Recently, I noticed about sorites problem. I thought that problem is serious to all of philosophical endeavor, but my friend told me that is problematic when you assume some kind of platonism. Is he right? Or is it equally problematic when we assume nominalism?

I think that the sorites paradox is a problem even for nominalists.

Suppose we line up 101 North American men by height, starting with the shortest man (who's 125 cm tall) and ending with the tallest man (who's 225 cm tall). Let's also suppose that each man except the shortest man is 1 cm taller than the man to his right. Clearly the shortest man is short. If 1 cm in height never makes the difference between a short man in the lineup and one who isn't short, then the tallest man is also short, which is clearly false. So there must be a tallest short man in the lineup. But who could that be? If we can't know who it is, then why not?

I think I've managed to state the problem in terms that even a nominalist can accept. If nominalism, as such, evades the problem, then I'd love to know how it does.

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