Foundations of mathematics: metaphysics, epistemology, structure

Stewart Shapiro

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation fir mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields. their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics.

Original languageEnglish
Pages (from-to)16-37
Number of pages22
JournalThe Philosophical Quarterly
Volume54
Issue number214
DOIs
Publication statusPublished - Jan 2004

Keywords

  • INDEFINITE EXTENSIBILITY

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