Putnam and the indispensability of mathematics

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Abstract

In this paper, I examine Putnam's nuanced views in the philosophy of mathematics, distinguishing three proposals: modalism (an interpretation of mathematics in terms of modal logic), quasi-empirical realism (that emphasizes the role and use of quasi-empirical methods in mathematics), and an indispensability view (that highlights the indispensable role of quantification over mathematical objects and the support such quantification provides for a realist interpretation of mathematics). I argue that, as he shifted through these views, Putnam aimed to preserve a semantic realist account of mathematics that avoids platonism. In the end, however, each of the proposals faces significant difficulties. A form of skepticism then emerges.

Original languageEnglish (US)
Pages (from-to)217-234
Number of pages18
JournalPrincipia
Volume17
Issue number2
DOIs
StatePublished - Aug 2013

Keywords

  • Indispensability argument
  • Modalism
  • Philosophy of mathematics
  • Putnam
  • Quine
  • Set

ASJC Scopus subject areas

  • Philosophy
  • History and Philosophy of Science

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