Figure, Ratio, Form: Plato's Five Mathematical Studies

Apeiron 32 (4):73-88 (1999)
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Abstract
A close reading of the five mathematical studies Socrates proposes for the philosopher-to-be in Republic VII, arguing that (1) each study proposes an object the thought of which turns the soul towards pure intelligibility and that (2) the sequence of studies involves both a departure from the sensible and a return to it in its intelligible structure.
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