29 September 2005

Eleatic Question: 2

How should one reply to the following?

It is clear that it is possible to think of plurality and imperfection. Consider a right triangle with unit sides. It has three sides (plurality); and its hypotenuse is essentially not commensurable with the sides (negation, imperfection).

But if plurality and imperfection do not exist, and we can think only of what exists ('it is'), then we do not in fact think of right triangles--we have only 'beliefs' about them.

That is, must Parmenides, on the standard reading, hold that mathematics too is an illusion, part of the deceitful web of mortal beliefs? But strange that thinking of mathematics should not be paradigmatic of thought. (One begins to wonder what thinking, then, is.)