Plato's Quinean Beard: Did Plato ever grow it?

Abstract

Quine may be taken to use the phrase ‘Plato's Beard’ to denote a solution to the following problem: How is it possible to speak of that which does not exist, of non-being or as Read has it, to denote a solution to the problem: ‘How can a sentence with empty names have meaning?’.

Quine writes:

Nonbeing must in some sense be, otherwise what is that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor.

To expand. If nonbeing in no sense is, then we cannot ever assert that it is not; yet if it in some sense is, then how can it remain nonbeing? Let us fill out with an example (coined from Quine). If Pegasus in no sense exists, then how can we ever assert that Pegasus does not exist?—yet we may clearly want to assert that Pegasus does not exist and affirm the proposition that it is false that Pegasus exists. If, on the other hand, Pegasus in some sense exists, how may we affirm that he does not? We shall be contradicting ourselves or be guilty of equivocation.