Front Page Titles (by Subject) SUPPLEMENT VIII - Critique of Pure Reason
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SUPPLEMENT VIII - Friedrich Max Müller, Critique of Pure Reason 
Immanuel Kant’s Critique of Pure Reason. In Commemoration of the Centenary of its First Publication. Translated into English by F. Max Mueller (2nd revised ed.) (New York: Macmillan, 1922).
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4. Space is represented as an infinite given quantity. Now it is quite true that every concept is to be thought as a representation, which is contained in an infinite number of different possible representations (as their common characteristic), and therefore comprehends them: but no concept, as such, can be thought as if it contained in itself an infinite number of representations. Nevertheless, space is so thought (for all parts of infinite space exist simultaneously). Consequently, the original representation of space is an intuition a priori, and not a concept.
Transcendental Exposition of the Concept of Space
I understand by transcendental exposition (Erörterung), the explanation of a concept, as of a principle by which the possibility of other synthetical cognitions a priori can be understood. For this purpose it is necessary, 1. That such cognitions really do flow from the given concept. 2. That they are possible only under the presupposition of a given mode of explanation of such concept.
Geometry is a science which determines the properties of space synthetically, and yet a priori. What then must be the representation of space, to render such a knowledge of it possible? It must be originally intuitive; for it is impossible from a mere concept to deduce propositions which go beyond that concept, as we do in geometry (Introduction V. See Suppl. VI). That intuition, however, must be a priori, that is, it must exist within us before any perception of the object, and must therefore be pure, not empirical intuition. For all geometrical propositions are apodictic, that is, connected with the consciousness of their necessity, as for instance the proposition, that space has only three dimensions; and such propositions cannot be empirical judgments, nor conclusions from them (Introduction II. See Suppl. IV. ii).
How then can an external intuition dwell in the mind anterior to the objects themselves, and in which the concept of objects can be determined a priori? Evidently not otherwise than so far as it has its seat in the subject only, as the formal condition under which the subject is affected by the objects and thereby is receiving an immediate representation, that is, intuition of them; therefore as a form of the external sense in general.
It is therefore by our explanation only that the possibility of geometry as a synthetical science a priori becomes intelligible. Every other explanation, which fails to account for this possibility, can best be distinguished from our own by that criterion, although it may seem to have some similarity with it.