Solutions to the Third Man Argument (TMA)
Historically, the most common response to the TMA is to assign forms and particulars to radically different categories, so that only particulars can be said to partake of forms (this is essentially Aristotle’s response). Since Plato frequently asserts self-predication of the forms (e.g. “the beautiful is beautiful”), some have therefore interpreted such self-predication as either an identity statement (“the beautiful is the form of beauty”) or what is called “Pauline predication” (“every beautiful thing is beautiful”). This interpretation misses the metaphysical import of Plato’s theory of forms. In particular, a fundamental aspect of the theory of forms is that something that is beautiful is only beautiful insofar as it partakes of the beautiful. For this to be possible, at least for Plato, the beautiful itself must be beautiful. Otherwise, how could the beautiful impart beauty to beautiful things? Instead of rejecting self-predication to solve the TMA, the only option we seem to have left is to assert that forms partake of themselves. This resolves the TMA, since there would not be a separate form of beauty in virtue of which the form of beauty is beautiful, as the form of beauty would be beautiful in virtue of itself. The problem, however, is that we immediately run into Russell’s paradox: take the form F corresponding to the property “being a form that does not partake of itself”. Then F partakes of itself iff F does not partake of itself. Hence, in order for our theory to be consistent, we need to either limit what a form is, or have some type of predication peculiar to forms.
Interestingly, the latter option finds support in the works of Plato himself. Plato (seems to) distinguish between predication pros ta alla and predication pros heauto. The former applies when particulars partake of forms, and also when forms partake of other forms. The latter applies when something is predicated of a form that is essential to the form itself. Clearly, self-predication would be pros heauto.
References
- Francis Pelletier, Edward Zalta, How to Say Goodbye to the Third Man. https://mally.stanford.edu/plato.pdf
Plato Plato’s Forms Predication Participation Russell’s Paradox Aristotle Edward Zalta