FOM: naive or brainwashed?

[Charles Silver]

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.

On Fri, 13 Mar 1998, Reuben Hersh wrote:
> I find your statement that according to me it is not necessary to
> read a book in order to know its contents absurd, grotesque, and
> incredible.

	I am trying only to get you to attend to what I think is a crucial
error in your account.  Other kinds of counter-examples posed by several
people on this list did not seem to catch your attention in a serious
way. 


> However, I appreciate your latest message denying any intention to
> offend.

	Well, obviously I am kidding around by applying your views to the
reading of your own book.  The serious point behind it is to call your
attention to the need to de-emphasize the external social concomitants of
mathematical agreement and to focus on the internal features underlying
it.  I am not altogether hostile to your viewpoint.  I believe you could
shift your views slightly [?] and still pursue the emphasis you want.  In
particular, I think you could maintain your objections to Platonism.


> You could correctly define my book by title, author & publisher.
> This would single it out from all other books, and make it
> possible for anyone to know if they had that book or some other book.

	In my view, you are seizing on unimportant features of my example
and not attending to the main point about the uninformativeness of any
purely sociological account of mathematics.

> As I understand defining, it's like in a dictionary, which you know
> of course is full of definitions.  The definition of "broom" is meant
> to enable you to tell a broom from a basketball, not to give the
> whole theory and practise of sweeping.

	The same point applies.  Change "define" to "determine".  That is,
in your view what *determines* what math is are sociological facts.
Therefore, what determines what your book is are also sociological facts.
Since the same facts determine an astrology book as well (given my
trumped-up example), you have no way (within your philosophy) to
distinguish your book from one in astrology.

> Read the book or not, whatever you want.  Possibly if you do
> read it we could have a more profitable discussion.

	I am looking forward to reading it.  I have read previous works of
yours with great enjoyment.  For example, I enjoyed _The Mathematical
Experience_ very much.  But, I think another way our discussion could be
made more profitable would be for you to acknowledge that the sociology of
mathematical agreement is insufficient to determine what mathematics is,
really. 

Charlie Silver