Logic Journal of IGPL· 2012Q2
Mathematical pluralism
- 92citations
- Q2SCImago
- 2012year
Short summary
This paper argues that the diversity of mathematical practices, including those using non-classical logics, cannot be reduced to Zermelo-Fraenkel set theory, proposing an analogy to the plurality of games.
AI-generated from the title and abstract; the full text is not read.
Key points
- Mathematical investigations are diverse and cannot all be reduced to Zermelo-Fraenkel set theory.
- Non-classical logics, such as those in intuitionist mathematics, demonstrate this diversity.
- The paper proposes an analogy between the plurality of mathematical systems and the plurality of games.
- Objections concerning pernicious relativism are considered and rejected.
AI-generated from the title and abstract; the full text is not read.
Abstract
There is a plurality of mathematical investigations. These cannot all be reduced to proofs within the framework of Zermelo Fraenkel set theory, if only because some of them use non-classical logic (such as the various branches of intuitionist mathematics). How is one to understand this situation? In this article, I suggest that one should see this plurality as analogous to the plurality of games, any of which may be played. Various objections are considered and rejected, including the charge that the picture engenders a pernicious relativism.
The authors' abstract, as published at the source. Logic Journal of IGPL, 2012 · DOI ↗
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Field: Theoretical Computer Science
Theoretical Computer ScienceMathematics