Third Argument and the Transcendental Exposition.=--The third argument ought to have been omitted in the second edition, and its substance incorporated in the new transcendental exposition, as was done with the corresponding argument concerning space. The excuse which Kant offers for not making the change, namely, his desire for brevity, is not valid. By insertion in the new section the whole matter could have been stated just as briefly as before.

The purpose of the transcendental exposition has been already defined. It is to show how time, when viewed in the manner required by the results of the metaphysical deduction, as an a priori intuition, renders synthetic a priori judgments possible.

This exposition, as it appears in the third argument of the first edition, grounds the apodictic character of two axioms in regard to time[503] on the proved apriority of the representation of time, and then by implication finds in these axioms a fresh proof of the apriority of time.

The new transcendental exposition extends the above by two further statements: (a) that only through the intuition of time can any conception of change, and therewith of motion (as change of place), be formed; and (b) that it is because the intuition of time is an a priori intuition that the synthetic a priori propositions of the “general doctrine of motion” are possible. To take each in turn. (a) Save by reference to time the conception of motion is self-contradictory. It involves the ascription to one and the same thing of contradictory predicates, e.g. that an object both is and is not in a certain place. From this fact, that time makes possible what is not possible in pure conception, Kant, in his earlier rationalistic period, had derived a proof of the subjectivity of time.[504] (b) In 1786 in the Metaphysical First Principles of Natural Science Kant had developed the fundamental principles of the general science of motion. He takes the opportunity of the second edition (1787) of the Critique to assign this place to them in his general system. The implication is that the doctrine of motion stands to time in the relation in which geometry stands to space. Kant is probably here replying, as Vaihinger has suggested,[505] to an objection made by Garve to the first edition, that no science, corresponding to geometry, is based on the intuition of time. For two reasons, however, the analogy between mechanics and geometry breaks down. In the first place, the conception of motion is empirical; and in the second place, it presupposes space as well as time.[506]

Kant elsewhere explicitly disavows this view that the science of motion is based on time. He had already done so in the preceding year (1786) in the Metaphysical First Principles. He there points out[507] that as time has only one dimension, mathematics is not applicable to the phenomena of inner sense. At most we can determine in regard to them (in addition, of course, to the two axioms already cited) only the law that all these changes are continuous. Also in Kant’s Ueber Philosophie überhaupt (written some time between 1780 and 1790, and very probably in or about the year 1789) we find the following utterance:

“The general doctrine of time, unlike the pure doctrine of space (geometry), does not yield sufficient material for a whole science.”[508]

Why, then, should Kant in 1787 have so inconsistently departed from his own teaching? This is a question to which I can find no answer. Apparently without reason, and contrary to his more abiding judgment, he here repeats the suggestion which he had casually thrown out in the Dissertation[509] of 1770:

“Pure mathematics treats of space in geometry and of time in pure mechanics.”

But in the Dissertation the point is only touched upon in passing. The context permits of the interpretation that while geometry deals with space, mechanics deals with time in addition to space.

KANT’S VIEWS REGARDING THE NATURE OF ARITHMETICAL SCIENCE

In the Dissertation, and again in the chapter on Schematism in the Critique itself, still another view is suggested, namely, that the science of arithmetic is also concerned with the intuition of time. The passage just quoted from the Dissertation proceeds as follows:

“Pure mathematics treats of space in geometry and of time in pure mechanics. To these has to be added a certain concept which is in itself intellectual, but which demands for its concrete actualisation (actuatio) the auxiliary notions of time and space (in the successive addition and in the juxtaposition of a plurality). This is the concept of number which is dealt with in Arithmetic.”[510]

This view of arithmetic is to be found in both editions of the Critique. Arithmetic depends upon the synthetic activity of the understanding; the conceptual element is absolutely essential.

“Our counting (as is easily seen in the case of large numbers) is a synthesis according to concepts, because it is executed according to a common ground of unity, as, for instance, the decade (Dekadik).”[511] “The pure image ... of all objects of the senses in general is time. But the pure schema of quantity, in so far as it is a concept of the understanding, is number, a representation which combines the successive addition of one to one (homogeneous). Thus number is nothing but the unity of the synthesis of the manifold of a homogeneous intuition in general, whereby I generate time itself in the apprehension of the intuition.”[512]

This is also the teaching of the Methodology.[513] Now it may be observed that in none of these passages is arithmetic declared to be the science of time, or even to be based on the intuition of time. In 1783, however, in the Prolegomena, Kant expresses himself in much more ambiguous terms, for his words imply that there is a parallelism between geometry and arithmetic.

“Geometry is based upon the pure intuition of space. Arithmetic produces its concepts of number through successive addition of units in time, and pure mechanics especially can produce its concepts of motion only by means of the representation of time.”[514]

The passage is by no means explicit; the “especially” (vornehmlich) seems to indicate a feeling on Kant’s part that the description which he is giving of arithmetic is not really satisfactory. Unfortunately this casual statement, though never repeated by Kant in any of his other writings, was developed by Schulze in his Erläuterungen.

“Since geometry has space and arithmetic has counting as its object (and counting can only take place by means of time), it is evident in what manner geometry and arithmetic, that is to say pure mathematics, is possible.”[515]

Largely, as it would seem,[516] through Schulze, whose Erläuterungen did much to spread Kant’s teaching, this view came to be the current understanding of Kant’s position. The nature of arithmetic, as thus popularly interpreted, is expounded by Schopenhauer in the following terms:

“In time every moment is conditioned by the preceding. The ground of existence, as law of the sequence, is thus simple, because time has only one dimension, and no manifoldness of relations can be possible in it. Every moment is conditioned by the preceding; only through the latter can we attain to the former; only because the latter was, and has elapsed, does the former now exist. All counting rests upon this nexus of the parts of time; its words merely serve to mark the single steps of the succession. This is true of the whole of arithmetic, which throughout teaches nothing but the methodical abbreviations of counting. Every number presupposes the preceding numbers as grounds of its existence; I can only reach them through all the preceding, and only by means of this insight into the ground of its existence do I know that, where ten are, there are also eight, six, four.”[517]

Schulze was at once challenged to show that this was really Kant’s teaching, and the passage which he cited was Kant’s definition of the schema of number, above quoted.[518] It is therefore advisable that we should briefly discuss the many difficulties which this passage involves. What does Kant mean by asserting that in the apprehension of number we generate time? Does he merely mean that time is required for the process of counting? Counting is a process through which numerical relations are discovered; and it undoubtedly occupies time. But so do all processes of apprehension, in the study of geometry no less than of arithmetic. That this is not Kant’s meaning, and that it is not even what Schulze, notwithstanding his seemingly explicit mode of statement, intends to assert, is clearly shown by a letter written by Kant to Schulze in November 1788. Schulze, it appears, had spoken of this very matter.

“Time, as you justly remark, has no influence upon the properties of numbers (as pure determinations of quantity), such as it may have upon the nature of those changes (of quantity) which are possible only in connection with a specific property of inner sense and its form (time). The science of number, notwithstanding the succession which every construction of quantity demands, is a pure intellectual synthesis which we represent to ourselves in thought. But so far as quanta are to be numerically determined, they must be given to us in such a way that we can apprehend their intuition in successive order, and such that their apprehension can be subject to time....”[519]

No more definite statement could be desired of the fact that though in arithmetical science as in other fields of study our processes of apprehension are subject to time, the quantitative relations determined by the science are independent of time and are intellectually apprehended.

But if the above psychological interpretation of Kant’s teaching is untenable, how is his position to be defined? We must bear in mind the doctrine which Kant had already developed in his pre-Critical period, that mathematical differs from philosophical knowledge in that its concepts can have concrete individual form.[520] In the Critique this difference is expressed in the statement that the mathematical sciences alone are able to construct their concepts. And as they are pure mathematical sciences, this construction is supposed to take place by means of the a priori manifold of space and of time. Now though Kant had a fairly definite notion of what he meant by the construction of geometrical figures in space, his various utterances seem to show that in regard to the nature of arithmetical and algebraic construction he had never really attempted to arrive at any precision of view. To judge by the passage already quoted[521] from the Dissertation, Kant regarded space as no less necessary than time to the construction or intuition of number. ”[The intellectual concept of number] demands for its concrete actualisation the auxiliary notions of time and space (in the successive addition and in the juxtaposition of a plurality)” A similar view appears in the Critique in A 140 = B 179 and in B 15. In conformity, however, with the general requirements of his doctrine of Schematism, Kant defines the schema of number in exclusive reference to time; and, as we have noted, it is to this definition that Schulze appeals in support of his view of arithmetic as the science of counting and therefore of time. It at least shows that Kant perceived some form of connection to exist between arithmetic and time. But in this matter Kant’s position was probably simply a corollary from his general view of the nature of mathematical science, and in particular of his view of geometry, the “exemplar”[522] of all the others. Mathematical science, as such, is based on intuition;[523] therefore arithmetic, which is one of its departments, must be so likewise. No attempt, however, is made to define the nature of the intuitions in which it has its source. Sympathetically interpreted, his statements may be taken as suggesting that arithmetic is the study of series which find concrete expression in the order of sequent times. The following estimate, given by Cassirer,[524] does ample justice both to the true and to the false elements in Kant’s doctrine.

”[Even discounting Kant’s insistence upon the conceptual character of arithmetical science, and] allowing that he derives arithmetical concepts and propositions from the pure intuition of time, this teaching, to whatever objections it may lie open, has certainly not the merely psychological meaning which the majority of its critics have ascribed to it. If it contained only the trivial thought, that the empirical act of counting requires time, it would be completely refuted by the familiar objection which B. Beneke has formulated: ‘The fact that time elapses in the process of counting can prove nothing; for what is there over which time does not flow?’ It is easily seen that Kant is only concerned with the ‘transcendental’ determination of the concept of time, according to which it appears as the type of an ordered sequence. William [Rowan] Hamilton, who adopts Kant’s doctrine, has defined algebra as ‘science of pure time or order in progression.’ That the whole content of arithmetical concepts can really be obtained from the fundamental concept of order in unbroken development, is completely confirmed by Russell’s exposition. As against the Kantian theory it must, of course, be emphasised, that it is not the concrete form of time intuition which constitutes the ground of the concept of number, but that on the contrary the pure logical concepts of sequence and of order are already implicitly contained and embodied in that concrete form.”

Much of the unsatisfactoriness of Kant’s argument is traceable to his mode of conceiving the “construction”[525] of mathematical concepts. All concepts, he seems to hold, even those of geometry and arithmetic, are abstract class concepts--the concept of triangle representing the properties common to all triangles, and the concept of seven the properties common to all groups that are seven. Mathematical concepts differ, however, from other concepts in that they are capable of a priori construction, that is, of having their objects represented in pure intuition. Now this is an extremely unfortunate mode of statement. It implies that mathematical concepts have a dual mode of existence, first as abstracted, and secondly as constructed. Such a position is not tenable. The concept of seven, in its primary form, is not abstracted from a variety of particular groups of seven; it is already involved in the apprehension of each of them as being seven. Nor is it a concept that is itself constructed. It may perhaps be described as being the representation of something constructed; but that something is not itself. It represents the process or method generative of the complex for which it stands. Thus Kant’s distinction between the intuitive nature of mathematical knowledge and the merely discursive character of conceptual knowledge is at once inspired by the very important distinction between the product of construction and the product of abstraction, and yet at the same time is also obscured by the quite inadequate manner in which that latter distinction has been formulated. Kant has again adhered to the older logic even in the very act of revising its conclusions; and in so doing he has sacrificed the Critical doctrines of the Analytic to the pre-Critical teaching of the Dissertation and Aesthetic. Mathematical concepts are of the same general type as the categories; their primary function is not to clarify intuitions, but to make them possible. They are derivable from intuition only in so far as they have contributed to its constitution. If intuition contains factors additional to the concepts through which it is interpreted, these factors must remain outside the realm of mathematical science, until such time as conceptual analysis has proved itself capable of further extension.

I may now summarise this general discussion. Though Kant in the first edition of the Critique had spoken of the mathematical sciences as based upon the intuition of space and time, he had not, despite his constant tendency to conceive space and time as parallel forms of existence, based any separate mathematical discipline upon time. His definition of number, in the chapter on Schematism, had recognised the essentially conceptual character of arithmetic, and had connected it with time only in a quite indirect manner. A passage in the Prolegomena is the one place in all Kant’s writings in which he would seem to assert, though in brief and quite indefinite terms, that arithmetic is related to time as geometry is related to space. No such view of arithmetic is to be found in the second edition of the Critique. In the transcendental exposition of time, added in the second edition, only pure mechanics is mentioned. This would seem to indicate that Kant had made the above statement carelessly, without due thought, and that on further reflection he found himself unable to stand by it. The omission is the more significant in that Kant refers to arithmetic in the passages added in the second edition Introduction. The teaching of these passages, apart from the asserted necessity of appealing to fingers or points,[526] harmonises with the view so briefly outlined in the Analytic. Arithmetic is a conceptual science; though it finds in ordered sequence its intuitional material, it cannot be adequately defined as being the science of time.

CONCLUSIONS FROM THE PRECEDING CONCEPTS[527]

These Conclusions do not run parallel with the corresponding Conclusions in regard to space. In the first paragraph there are two differences. (a) Kant takes account of a view not considered under space, viz. that time is a self-existing substance. He rejects it on a ground which is difficult to reconcile with his recognition of a manifold of intuition as well as a manifold of sense, namely that it would then be something real without being a real object. In A 39 = B 57 and B 70 Kant describes space and time, so conceived, as unendliche Undinge. (b) Kant introduces into his first Conclusion the argument[528] that only by conceiving time as the form of inner intuition can we justify a priori synthetic judgments in regard to objects.

=Second Paragraph (Conclusion b).=--This latter statement is repeated at the opening of the second Conclusion. The emphasis is no longer, however, upon the term “form” but upon the term “inner”; and Kant proceeds to make assertions which by no means follow from the five arguments, and which must be counted amongst the most difficult and controversial tenets of the whole Critique. (a) Time is not a determination of outer appearances. For it belongs neither to their shape nor to their position--and prudently at this point the property of motion is smuggled out of view under cover of an etc. Time does not determine the relation of appearances to one another, but only the relation of representations in our inner state.[529] It is the form only of the intuition of ourselves and of our inner state.[530] Obviously these are assertions which Kant cannot possibly hold to in this unqualified form. In the very next paragraph they are modified and restated. (b) As this inner intuition supplies no shape (Gestalt), we seek to make good this deficiency by means of analogies. We represent the time-sequence through a line progressing to infinity in which the manifold constitutes a series of only one dimension. From the properties of this line, with the one exception that its parts are simultaneous whereas those of time are always successive, we conclude to all the properties of time.

The wording of the passage seems to imply that such symbolisation of time through space is helpful but not indispensably necessary for its apprehension. That it is indispensably necessary is, however, the view to which Kant finally settled down.[531] But he has not yet come to clearness on this point. The passage has all the signs of having been written prior to the Analytic. Though Kant seems to have held consistently to the view that time has, in or by itself, only one dimension,[532] the difficulties involved drove him to recognise that this is true only of time as the order of our representations. It is not true of the objective time apprehended in and through our representations. When later Kant came to hold that consciousness of time is conditioned by consciousness of space, he apparently also adopted the view that, by reference to space, time indirectly acquires simultaneity as an additional mode. The objective spatial world is in time, but in a time which shows simultaneity as well as succession. In the Dissertation[533] Kant had criticised Leibniz and his followers for neglecting simultaneity, “the most important consequence of time.”

“Though time has only one dimension, yet the ubiquity of time (to employ Newton’s term), through which all things sensuously thinkable are at some time, adds another dimension to the quantity of actual things, in so far as they hang, as it were, upon the same point of time. For if we represent time by a straight line extended to infinity, and simultaneous things at any point of time by lines successively erected [perpendicular to the first line], the surface thus generated will represent the phenomenal world both as to substance and as to accidents.”

Similarly in A 182 = B 226 of the Critique Kant states that simultaneity is not a mode of time,[534] since none of the parts of time can be simultaneous, and yet also teaches in A 177 = B 219 that, as the order of appearances, time possesses in addition to succession the two modes, duration and simultaneity. The significance of this distinction between time as the order of our inner states, and time as the order of objective appearances, we shall consider immediately.

A connected question is as to whether or not Kant teaches the possibility of simultaneous apprehension. In the Aesthetic and Dialectic he certainly does so. Space is given as containing coexisting parts, and[535] can be intuited as such without successive synthesis of its parts. In the Analytic, on the other hand, the opposite would seem to be implied.[536] The apprehension of a manifold can only be obtained through the successive addition or generation of its parts.

(c) Lastly, Kant argues that the fact that all the relations of time can be expressed in an outer intuition is proof that the representation of time is itself intuition. But surely if, as Kant later taught, time can be apprehended at all only in and through space, that, taken alone, would rather be a reason for denying it to be itself intuition. In any case it is difficult to follow Kant in his contention that the intuition of time is similar in general character to that of space.[537]

=Third Paragraph (Conclusion c).=--Kant now reopens the question as to the relation in which time stands to outer appearances. As already noted, he has argued in the beginning of the previous paragraph that it cannot be a determination of outer appearances, but only of representations in our inner state. External appearances, however, as Kant recognises, can be known only in and through representations. To that extent they belong to inner sense, and consequently (such is Kant’s argument) are themselves subject to time. Time, as the immediate condition of our representations, is also the mediate condition of appearances. Therefore, Kant concludes, “all appearances, i.e. all objects of the senses, are in time, and necessarily stand in time-relations.”

Now quite obviously this argument is invalid if the distinction between representations and their objects is a real and genuine one. For if so, it does not at all follow that because our representations of objects are in time that the objects themselves are in time. In other words, the argument is valid only from the standpoint of extreme subjectivism, according to which objects are, in Kant’s own phraseology, blosse Vorstellungen. But the argument is employed to establish a realist conclusion, that outer objects, as objects, stand in time-relations to one another. In contradiction of the previous paragraph he is now maintaining that time is a determination of outer appearances, and that it reveals itself in the motion of bodies as well as in the flux of our inner states.

The distinction between representations and their objects also makes it possible for Kant both to assert and to deny that simultaneity is a mode of time. “No two years can be coexistent. Time has only one dimension. But existence (das Dasein), measured through time, has two dimensions, succession and simultaneity.” There are, for Kant, two orders of time, subjective and objective. Recognition of the latter (emphasised and developed in the Analytic)[538] is, however, irreconcilable with his contention that time is merely the form of inner sense.

We have here one of the many objections to which Kant’s doctrine of time lies open. It is the most vulnerable tenet in his whole system. A mere list of the points which Kant leaves unsettled suffices to show how greatly he was troubled in his own mind by the problems to which it gives rise. (1) The nature of the a priori knowledge which time yields. Kant ascribes to this source sometimes only the two axioms in regard to time, sometimes pure mechanics, and sometimes also arithmetic. (2) Whether time only allows of, or whether it demands, representation through space. Sometimes Kant makes the one assertion, sometimes the other. (3) Whether it is possible to apprehend the coexistent without successive synthesis of its parts. This possibility is asserted in the Aesthetic and Dialectic, denied in the Analytic. (4) Whether simultaneity is a mode of time. (5) Whether, and in what manner, appearances of outer sense are in time. Kant’s answer to 4 and to 5 varies according as he identifies or distinguishes representations and empirical objects.

The manifold difficulties to which a theory of time thus lies open are probably the reason why Kant, in the Critique, reverses the order in which he had treated time and space in the Dissertation.[539] But the placing of space before time is none the less unfortunate. It greatly tends to conceal from the reader the central position which Kant has assigned to time in the Analytic. Consciousness of time is the fundamental fact, taken as bare fact, by reference to which Kant gains his transcendental proof of the categories and principles of understanding.[540] In the Analytic space, by comparison, falls very much into the background. A further reason for the reversal may have been Kant’s Newtonian view of geometry as the mathematical science par excellence.[541] In view of his formulation of the Critical problem as that of accounting for synthetic a priori judgments, he would then naturally be led to throw more emphasis on space.

To sum up our main conclusions. Kant’s view of time as a form merely of inner sense, and as having only one dimension, connects with his subjectivism. His view of it as inhering in objects, and as having duration and simultaneity as two of its modes, is bound up with his phenomenalism. Further discussion of these difficulties must therefore be deferred until we are in a position to raise the more fundamental problem as to the nature of the distinction between a representation and its object.[542] Motion is not an inner state. Yet it involves time as directly as does the flow of our feelings and ideas. Kant’s assertion that “time can no more be intuited externally than space can be intuited as something in us,”[543] if taken quite literally, would involve both the subjectivist assertion that motion of bodies is non-existent, and also the phenomenalist contention that an extended object is altogether distinct from a representation.

The fourth and fifth paragraphs call for no detailed analysis.[544] Time is empirically real, transcendentally ideal--these terms having exactly the same meaning and scope as in reference to space.[545] The fourth sentence in the fifth paragraph is curiously inaccurate. As it stands, it would imply that time is given through the senses. In the concluding sentences Kant briefly summarises and applies the points raised in these fourth and fifth paragraphs.

ELUCIDATION

=First and Second Paragraphs.=--Kant here replies to a criticism which, as he tells us in his letter of 1772 to Herz, was first made by Pastor Schulze and by Lambert.[546] In that letter the objection and Kant’s reply are stated as follows.

“In accordance with the testimony of inner sense, changes are something real. But they are only possible on the assumption of time. Time is, therefore, something real which belongs to the determinations of things in themselves. Why, said I to myself, do we not argue in a parallel manner: ‘Bodies are real, in accordance with the outer senses. But bodies are possible only under the condition of space. Space is, therefore, something objective and real which inheres in the things themselves.’ The cause [of this differential treatment of space and of time] is the observation that in respect to outer things we cannot infer from the reality of representations the reality of their objects, whereas in inner sense the thought or the existing of the thought and of myself are one and the same. Herein lies the key to the difficulty. Undoubtedly I must think my own state under the form of time, and the form of the inner sensibility consequently gives me the appearance of changes. Now I do not deny that changes are something real any more than I deny that bodies are something real, but I thereby mean only that something real corresponds to the appearance. I may not even say the inner appearance undergoes change (verändere sich), for how could I observe this change unless it appeared to my inner sense? To the objection that this leads to the conclusion that all things in the world objectively and in themselves are unchangeable, I would reply that they are neither changeable nor unchangeable. As Baumgarten states in § 18 of his Metaphysica, the absolutely impossible is hypothetically neither possible nor impossible, since it cannot be mentally entertained under any condition whatsoever; so in similar manner the things of the world are objectively or in themselves neither in one and the same state nor in different states at different times, for thus understood [viz. as things in themselves] they are not represented in time at all.”[547]

Thus Kant’s contention, both in this letter and in the passage before us, is that even our inner states would not reveal change if they could be apprehended by us or by some other being apart from the subjective form of our inner sense. We may not say that our inner states undergo change, or that they succeed one another, but only that to us they necessarily appear as so doing.[548] Time is no more than subjectively real.[549] As Körner writes to Schiller: “Without time man would indeed exist but not appear. Not his reality but only his appearance is dependent upon the condition of time.” “Man is not, but only appears, when he undergoes change.”[550] The objects of inner sense stand in exactly the same position as those of outer sense. Both are appearances, and neither can be identified with the absolutely real. As Kant argues later in the Critique,[551] inner processes are not known with any greater certainty or immediacy than are outer objects; the reality of time as subjective proves its unreality in relation to things in themselves. The statement that the constitution of things in themselves is “problematic” is an exceptional mode of expression for Kant. Usually--as indeed throughout the whole context of this passage[552]--he asserts that though things in themselves are unknowable, we can with absolute certainty maintain that they are neither in space nor in time. Upon this point we have already dwelt in discussing Trendelenburg’s controversy with Fischer.[553]

=Third Paragraph.=--The third and fourth paragraphs of this section ought to have had a separate heading. They summarise the total argument of the Aesthetic in regard to space as well as time, distinguish its tenets from those of Newton and of Leibniz, and draw a general conclusion. The summary follows the strict synthetic method. The opening sentences illustrate Kant’s failure to distinguish between the problems of pure and of applied mathematics, and also show how completely he tends to conceive mathematics as typified by geometry. The criticism of alternative views traverses the ground of the famous controversy between Leibniz and Clarke. Their Streitschriften were, as we have good circumstantial grounds for believing,[554] a chief influence in the development of Kant’s own views. Kant, who originally held the Leibnizian position, was by 1768[555] more or less converted to the Newtonian teaching, and in the Dissertation of 1770 developed his subjectivist standpoint with the conscious intention of retaining the advantages while remedying the defects of both alternatives.[556] For convenience we may limit the discussion to space. (a) The view propounded by Newton, and defended by Clarke, is that space has an existence in and by itself, independent alike of the mind which apprehends it and of the objects with which it is filled. (b) The view held by Leibniz is that space is an empirical concept abstracted from our confused sense-experience of the relations of real things.[557]

The criticism of (a) is twofold. First, it involves belief in an eternal and infinite Unding. Secondly, it leads to metaphysical difficulties, especially in regard to the existence of God. If space is absolutely real, how is it to be reconciled with the omnipresence of God? Newton’s view of space as the =sensorium Dei= can hardly be regarded as satisfactory.

The objection to (b) is that it cannot account for the apodictic certainty of geometry, nor guarantee its application to experience. The concept of space, when regarded as of sensuous origin, is something that may distort (and according to the Leibnizian teaching does actually distort) what it professes to represent, and is something from which restrictions that hold in the natural world have been omitted.[558] As empirical, it cannot serve as basis for the universal and necessary judgments of mathematical science.[559]

The first view has, however, the advantage of keeping the sphere of appearances open for mathematical science. As space is infinite and all-comprehensive, its laws hold universally. The second view has the advantage of not subjecting reality to space conditions. These advantages are retained, while the objections are removed, by the teaching of the Aesthetic.

Kant further criticises the former view in A 46 ff. = B 64 ff. There is no possibility of accounting for the a priori synthetic judgments of geometry save by assuming that space is the pure form of outer intuition. For though the Newtonian view will justify the assertion that the laws of space hold universally, it cannot explain how we come to know them a priori. And assuming, as Kant constantly does, that space cannot be both an a priori form of intuition and also independently real, he concludes that it is the former only.

In B 71 Kant also restates the metaphysical difficulties to which the Newtonian view lies open. In natural theology we deal with an existence which can never be the object of sensuous intuition, and which has to be freed from all conditions of space and time. This is impossible if space is so absolutely real that it would remain though all created things were annihilated.

=Fourth Paragraph.=--Space and time are the only two forms of sensibility; all other concepts belonging to the senses, such as motion and change, are empirical.[560] As Kant has himself stated, no reason can be given why space and time are the sole forms of our possible intuition:

“Other forms of intuition than space and time, ... even if they were possible, we cannot render in any way conceivable and comprehensible to ourselves, and even assuming that we could do so, they still would not belong to experience, the only kind of knowledge in which objects are given to us.”[561]

The further statement,[562] frequently repeated in the Critique, that time itself does not change, but only what is in time,[563] indicates the extent to which Kant has been influenced by the Newtonian receptacle view. As Bergson very justly points out, time, thus viewed as a homogeneous medium, is really being conceived on the analogy of space. “It is merely the phantom of space obsessing the reflective consciousness.”[564]

GENERAL OBSERVATIONS ON THE TRANSCENDENTAL AESTHETIC

=I. First Paragraph.=--“To avoid all misapprehension” Kant proceeds to state “as clearly as possible” his view of sensuous knowledge. With this end in view he sets himself to enforce two main points: (a) that as space and time are only forms of sensibility, everything apprehended is only appearance; (b) that this is not a mere hypothesis but is completely certain. Kant expounds (a) indirectly through criticism of the opposing views of Leibniz and of Locke. But before doing so he makes in the next paragraph a twofold statement of his own conclusions.

=Second Paragraph.=--This paragraph states (a) that through intuition we can represent only appearances, not things in themselves, and (b) that the appearances thus known exist only in us. Both assertions have implications, the discussion of which must be deferred to the Analytic. The mention of the “relations of things by themselves” may, as Vaihinger suggests,[565] be a survival from the time when (as in the Dissertation[566]) Kant sought to reduce spatial to dynamical relations. The assertion that things in themselves are completely unknown to us goes beyond what the Aesthetic can establish and what Kant here requires to prove. His present thesis is only that no knowledge of things in themselves can be acquired either through the forms of space and time or through sensation; space and time are determined solely by our pure sensibility, and sensations by our empirical sensibility. Failure to recognise this is, in Kant’s view, one of the chief defects of the Leibnizian system.

=Third and Fourth Paragraphs. Criticism of the Leibniz-Wolff Interpretation of Sensibility and of Appearance.=--Leibniz vitiates both conceptions. Sensibility does not differ from thought in clearness but in content. It is a difference of kind.[567] They originate in different sources, and neither can by any transformation be reduced to the other.

“Even if an appearance could become completely transparent to us, such knowledge would remain toto coelo different from knowledge of the object in itself.”[568] “Through observation and analysis of appearances we penetrate to the secrets of nature, and no one can say how far this may in time extend.... [But however far we advance, we shall never be able by means of] so ill-adapted an instrument of investigation [as our sensibility] to find anything except still other appearances, the non-sensuous cause of which we yet long to discover.”[569]

We should still know only in terms of the two inalienable forms of our sensibility.[570] The dualism of thought and sense can never be transcended by the human mind. By no extension of its sphere or perfecting of its insight can sensuous knowledge be transformed into a conceptual apprehension of purely intelligible entities.

Leibniz’s conception of appearances as things in themselves confusedly apprehended is equally false, and for the same reasons.[571] Appearance and reality are related as distinct existences, each of which has its own intrinsic character and content. Through the former there can be no hope of penetrating to the latter. Appearance is subjective in matter as well as in form. For Leibniz our knowledge of appearances is a confused knowledge of things in themselves. Properly viewed, it is the apprehension, whether distinct or confused, of objects which are never things in themselves. Sense-knowledge, such as we obtain in the science of geometry, has often the highest degree of clearness. Conceptual apprehension is all too frequently characterised by obscurity and indistinctness.

This criticism of Leibniz, as expounded in these two paragraphs, is thoroughly misleading if taken as an adequate statement of Kant’s view of the relations between sense and understanding, appearance and reality. These paragraphs are really a restatement of a passage in the Dissertation.

“It will thus be seen that we express the nature of the sensuous very inappropriately when we assert that it is the more confusedly known, and the nature of the intellectual when we describe it as the distinctly known. For these are merely logical distinctions, and obviously have nothing to do with the given facts which underlie all logical comparison. The sensuous may be absolutely distinct, and the intellectual extremely confused. That is shown on the one hand in geometry, the prototype of sensuous knowledge, and on the other in metaphysics, the instrument of all intellectual enquiry. Every one knows how zealously metaphysics has striven to dispel the mists of confusion which cloud the minds of men at large and yet has not always attained the happy results of the former science. Nevertheless each of these kinds of knowledge preserves the mark of the stock from which it has sprung. The former, however distinct, is on account of its origin entitled sensuous, while the latter, however confused, remains intellectual--as e.g. the moral concepts, which are known not by way of experience, but through the pure intellect itself. I fear, however, that Wolff by this distinction between the sensuous and the intellectual, which for him is merely logical, has checked, perhaps wholly (to the great detriment of philosophy), that noblest enterprise of antiquity, the investigation of the nature of phenomena and noumena, turning men’s minds from such enquiries to what are very frequently only logical subleties.”[572]

The paragraphs before us give expression only to what is common to the Dissertation and to the Critique, and do so entirely from the standpoint of the Dissertation. Thus the illustration of the conception of “right” implies that things in themselves can be known through the understanding. The conception, as Kant says, represents “a moral property which belongs to actions in and by themselves.” Similarly, in distinguishing the sensuous from “the intellectual,” he says that through the former we do not apprehend things in themselves, thus implying that things in themselves can be known through the pure intellect. The view developed in the Analytic, alike of sensibility and of appearance, is radically different. Sensibility and understanding may have a common source; and both are indispensably necessary for the apprehension of appearance. Neither can function save in co-operation with the other. Appearance does not differ from reality solely through its sensuous content and form, but also in the intellectual order or dispensation to which it is subject. But in the very act of thus deepening the gulf between appearance and reality by counting even understanding as contributing to the knowledge only of the former, he was brought back to a position that has kinship with the Leibnizian view of their interrelation. Since understanding is just as essential as sensibility to the apprehension of appearances, and since understanding differs from sensibility in the universality of its range, it enables us to view appearances in their relation to ultimate reality, and so to apprehend them as being, however subjective or phenomenal, ways in which the thing in itself presents itself to us. Such a view is, however, on Kant’s principles, quite consistent with the further contention, that appearance does not differ from reality in a merely logical manner. Factors that are peculiar to the realm of appearance have intervened to transform the real; and in consequence even completed knowledge of the phenomenal--if such can be conceived as possible--would not be equivalent to knowledge of things in themselves.

=Fifth Paragraph. Criticism of Locke’s View of Appearance.=--This paragraph discusses Locke’s doctrine[573] that the secondary qualities are subjective, and that in the primary qualities we possess true knowledge of things in themselves. The distinction is drawn upon empirical grounds, namely, that while certain qualities are uniform for more than one sense, and belong to objects under all conditions, others are peculiar to the different senses, and arise only through the accidental relation of objects to the special senses.[574] This distinction is, Kant says, entirely justified from the physical standpoint.[575] A rainbow is an appearance of which the raindrops constitute the true empirical reality. But Locke and his followers interpret this distinction wrongly. They ignore the more fundamental transcendental (i.e. metaphysical) distinction between empirical reality and the thing in itself. From the transcendental standpoint the raindrops are themselves merely appearance. Even their round shape, and the very space in which they fall; are only modifications of our sensuous intuition. The ‘transcendental object’[576] remains unknown to us.

When Kant thus declares that the distinction between primary and secondary qualities is justified (richtig) from the physical standpoint, he is again[577] speaking from a phenomenalist point of view. And it may be noted that in developing his transcendental distinction he does not describe the raindrops as mere representations. His phrase is much more indefinite. They are “modifications or fundamental forms (Grundlagen) of our sensuous intuition.”

Kant does not here criticise the view of sensibility which underlies Locke’s view of appearance. But he does so in A 271 = B 327, completing the parallel and contrast between Leibniz and Locke.

“Leibniz intellectualised appearances, just as Locke, according to his system of noogony (if I may be allowed these expressions), sensualised all concepts of the understanding, i.e. interpreted them as simply empirical or abstracted concepts of reflection. Instead of interpreting understanding and sensibility as two quite different sources of representations, which yet can supply objectively valid judgments of things only in conjunction with each other, each of these great men holds only to one of the two, viewing it as in immediate relation to things in themselves. The other faculty is regarded as serving only to confuse or to order the representations which this selected faculty yields.”[578]

=Proof that the above View of Space and Time is not a mere Hypothesis, but completely certain.=[579]--The proof, which as here recapitulated and developed follows the analytic method, has already been considered in connection with A 39 = B 56. It proceeds upon the assumption that space cannot be both an a priori form of intuition and also independently real. The argument as a whole lacks clearness owing to Kant’s failure to distinguish between the problems of pure and applied geometry, between pure intuition and form of intuition. This is especially obvious in the very unfortunate and misleading second application of the triangle illustration.[580] Kant’s tendency to conceive mathematical science almost exclusively in terms of geometry is likewise illustrated.

“There is in regard to both [space and time] a large number of a priori apodictic and synthetic propositions. This is especially true of space, which for this reason will be our chief illustration in this enquiry.”[581]

=II. Paragraphs added in the Second Edition.=[582]--Kant proceeds to offer further proof of the ideality of the appearances (a) of outer and (b) of inner sense. Such proof he finds in the fact that these appearances consist solely of relations. (a) Outer appearances reduce without remainder to relations of position in intuition (i.e. of extension), of change of position (motion), and to the laws which express in merely relational terms the motive forces by which such change is determined. What it is that is thus present in space, or what the dynamic agencies may be to which the motion is due, is never revealed. But a real existent (Sache an sich) can never be known through mere relations. Outer sense consequently reveals through its representations only the relation of an object to the subject, not the intrinsic inner nature of the object in itself (Object an sich). Kant’s avoidance of the term Ding an sich may be noted.[583]

(b) The same holds true of inner sense, not only because the representations of outer sense constitute its proper (eigentlichen) material, but also because time, in which these are set, contains only relations of succession, coexistence, and duration. This time (which as consisting only of relations can be nothing but a form[584]) is itself, in turn, a mere relation. It is only the manner in which through its own activity the mind is affected by itself. But in order to be affected by itself it must have receptivity, in other words, sensibility. Time, consequently, must be regarded as the form of this inner sense.

That everything represented in time, like that which is represented in space, consists solely of relations, Kant does not, however, attempt to prove. He is satisfied with repeating the conclusion reached in the first edition of the Aesthetic, that, as time is the object of a sense, it must of necessity be appearance. This, like everything which Kant wrote upon inner sense, is profoundly unsatisfactory. The obscurities of his argument are not to be excused on the ground that “the difficulty, how a subject can have an internal intuition of itself, is common to every theory.” For no great thinker,[585] except Locke, has attempted to interpret inner consciousness on the analogy of the senses. Discussion of the doctrine must meantime be deferred.[586]

=III. B 69.=--Kant here formulates the important distinction between appearance (Erscheinung) and illusion (Schein). The main text is clear so far as it goes; but the appended note is thoroughly confused. Together they contain no less than three distinct and conflicting views of illusion.[587] According to the main text, Schein signifies a representation, such as may occur in a dream, to which nothing real corresponds. Erscheinung, on the other hand, is always the appearance of a given object; but since the qualities of that object depend solely on our mode of intuition, we have to distinguish the object as appearance from the object as thing in itself.

”[Every appearance] has two sides, the one by which the object is viewed in and by itself, ... the other by which the form of the intuition of the object is taken into account....”[588]

Obviously, when illusion is defined in the above manner, the assertion that objects in space are mere appearances cannot be taken as meaning that they are illusory.

But this view of illusion is peculiar to the passage before us and to A 38 = B 55. It occurs nowhere else, either in the Critique or in the Prolegomena; and it is not, as Kant has himself admitted,[589] really relevant to the purposes of the Critique. The issues are more adequately faced in the appended note, which, however, at the same time, shows very clearly that Kant has not yet properly disentangled their various strands. The above definition of appearance is too wide. It covers illusory sense perception as well as appearance proper. The further qualification must be added, that the predicates of appearance are constant and are inseparable from its representation. Thus the space predicates can be asserted of any external object. Redness and scent can be ascribed to the rose. All of these are genuine appearances. If, on the other hand, the two handles, as observed by Galileo, are attributed to Saturn, roundness to a distant square tower, bentness to a straight stick inserted in water, the result is mere illusion. The predicates, in such cases, do not stand the test of further observation or of the employment of other senses. Only in a certain position of its rings, relatively to the observer, does Saturn seem (scheint) to have two handles. The distant tower only seems to be round. The stick only seems to be bent. But the rose is extended and is red. Obviously Kant is no longer viewing Schein as equivalent to a merely mental image. It now receives a second meaning. It is illusion in the modern, psychological sense. It signifies an abnormal perception of an actually present object. The distinction between appearance and illusion is now reduced to a merely relative difference in constancy and universality of appearance. Saturn necessarily appears to Galileo as possessing two handles. A square tower viewed from the distance cannot appear to the human eye otherwise than round. A stick inserted in water must appear bent. If, however, Saturn be viewed under more favourable conditions, if the distance from the tower be diminished, if the stick be removed from the water, the empirical object will appear in a manner more in harmony with the possible or actual experiences of touch. The distinction is practical, rather than theoretical, in its justification. It says only that certain sets of conditions may be expected to remain uniform; those, for instance, physical, physiological, and psychical, which cause a rose to appear red. Other sets of conditions, such as those which cause the stick to appear bent, are exceptional, and for that reason the bentness may be discounted as illusion. Among the relatively constant are the space and time properties of bodies. To employ the terms of the main text, it is not only by illusion that bodies seem to exist outside me; they actually are there.

So long as we keep to the sphere of ordinary experience, and require no greater exactitude than practical life demands, this distinction is, of course, both important and valid. But Kant, by his references to Saturn, raises considerations which, if faced, must complicate the problem and place it upon an entirely different plane. If, in view of scientific requirements, the conditions of observation are more rigorously formulated, and if by artificial instruments of scientific precision we modify the perceptions of our human senses, what before was ranked as appearance becomes illusion; and no limit can be set to the transformations which even our most normal human experiences may thus be made to undergo. Even the most constant perceptions then yield to variation. The most that can be asserted is that throughout all change in the conditions of observation objects still continue to possess, in however new and revolutionary a fashion, some kind of space and time predicates. The application of this more rigorous scientific standard of appearance thus leads to a fourfold distinction between ultimate reality, scientific appearances, the appearances of ordinary consciousness, and the illusions of ordinary consciousness. The appearances of practical life are the illusions of science, and the appearances of science would similarly be illusions to any being who through ‘intuitive understanding’ could apprehend things in themselves.

But if the distinction between appearance and illusion is thus merely relative to the varying nature of the conditions under which observation takes place, it can afford no sufficient answer to the criticisms which Kant is here professing to meet. Kant has in view those critics (such as Lambert, Mendelssohn, and Garve) who had objected that if bodies in space are representations existing, as he so often asserts, only “within us,” their appearing to exist “outside us” is a complete illusion. These critics have, indeed, found a vulnerable point in Kant’s teaching. The only way in which he can effectively meet it is by frank recognition and development of the phenomenalism with which his subjectivism comes into so frequent conflict.[590] That certain perceptions are more constant than others does not prove that all alike may not be classed as illusory. The criticism concerns only the reality of extended objects. From Kant’s own extreme subjectivist position they are illusions of the most thoroughgoing kind. If, as Kant so frequently maintains, objects are representations and exist only “within us,” their existence “outside us” must be denied. The criticism can be met only if Kant is prepared consistently to formulate and defend his own alternative teaching, that sensations arise through the action of external objects upon the sense-organs, and that the world of physical science has consequently a reality not reducible to mere representations in the individual mind.

It may be objected that Kant has in the main text cited one essential difference between his position and that which is being ascribed to him. Extended objects, though mere representations, are yet due to, and conditioned by, things in themselves. They are illusory only in regard to their properties, not in regard to their existence. But this distinction is not really relevant. The criticism, as just stated, is directed only against Kant’s view of space. The fact that the spatial world is a grounded and necessary illusion is not strictly relevant to the matter in dispute. Kant has, indeed, elsewhere, himself admitted the justice of the criticism. In A 780 = B 808 he cites as a possible hypothesis, entirely in harmony with his main results, though not in any degree established by them, the view

“that this life is an appearance only, that is, a sensuous representation of purely spiritual life, and that the whole sensible world is a mere image (ein blosses Bild) which hovers before our present mode of knowledge, and like a dream has in itself no objective reality.”

Kant’s reply is thus really only verbal. He claims that illusion, if constant, has earned the right to be called appearance. He accepts the criticism, but restates it in his own terms. The underlying phenomenalism which colours the position in his own thoughts, and for which he has not been able to find any quite satisfactory formulation, is the sole possible justification, if any such exists, for his contention that the criticism does not apply. Such phenomenalism crops out in the sentence, already partially quoted:

“If I assert that the quality of space and time, according to which, as a condition of their existence, I posit both external objects and my own soul, lies in my mode of intuition and not in these objects in themselves, I am not saying that only by illusion do bodies seem to exist outside me or my soul to be given in my self-consciousness.”[591]

But, so far, I have simplified Kant’s argument by leaving out of account a third and entirely different view of illusion which is likewise formulated in the appended note. In the middle of the second sentence, and in the last sentence, illusion is defined as the attribution to the thing in itself of what belongs to it only in its relation to the senses. Illusion lies not in the object apprehended, but only in the judgment which we pass upon it. It is due, not to sense, but to understanding.[592] Viewing illusion in this way, Kant is enabled to maintain that his critics are guilty of “an unpardonable and almost intentional misconception,”[593] since this is the very fallacy which he himself has been most concerned to attack. As he has constantly insisted, appearance is appearance just because it can never be a revelation of the thing in itself.

Now the introduction of this third view reduces the argument of the appended note to complete confusion. Its first occurrence as a parenthesis in a sentence which is stating an opposed view would seem to indicate that the note has been carelessly recast. Originally containing only a statement of the second view, Kant has connected therewith the view which he had already formulated in the first edition and in the Prolegomena. But the two views cannot be combined. By the former definition, illusion is necessitated but abnormal perception; according to the latter, it is a preventable error of our conscious judgment. The opposite of illusion is in the one case appearance, in the other truth. The retention of the reference to Saturn, in the statement of the third view at the end of the note, is further evidence of hasty recasting. While the rose and the extended objects are there treated as also things in themselves, Saturn is taken only in its phenomenal existence. In view of the general confusion, it is a minor inconsistency that Kant should here maintain, in direct opposition to A 28-9, that secondary qualities can be attributed to the empirical object.

This passage from the second edition is a development of Prolegomena, § 13, iii. Kant there employs the term appearance in a quite indefinite manner. For the most part he seems to mean by it any and every sense-experience, whether normal or abnormal, and even to include under it dream images. But it is also employed in the second of the above meanings, as signifying those sense-perceptions which harmonise with general experience. Illusion is throughout employed in the third of the above meanings. Kant’s illustration, that of the apparently retrograde movements of the planets, necessitates a distinction between apparent and real motion in space, and consequently leads to the fruitful distinction noted above. Kant gives, however, no sign that he is conscious of the complicated problems involved.

In the interval between the Prolegomena (1783) and the second edition of the Critique (1787) Mendelssohn had published (1785) his Morgenstunden. In its introduction, entitled Vorerkenntniss von Wahrheit, Schein und Irrthum,[594] he very carefully distinguishes between illusion (Sinnenschein) and error of judgment (Irrthum). This introduction Kant had read. In a letter to Schütz[595] he cites it by title, and praises it as “acute, original, and of exemplary clearness.” It is therefore the more inexcusable that he should again in the second edition of the Critique have confused these two so radically different meanings of the term Schein. Mendelssohn, however, drew no distinction between Schein and Erscheinung. They were then used as practically synonymous,[596] though of course Schein was the stronger term. Kant seems to have been the first to distinguish them sharply and to attempt to define the one in opposition to the other. But the very fact that Erscheinung and Schein were currently employed as equivalent terms, and that the distinction, though one of his own drawing, had been mentioned only in the most cursory manner in the first edition of the Critique,[597] removes all justification for his retort upon his critics of “unpardonable misconception.” His anger was really due, not to the objection in itself, but to the implied comparison of his position to that of Berkeley. Such comparison never failed to arouse Kant’s wrath. For however much this accusation might be justified by his own frequent lapses into subjectivism of the most extreme type, even its partial truth was more than he was willing to admit. Berkeley represents in his eyes, not merely a subjectivist interpretation of the outer world, but the almost diametrical opposite of everything for which he himself stood. Discussion of Kant’s relation to Berkeley had best, however, be introduced through consideration of the passage immediately following in which Kant refers to Berkeley by name.

=III. (Second Part) B 70.=--Kant urges that his doctrine of the ideality of space and time, so far from reducing objects to mere illusion, is the sole means of defending their genuine reality. If space and time had an independent existence, they would have to be regarded as more real than the bodies which occupy them. For on this view space and time would continue to exist even if all their contents were removed; they would be antecedent necessary conditions of all other existences. But space and time thus interpreted are impossible conceptions.[598] The reality of bodies is thereby made to depend upon Undinge. If this were the sole alternative, “the good Bishop Berkeley [could] not be blamed for degrading bodies to mere illusion.” We should, Kant maintains, have to proceed still further, denying even our own existence. For had Berkeley taken account of time as well as of space, a similar argument, consistently developed in regard to time, would have constrained him to reduce the self to the level of mere illusion. Belief in the reality of things in themselves, whether spiritual or material, is defensible only if space and time be viewed as subjective. In other words, Berkeley’s idealism is an inevitable consequence of a realist view of space. But it is also its reductio ad absurdum.

[“Berkeley in his dogmatic idealism] maintains that space, with all the things of which it is the inseparable condition, is something impossible in itself, and he therefore regards the things in space as merely imaginary entities (Einbildungen). Dogmatic idealism is inevitable if space be interpreted as a property which belongs to things in themselves. For, when so regarded, space, and everything to which it serves as condition, is a non-entity (Unding). The ground upon which this idealism rests we have removed in the Transcendental Aesthetic.”[599]

The term Schein is not employed throughout this passage in either of the two meanings of the appended note, but in that of the main text. It signifies a representation, to which no existence corresponds.

KANT’S RELATION TO BERKELEY

By idealism[600] Kant means any and every system which maintains that the sensible world does not exist in the form in which it presents itself to us. The position is typified in Kant’s mind by the Eleatics, by Plato, and by Descartes, all of whom are rationalists. With the denial of reality to sense-appearances they combine a belief in the possibility of rationally comprehending its supersensible basis. Failing to appreciate the true nature of the sensible, they misunderstand the character of geometrical science, and falsely ascribe to pure understanding a power of intellectual intuition. Kant’s criticisms of Berkeley show very clearly that it is this more general position which he has chiefly in view. To Berkeley Kant objects that only in sense-experience is there truth, that it is sensibility, not understanding, which possesses the power of a priori intuition, and that through pure understanding, acting in independence of sensibility, no knowledge of any kind can be acquired. In other words, Kant classes Berkeley with the rationalists. And, as we have already seen, he even goes the length of regarding Berkeley’s position as the reductio ad absurdum of the realist view of space. Kant does, indeed, recognise[601] that Berkeley differs from the other idealists, in holding an empirical view of space, and consequently of geometry, but this does not prevent Kant from maintaining that Berkeley’s thinking is influenced by certain fundamental implications of the realist position. Berkeley’s insight--such would seem to be Kant’s line of argument--is perverted by the very view which he is attacking. Berkeley appreciates only what is false in the Cartesian view of space; he is blind to the important element of truth which it contains. Empiricist though he be, he has no wider conception of the function and powers of sensibility than have the realists from whom he separates himself off; and in order to comprehend those existences to which alone he is willing to allow true reality, he has therefore, like the rationalists, to fall back upon pure reason.[602]

That Kant’s criticism of Berkeley should be extremely external is not, therefore, surprising. He is interested in Berkeley’s positive teaching only in so far as it enables him to illustrate the evil tendencies of a mistaken idealism, which starts from a false view of the functions of sensibility and of understanding, and of the nature of space and time. The key to the true idealism lies, he claims, in the Critical problem, how a priori synthetic judgments can be possible. This is the fundamental problem of metaphysics, and until it has been formulated and answered no advance can be made.

“My so-called (Critical) idealism is thus quite peculiar in that it overthrows ordinary idealism, and that through it alone a priori cognition, even that of geometry, attains objective reality, a thing which even the keenest realist could not assert till I had proved the ideality of space and time.”[603]

In order to make Kant’s account of Berkeley’s teaching really comprehensible, we seem compelled to assume that he had never himself actually read any of Berkeley’s own writings. Kant’s acquaintance with the English language was most imperfect, and we have no evidence that he had ever read a single English book.[604] When he quotes Pope and Addison, he does so from German translations.[605] Subsequent to 1781 he could, indeed, have had access to Berkeley’s Dialogues between Hylas and Philonous[606] in a German translation; but in view of the account which he continues to give of Berkeley’s teaching, it does not seem likely[607] that he had availed himself of this opportunity. As to what the indirect sources of Kant’s knowledge of Berkeley may have been, we cannot decide with any certainty, but amongst them must undoubtedly be reckoned Hume’s statements in regard to Berkeley in the Enquiry,[608] and very probably also the references to Berkeley in Beattie’s Nature of Truth.[609] From the former Kant would learn of Berkeley’s empirical view of space and also of the sceptical tendencies of his idealist teaching. From it he might also very naturally infer that Berkeley denies all reality to objects. By Beattie Kant would be confirmed in this latter view, and also in his contention that Berkeley is unable to supply a criterion for distinguishing between reality and dreams. Kant may also have received some impressions regarding Berkeley from Hamann.

To take Kant’s criticisms of Berkeley more in detail. In the first edition of the Critique[610] Kant passes two criticisms, without, however, mentioning Berkeley by name: first, that he overlooks the problem of time, and, like Descartes, ascribes complete reality to the objects of inner sense. This is the cause of a second error, namely, that he views the objects of outer sense as mere illusion (blosser Schein). Proceeding, Kant argues that inner and outer sense are really in the same position. Though they yield only appearances, these appearances are conditioned by things in themselves. Through this relation to things in themselves they are distinguished from all merely subjective images. Berkeley is again referred to in the fourth Paralogism.[611] His idealism is distinguished from that of Descartes. The one is dogmatic; the other is sceptical. The one denies the existence of matter; the other only doubts whether it is possible to prove it. Berkeley claims, indeed, that there are contradictions in the very conception of matter; and Kant remarks that this is an objection which he will have to deal with in the section on the Antinomies. But this promise Kant does not fulfil; and doubtless for the reason that, however unwilling he may be to make the admission, on this point his own teaching, especially in the Dialectic, frequently coincides with that of Berkeley. So little, indeed, is Kant concerned in the first edition to defend his position against the accusation of subjectivism, that in this same section he praises the sceptical idealist as a “benefactor of human reason.”

“He compels us, even in the smallest advances of ordinary experience, to keep on the watch, lest we consider as a well-earned possession what we perhaps obtain only in an illegitimate manner. We are now in a position to appreciate the value of the objections of the idealist. They drive us by main force, unless we mean to contradict ourselves in our commonest assertions, to view all our perceptions, whether we call them inner or outer, as a consciousness only of what is dependent on our sensibility. They also compel us to regard the outer objects of these perceptions not as things in themselves, but only as representations, of which, as of every other representation, we can become immediately conscious, and which are entitled outer because they depend on what we call ‘outer sense’ whose intuition is space. Space itself, however, is nothing but an inner mode of representation in which certain perceptions are connected with one another.”[612]

These criticisms are restated in A 491-2 = B 519-20, with the further addition that in denying the existence of extended beings “the empirical idealist” removes the possibility of distinguishing between reality and dreams. This is a new criticism. Kant is no longer referring to the denial of unknowable things in themselves. He is now maintaining that only the Critical standpoint can supply an immanent criterion whereby real experiences may be distinguished from merely subjective happenings. This point is further insisted upon in the Prolegomena,[613] but is nowhere developed with any direct reference to Berkeley’s own personal teaching. Kant assumes as established that any such criterion must rest upon the a priori; and in this connection Berkeley is conveniently made to figure as a thoroughgoing empiricist.

The Critique, on its publication, was at once attacked, especially in the Garve-Feder review, as presenting an idealism similar to that of Berkeley. As Erdmann has shown, the original plan of the Prolegomena was largely modified in order to afford opportunity for reply to this “unpardonable and almost intentional misconception.”[614] Kant’s references to Berkeley, direct and indirect, now for the first time manifest a polemical tone, exaggerating in every possible way the difference between their points of view. Only the transcendental philosophy can establish the possibility of a priori knowledge, and so it alone can afford a criterion for distinguishing between realities and dreams. It alone will account for the possibility of geometrical science; Berkeley’s idealism would render the claims of that science wholly illusory. The Critical idealism transcends experience only so far as is required to discover the conditions which make empirical cognition possible; Berkeley’s idealism is ‘visionary’ and ‘mystical.’[615] Even sceptical idealism now comes in for severe handling. It may be called “dreaming idealism”; it makes things out of mere representations, and like idealism in its dogmatic form it virtually denies the existence of the only true reality, that of things in themselves. Sceptical idealism misinterprets space by making it empirical, dogmatic idealism by regarding it as an attribute of the real. Both entirely ignore the problem of time. For these reasons they underestimate the powers of sensibility (to which space and time belong as a priori forms), and exaggerate those of pure understanding.

“The position of all genuine idealists from the Eleatics to Berkeley is contained in this formula: ‘All cognition through the senses and experience is nothing but mere illusion, and only in the ideas of pure understanding and Reason is there truth.’ The fundamental principle ruling all my idealism, on the contrary, is this: ‘All cognition of things solely from pure understanding or pure Reason is nothing but mere illusion and only in experience is there truth.’”[616]

This is an extremely inadequate statement of the Critical standpoint, but it excellently illustrates Kant’s perverse interpretation of Berkeley’s teaching.

To these criticisms Kant gives less heated but none the less explicit expression in the second edition of the Critique. He is now much more careful to avoid subjectivist modes of statement. His phenomenalist tendencies are reinforced, and come to clearer expression of all that they involve. The fourth Paralogism with its sympathetic treatment of empirical idealism is omitted, and in addition to the above passage Kant inserts a new section, entitled Refutation of Idealism, in which he states his position in a much more adequate manner.

=IV. B 71.=--Kant continues the argument of A 39.[617] If space and time condition all existence, they will condition even divine existence, and so must render God’s omniscience, which as such must be intuitive, not discursive, difficult of conception. Upon this point Kant is more explicit in the Dissertation.[618]

“Whatever is, is somewhere and sometime, is a spurious axiom.... By this spurious principle all beings, even though they be known intellectually, are restricted in their existence by conditions of space and time. Philosophers therefore discuss every form of idle question regarding the locations in the corporeal universe of substances that are immaterial--and of which for that very reason there can be no sensuous intuition nor any possible spatial representation--or regarding the seat of the soul, and the like. And since the sensuous mixes with the intellectual about as badly as square with round, it frequently happens that the one disputant appears as holding a sieve into which the other milks the he-goat. The presence of immaterial things in the corporeal world is virtual, not local, although it may conveniently be spoken of as local. Space contains the conditions of possible interaction only when it is between material bodies. What, however, in immaterial substances constitutes the external relations of force between them or between them and bodies, obviously eludes the human intellect.... But when men reach the conception of a highest and extra-mundane Being, words cannot describe the extent to which they are deluded by these shades that flit before the mind. They picture God as present in a place: they entangle Him in the world where He is supposed to fill all space at once. They hope to make up for the [spatial] limitation they thus impose by thinking of God’s place per eminentiam, i.e. as infinite. But to be present in different places at the same time is absolutely impossible, since different places are mutually external to one another, and consequently what is in several places is outside itself, and is therefore present to itself outside itself--which is a contradiction in terms. As to time, men have got into an inextricable maze by releasing it from the laws that govern sense knowledge, and what is more, transporting it beyond the confines of the world to the Being that dwells there, as a condition of His very existence. They thus torment their souls with absurd questions, for instance, why God did not fashion the world many centuries earlier. They persuade themselves that it is easily possible to conceive how God may discern present things, i.e. what is actual in the time in which He is. But they consider that it is difficult to comprehend how He should foresee the things about to be, i.e. the actual in the time in which He is not yet. They proceed as if the existence of the Necessary Being descended successively through all the moments of a supposed time, and having already exhausted part of His duration, foresaw the eternal life that still lies before Him together with the events which [will] occur simultaneously [with that future life of His]. All these speculations vanish like smoke when the notion of time has been rightly discerned.”

The references in B 71-2 to the intuitive understanding are among the many signs of Kant’s increased preoccupation, during the preparation of the second edition, with the problems which it raises. Such understanding is not sensuous, but intellectual; it is not derivative, but original; the object itself is created in the act of intuition. Or, as Kant’s position may perhaps be more adequately expressed, all of God’s activities are creative, and are inseparable from the non-sensuous intuition whereby both they and their products are apprehended by Him. Kant’s reason for again raising this point may be Mendelssohn’s theological defence of the reality of space in his Morgenstunden.[619] Mendelssohn has there argued that just as knowledge of independent reality is confirmed by the agreement of different senses, and is rendered the more certain in proportion to the number of senses which support the belief, so the validity of our spatial perceptions is confirmed in proportion as men are found to agree in this type of experience with one another, with the animals, and with angelic beings. Such inductive inference will culminate in the proof that even the Supreme Being apprehends things in this same spatial manner.[620] Kant’s reply is that however general the intuition of space may be among finite beings, it is sensuous and derivative, and therefore must not be predicated of a Divine Being. For obvious reasons Kant has not felt called upon to point out the inadequacy of this inductive method to the solution of Critical problems. In A 42 Kant, arguing that our forms of intuition are subjective, claims that they do not necessarily belong to all beings, though they must belong to all men.[621] He is quite consistent in now maintaining[622] that their characteristics, as sensuous and derivative, do not necessarily preclude their being the common possession of all finite beings.

THE PARADOX OF INCONGRUOUS COUNTERPARTS

The purpose, as already noted, of the above sections II. to IV., as added in the second edition, is to afford ‘confirmation’ of the ideality of space and time. That being so, it is noticeable that Kant has omitted all reference to an argument embodied, for this same purpose, in § 13 of the Prolegomena. The matter is of sufficient importance to call for detailed consideration.[623]

As the argument of the Prolegomena is somewhat complicated, it is advisable to approach it in the light of its history in Kant’s earlier writings. It was to his teacher Martin Knutzen that Kant owed his first introduction to Newton’s cosmology; and from Knutzen he inherited the problem of reconciling Newton’s mechanical view of nature and absolute view of space with the orthodox Leibnizian tenets. In his first published work[624] Kant seeks to prove that the very existence of space is due to gravitational force, and that its three-dimensional character is a consequence of the specific manner in which gravity acts. Substances, he teaches, are unextended. Space results from the connection and order established between them by the balancing of their attractive and repulsive forces. And as the law of gravity is merely contingent, other modes of interaction, and therefore other forms of space, with more than three dimensions, must be recognised as possible.

“A science of all these possible kinds of space would undoubtedly be the highest enterprise which a finite understanding could undertake in the field of geometry.”[625]

In the long interval between 1747 and 1768 Kant continued to hold to some such compromise, retaining Leibniz’s view that space is derivative and relative, and rejecting Newton’s view that it is prior to, and pre-conditions, all the bodies that exist in it. But in that latter year he published a pamphlet[626] in which, following in the steps of the mathematician, Euler,[627] he drew attention to certain facts which would seem quite conclusively to favour the Newtonian as against the Leibnizian interpretation of space. The three dimensions of space are primarily distinguishable by us only through the relation in which they stand to our body. By relation to the plane that is at right angles to our body we distinguish ‘above’ and ‘below’; and similarly through the other two planes we determine what is ‘right’ and ‘left,’ ‘in front’ and ‘behind.’ Through these distinctions we are enabled to define differences which cannot be expressed in any other manner. All species of hops--so Kant maintains--wind themselves around their supports from left to right, whereas all species of beans take the opposite direction. All snail shells, with some three exceptions, turn, in descending from their apex downwards, from left to right. This determinate direction of movement, natural to each species, like the difference in spatial configuration between a right and a left hand, or between a right hand and its reflection in a mirror, involves in all cases a reference of the given object to the wider space within which it falls, and ultimately to space as a whole. Only so can its determinate character be distinguished from its opposite counterpart. For as Kant points out, though the right and the left hand are counterparts, that is to say, objects which have a common definition so long as the arrangement of the parts of each is determined in respect to its central line of reference, they are none the less inwardly incongruent, since the one can never be made to occupy the space of the other. As he adds in the Prolegomena, the glove of one hand cannot be used for the other hand. This inner incongruence compels us to distinguish them as different, and this difference is only determinable by location of each in a single absolute space that constrains everything within it to conform to the conditions which it prescribes. In three-dimensional space everything must have a right and a left side, and must therefore exhibit such inner differences as those just noted. Spatial determinations are not, as Leibniz teaches, subsequent to, and dependent upon, the relations of bodies to one another; it is the former that determine the latter.

“The reason why that which in the shape of a body exclusively concerns its relation to pure space can be apprehended by us only through its relation to other bodies, is that absolute space is not an object of any outer sensation, but a fundamental conception which makes all such differences possible.”[628]

Kant enforces his point by arguing that if the first portion of creation were a human hand, it would have to be either a right or a left hand. Also, a different act of creation would be demanded according as it was the one or the other. But if the hand alone existed, and there were no pre-existing space, there would be no inward difference in the relations of its parts, and nothing outside it to differentiate it. It would therefore be entirely indeterminate in nature, i.e. would suit either side of the body, which is impossible.

This adoption of the Newtonian view of space in 1768 was an important step forward in the development of Kant’s teaching, but could not, in view of the many metaphysical difficulties to which it leads, be permanently retained; and in the immediately following year--a year which, as he tells us,[629] “gave great light”--he achieved the final synthesis which enabled him to combine all that he felt to be essential in the opposing views. Though space is an absolute and preconditioning source of differences which are not conceptually resolvable, it is a merely subjective form of our sensibility.

Now it is significant that when Kant expounds this view in the Dissertation of 1770, the argument from incongruous counterparts is no longer employed to establish the absolute and pre-conditioning character of space, but only to prove that it is a pure non-conceptual intuition.

“Which things in a given space lie towards one side, and which lie towards the other, cannot by any intellectual penetration be discursively described or reduced to intellectual marks. For in solids that are completely similar and equal, but incongruent, such as the right and the left hand (conceived solely in terms of their extension), or spherical triangles from two opposite hemispheres, there is a diversity which renders impossible the coincidence of their spatial boundaries. This holds true, even though they can be substituted for one another in all those respects which can be expressed in marks that are capable of being made intelligible to the mind through speech. It is therefore evident that the diversity, that is, the incongruity, can only be apprehended by some species of pure intuition.”[630]

There is no mention of this argument in the first edition of the Critique, and when it reappears in the Prolegomena it is interpreted in the light of an additional premiss, and is made to yield a very different conclusion from that drawn in the Dissertation, and a directly opposite conclusion from that drawn in 1768. Instead of being employed to establish either the intuitive character of space or its absolute existence, it is cited as evidence in proof of its subjectivity. As in 1768, it is spoken of as strange and paradoxical, and many of the previous illustrations are used. The paradox consists in the fact that bodies and spherical figures, conceptually considered, can be absolutely identical, and yet for intuition remain diverse. This paradox, Kant now maintains[631] in opposition to his 1768 argument, proves that such bodies and the space within which they fall are not independent existences. For were they things in themselves, they would be adequately cognisable through the pure understanding, and could not therefore conflict with its demands. Being conceptually identical, they would necessarily be congruent in every respect. But if space is merely the form of sensibility, the fact that in space the part is only possible through the whole will apply to everything in it, and so will generate a fundamental difference between conception and intuition.[632] Things in themselves are, as such, unconditioned, and cannot, therefore, be dependent upon anything beyond themselves. The objects of intuition, in order to be possible, must be merely ideal.

Now the new premiss which differentiates this argument from that of 1768, and which brings Kant to so opposite a conclusion, is one which is entirely out of harmony with the teaching of the Critique. In this section of the Prolegomena Kant has unconsciously reverted to the dogmatic standpoint of the Dissertation, and is interpreting understanding in the illegitimate manner which he so explicitly denounces in the section on Amphiboly.

“The mistake ... lies in employing the understanding contrary to its vocation transcendentally [i.e. transcendently] and in making objects, i.e. possible intuitions, conform to concepts, not concepts to possible intuitions, on which alone their objective validity rests.”[633]

The question why no mention of this argument is made in the second edition of the Critique is therefore answered. Kant had meantime, in the interval between 1783 and 1787,[634] become aware of the inconsistency of the position. So far from being a paradox, this assumed conflict rests upon a false view of the function of the understanding.[635] The relevant facts may serve to confirm the view of space as an intuition in which the whole precedes the parts;[636] but they can afford no evidence either of its absoluteness or of its ideality. In 1768 they seem to Kant to prove its absoluteness, only because the other alternative has not yet occurred to him. In 1783 they seem to him to prove its ideality, only because he has not yet completely succeeded in emancipating his thinking from the dogmatic rationalism of the Dissertation.

As already noted,[637] Kant’s reason for here asserting that space is intuitive in nature, namely, that in it the parts are conditioned by the whole, is also his reason for elsewhere describing it as an Idea of Reason. The further implication of the argument of the Prolegomena, that in the noumenal sphere the whole is made possible only by its unconditioned parts, raises questions the discussion of which must be deferred. The problem recurs in the Dialectic in connection with Kant’s definition of the Idea of the unconditioned. In the Ideas of Reason Kant comes to recognise the existence of concepts which do not conform to the reflective type analysed by the traditional logic, and to perceive that these Ideas can yield a deeper insight than any possible to the discursive understanding. The above rationalistic assumption must not, therefore, pass unchallenged. It may be that in the noumenal sphere all partial realities are conditioned by an unconditioned whole.

* * * * *

=Concluding Paragraph.=[638]--The wording of this paragraph is in keeping with the increased emphasis which in the Introduction to the second edition is given to the problem, how a priori synthetic judgments are possible. Kant characteristically fails to distinguish between the problems of pure and applied mathematics, with resulting inconsecutiveness in his argumentation.

THE TRANSCENDENTAL DOCTRINE OF ELEMENTS

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Introduction

=I. Concerning Logic in General.=--This Introduction[639] which falls into four divisions, is extremely diffuse, and contributes little that is of more than merely architectonic value. It is a repetition of the last section of the general Introduction, and of the introductory paragraphs of the Aesthetic, but takes no account of the definitions given in either of those two places. It does not, therefore, seem likely that it could have been written in immediate sequence upon the Aesthetic. It is probably later than the main body of the Analytic.[640] In any case it is externally tacked on to it; as Adickes has noted,[641] it is completely ignored in the opening section of the Analytic.[642]

In treating of intuition in the first sentence, Kant seems to have in view only empirical intuition.[643] Yet he at once proceeds to state that intuition may be pure as well as empirical.[644] Also, in asserting that “pure intuition contains only the form under which something is intuited,” Kant would seem to be adopting the view that it does not yield its own manifold, a conclusion which he does not, however, himself draw.

In defining sensibility,[645] Kant again ignores pure intuition. Sensuous intuition, it is stated, is the mode in which we are affected by objects.[646] Understanding, in turn, is defined only in its opposition to sensibility, in the ordinary meaning of that term. Understanding is the faculty which yields thought of the object to which sense-affection is due. It is “the power of thinking the object of sensuous intuition”; and acts, it is implied, in and through pure concepts which it supplies out of itself.

“Without sensibility objects would not be given to us [i.e. the impressions, in themselves merely subjective contents, through which alone independent objects can be revealed to us, would be wanting]; without understanding they would not be thought by us [i.e. they would be apprehended only in the form in which they are given, viz. as subjective modes of our sensibility].”

Kant has not yet developed the thesis which the central argument of the Analytic is directed to prove, namely, that save through the combination of intuition and conception no consciousness whatsoever is possible. In these paragraphs he still implies that though concepts without intuition are empty they are not meaningless, and that though intuitions without concepts are blind they are not empty.[647] Their union is necessary for genuine knowledge, but not for the existence of consciousness as such.

“It is just as necessary to make our concepts sensuous, i.e. to add to them their object in intuition, as to make our intuitions intelligible, i.e. to bring them under concepts.”

Kant’s final Critical teaching is very different from this. Concepts are not first given in their purity, nor is “their object” added in intuition. Only through concepts is apprehension of an object possible, and only in and through such apprehension do concepts come to consciousness. Nor are intuitions “made intelligible” by being “brought under concepts.” Only as thus conceptually interpreted can they exist for consciousness. The co-operation of concept and intuition is necessary for consciousness in any and every form, even the simplest and most indefinite. Consciousness of the subjective is possible only in and through consciousness of the objective, and vice versa. The dualistic separation of sensibility from understanding persists, however, even in Kant’s later utterances; and, as above stated,[648] to this sharp opposition are due both the strength and the weakness of Kant’s teaching. Intuition and conception must, he here insists, be carefully distinguished. Aesthetic is the “science of the rules of sensibility in general.” Logic is the “science of the rules of understanding in general.”

Kant’s classification of the various kinds of logic[649] may be exhibited as follows:

{ pure { general { applied Logic { special { transcendental

Adickes[650] criticises Kant’s classification as defective, owing to the omission of the intermediate concept ‘ordinary.’ Adickes therefore gives the following table:

Logic =========================================== || | ||transcendental | ordinary || |_________________________ || | | || | special | general || | |_______________ || | | | || | | pure | applied || | | |

General logic is a logic of elements, i.e. of the absolutely necessary laws of thought, in abstraction from all differences in the objects dealt with, i.e. from all content, whether empirical or transcendental. It is a canon of the understanding in its general discursive or analytic employment. When it is pure, it takes no account of the empirical psychological conditions under which the understanding has to act. When it is developed as an applied logic, it proceeds to formulate rules for the employment of understanding under these subjective conditions. It is then neither canon, nor organon, but simply a catharticon of the ordinary understanding. Special logic is the organon of this or that science, i.e. of the rules governing correct thinking in regard to a certain class of objects. Only pure general logic is a pure doctrine of reason. It alone is absolutely independent of sensibility, of everything empirical, and therefore of psychology. Such pure logic is a body of demonstrative teaching, completely a priori. It stands to applied logic in the same relation as pure to applied ethics.

“Some logicians, indeed, affirm that logic presupposes psychological principles. But it is just as inappropriate to bring principles of this kind into logic as to derive the science of morals from life. If we were to take the principles from psychology, that is, from observations on our understanding, we should merely see how thought takes place, and how it is affected by the manifold subjective hindrances and conditions; so that this would lead only to the knowledge of contingent laws. But in logic the question is not of contingent, but of necessary laws; not how we do think, but how we ought to think. The rules of logic, then, must not be derived from the contingent, but from the necessary use of the understanding which without any psychology a man finds in himself. In logic we do not want to know how the understanding is and thinks, and how it has hitherto proceeded in thinking, but how it ought to proceed in thinking. Its business is to teach us the correct use of reason, that is, the use which is consistent with itself.”[651]

By a canon Kant means a system of a priori principles for the correct employment of a certain faculty of knowledge.[652] By an organon Kant means instruction as to how knowledge may be extended, how new knowledge may be acquired. A canon formulates positive principles through the application of which a faculty can be directed and disciplined. A canon is therefore a discipline based on positive principles of correct use. The term discipline is, however, reserved by Kant[653] to signify a purely negative teaching, which seeks only to prevent error and to check the tendency to deviate from rules. When a faculty has no correct use (as, for instance, pure speculative reason), it is subject only to a discipline, not to a canon. A discipline is thus “a separate, negative code,” “a system of caution and self-examination.” It is further distinguished from a canon by its taking account of other than purely a priori conditions. It is related to a pure canon much as applied is related to general logic. As a canon supplies principles for the directing of a faculty, its distinction from an organon obviously cannot be made hard and fast. But here as elsewhere Kant, though rigorous and almost pedantic in the drawing of distinctions, is correspondingly careless in their application. He describes special logic as the organon of this or that science.[654] We should expect from the definition given in the preceding sentence that it would rather be viewed as a canon. In A 46 = B 63 Kant speaks of the Aesthetic as an organon.

=II. Concerning Transcendental Logic.=--It is with the distinction between general and transcendental logic that Kant is chiefly concerned. It is a distinction which he has himself invented, and which is of fundamental importance for the purposes of the Critique. Transcendental logic is the new science which he seeks to expound in this second main division of the Doctrine of Elements. The distinction, from which all the differences between the two sciences follow, is that while general logic abstracts from all differences in the objects known, transcendental logic abstracts only from empirical content. On the supposition, not yet proved by Kant, but asserted in anticipation, that there exist pure a priori concepts which are valid of objects, there will exist a science distinct in nature and different in purpose from general logic. The two logics will agree in being a priori, but otherwise they will differ in all essential respects.

The reference in A 55 = B 79 to the forms of intuition is somewhat ambiguous. Kant might be taken as meaning that in transcendental logic abstraction is made not only from everything empirical but also from all intuition. That is not, however, Kant’s real view, or at least not his final view. In sections A 76-7 = B 102, A 130-1 = B 170, and A 135-6 = B 174-5, which are probably all of later origin, he states his position in the clearest terms. Transcendental logic, he there declares, differs from general logic in that it is not called upon to abstract from the pure a priori manifolds of intuition.[655] This involves, it may be noted, the recognition, so much more pronounced in the later developments of Kant’s Critical teaching, of space and time as not merely forms for the apprehension of sensuous manifolds but as themselves presenting to the mind independent manifolds of a priori nature.

As the term transcendental indicates, the new logic will have as its central problems the origin, scope, conditions and possibility of valid a priori knowledge of objects. None of these problems are treated in general logic, which deals only with the understanding itself. The question which it raises is, as Kant says in his Logic,[656] How can the understanding know itself? The question dealt with by transcendental logic we may formulate in a corresponding way: How can the understanding possess pure a priori knowledge of objects? It is a canon of pure understanding in so far as that faculty is capable of synthetic, objective knowledge a priori.[657] General logic involves, it is true, the idea of reference to objects,[658] but the possibility of such reference is not itself investigated. In general logic the understanding deals only with itself. It assumes indeed that all objects must conform to its laws, but this assumption plays no part in the science itself.

A further point, not here dwelt upon by Kant, calls for notice, namely, that the activities of understanding dealt with by general logic are its merely discursive activities,--those of discrimination and comparison; whereas those dealt with by transcendental logic are the originative activities through which it produces a priori concepts from within itself, and through which it attains, independently of experience, to an a priori determination of objects. Otherwise stated, general logic deals only with analytic thinking, transcendental logic with the synthetic activities that are involved in the generation of the complex contents which form the subject matter of the analytic procedure.

=III. Concerning the Division of General Logic into Analytic and Dialectic.=[659]--The following passage from Kant’s Logic[660] forms an excellent and sufficient comment upon the first four paragraphs of this section:

“An important perfection of knowledge, nay, the essential and inseparable condition of all its perfection, is truth. Truth is said to consist in the agreement of knowledge with the object. According to this merely verbal definition, then, my knowledge, in order to be true, must agree with the object. Now I can only compare the object with my knowledge by this means, namely by having knowledge of it. My knowledge, then, is to be verified by itself, which is far from being sufficient for truth. For as the object is external to me, I can only judge whether my knowledge of the object agrees with my knowledge of the object. Such a circle in explanation was called by the ancients Diallelos. And, indeed, the logicians were accused of this fallacy by the sceptics, who remarked that this account of truth was as if a man before a judicial tribunal should make a statement, and appeal in support of it to a witness whom no one knows, but who defends his own credibility by saying that the man who had called him as a witness is an honourable man. The charge was certainly well-founded. The solution of the problem referred to is, however, absolutely impossible for any man.

“The question is in fact this: whether and how far there is a certain, universal, and practically applicable criterion of truth. For this is the meaning of the question, What is truth?...

“A universal material criterion of truth is not possible; the phrase is indeed self-contradictory. For being universal it would necessarily abstract from all distinction of objects, and yet being a material criterion, it must be concerned with just this distinction in order to be able to determine whether a cognition agrees with the very object to which it refers, and not merely with some object or other, by which nothing would be said. But material truth must consist in this agreement of a cognition with the definite object to which it refers. For a cognition which is true in reference to one object may be false in reference to other objects. It is therefore absurd to demand a universal material criterion of truth, which is at once to abstract and not to abstract from all distinction of objects.

“But if we ask for a universal formal criterion of truth, it is very easy to decide that there may be such a criterion. For formal truth consists simply in the agreement of the cognition with itself when we abstract from all objects whatever, and from every distinction of objects. And hence the universal formal criteria of truth are nothing but universal logical marks of agreement of cognitions with themselves, or, what is the same thing, with the general laws of the understanding and the Reason. These formal universal criteria are certainly not sufficient for objective truth, but yet they are to be viewed as its conditio sine qua non. For before the question, whether the cognition agrees with the object, must come the question, whether it agrees with itself (as to form). And this is the business of logic.”[661]

The remaining paragraphs[662] of Section III. may similarly be compared with the following passage from an earlier section of Kant’s Logic:[663]

“Analytic discovers, by means of analysis, all the activities of reason which we exercise in thought. It is therefore an analytic of the form of understanding and of Reason, and is justly called the logic of truth, since it contains the necessary rules of all (formal) truth, without which truth our knowledge is untrue in itself, even apart from its objects. It is therefore nothing more than a canon for deciding on the formal correctness of our knowledge.

“Should we desire to use this merely theoretical and general doctrine as a practical art, that is, as an organon, it would become a dialectic, i.e. a logic of semblance (ars sophistica disputatoria), arising out of an abuse of the analytic, inasmuch as by the mere logical form there is contrived the semblance of true knowledge, the characters of which must, on the contrary, be derived from agreement with objects, and therefore from the content.

“In former times dialectic was studied with great diligence. This art presented false principles in the semblance of truth, and sought, in accordance with these, to maintain things in semblance. Amongst the Greeks the dialecticians were advocates and rhetoricians who could lead the populace wherever they chose, because the populace lets itself be deluded with semblance. Dialectic was therefore at that time the art of semblance. In logic, also, it was for a long time treated under the name of the art of disputation, and during that period all logic and philosophy was the cultivation by certain chatterboxes of the art of semblance. But nothing can be more unworthy of a philosopher than the cultivation of such an art. Dialectic in this form, therefore, must be altogether suppressed, and instead of it there must be introduced into logic a critical examination of this semblance.

“We should then have two parts of logic: the analytic, which will treat of the formal criteria of truth, and the dialectic, which will contain the marks and rules by which we can know that something does not agree with the formal criteria of truth, although it seems to agree with them. Dialectic in this form would have its use as a cathartic of the understanding.”

Dialectic is thus interpreted in a merely negative sense. It is, Kant says, a catharticon. So far from being an organon, it is not even a canon. It is merely a discipline.[664] By this manner of defining dialectic Kant causes some confusion. It does not do justice to the scope and purpose of that section of the Critique to which it gives its name.[665]

=IV. Concerning the Division of Transcendental Logic into Transcendental Analytic and Dialectic.=--The term object[666] is used throughout this section in two quite distinct senses. In the second and third sentences it is employed in its wider meaning as equivalent to content or matter. In the fourth sentence it is used in the narrower and stricter sense, more proper to the term, namely, as meaning ‘thing.’ Again, in the fifth sentence content (Inhalt) would seem to be identified with object in the narrower sense, while in the sixth sentence matter (Materie, a synonym for content) appears to be identified with object in the wider sense. Transcendental Dialectic, in accordance with the above account of its logical correlate, is defined in a manner which does justice only to the negative side of its teaching. Its function is viewed as merely that of protecting the pure understanding against sophistical illusions.[667]

THE TRANSCENDENTAL LOGIC

DIVISION I

THE TRANSCENDENTAL ANALYTIC

The chief point of this section[668] lies in its insistence that, as the Analytic is concerned only with the pure understanding, the a priori concepts with which it deals must form a unity or system. Understanding is viewed as a separate faculty, and virtually hypostatised. As a separate faculty, it must, it is implied, be an independent unity, self-containing and complete. Its concepts are determined in number, constitution, and interrelation, by its inherent character. They originate independently of all differences in the material which they are employed to organise.

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I. THE ANALYTIC OF CONCEPTS

=Introductory Paragraph.=--Kant’s view of the understanding as a separate faculty is in evidence again in this paragraph.[669] The Analytic is a “dissection of the faculty of the understanding.” A priori concepts are to be sought nowhere but in the understanding itself, as their birthplace. There “they lie ready till at last, on the occasion of experience, they become developed.” But such statements fail to do justice to Kant’s real teaching. They would seem to reveal the persisting influence of the pre-Critical standpoint of the Dissertation.

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