FOM: naive or brainwashed?

[Lincoln Wallen]

Charles Silver writes:

   Date: Sat, 14 Mar 1998 07:50:31 -0500 (EST)
   From: Charles Silver <csilver at sophia.smith.edu>

   BACKGROUND: I argued in an earlier post that Hersh's philosophy of
   mathematics has the unfortunate consequence that one need not read his
   book to know what it is about.  All one has to do (acc. to his view) is to
   attend to various sociological factors pertaining to it.  I further posed
   what I thought was a dilemma for his view in so far as it applies to his
   own book, which is that there could be the exact same sociological
   phenomena associated with an astrology book.  According to his philosophy
   (as expressed on this list), the two books would then be identical, since
   his view is that these sociological factors suffice to determine what the
   book is.  Or, put another way, one could correctly say (in terms of
   Hersh's own view) that his book is really about astrology (since his view
   provides us with no way of distinguishing his math book from the one on
   astrology).  The dilemma I see here is that Hersh needs to repudiate this
   view or accept the consequence that (apparently without knowing it) he has
   written an astrology book.

Even the approach which goes under the name "sociology of science" ---
which I would criticize at least on the grounds that it renders the
sociologist more capable of recognising the material pertaining to a
domain than the participants themselves --- would be able to
distinguish between the product (the book) of astrologers and the
product of a mathematician, or a philosopher, or a physicist etc.
Indeed this is the central phenomena such ideas seek to explain.  So I
have to disagree with the thrust of this argument.  If Hersh does
associate his thinking with such ideas then there are interesting
problems with such an account, but distinguishing the products of
different professions isn;t one of them.

I think Shipman has offered the central challenge, which I also tried
to get people to focus on: *what* is it about mathematical practice and
forms of expression which makes it recognisably mathematical (with all
the attendant properties).  Arguing about the status of mathematical
objects (existence etc) must come after a thorough understanding of
the way such "objects" are actually used in mathematical practice,
both written and interactive.  In this sense, f.o.m. requires certain
types of empirical analysis of mathematical practice, more akin to
that of anthropology, than what most understand as sociology.

That is to say: what mathematician's actually *do* is central to
f.o.m. 

Disclaimer: I have not read Hersh's book, so I don;t really know what
his position is.

Lincoln Wallen