FOM: social construction?

[Martin Davis]

At 10:50 AM 3/19/98 -0700, Randall Holmes wrote:

> It is quite difficult to see how mathematical
>discourse can refer on a materialist view; that is why I am not a
>materialist.

I have agreed with everything Holmes said in this posting EXCEPT this. Here
(and only here) I stand with Reuben Hersh.

I note that Holmes said "difficult" - not "impossible".

I've tried to deal with this issue in previous postings. For me the crucial
aspect of "refering" or "existence" of the objects of mathematical discourse
is the OBJECTIVITY of their properties. 

Simple-minded Platonism doesn't help: there are too many abstract items out
there in a Platonist's wonderland happy to serve as the TRUE number 7 or
sqrt(2). I think (as Bill Tait has I believe emphasized) we tend to be
bewitched by the thought processes initiated by grammatical conventions
surrounding the word "exists". One can see this very clearly in the
seriousness with which very smart people have regarded the (silly)
ontological proof of the EXISTENCE of God. It is a FACT of mathematical
experience that we come to have knowledge of mathematical entities and that
we have no ability to alter what we discover about them. Why and how this is
so is the main business of f.o.m. But what we mean by existence is no more
than that FACT.

Martin