FOM: naive or brainwashed?
csilver at sophia.smith.edu
Sun Mar 15 08:36:32 EST 1998
On Sun, 15 Mar 1998, Lincoln Wallen wrote:
> Charles Silver writes:
> 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.
> 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).
> That is to say: what mathematician's actually *do* is central to
It's roughly the same point. What the above misses, though, is
how mathematical truth is established. For example, contrast the
verification of FLT with the verification of the statement "Food is now
being sent to the astronauts on MIR". Or, to make this sharper and to
bring it back to my example, contrast the verification of FLT with the
statement "Hersh wrote his book because he's a Leo".
More information about the FOM