The Academy at Work
Zeno’s argument against plurality in the Parmenides does not support the view that there is only one object in the world—only the view that every object in the world is one. Socrates counters that every sensible object can be many by participating in Forms, but none of the Forms can be many. Parmenides retorts that participation is not consistent with the Forms’ unity. The dialectic Parmenides offers derives a series of contradictions from supposing either that each Form is one or that it is many (that is, qualified by any other feature). The implicit solution is that participation must allow the Forms to participate in one another without losing their essential unity. The net result, central to the Academy’s educational programme, is to articulate, for the first time, the concept of predication as we understand it today. Its results are summarized in the Sophist’s discussion of ‘Greatest Kinds’.