FOM: Jurassic pebbles
Kanovei
kanovei at wminf2.math.uni-wuppertal.de
Wed Mar 18 04:21:29 EST 1998
<Date: Tue, 17 Mar 1998 09:26:45 -0800
<From: Vaughan Pratt <pratt at cs.stanford.edu>
<1. Would it be fair to infer from this that you believe that mathematics
<is not frozen in time but rather reflects what we know?
As it is clear that the amount of Math now and in 18 century
is obviously different, I think what you are asking is whether
(I believe that) if XXX is once put and properly recognized
as a correct mathematical result, as the LT has been, then
a) it will remain such (in the frameworks of the terrestrial
form of Mathematics ?)
b) it always existed in the past.
I would agree with a).
My reason is that, at the very end,
mathematics reflects the physical counting (including
measurements as a form of counting: counting of measure
units). And, since counting a very stable (or: absolutely
stable) process (shall one add: in our universe), this,
through many steps, results in the stability and
unchangeability of our mathematics.
However there can be reservations. For instnse, once they
may think to change the whole setup of arithmetics to
reflect the fact that the universe contains only finite
amonut of particles. Who knows.
b) Perhaps this depends on how you view the LT. If you
think that the whole setup of arithmetic is in 1-1 way
determined by the physical setup of the universe
(there are reasons to think so), then PA, and LT as a
logical consequence of PA, "always existed". In this sense,
Lagrange only *discovered* rather than *created* the
theorem (similarly to the discovery of Amerika by Columbus).
However the existence of the LT as a social phenomenon
begins from its proof by L.
Vladimir Kanovei
PS. You comment (in another post) upon a letter of Harrington.
Can you copy it for me (assuming it is a regular fom-list
mailing), as I have not received it.
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