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The Adventure of ReasonInterplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940$
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Paolo Mancosu

Print publication date: 2010

Print ISBN-13: 9780199546534

Published to Oxford Scholarship Online: May 2011

DOI: 10.1093/acprof:oso/9780199546534.001.0001

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Harvard 1940–1941: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science

Harvard 1940–1941: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science

Chapter:
(p.361) 13 Harvard 1940–1941: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science
Source:
The Adventure of Reason
Author(s):

Paolo Mancosu (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199546534.003.0013

Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among them during the year. These conversations centred around semantical issues related to the analytic/synthetic distinction and on the project of a finitist/nominalist construction of mathematics and science. Carnap’s Nachlass in Pittsburgh contains a set of detailed notes, amounting to more than 80 typescripted pages, taken by Carnap while these discussions were taking place. This Chapter presents a survey of these notes with special emphasis on Tarski’s rejection of the analytic/synthetic distinction, the passage from typed languages to first-order languages, Tarski’s finitism/nominalism, and the construction of a finitist language for mathematics and science.

Keywords:   Keywords: Carnap, Tarski, finitism, nominalism, typed languages, analytic, synthetic

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