FOM: objectivity, postmodernism, multiculturalism, feminist etc.

eva hersh evahersh at
Sat Jan 10 22:34:16 EST 1998

Dear Professor Simpson,

Since you rely on the New York Times to tell you what
I think, may I be permitted to quote from my book,
"What is Mathematics, Really?"

As to objectivity, which you and some other members
of this list assert I do not believe in:

page 11, "The mystery of mathematics is its objectivity, its seeming
certainty or near-certainty, and its near-independence of persons,
cultures, and historical epochs."  "Platonism of the ordinary
mathematician or student is a recognition that the facts of
mathematics are independent of her or his wihes.  This is the quality
that makes mathematics
exceptional."  page 16  "Once created and communicated, mathematical
objects are *there.*  They detach from their originators and become
part of human culture.  We learn of them as external objects, with
known properties and unknown propeties.  Of the unknown properties,
there are some we are able to discover.  Some we can't discover, even
though they are our own creations."  p. 17  "Mathematical objects cn
have well-determined properties because mathematical problems can have
well-determined answers."  p. 18
"The observable reality  of mathematics is this:  an evolving network
of ideas with objective properties."

p. 19  

'A world of ideas exists, created by human beings, existing in their
shared consciousness.  These ideas have objective properties, in the
same sense that material objects have objective properties.
The construction of proof and counterexample is the method of
discovering the properties of these ideas.  This branch of knowledge
is called mathematics."

p. 181  "To each of us, mathematics is an external reality.  Working
with it demands we submit to its objective character.  It's what is
is, not what we want it to be."

	Is that enough about objectivity?

	Then you repeat Rothsteins' canard that "feminist
and Afro-American mathematics are mentioned prominently."  The only
sentences that
can be construed as such "prominent mention" are on
page xv of the preface.  May I please with your
permission quote them?  "Some people think female mathematicians and
mathematicians of color see the nature of mathematics differently than
do white male mathematicians.  I'm not convinced such differences are
present.  If they are, I'm unqualified to write about
them."  That's all.  Not another word.  This is a funny kind of
"prominent mention.".

	You also quote Rothstein to the effect that I claim my so-called
anti-objectivist views would bring more students of different races
and cultures into
mathematics.  My book contains not a single word about students of
different races and cultures.  I did say that in my opinion formalist
and Platonist philosophies can be educationally harmful, and that
humanist  philosophy might be educationally beneficial.  Where do you
or Rothstein get your "different races and cultures?"  Do you call
this honest, accurate, or responsible?

There is absolutely nothing "multiculturalist" or 
"postmodernist" in my book.   Multiculturalism, to
my understanding, advocates bringing into the schools the cultures of
Africa, Asia, and Latin America, in
addition to our present Anglo-European cultures.  This
has no application to mathematics, and is nowhere 
considered or contemplated in my book.

I have a a 3-page section reviewing the
book by Marcia Ascher on "ethnomathematics."  I
can't imagine how it could offend you, if you bothered to read it.

As for "postmodernism", I once tried to find out what
it is, and failed.  In the present connection, however, I think I can
see what it is.  Isn't it a stick to beat an author whose ideas you
dislike so much you can't bear to pick up his book?

With all due respect,

Reuben Hersh

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