FOM: Re: A howler

Reuben Hersh rhersh at
Tue Mar 24 09:56:01 EST 1998

On Tue, 24 Mar 1998, Charles Silver wrote:

> 	On p. 236, Hersh says: "mathematics [is] the study of certain
> social-cultural-historic objects...."  This is a howler.  I think that
> Hersh, as a scientist, should just admit that this view is palpably wrong,
> and he should now consider how it might be modified in order to preserve
> his many insights (rather than continuing to engage in distracting verbal
> swordsplay). 
> Charlie Silver

Thanks, Charlie, for your friendly invitation.

I am trying to see how my statement is a howler.  (Not just
mistaken, but absurd, senseless, unworthy of response.)

My difficulty is that my effort to understand may seem to you
as distracting verbal swordsplay.  (Although I kind of like that
image of myself as a verbal Douglas Fairbanks defending Mary
Pickford from a swarm of ugly pirates.)> (Just kidding.)

I wrote, "By recognizing mathematics as the study of certain
social-cultural-historic objects, humanism connects philosophy
of mathematics to the rest of philosophy."

I think any statement of the form "mathematics is..." is bound
to be incomplete and oversimplified.  Mathematics, like art
or philosophy, is  too big, too rich, to be captured in any
compact formulation.

Probably it would have been better to write, "mathematics, as
among other things, the study of..."
Is it a howler to say that math is, among other things, the study
of certain social-cultural-historic objects?

Math is a practise, more than a study, but it is also a study, don't
you think?

If so, is it a study of objects?  Well, more of processes than objects,
I think, and maybe of even other things besides processes and objects.
But among the things math studies, to the extent that it is a study,
are certain objects, don't you agree?  Perhaps not.  But that is
probably not your major objection.

Well, if it does study objects, what sorts of objects might they be?
Like, numbers, functions, operators, curves, surfaces, relations,
operations, isomorphisms and homomorphisms, etc. etc. etc.

Now, one could just say, "mathematical objects," and no one probably
would call that a howler.  But it would be kind of a cowardly evasion.

One could say mental objects, as I believe did L.E.J. Brouwer, and
Danny Isaacson, and some others.  Many would disagree, but a howler?
I don't think so.

One could say physical objects or mathematical aspects of physical
objects.  A howler?  I wouldn't say so, others might.

I say that, for example, Cantor's diagonal argument, or Dirichlet's
zero-one function, or Lagrange's theorem for n > Skewes' number, are
ideas, inventions of humans, absorbed and integrated into the
practise of mathematics, which is a human practise, not primarily
of individuals but of people in communication with each other, in
other words a social practise.   So I thought it was OK to describe
such things as certain social-cultural-historic objects.

I understand many fom'ers disagree, not just strongly but
angrily and indignantly.  OK.  But I don't know what makes you react
to one more statement of my opinion as a howler, any more than
any of the many other statements.

I am willing to say that in my opinion math objects can "profitably
be viewed as s-c-h objects," allowing other people to view them
otherwise.  I would, however, have to admit that viewing them
as changeless, timeless, immaterial, insubstantial, inhuman
is in my opinion an illusion.  I am willing to stop saying
"superstition" or "delusion," for the sake of cutting back on
flashy verbal swordsplay.


More information about the FOM mailing list