[FOM] Bivalence and Law of Excluded Middle
William Tait
williamtait at mac.com
Wed Feb 20 15:14:06 EST 2008
On Feb 18, 2008, at 9:22 AM, Joseph Vidal-Rosset wrote:
> I would be happy to hear the opinions and the arguments of FOM
> subscribers about the question that Sayward asked in the title of this
> paper. Does the LEM require Bivalence?
>
> Joseph Vidal-Rosset
If one takes the meaning of a mathematical proposition to be given by
what counts as a proof of it, which I think is a highly defensible
position, then it would seem that the proposition that P and the
proposition that P is true are the same. How would one prove the one
without it counting as a proof of the other?
Incidentally, I discussed this in section 3 of a paper "Beyond the
axioms: The question of objectivity in mathematics," Philosophia
Mathematica 9 (2001): 21-36.
I don't see where the concept of truth---as opposed to the concept of
a formal sentence being true in a structure---really occurs in math.
(The two concepts do indeed get confused.)
Best regards,
Bill Tait
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