Analysis of Plato's and Aristotle's Criticism of Parmenides' Unity of What-Is

In this article, I analyze one version of the criticism of Parmenides' thesis “what-is is one” in Plato (Soph. 244c8-9) and two versions of criticism of this thesis in Aristotle (Phys. A, 3). Plato bases his refutation on the assumption that Parmenides, who pronounced his thesis, must agree with the presence of two different entities - the name “what-is” and the name “one”, but it contradicts his thesis. The first version of Aristotle's criticism asserts that in Parmenides' thesis “one” as a property is different from “what-is” as a property, ergo etc. The second version of Aristotle's criticism asserts that in Parmenides' thesis “what-is” as a property is different from what it is inhered in, ergo etc. I have shown that all three versions of criticism are effective against Parmenides' thesis in the case of the interpretation of “what-is” in it as a real object. I have also shown that in the case of the interpretation of “what-is” Parmenides' thesis as a mental object, which is an internal object of the act of thinking, none of the versions refutes this thesis. In justifying my conclusions, I have used the notation for propositional attitudes reports with epistemic operators. Also, I have interpreted an internal object of thinking as an abstract object that encodes the characteristics, which are attributing to it in the act of thinking, but at the same time this abstract object is also capable of exemplifying some characteristics. I have used the exemplification-encoding distinction from E. Zalta's theory of abstract objects. In rewriting the three versions of Parmenides' refutation for the case of mental objects, I have replaced “names” and “what a property is inherent in” with abstract mental objects, and “properties” with characteristics encoded by abstract objects, whose characteristics are also mental objects. I have shown that the formalization of the first version of Aristotle's criticism could contain non-predicative functions in the sense of Principia Mathematica. I have revealed the structural similarity of Plato's refutation with the second version of Aristotle's refutation. The same can be said about the blocking of these refutations that I have considered.

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