FOM: Hersh's dubious doubts/Davis' examples
Robert S Tragesser
RTragesser at compuserve.com
Mon Jan 5 14:17:39 EST 1998
Likely Reuben Hersh must fail to appreciate
Davis' examples exactly because he (Hersh)
proceeds by the method of (dubious) doubt rather
than by aiming at positive characterization
(through thought experiments with living
mathematical thinking).
I've been trying to say that Reuben Hersh is
building his humanistic/consensual philosophy of
mathematical knowledge on dubious (=
unreasonable = irresponsible doubts --
"irresponsible" because unresponsive to the
problem of capturing postiviely what is so
distinctive and peculiarly cogent about
mathematical knowledge).
[It was pointed out to me that most people
on FOM would not have picked up on the
reference of 'skeptical terror' to Cavell, so that
my remarks seem vapid and vague.--Sorry, if
so.]
Hersh has built his humanistic philosophy
of mathematics and his view of mathematics as
sustained by consensus on blanket (and dubious)
doubts -- that all mathematical theorems are
dubious, even the most elementary.
When Hobbes (quoted by Lakatos) and
Locke call mathematical knowledge "certain",
they are using that word to indicate that there is
something distinctive about mathematics (in
contrast to empirical science, "natural
philosophy"), NOT that mathematical
knowledge is absolutely infallible. There
remains the task of characterizing what is so
distinctive about mathematics.
Feferman had objected to Lakatos' excesses
of falliblism -- that, against Lakatos, there is an
end to guesswork, that there are "successful
struggle[s] to solve a problem or complete a
proof". Rota insists that there are abiding
mathematical facts. (Both Feferman and Rota do
point out that -- as Feferman puts it --
"results are viewed in changing perspective
over historical periods. Their significance is
reassessed, they are generalized and
understood in wider settings. . . .But this is
quite a different picture from that given by
Lakatos of endless guesswork.")
What is there about mathematical that it supports
definitive solutions?
rbrttragesser
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