FOM: social construction of mathematics?

Charles Silver csilver at
Thu Mar 19 07:18:14 EST 1998

	I don't mean by writing what I do below that I fully agree with
everything that Randall Holmes said (though I do like some of his points) 
or that I completely disagree with everything that Reuben Hersh said (I
like some of his points too).  But, I want to call attention to one point
that Hersh made: 

Reuben Hersh:
> 	The view that mathematics is a social construction comes,
> 	on the contrary, from (1) being a mathematician and
> 	watching what mathematicians say and do (2) rejecting
> 	the other possibilities, that it is a transcendental
> 	immaterial "reality" (Platonism) or a mental process
> 	(Brouwer) or meaningless formal calculations (formalism.)

	Let's dispense with (1), because it could mean that you've been
around longer than Holmes and therefore you know what math is better than
he does, which I'm sure you do not intend.  (2) is the important one to
me.  It suggests that you are reluctant to fiddle with positions and to
offer your own original insights in a way that would create a completely
new philosophy of mathematics.  As I recall, you said something to the
effect that you found the view you were looking for in the article by
White in Newman's _The World of Math._.  Do I have that right?  Anyway, my
point is that it is not necessarily correct to choose among the
already-available alternatives.  As I understand you--please correct me if
I am wrong--you were repulsed by certain views about the nature of math
(particularly Platonism), but you were attracted to the sort of position
advocated by White in his article.  I'm not saying I think you were
absolutely wrong to do this, but that position by itself has fundamental
problems too (which I don't think you want to acknowledge).  I'm claiming
you should now not just stick with the White choice (or whatever), but use
some ingenuity in fashioning an improved view from the criticisms of it
that you've received. I haven't thought this through, but it seems to me
that you could preserve your anti-Platonic position and still be able to
emphasize the social-cultural aspects of mathematical activity, but not in
the way you presently do (because the way you now do seems to be a kind of
"use-mention confusion"). (A Feferman-like view might be helpful to look
at in concocting your own, though I personally don't like the "only" in
his stated view that mathematical objects are "only in the imagination".)

Charlie Silver
Smith College

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