[FOM] Clarity in fom and problem solving
Mark van Atten
Mark.vanAtten at univ-paris1.fr
Thu Apr 6 05:00:42 EDT 2006
On Wed, 05 Apr 2006 02:40:54 -0400, Harvey Friedman quoted from p.314 of
Gödel CW III and commented:
> Obviously, these are very imaginative and thought provoking arguments by
> Godel in favor of realism or Platonism in mathematics.
The arguments quoted are not specific enough to make a case for
platonism as distinct from, or opposed to, certain other positions, e.g.
intuitionism. As Gödel also observed,
`Brouwer does not mean arbitrary creations. Rather he means cre-
ation according to certain principles. The central and appropriate
concept for Brouwer is construction rather than creation. We con-
struct something out of something given ... Creation in this sense
does not exclude Platonism.' [Wang, Logical Journey, p.248]
Intuitionism is the exploration of this `something given'; and an
intuitionist could have produced Gödel's three arguments that prof.
Friedman quoted. But obviously the Platonism that this (according to the
quote above) amounts to, is Platonism in a weaker sense than usual. In
particular, it is weaker than the kind Gödel himself wished to argue
for. For intuitionistic ontology, mind suffices; the platonist needs in
addition a realm of objects that are not in the mind.
Mark van Atten.
IHPST (Paris 1/CNRS/ENS)
13 rue du Four, F-75006 Paris, France
tel ++ 33 (0)1 43 54 94 60
fax ++ 33 (0)1 43 25 29 48
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