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Date: | Fri Dec 29 12:24:35 2006 |
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Roy,
Well, you are the expert on this, but
I would submit that there is an underlying
principle common to at least the Bourbaki
and Hilbert programs as well as the Euclid
program. That underlying program is best
described as being Occam's Razor, a kind
of intellectual optimization: how do we
prove the useful results we want to have
proven with the smallest set of assumptions/
axioms. You are right, although you did not
quite state it this way, that for many of
these folks, especially the Bourbakists, this
optimization goal was probably more important
than the absolute reality or lack thereof of
the axioms.
Euclid may not have formulated in precisely
these terms, as Hilbert pretty clear did (even
if he did not specifically cite Occam [or Ockham]),
but having a heuristic goal would tend to lead
one to such a simplification. Perhaps we might
think of Euclid as having been a satisficer in
this realm, with wanting to have as few axioms
as possible, but with the constraint that they
appeal to common sense and at least appear to
be true.
Barkley Rosser
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