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.

This paper offers an interpretation of self-Predication (the idea that justice is just) in plato, Given that self-Predication is accepted as obvious both by plato and by his audience, Which entails that "all" self-Predications are clearly, Though not trivially, True. More strongly, It is suggested that "only" self-Predications can be accepted as clearly true by plato. This is to deny that plato had at his disposal an articulated notion of predication, And his middle theory of forms, Primarily the relation of (...) participation, Is seen as his attempt to arrive at that notion. It is argued that his metaphysical and semantical views are heavily influenced by eleatic monism. But this monism is incompatible with the very idea of predication. It is only in his later works, Where he attacks parmenides directly, That plato manages to lay the groundwork for what can be considered as the discovery of predication. (shrink)