The logic of the third man

Philosophical Review 80 (4):448-475 (1971)
Abstract
The main lines of interpretation offered to date of the Third Man Argument in Plato's Parmenides (132a1-b2) are considered and rejected. A new, set-theoretic, reconstruction of the argument is offered. It is concluded that the philosophical point of the argument is different from what it has been generally supposed to be: Plato is pointing out the logical shortcomings in his earlier formulated principle of One-Over-Many.
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Phil Corkum (2012). Aristotle on Mathematical Truth. British Journal for the History of Philosophy 20 (6):1057-1076.
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