Hilary Putnam on the philosophy of logic and mathematics

  1. Sagüillo Fernández-Vega, José Miguel
Journal:
Theoria: an international journal for theory, history and foundations of science

ISSN: 0495-4548

Year of publication: 2018

Volume: 33

Issue: 2

Pages: 183-200

Type: Article

DOI: 10.1387/THEORIA.17626 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Theoria: an international journal for theory, history and foundations of science

Abstract

This paper focuses on Putnam’s conception of logical truth as grounded in his picture of mathematical practice and ontology. Putnam’s 1971 book Philosophy of Logic came one year later than Quine’s homonymous volume. In the first section, I compare these two Philosophies of Logic which exemplify realist-nominalist viewpoints in a most conspicuous way. The next section examines Putnam’s views on modality, moving from the modal qualification of his intuitive conception to his official generalized non-modal second-order set-theoretic concept of logical truth. In the third section, I emphasize how Putnam´s “mathematics as modal logic” departs from Quine’s “reluctant Platonism”. I also suggest a complementary view of Platonism and modalism showing them perhaps interchangeable but underlying different stages of research processes that make up a rich and dynamic mathematical practice. The final, more speculative section, argues for the pervasive platonistic conception enhancing the aims of inquiry in the practice of the working mathematician

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* I am grateful to the participants in the workshop “Updating indispensabilities: Hilary Putnam in Me-moriam” held in Santiago de Compostela at the end of November 2016 for discussion that followed my presentation. I am grateful to Concha Martínez, Matteo Plebani, Otávio Bueno, and John Corco-ran for comments on a previous version. My special thanks also go to two anonymous referees of Theo-ria for their insightful suggestions that significantly improved the present version. One report was es-pecially constructive, dialogical and detailed. 1 The research for this paper was supported by the Spanish Ministry of Economy and Competitivity and FEDER via the research projects FFI 2013-41415-P and FFI2017-82534-P.

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