Since Proclus replies at length to the Third Man Argument
in his Commentary on the Parmenides, we cannot supposc that his metaphysical system was entirely the product of this fallacy (p.
As Lewis reads him, the Aristotle of the Categories takes the moral of the Third Man Argument to be that relations of ontological dependence must be unmediated or "one step" relations.
As Lewis notes, neither his account of the role of the Third Man Argument nor the claim of one step dependence can be substantiated directly by any single text or series of texts.
Furthermore, Lewis' own account of the said of and present in relations calls into question his reading of the relationship between the Third Man Argument and the ontological theory of the Categories.
Vlastos cites Protagoras 330c-d as containing "the star instance of Self-Predication in Plato" ("The Third Man Argument
in the Parmenides" [Philosophical Review 63 (1954): 319-49], p.
Vlastos's original article on the elenchus was a classic like his great article on the Third Man Argument
in the Parmenides (1954): both spawned scholarly cottage-industries, and both have been superseded in important respects.
This renders them vulnerable to the Third Man argument.
Each of the authors Malcolm discusses has tried, in his own way, to explain the central paradoxes that seem to make the theory of Forms succumb to the Third Man argument.