of each is an intuition.  The a priori, immediate intuition of the one space is entirely different from the empirical, general conception of space, which is abstracted from the various spaces. (4) Determinate periods of time arise by limitation of the one, fundamental time.  Consequently this original time must be unlimited or infinite, and the representation of it must be an intuition, not a concept.  Time contains in itself an endless number of representations (its parts, times), but this is never the case with a generic concept, which, indeed, is contained as a partial representation in an endless number of representations (those of the individuals having the same name), and, consequently, comprehends them all under itself, but which never contains them in itself.  The general concept horse is contained in each particular representation of a horse as a general characteristic, and that of justice in each representation of a definite just act; time, however, is not contained in the different times, but they are contained in it.  Similarly the relation of infinite space to the finite spaces is not the logical relation of a concept to examples of it, but the intuitive relation of an unlimited whole to its limited parts.

The Prolegomena employs as a fifth proof for the intuitive character of space, an argument which had already appeared in the essay On the Ultimate Ground of the Distinction of Positions in Space.  There are certain spatial distinctions which can be grasped by intuition alone, and which are absolutely incapable of comprehension through the understanding—­for example, those of right and left, above and below, before and behind.  No logical marks can be given for the distinction between the object and its image in the mirror, or between the right ear and the left.  The complete description of a right hand must, in all respects (quality, proportionate position of parts, size of the whole), hold for the left as well; but, despite the complete similarity, the one hand cannot be exactly super-imposed on the other; the glove of the one cannot be worn on the other.  This difference in direction, which has significance only when viewed from a definite point, and the impossibility mentioned of a congruence between an object (right hand) and its reflected image (left hand) can be understood only by intuition; they must be seen and felt, and cannot be made clear through concepts, and, consequently, can never be explained to a being which lacks the intuition of space.

In the “transcendental” exposition of space and time Kant follows this “metaphysical” exposition, which had to prove their non-empirical, and non-discursive, hence their a priori and intuitive, character, with the proof that only such an explanation of space and time could make it conceivable how synthetic cognitions a priori can arise from them.  The principles of mathematics are of this kind.  The synthetic character of geometrical truths is explained by the intuitive nature of space, their apodictic character by its apriority, and their objective reality or applicability to empirical objects by the fact that space is the condition of (external) perception.  The like is true of arithmetic and time.