Ebook: Plato's Mathematical Imagination: The Mathematical Passages in the Dialogues and their Interpretation

For two thousand years certain “mathematical” passages have puzzled Plato’s readers. Humanistic scholars have generally chosen to ignore them in favor of passages of more literary interest. Neo-Platonic enthusiasts have tended to center attention on them, with the apparent expectation that some mysterious, occult key to Plato’s philosophy and to the nature of reality had been enciphered there. Modern treatments tend to fall into one or the other of these traditions. On the one hand, the humanistic scholar who reads his Plato as belles-lettres uses the term “literary effect” to bypass explanation of obscure mathematical passages. In literature, it may be allowable to introduce meaningless passages to create an effect of difficulty; in philosophy, it is not.

In this study, the theory has been advanced that the “mathematical” passages in Plato which have seemed nonsense or riddles to previous students in fact describe diagrams which Plato had designed, and were intended to accompany and clarify his text. The result has been the recovery of new primary source material for the study of Plato.