Article ID: CBB678905232

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

unapi

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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Authors & Contributors
Poincaré, Henri
Heinzmann, Gerhard
Lê, François
Duarte, German A.
Anne-Sandrine Paumier
Molaro, Aurelio
Concepts
Geometry
Mathematics
Philosophy of science
Philosophy
Epistemology
Psychology
Time Periods
19th century
20th century, early
20th century
18th century
17th century
Places
France
Europe
England
Italy
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