Page:The World and the Individual, First Series (1899).djvu/563

This page needs to be proofread.

544

SUPPLEMENTARY ESSAY

by Bolzano, in the passage of his Paradoxien des Unendlichen, already cited, the typical instance chosen to exemplify the infinite is that system of truth, or of wahre Sätze, whose validity follows from any primary Satz, or from any collection of such Sätze. If the proposition A is true, it follows, as Bolzano points out, that the proposition which asserts that “A is true,” is also true. Call this proposition A’. Then the proposition “A’ is true,” is also true; and so on endlessly. While Bolzano has not Dedekind’s exact conception of the nature of a Kette, and does not expressly use Dedekind’s positive definition of the infinite, his example of the series of true propositions, A, A’, A’’, etc., — each of which is different from its predecessor, since it makes its predecessor the subject of which it asserts the predicate true, — is an example chosen wholly in the spirit of Dedekind’s later selection of the Gedankenwelt, and is an extremely simple instance of a self-representative system.^[1]

Realism, and the Third Conception of Being in our list, share alike, then, whatever difficulties may cluster about the conception of an infinitely self-representative system. What conception of Being can escape from this fate? Our own Fourth Conception?

No, as we must now expressly point out, our own conception of what it is to be makes the Real a Kette of the present type.

↑ The parallel Kette of knowledge was observed by Spinoza, Ethics, P. II, Prop. 43. In the tract, De Intell. Emendat., however, Spinoza tries to explain away the significance of the endlessness of the resulting series. In the Ethics he says that whoever knows, knows that he knows, so that to an adequate idea, an adequate idea of this idea is necessarily joined by God and man. But in the Tractatus he asserts that the idea of the idea is not a necessary accompaniment of the adequate idea, but merely may follow upon the adequate idea if we choose. The contrast of expression in the two passages is remarkable; and the question is of the most critical importance for the whole system of Spinoza. For if the idea, when adequate, is actually self-representative, the form of parallelism between extension and thought, asserted by Spinoza, finally breaks down, since, to avoid the troubles about the infinite, Spinoza expressly makes extended substance indivisible, so as to avoid making it a self-representative system. Furthermore, in any case, no precisely parallel process to the idea of the idea is to be found in extended substance.

[1] The parallel Kette of knowledge was observed by Spinoza, Ethics, P. II, Prop. 43. In the tract, De Intell. Emendat., however, Spinoza tries to explain away the significance of the endlessness of the resulting series. In the Ethics he says that whoever knows, knows that he knows, so that to an adequate idea, an adequate idea of this idea is necessarily joined by God and man. But in the Tractatus he asserts that the idea of the idea is not a necessary accompaniment of the adequate idea, but merely may follow upon the adequate idea if we choose. The contrast of expression in the two passages is remarkable; and the question is of the most critical importance for the whole system of Spinoza. For if the idea, when adequate, is actually self-representative, the form of parallelism between extension and thought, asserted by Spinoza, finally breaks down, since, to avoid the troubles about the infinite, Spinoza expressly makes extended substance indivisible, so as to avoid making it a self-representative system. Furthermore, in any case, no precisely parallel process to the idea of the idea is to be found in extended substance.

[1]