Norbert Wiener 1894–1964 by Pesi R. Masani

By Pesi R. Masani

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Gibbs on statistical mechanics and the Einstein-Smoluchowski papers on the Brownian motion, which were to prove of lasting value, cf. § 7D below. One wonders whether Wiener would have received the wise counsel he obtained from Russell had he been a student in our present fragmented and watered-down universities. The work of the logical school in Cambridge (c. 1914) was constricted by the absence of metamathematics. The only contribution to axiomatic set theory that came from Wiener's contacts with Russell was his theoretical definition of the ordered pair as a set [14a].

In this approach we see an inclination on Wiener's part towards the concept of metalanguage and towards the thought that was to come with Wittgenstein in 1919, to wit, "What we cannot talk about we must pass over in silence" {W14, p. 15I}. Relativism is Wiener's term for the philosophical position that denies the possibility of certitude in human knowledge, but not the existence of certainty. It is not to be confused with pragmatism. Indeed Wiener questions the Protagorean formula "man is the measure of all things ...

For each of the sets {l, 2, 3, ... }, {2, 3, 4, ... }, {3, 4, 5, ... }, etc. is infinite and therefore a member of I, and there are infinitely many of thcm. Thus I is itself an infinite set, and so IE 1. Now consider Russell's set R, which by definition has as members all and only those sets X which are not members of themselves; in brief, X ER if & only if X $ X. (1) Given a set A, the formula (1) enables us to give a direct answer to the question: Is A a member of R? It is, if A $ A; it is not, if A E A.

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