The problems of the third division of the _Dialectic_ arises from an attempt to think of a whole which shall include both the known world and the mind that knows. This attempt, which Kant calls the ideal of pure reason, leads to proofs of the existence of God.
As the _Dialectic_ proceeds, it becomes clear that Kant has another list to hand. He enumerates, as the three great objects of metaphysical inquiry, God, Freedom, and immortality, and in his discussion of the ideas of reason he treats them principally as attempts to give definite and dogmatic answers to the problems suggested by these three topics.
Immortality is the subject of what Kant calls the paralogisms of rational psychology. He argues that all attempts to prove the immortality of the soul by a priori arguments involve an argument of this kind: they begin by noting that death is always dissolution of some kind, that, therefore, what is not made up of parts and cannot be dissolved, cannot die. Then they urge that the soul is not made up of parts, and therefore cannot die. The fallacy in this argument is that it treats the unity of the self as though it were an object of knowledge. We can show that knowledge is only possible if the self has a unity other than that of a spatial whole, but we cannot therefore argue that it must be exactly like a spatial whole, in the sense that death in it can only be brought about by dissolution, but unlike a spatial whole in that in it there is nothing to be dissolved. The real nature of the unity of the self, Kant argues, cannot be known. All we can do is to reject a priori arguments either for or against its immortality.
Freedom is treated in the third antinomy of pure reason, and to that Kant devotes most attention, but others of the antinomies are concerned with the difficulties arising from the application of spatial and temporal determinations to reality as a whole, and to the category of necessity. Kant makes a distinction between the first two and the second two antinomies. It is the first two that express the inadequacy of temporal or spatial determination to reality as a whole. All such determination implies measurement, and measurement is always a relation of part to part. The antitheses of both antinomies express the inadequacy of any number to the expression of the nature of the whole, the thesis the inadequacy of regarding reality as an aggregate or addition of any kind. Each is strong in what it denies, and Kant’s solution is that both thesis and antithesis are false, because you cannot apply spatial or temporal determination to the world as a whole.