In like manner, the apparent antinomies on which such a scepticism builds will be found to resolve themselves for a system based on a deeper insight into the nature of things.
These antinomies are four - two mathematical, two dynamical - connected with (I) the limitation of the universe in respect of space and time, (2) the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist), (3) the problem of freedom in relation to universal causality, (4) the existence of a universal being - about each of which pure reason contradicts the empirical, as thesis and antithesis.
Resultant determinate judgments, presumes of course Doivi the doctrine of the interpenetration of ideas laid down in the Sophistes as the basis of predication, but its use precedes the positive development of that formula, though not, save very vaguely, the exhibition of it, negatively, in the antinomies of the one and the many in the Parmenides.
Due attention to the relation between understanding and reason enables us to solve the antinomies and to discover their precise origin and significance.
The antinomies with which it concludes are more naturally taken as a prelude to the discussion of the Sophistes than as an unnecessary retreatment of the doctrine of the one and the many in a more negative form.