[FOM] Bivalence and Law of Excluded Middle

[William Tait]

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