Mathematics and the conversion of the mind: Republic VII 522c1-531e

Ancient Philosophy 15 (2):359-391 (1995)

An account of how the mathematical sciences turn the mind away from becoming and towards being. There are four main conclusions. 1. The study of numbers, when treated independently of the other sciences, uses a particular conception of the nature of numbers to detach the mind from the influence of perceptible objects. 2. The study of ratios and proportions, explicitly the core of Plato's harmonics, is fundamental also to plane and solid geometry and astronomy. 3. Ratios and proportion form the basis for the synoptic vision of all the mathematical sciences. This vision is an essential preparation for dialectic because it makes mathematicians become aware of the limitations of the mathematics they have been engaged in but it also shows them how they can begin to overcome those limitations. 4. The main purpose of the study of numbers, treated finally in relation to the other sciences, is to calculate ratios.
Keywords Ancient Philosophy  Classical Studies  History of Philosophy
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ISBN(s) 0740-2007
DOI 10.5840/ancientphil19951523
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Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line.Miriam Byrd - 2018 - International Journal of the Platonic Tradition 12 (2):111-131.

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