[FOM] Scope questions

[Mícheál Mac an Airchinnigh]

At 14:25 -0400 2003/21/04, Harvey Friedman wrote:
>Reply to Pratt 4/21/03 10:41PM.
>
>I can only speak for myself, and guess about others.
>
>>Having participated in this list some years ago, and having returned this
>>year, largely in observer mode, I'm prompted to ask to what extent the
>>subject of foundations of mathematics is defined by the interests and
>>technical specialties of its contributors.
>
>I try to have an overarching idea of foundations of mathematics 
>that, at least in principle, allows for serious consideration of 
>approaches that differ greatly from the conventional 
>Frege/Russell/Zermelo/Frankel/Bernays/von 
>Neumann/Gentzen/Hilbert/Turing/Godel approach.
>
>I do not believe that any serious competitor to this standard 
>approach to the foundations of mathematics has emerged, although 
>some alternative approaches definitely give one the impression that 
>they could become a viable alternative. However, in my opinion, none 
>has been carried through with enough powerful ideas in order to do 
>anywhere near the work that the standard approach does. This doesn't 
>mean that it can't be done.

[[rest elided...]]

I do believe that the very recent text

"Sets for Mathematics"
F. William Lawvere and Robert Rosebrugh
Cambridge University Press, 2003

is worth looking at "foundationally".

I have just finished it!
It is impressive!
The beginning of a different approach?

Micheal
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Mícheál Mac an Airchinnigh
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