[15] It is difficult to see how Kant could meet the criticism that here, contrary to his intention, he is treating physical objects as things in themselves. Cf. p. 265.
[16] B. 182-3, M. 110-11.
[17] B. 207-18, M. 125-32.
[18] The italics are mine.
CHAPTER XI
THE MATHEMATICAL PRINCIPLES
As has been pointed out,[1] the aim of the second part of the Analytic of Principles is to determine the a priori principles involved in the use of the categories under the necessary sensuous conditions. These principles Kant divides into four classes, corresponding to the four groups of categories, and he calls them respectively 'axioms of perception', 'anticipations of sense-perception', 'analogies of experience', and 'postulates of empirical thought'. The first two and the last two classes are grouped together as 'mathematical' and 'dynamical' respectively, on the ground that the former group concerns the perception of objects, i. e. their nature apprehended in perception, while the latter group concerns their existence, and that consequently, since assertions concerning the existence of objects presuppose the realization of empirical conditions which assertions concerning their nature do not, only the former possesses an absolute necessity and an immediate evidence such as is found in mathematics.[2] These two groups of principles are not, as their names might suggest, principles within mathematics and physics, but presuppositions of mathematics and physics respectively. Kant also claims appropriateness for the special terms used of each minor group to indicate the kind of principles in question, viz. 'axioms', 'anticipations', 'analogies', 'postulates'. But it may be noted as an indication of the artificiality of the scheme that each of the first two groups contains only one principle, although Kant refers to them in the plural as axioms and anticipations respectively, and although the existence of three categories corresponding to each group would suggest the existence of three principles.
The axiom of perception is that 'All perceptions are extensive quantities'. The proof of it runs thus: