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Article ID: CBB678905232

Poincaré on the Foundations of Arithmetic and Geometry. Part 2: Intuition and Unity in Mathematics (2017)

Dunlop, Katherine (Author)

HOPOS
Volume: 7
Issue: 1
Pages: 88-107

DOI: 10.1086/691130

URI: http://www.journals.uchicago.edu/doi/abs/10.1086/691130

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Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in this manner, intuition serves the epistemological function of warranting generalizations and justifying practices. In particular, it justifies the application of group-theoretic notions in geometry but not the use of set-theoretic notions in arithmetic.

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