Mathematics Without Foundation Putnam Pdf

Theoria: An International Journal for Theory, History and Foundations of Science

journal article

Hilary Putnam on the philosophy of logic and mathematics

Theoria: An International Journal for Theory, History and Foundations of Science

Published By: University of the Basque Country (UPV/EHU)

Theoria: An International Journal for Theory, History and Foundations of Science

https://www. jstor .org/stable/26450642

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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 view-points 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. 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.

Journal Information

Established in 1952 by Miguel Sánchez-Mazas, Theoria is one of the leading philosophy journals in the Spanish-speaking world. THEORIA cooperates with two Spanish philosophical societies: SOLOFICI and SEFA. It is regularly indexed in the following databases: Arts & Humanities Citation Index®, ISI Alerting Services, SCOPUS, Scimago, Current Contents®/Arts & Humanities, DOAJ, Bulletin Signaletique 519, ICYT, ISOC, MathSci,Mathematical Reviews, Current Mathematical Publications, Philosopher's Index, Repertoire bibliographique de la Philosophie. It also features prominently in national databases such as DICE and MIAR.

Publisher Information

The University of the Basque Country is a unique custodian of our age-old linguistic heritage: we have raised Basque language (the only pre Indo-European tongue still spoken) to the highest educational level.