FOM: Platonism v. social constructivism
csilver at sophia.smith.edu
Sun Mar 1 07:52:18 EST 1998
To Reuben Hersh:
First, I want to thank you or whoever-was-responsible for my
receiving a free copy of your very attractive looking book. I hope to
have time to read it soon.
I think you still fail to appreciate a very fundamental point,
which is that mere agreement does not inform us as to what that agreement
is *about*. Since I've already tried some examples (some goofy ones, I'll
admit, like King Kong), and they didn't seem to catch your interest, I
won't bother with that any more. But, I'll say this (I think several
others have made essentially the same point): one thing that distinguishes
mathematical agreement from other kinds of agreements are its verification
principles. That is, the kinds of demonstrations that establish that
something is true mathematically. These demonstrations differ greatly
from the kinds of demonstrations of truth in other fields. I think you
miss this crucial point and some others, but I don't want to go on with
this. What I'd like to ask you about here is not what you are *for*, but
what you are *against*.
My guess is that you are reacting to a kind of Platonism in
mathematics that you think distorts the picture of what mathematics
It would be instructive, for me at least, if you would spell out
some of the things you object to, which led you to your present position.
In case you sense a trap here, let me put my cards on the table. I think
that you probably do have some legitimate objections to Platonism and/or
other philosophies of mathematics. But, my impression is that in order to
correct these ills, you over-corrected and went too far in the direction
of new-age thought. This is my impression, at any rate. I would
appreciate any explanation of what's at the bottom of your rejection of
the standard views of mathematics. That is, what don't you like about
what mathematics is thought to be, really?
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