Third Man Argument

The Third Man Argument is the most famous objection to the Theory of Forms — raised by Plato himself against the young Socrates in the Parmenides, and named by Aristotle. If many large things are large by sharing in one Form, Largeness, then Largeness together with those things forms a new plurality needing a further Form — a second Largeness — and that a third, without end.

The hidden assumptions

The regress turns on two premises later made explicit: self-predication (Largeness is itself large) and non-identity (a Form is not identical with the things that share it). Whether Plato meant it to refute the Forms or to refine them is debated; the Parmenides presents it as a challenge the theory must survive, and the Neoplatonists answered by denying that the One-over-many is merely “one more” of the same kind.