Hilary Putnam on the philosophy of logic and mathematics

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

ISSN: 0495-4548

Ano de publicación: 2018

Volume: 33

Número: 2

Páxinas: 183-200

Tipo: Artigo

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

Outras publicacións en: Theoria: an international journal for theory, history and foundations of science

Resumo

Este artículo estudia la concepción de Putnam de verdad lógica que emana de su visión de la práctica de la matemática y de su ontología. Philosophy of Logic, el libro de 1971 de Putnam surge un año más tarde que el homónimo de Quine. En la primera sección, se comparan estas dos Filosofías de la Lógica que ejemplifican los puntos de vista del realismo y del nominalismo de modo conspicuo. La siguiente sección examina el enfoque de la modalidad de Putnam, que va desde la cualificación modal de su caracterización intuitiva de validez lógica a su concepción oficial generalizada no-modal conjuntista de segundo orden. La tercera sección subraya el modo en que «la matemática como lógica modal» de Putnam se distancia del «Platonism a regañadientes» de Quine. Aquí se sugiere una visión complementaria del Platonism y del modalismo, los cuales, aunque quizás intercambiables, se muestran subyaciendo a los diferentes estadios del proceso de investigación de una práctica de la matemática rica y dinámica. La sección final, más especulativa, conjetura algunas razones de la persistente concepción platónica implícita en la práctica del matemático.

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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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