On what Ontology Is and not-Is

TL;DR

This paper explores the relationship between logic and metaphysics in Plato's participation theory, revealing that his system's underlying logic is likely paraconsistent, which challenges traditional views.

Contribution

It provides a detailed analysis of Plato's participation theory, demonstrating its paraconsistent logical structure through textual and technical examination.

Findings

Plato's participation theory is linked to paraconsistent logic.

The contradiction principle was explicitly formulated by Plato.

Textual evidence supports the paraconsistent interpretation.

Abstract

In this paper I study the connection between logic and metaphysics in Plato's participation theory, from the structural properties of the latter. Although Plato was the first ever to formulate the contradiction principle explicitly (in the Phaedo), the logic underlying his system appears to be paraconsistent. This confirms an earlier suggestion by G. Priest. Its technical characteristics and the textual evidence supporting this interpretation are both studied in detail.