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]
[2] The assertion that all perceptions (i. e. all objects of perception) are extensive quantities relates, according to Kant, to the nature of objects, while the assertion that an event must have a necessary antecedent affirms that such an antecedent must exist, but gives no clue to its specific nature. Compare "But the existence of phenomena cannot be known _a priori_, and although we could be led in this way to infer the fact of some existence, we should not know this existence determinately, i. e. we could not anticipate the respect in which the empirical perception of it differed from that of other existences". (B. 221, M. 134). Kant seems to think that the fact that the dynamical principles relate to the existence of objects is a sufficient justification of their name.
It needs but little reflection to see that the distinctions which Kant draws between the mathematical and the dynamical principles must break down.
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.