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Elaine Landry reconsiders the relationship between Plato and mathematical Platonism. Reading the Divided Line and Book 7 of the Republic, she argues that Plato distinguishes the methods of mathematics from those of philosophical inquiry. The mathematician can proceed from hypotheses treated as first principles without first providing a metaphysical account of the objects involved.
The discussion compares interpretations of Plato, follows the changes between the Republic’s accounts, and develops the idea of methodological ‘as-if’ realism. Sections on the good in mathematics and on mathematics versus metaphysics connect this close reading to questions about mathematical practice, foundations and applicability. The book is an adult philosophical study, with its argument, diagram, notes and bibliography preserved in the original edition.
Elaine Landry. Plato Was Not a Mathematical Platonist. Cambridge University Press, 2023. https://doi.org/10.1017/9781009313797. Licensed CC BY-NC 4.0; the unchanged original edition and its required notices are retained.