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Additional info for Carnap, Tarski, and Quine at Harvard: Conversations on Logic, Mathematics, and Science
CHWISTEK’S ‘NOMINALISM’ In May 1940, months before the finitist-nominalist project is proposed and explored, Tarski visited the University of Chicago, where he and Carnap had an extended and wide-ranging discussion. Carnap’s notes record that Tarski said With the higher types, Platonism begins. The tendencies of Chwistek and others (“Nominalism”) to talk only about describable things are healthy. The only problem is finding a good execution. ], but perhaps with unrestricted operators; in the second language, individuals that are identical to or correspond to the sentential functions in the first language, so properties of natural numbers expressible in the first language; in the third language, as individuals those properties expressible in the second lan- 22.
T he obser vat io n al ter ms. First Justification: Verständlichkeit 33 mathematics is effected by means of the rules of application” of pure mathematics to synthetic sentences (Carnap 1934/1937, 327). 1. But what is the point of producing such a partial interpretation? What does it achieve? In Foundations, Carnap first introduces the issue of the understandability of a physical theory in the following terms: (how) can a layperson understand the content of the theory? Suppose that we intend to construct an interpreted system of physics— or the whole of science.
He calls numbers—which, on his preferred analysis, are classes of classes—‘fictions of fictions’: Numbers are classes of classes, and classes are logical fictions, so that numbers are, as it were, fictions at two removes, fictions of fictions. Therefore, you do not have as ultimate constituents of your world, these queer things that you are inclined to call numbers. (Russell 1918/1956, 270) The fact that the leading philosophical luminary of Carnap, Tarski, and Quine’s early careers called classes ‘fictions’ and declared numbers, the things successfully manipulated by six-year-old children, to be ‘queer things’ could play some role in inclining Tarski, Quine, and others to consider the refusal to allow numbers into the universe of discourse prima facie plausible or reasonable.
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