Joao Leao wrote:
>
>CMR wrote:
>
> > Gödel's incompleteness theorems have and justly should be
>judged/interpreted
> > purely on the merits of the arguments themselves, not the author's
> > subjective(prejudiced?) interpretation, no?
> >
> > He was as much a victim(beneficiary?) of his "discoveries" as was
>anyone...
>
>Precisely! The implication I was drawing is that, as he stated quite well,
>his mathematical results reinforced his Platonist conviction. Unless you
>are implying that mathematical reality favours the ones who submit to
>it (an enticing possibility, for sure), I don't see how it could have been
>otherwise...
Yes, a Platonist can feel as certain of the statement "the axioms of Peano
arithmetic will never lead to a contradiction" as he is of 1+1=2, based on
the model he has of what the axioms mean in terms of arithmetic. It's hard
to see how non-Platonist could justify the same conviction, though, given
Godel's results. Since many mathematicians probably would be willing to bet
anything that the statement was true, this suggests a lot of them are at
least closet Platonists.
Of course, Platonism in the mathematical realm is a little different than
Platonism in the realm of ordinary language. I don't believe there is such a
thing as an "ideal apple", for example.
Jesse
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Received on Mon Jun 16 2003 - 13:41:15 PDT