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Summary: Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.
Comment: This would be useful in an advanced undergraduate course on metaphysics, epistemology or philosophy of logic and mathematics. This is not an easy paper, but Leng does an excellent job of making clear some difficult ideas. The view defended is an important one in both philosophy of logic and philosophy of mathematics. Any reasonably comprehensive treatment of nominalism should include this paper.Export citation in BibTeX formatExport text citationView this text on PhilPapersExport citation in Reference Manager formatExport citation in EndNote formatExport citation in Zotero format
- Science, Logic & Mathematics
- Philosophy of Mathematics
- Epistemology of Mathematics
- What’s there to know?
What’s there to know?
Leng, Mary. What’s there to know?
2007, In M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge. OUP