[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 


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