2. French Criticism and the Philosophy of Discontinuity
In France, after the middle of the nineteenth century, the critical school is represented by the vigorous thinker Charles Renouvier (1815-1903), who in the name of logic and ethics attacks all idealistic and realistic attempts to construe being as a continuous totality. He directed his polemics with particular force against the concept of actual infinity, which he regarded as a logical contradiction and an empirical falsehood. For an infinite which is at the same time regarded as a determinate whole is a contradiction, and experience teaches us that the principle of definite number applies to everything. With actual infinity continuity is likewise destroyed, — for continuity must indeed presuppose infinitely many gradations, — and with continuity necessity. In opposition to Kant's attempt to prove the principle' of causality, Renouvier returns to Hume's position and thus attains a radical philosophy of discontinuity. He regards every distinction as a discontinuity. And as a matter of fact it is not only in our knowledge of nature that we are constantly compelled to recognize leaps. The first principles of our knowledge are postulated by a leap, i.e. by an act of choice. Renouvier was profoundly influenced by Kant's antinomies; it is his opinion however that, if we wish to retain the principles of logic, we are obliged to accept the theses and reject the antitheses.
Renouvier has published a sketch of his philosophical development in an exceedingly interesting essay found in Equisse d'une classification des systemes philosophiques (1885) (Comment je suis arrive a cette conclusion, ibid., II, pp. 355-405).—For the various phases
