FOM: naive or brainwashed?
rhersh at math.unm.edu
Wed Mar 11 17:43:40 EST 1998
Thanks for including me in your interesting posting. I'm surprised
that anti-foundationalism is now an industry, but if so, all to the
good. And I cherish your image of me "leading the charge," sword
in hand? or just a pen? word-processor in hand seems visually wrong.
May I apologize to Frege, Hilbert, and Brouwer, if you think I
trivialize them? I am glad to acknowledge all three as great
thinkers. Of course it wasn't my purpose to expound at length
their contributions to mathematics and logic, although if you
take a look at my book I think you will have to admit that I
presented more than mere slogans. I contended that all three
programs to restore indubitable foundations to mathematics had
not attained their goals, and are no longer being pursued for
that goal. I don't think that is a controversial statement.
You also list Godel as a great man whom I dissed. Well, I
included Boolos proof of Godel's incompleteness theorem. But
I did quote Godel mainly as the outstanding Platonist. If
Volume 3 of his collected works had been available, I would
have quoted him in more detail. I might not have tried to
refute him in detail, since a critique of Platonism in general
is one of the main threads of my book. I don't see that I
"Reuben Hersh makes the remarkable discovery that mathematical activity
is a social process."
May I be forgiven for guessing that the "remarkable" is sarcasm?
To me it's interesting that there are two popular responses to my
unremarkable observation (not discovery.) A fair number of fom'ers
respond with indignation, fury, mockery, etc. And then a few
others respond, "So what? Of course! What else is new?"
Can you account for this interesting duality? Everybody
agrees I'm all wet, but from two opposite reasons.
It's not a remarkable discovery. It is an important
fact, which philosophers of math (with a few exceptions whom
I credit) has consistently ignored. Not only ignored hitherto,
but insists on continuing to ignore, even after I suggest
some attention be paid. As you know, since (I think) you have
read my book, I attempt to show how this commonplace fact
can be useful in unraveling some philosophical puzzles.
I hope I won't be overstepping the bounds of friendship if
I remind you of our conversation last summer in your house in Berkeley.
You told me that you are a Platonist about the natural numbers,
an agnostic about the rest. As you mentioned in your posting
about Lagrange's theorem, it's clear to you that such a theorem about the
natural numbers was true before there were people,
and I suppose before there was an Earth or a Sun. Anyway,
I said that to me, as a materialist, such a view was hard to
connect or relate to my overall materialist philosophy. You
said that you also didn't know how to make such a connection.
To me, that's a reason why Platonism is untenable. To
you, evidently, this gap does not prevent you from continuing
as a Platonist.
Understand, I am not dreaming of convincing you of anything or
changing your mind about anything. Just trying to get you
to see why someone in his right mind might find Platonism indigestible.
In my view, locating math in social interactions is a materialist
explanation of the nature of math. I give long lists of other
social realities just to drive home the obvious but often
ignored fact that reality does include social reality--naturally,
based on a physical basis. Just as the mind is based on the
brain, but is not the same thing as the brain. (Surely that familiar fact
doesn't require justification?)
It's not a matter of finding a physical location for 7. It's
a matter of explaining the sense in which we can say it
exists. Its objectivity is not an explanation of that.
Good luck with your talk. I hope you send me a copy.
More information about the FOM