We need only draw attention to three points. Firstly, no justification is given of the term 'axiom'. Secondly, the argument does not really appeal to the doctrine of the categories, but only to the character of space and time as forms of perception. Thirdly, it need not appeal to space and time as forms of perception in the proper sense of ways in which we apprehend objects, but only in the sense of ways in which objects are related[5]; in other words, it need not appeal to Kant's theory of knowledge. The conclusion follows simply from the nature of objects as spatially and temporally related, whether they are phenomena or not. It may be objected that Kant's thesis is that _all_ objects of perception are extensive quantities, and that unless space and time are allowed to be ways in which _we must perceive_ objects, we cannot say that all objects will be spatially and temporally related, and so extensive quantities. But to this it may be replied that it is only true that all objects of perception are extensive quantities if the term 'object of perception' be restricted to parts of the physical world, i. e. to just those realities which Kant is thinking of as spatially and temporally related,[6] and that this restriction is not justified, since a sensation or a pain which has only intensive quantity is just as much entitled to be called an object of perception.
[6] The context shows that Kant is thinking only of such temporal relations as belong to the physical world, and not of those which belong to us as apprehending it. Cf. p. 139.
The anticipation of sense-perception consists in the principle that 'In all phenomena, the real, which is an object of sensation, has intensive magnitude, i. e. a degree'. The proof is stated thus:
"Apprehension merely by means of sensation fills only one moment (that is, if I do not take into consideration the succession of many sensations). Sensation, therefore, as that in the phenomenon the apprehension of which is not a successive synthesis advancing from parts to a complete representation, has no extensive quantity; the lack of sensation in one and the same moment would represent it as empty, consequently = 0. Now that which in the empirical perception corresponds to sensation is reality (_realitas phaenomenon_); that which corresponds to the lack of it is negation = 0. But every sensation is capable of a diminution, so that it can decrease and thus gradually vanish. Therefore, between reality in the phenomenon and negation there exists a continuous connexion of many possible intermediate sensations, the difference of which from each other is always smaller than that between the given sensation and zero, or complete negation. That is to say, the real in the phenomenon has always a quantity, which, however, is not found in apprehension, since apprehension takes place by means of mere sensation in one moment and not by a successive synthesis of many sensations, and therefore does not proceed from parts to the whole. Consequently, it has a quantity, but not an extensive quantity."