Plato Was Not a Mathematical Platonist

Elaine Landry

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English

Cambridge University Press
26 January 2023

Western philosophy: Ancient, to c 500; Philosophy of mathematics; History of mathematics

Series: Elements in the Philosophy of Mathematics

This Element shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's hypothetical method, by contrast, takes hypotheses as if they were first principles, so no metaphysical account of their truth is needed. Thus, we come to Plato's methodological as-if realism: in mathematics, we treat our hypotheses as if they were first principles, and, consequently, our objects as if they existed, and we do this for the purpose of solving problems. Taking the road suggested by Plato's Republic, this Element shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability. This title is also available as Open Access on Cambridge Core.

By: Elaine Landry
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 230mm, Width: 154mm, Spine: 5mm
Weight: 150g
ISBN: 9781009313780
ISBN 10: 1009313789
Series: Elements in the Philosophy of Mathematics
Pages: 62
Publication Date: 26 January 2023
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

Reviews for Plato Was Not a Mathematical Platonist

'… Landry's response to the Platonic call for collaboration with his text opens up the possibility of very fruitful debates.' Susanna Saracco, Metascience