Third Man Argument

The most famous objection to the Theory of Forms, pressed by the aged Parmenides against young Socrates in Plato's Parmenides (132a–133a): positing one Form over many instances generates an unlimited regress of Forms. If many large things are large by participating in the Large itself, then surveying the Large together with the large things yields a new large thing "by which all these appear large" — a second Largeness, then a third, "and so each of your forms will no longer be one, but unlimited in multitude" (132b). The argument is named for the version Aristotle later gives (the "third man," tritos anthrōpos, Metaphysics) and has been the central focus of twentieth-century analytic Plato scholarship. Crucially, Plato voices it against his own theory — and retains the theory anyway.

Key Points

  • Two versions in the Parmenides: (1) the largeness regress (132a–b) — the one-over-many move, reapplied to the Form-plus-instances, never terminates; (2) the likeness/paradigm regress (132d–133a) — if Forms are "patterns … and other things resemble them," resemblance is symmetric, so Form and participant are alike "by partaking of the same one form," requiring a further form, "and a fresh form will never cease emerging."
  • The failed escape between them (132b–c): making Forms thoughts (noēmata) does not stop the regress — a thought is a thought of "some one character … over all the instances," which is again a Form.
  • The two tacit premises: the regress needs self-predication (the Form of Large is itself large) and non-self-identity (the new Form is distinct from the first). Neither is stated by Plato as a commitment — and a defender of Forms may deny self-predication, blocking the regress.
  • Aristotle's reception: the tritos anthrōpos is named and pressed by the philosopher Aristotle in the Metaphysics against the Forms — while in the dialogue the regress-argument's respondent is a character named "Aristotle" (one of the Thirty), a double irony.
  • Plato does not abandon the Forms: immediately after the six objections, Parmenides insists that without Forms "the power of dialectic" is destroyed (135b–c). The TMA is self-criticism, not a refutation Plato accepts.

What the Concept Does

  • Exposes the cost of separation + self-predication — it shows that treating a Form both as the one explanatory ground of a property and as itself a possessor of that property generates a vicious infinite series. Either the Form is not itself F, or the one-over-many principle must be restricted.
  • Forces the participation relation into the open — together with the whole-or-part dilemma, it makes the Phaedo's undefined "sharing in" (methexis) the theory's central unsolved problem.

What It Rejects

  • The naïve one-over-many assumption — that every collection sharing a predicate F is unified by a further single F-thing standing over it (including the Form itself among the F-things).

Stakes

If self-predication is a genuine Platonic commitment, the TMA is close to fatal and the Theory of Forms cannot stand in its Phaedo form. If it is not — if "the Large is large" is a category mistake or a harmless façon de parler — the regress never starts. The argument thus turns the whole interpretation of the Forms on a single question (does Plato hold that Forms are self-predicating paradigms?), and it is the historical seed of every "ideal exemplar" critique down to the present. Plato's own response is not to answer it but to retain the Forms as the condition of discourse and route the difficulty forward to the Sophist's relational revision. See claims#parmenides-self-critique-retains-forms (candidate).

Connections

  • critiques theory-of-forms — the regress targets the one-over-many + self-predication structure of the Phaedo/Republic Forms; the most-discussed internal objection.
  • requires (as a tacit premise) self-predication — the unstated assumption that a Form possesses the property it grounds; a defender's denial of it dissolves the argument.
  • is named and pressed by aristotle — the tritos anthrōpos of the Metaphysics, turned against the Forms by Plato's own student.
  • is part of the self-critique in plato-parmenides — alongside the whole-or-part dilemma and the "Greatest Difficulty."

Open Questions

  • Is self-predication a real Platonic commitment, or an artifact of the "X-itself" idiom? The dialogue does not say, and the answer decides the argument's force.
  • Does the Sophist's relational Forms (the communion of kinds) actually answer the TMA, or only change the subject? The Parmenides routes the problem forward but the connection is the reader's to draw.

Sources

  • plato-parmenides — the two regress-versions (132a–b, 132d–133a), the Forms-as-thoughts escape (132b–c), and the retention of the Forms (135b–c).