FOM: membership

[Hilary Putnam]

On Sun, 19 Oct 1997, John Baldwin wrote:

> Vaughn Pratt's note reminded me of a fancy word I learned at
> the meeting for Bill Tait's retirement that seems relevant to
> this discussion.  The word was structuralism and I while I'll
> yield to the philosophers for the proper technical usage my
> interpretation was this.  One should understand mathematical
> structures in terms of the relationships amongst the objects
> of the structure with our regard to their internal properties.
> Thus we study the reals as a complete ordered field, not
> Cauchy sequences of equivalence classes of integers.
> 
> So I suppose the question to Steve  is whether any analysis
> beginning at this level could be viewed as foundational?
> 
> Another point that I made in my essay and think bears repeating is
> that it seems fruitful to look not only a single global FOM
> but a foundationS of mathematics where different techniques and
> viewpoints are appropriate for various areas of mathematics.
> 
How sensible! Hilary P