`Mathematical Platonism' Versus Gathering the Dead: What Socrates teaches Glaucon

Philosophia Mathematica 13 (2):115-134 (2005)
Glaucon in Plato's Republic fails to grasp intermediates. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. He says mathematical objects are eternal. Socrates urges a seriously debatable, and seriously defensible, alternative centered on the destruction of hypotheses. He offers his version of geometry and astronomy as refuting the charge that he impiously ‘ponders things up in the sky and investigates things under the earth and makes the weaker argument the stronger’. We relate his account briefly to mathematical developments by Plato's associates Theaetetus and Eudoxus, and then to the past 200 years' developments in geometry
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DOI 10.1093/philmat/nki010
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C. McLarty (2012). Introduction: Hypotheses and Progress. Philosophia Mathematica 20 (2):135-142.

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