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 language | English (US) |
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Pages (from-to) | 217-234 |
Number of pages | 18 |
Journal | Principia |
Volume | 17 |
Issue number | 2 |
DOIs | |
State | Published - Aug 2013 |
Keywords
- Indispensability argument
- Modalism
- Philosophy of mathematics
- Putnam
- Quine
- Set
ASJC Scopus subject areas
- Philosophy
- History and Philosophy of Science