Willard Van Orman Quine

260 daniel isaacson
15. “I had been fascinated by a symmetrical little formula in Couturat
[Algebra of Logic, cited p. 59] having to do with ways of combining
classes. By trial and error I found the general law of which that formula
was a special case. The goal I set myself for my honors thesis was a
proof of this law within the system of Principia....Theproof took eighteen
pages of symbols. Three years later in Vienna I got the eighteen
pages down to three for the Journal of the London Mathematical Society
[“A Theorem in the Calculus of Classes,” vol. 8 (1933): 89–95]”
(TL 72–3).
16. “Nobody at Oberlin knew modern logic; however, the chairman of the
mathematics department, William D. Cairns, made inquiries and got
me the books. They were Venn’s Symbolic Logic, Peano’s Formulaire
de mathématiques, Couturat’s Algebra of Logic, Whitehead’s Introduction
to Mathematics, Keyser’s Mathematical Philosophy, Russell’s Principles
of Mathematics, and the crowning glory, Whitehead and Russell’s
Principia Mathematica” (TL 59).
17. “I went to Whitehead’s flat every two weeks to report my progress and
problems. He would listen until I reached a point suited to a philosophical
tangent on his part. The sessions impressed me but yielded little
logic” (TL 84).
18. Intensional is opposed to extensional. A predicate is extensional if it is
determined by the things to which it applies, extensional if not. An operation
that applies to sentences is extensional if the outcome depends
only on the truth-value(s) of the sentence(s) to which it applies – e.g., the
operation that goes from sentences ‘p’ and ‘q’ to the sentence ‘p if and
only if q’ as opposed to the operation that goes from sentences ‘p’ and
‘q’ to the sentence ‘p means the same as q’. Similarly ‘not p’ as opposed
to ‘necessarily p’ or ‘so-and-so believes that p’. For a taste of Quine’s
strictures on modal logic, see TGMI.
19. This recollection by Quine seems odd, given that, also by his account,
he had come to Vienna in part on the advice of Herbert Feigl, who had
been a member of the Vienna Circle from its informed inception in 1924
(see Feigl 1974, 7), and that the circle had gone public, with publication
of its manifesto, by the time Feigl met Quine at Harvard in 1930.
20. Quine republished this passage in both of his autobiographies (A 12–3
and TL 98).
21. There was a fourth lecture, entitled “Logical Positivism,” which Quine
delivered at Radcliffe College on December 17, 1934, but no complete
text seems to have survived (Creath 1990, ix). The aim of this lecture
was to make some of this material available to the female students of
Radcliffe College, who at that time were taught separately from Harvard
men.
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