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From: Transfer Principle on 9 Jun 2010 20:42
On Jun 8, 6:32 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Transfer Principle <lwal...(a)lausd.net> writes:
> > If it does turn out that ZF is inconsistent, then there would have
> > been some underlying reason that the proof wasn't discovered for over
> > a century after the axioms were first given.
> What's there to rule out the possibility that the simplest proof of a
> contradiction in ZF is inhumanely complex, utterly beyond our
> comprehension, invoking, say, an obscure instance of
> Pi-20^20^20^20^4546^3214532 + 4145624^7542 + 897412 replacement?

Ah yes, I do acknowledge that a proof may be difficult to find
if it involves large numbers. Indeed, this is exactly what Ed
Nelson is doing. He is attempting to find a proof that PA is
inconsistent, involving the large numbers that appear via the
operation of tetration.
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