To understand the title, we should first distinguish between lowercase-p platonism and capital-P Platonism: The former platonism refers to realism as an answer to the problem of universals, the latter Platonism refers to membership in the specific institution which Plato himself founded (the Academy, a school of philosophy at Athens). Plato is ergo a Platonist by definition, having founded the school at Athens. Since this essay deals with the problem of universals, we should also define this matter. The problem of universals was first framed in Plato's Parmenides, with an aporia which has endured for over two millennia. It is probably the oldest unresolved philosophical problem in history. The dialogue takes place during the festival known as the Great Panathenaea, in the deme Keramis of Athens, the site of a (fictional?) meeting between three famous philosophers of three different ages: Socrates (probably ~20), Zeno (~40), and Parmenides (~65). Parmenides was an established Italian philosopher, recorded with prestige in every ancient biography of the pre-Socratic philosophers. Zeno was Parmenides' student at his school in Italy. The Parmenides begins with Zeno reciting one of his many lost philosophical treatises (which remains anonymous in the dialogue). Socrates probes him on an argument advanced therein: an argument which, “maintain[s], in opposition to everything that is commonly said, that things are not many (127e).” This was the characteristic thrust of that Italian school of philosophy: that what exists is one and not many.

Socrates produces a counterargument for Zeno, using a metaphysical principle which Socrates had already invented in prior dialogues like Phaedo1: The principle of Separation (chorismos) between universals and particulars, that forms exist “themselves by themselves,&rqduo; (Phaedo 100b, Parmenides 129a; ipsa pro se or auto kath' auto). In fact, there is considerable difficulty in translating the Greek phrase auto kath' auto, since neither the Latin preposition pro nor the English preposition by resemble the exact meaning of the Greek preposition kata (here contracted to kath'). Given the relevant context and grammar, kata can be interpreted as any of the English prepositions “in,” “for,” or “according to”. It is therefore difficult to interpret Socrates' principle of Separation in modern English or in modern logic. So I go for recourse to Dr. Gregory Vlastos (1907-91), certainly the last great scholar of Classical philosophy and Plato to have been born in Constantinople. In 1954, Vlastos' Third man argument in the Parmenides was published, an essay concerning those, “two passages in the Parmenides purporting to prove that the Theory of Forms involves an infinite regress, which came to be dubbed within Plato's lifetime the 'Third Man' Argument (319).” The “Third Man” argument in fact refers to Aristotle's reconstruction of the same one advanced in the Parmenides, with different terms but the same form—a reconstruction which has been lost outside of secondary testimony3. In fact, the original Platonic version of this argument was advanced by Parmenides in response to Socrates' argument against Zeno, and it uses as a premise the same Separation principle which Socrates assumed in his argument. When academics refer to the “Theory of Forms” or especially the “High Theory of Form” or the “Early Theory of Form,” they generally mean a theory of form which adheres to the sort of Separation principle highlighted in the Parmenides.

This article is a work in progress– finishing soon.