Plato Was Not a Mathematical Platonist

This Element shows that Plato was not a mathematical Platonist, and kept a clear distinction between mathematical and metaphysical realism.

Elaine Landry (Author)

9781009313780, Cambridge University Press

Paperback / softback, published 26 January 2023

58 pages
23 x 15.4 x 0.5 cm, 0.15 kg

'… the author contends that Plato should not be read as a mathematical Platonist but rather as a methodological realist - or mathematical as-ifist - who treats mathematical objects as hypothetically real tools for solving problems, rather than as metaphysically existent entities … For contemporary philosophy of mathematics, this reading calls for renewed attention to actual mathematical practice and methodology, rather than the imposition of metaphysical assumptions that distort both Plato's views and the nature of mathematics itself.' Luis Giraldo González Ricardo, MathSciNet

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.

1. Introduction
2. The interprative lay of the land
3. The divided line
4. Book 7
5. The good in mathematics
6. Mathematics versus metaphysics
References.

Subject Areas: History of mathematics [PBX], Philosophy of mathematics [PBB], Western philosophy: Ancient, to c 500 [HPCA]