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Crossover QueriesDwelling with Negatives, Embodying Philosophy's Others$
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Edith Wyschogrod

Print publication date: 2006

Print ISBN-13: 9780823226061

Published to Fordham Scholarship Online: March 2011

DOI: 10.5422/fso/9780823226061.001.0001

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The Mathematical Model in Plato and Some Surrogates in a Jain Theory of Knowledge

The Mathematical Model in Plato and Some Surrogates in a Jain Theory of Knowledge

(p.464) 30 The Mathematical Model in Plato and Some Surrogates in a Jain Theory of Knowledge
Crossover Queries

Edith Wyschogrod

Fordham University Press

This view of arithmetic structure permits a solution of what has been called the “ontological methexis” problem, that is, the question of how each object remaining solidary (monadic) can combine with other objects into groups or assemblages. The solution is suggested by the nature of Ideal and Mathematical Numbers. Existing objects can participate in a genus since the genus exhibits the mode of being each ideal number, yet its members, like the homogeneous monads in the realm of Mathematical Number (which are themselves outside change and time) can nevertheless be arranged into definite numbers. It is clear that, for Plato, the sense world is transcended by organizing the multiplicity of sensibles into more comprehensive assemblages and by using the objects of arithmetic and geometry to provide a model for the world of Forms. The Jain scheme depends on no such model, for it assumes that no objects or relations in that world, and no faculty commensurate with it, however complex, can serve as a paradigm for ultimate knowledge.

Keywords:   ontological methexis, Mathematical Number, Plato, arithmetic, geometry, Forms, Jain scheme, knowledge

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