[FOM] Richard Epstein's view
Timothy Y. Chow
tchow at alum.mit.edu
Mon Apr 2 10:40:34 EDT 2012
On Mon, 2 Apr 2012, Sara L. Uckelman wrote:
> Buridan discusses the insoluble "Every proposition is affirmative,
> therefore no proposition is negative." Such an inference is problematic
> on Buridan's view because of the token-based approach to propositions
> that he (and other medieval logicians) took. It is certainly *possible*
> that every (token) proposition that happens to exist is affirmative, and
> thus it is *possible* that no proposition is negative, but it will never
> be possibly-true that no proposition is negative, for in order for this
> proposition to have a truth value, it must exist, and it itself is
> negative, and thus its very existence falsifies itself.
I don't find this objection convincing. In particular, I would blame the
implicit theory of "possibility" being invoked here, rather than the
theory of truth. In what sense is it possible that every proposition that
happens to exist is affirmative? Presumably, some version of the theory
of possible worlds, currently very fashionable in philosophy, is being
appealed to. But I don't see why we should think that such a theory is
relevant to a discussion of mathematical statements. For example, all
conditionals that appear in formal mathematical discourse are material
conditionals, not counterfactual conditionals. "The Riemann hypothesis
might be true" just means "We don't know that the Riemann hypothesis is
false" and is not something that ever appears in an official conjecture or
theorem.
Tim
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