[FOM] re "understanding Putnam on understanding mathematics

[William Tait]

On Jul 25, 2007, at 6:24 PM, Gabriel Stolzenberg wrote:
>    The exact remark is in "On the Infinite."  In "From Frege to  
> Goedel,"
> it's in the second paragraph on p. 379.  Here is part of it.
>
>        In any case, those logical laws that man has always used
>        since he began to think, the very ones that Aristotle
>        taught, do not hold.

The other part of it, which is essential for understanding what  
Hilbert was saying, is "In the domain of finitary propositions". He  
is speaking about the methodological position he wants to take  
(finitism) in order to prove the consistency of what he calls the  
laws of Aristotelian logic. Further down in the same paragraph: "we  
just do not want to renounce the use of the simple laws of  
Aristotelian logic..."

Bill Tait