ENGLISH

Plato Was Not a Mathematical Platonist

By Elaine Landry

Book information

Publisher
Cambridge University Press
Year
2023
ISBN
1009313789, 9781009313780, 9781009313797
Language
english
Format
PDF
Filesize
1 MB (1154487 bytes)
Series
Elements in the Philosophy of Mathematics
Pages
\58
Time added
2023-01-27 14:08:48

Description

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. Cover Title page Copyright page Plato Was Not a Mathematical Platonist Contents 1 Introduction 2 The Interpretive Lay of the Land 3 The Divided Line 4 Book 7 5 The Good in Mathematics 6 Mathematics Versus Metaphysics References Acknowledgments

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