The Problem is not Mathematics, but Mathematicians: Plato and the Mathematicians Again

Philosophia Mathematica 20 (2):170-199 (2012)
I argue against a formidable interpretation of Plato’s Divided Line image according to which dianoetic correctly applies the same method as dialectic. The difference between the dianoetic and dialectic sections of the Line is not methodological, but ontological. I maintain that while this interpretation correctly identifies the mathematical method with dialectic, ( i.e. , the method of philosophy), it incorrectly identifies the mathematical method with dianoetic. Rather, Plato takes dianoetic to be a misapplication of the mathematical method by a subset of practicing mathematicians. Thus, Plato’s critique of dianoetic is a not a critique of mathematics, as such, but of mathematicians.
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DOI 10.1093/philmat/nkq029
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S. Pollard (2013). Dianoia Left and Right. Philosophia Mathematica 21 (3):309-322.

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