A Commentary to Kant's 'Critique of Pure Reason'

by Norman Kemp Smith

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.