FOM: membership

[John Baldwin]

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.