[FOM] Clarity in fom and problem solving

[Mark van Atten]

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.

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