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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