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Tolerance and Analyticity in Carnap's Philosophy of Mathematics

Michael Friedman

in Future Pasts

Published in print September 2001 | ISBN: 9780195139167
Published online November 2003 | e-ISBN: 9780199833214 | DOI: http://dx.doi.org/10.1093/019513916X.003.0011
 Tolerance and Analyticity in Carnap's Philosophy of Mathematics

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This essay is an interpretation of Carnap’s principle of tolerance in his 1934 Logical Syntax of Language, as expressed in his philosophy of mathematics. Friedman argues that Carnap’s deepest philosophical motivation was to offer scientifically minded philosophers an intellectual responsible, undogmatic way out of their philosophical perplexities. Carnap’s dream of replacing dogmatic metaphysical dispute with the construction of formalized languages failed, for interesting reasons internal to the development of logic. Carnap hoped to provide a purely formal characterization of the intuitive distinction between questions which concern the real natures of objects and those which merely concern alternative ways of speaking. Yet in relying on Gödel’s arithmetization of syntax to formulate a language-relative distinction between synthetic and analytic truth, Carnap’s Syntax philosophy foundered on the incompleteness theorem, for that result shows that there is in principle no wholly formal (philosophical neutral) way to survey the logical consequences of each and every alternative theory of mathematics. This left Carnap with no way to formulate his principle of tolerance neutrally.

Keywords: Carnap; logical syntax; principle of tolerance; analytic/synthetic distinction; Gödel’s incompleteness theorem; history of analytic philosophy; foundations of mathematics

Chapter.  18024 words. 

Subjects: History of Western Philosophy

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