A Mathematical Model for Plato's Theory of Forms

Abstract

Aims/ Objectives: In this article we construct a mathematical/topological framework for comprehending fundamental concepts in Plato's theory of Forms; specically the dual processes of: 1. The participation/partaking-methexis of the many particulars predicated as F to the Form-essence F, according to their degree of participation to it. 2. The presence-parousia of the Form-essence F to the particulars predicated as F, in analogy to their degree of participation to F as in 1. The theoretical foundation of our model is primarily based on a combination of both the Approximationist and Predicationalist approaches for Plato's theory of Forms, taking into account the degree of participation of the particulars to the Form, that are predicated to. In constructing our model we assume that there exists exactly one Form corresponding to every predicate that has a Form (Plato's `uniqueness thesis'), and to support our main theses we analyze textual evidence from various Platonic works. The mathematical model is founded on the dual notions of projective and inductive topologies, and their projective and inductive limits respectively.