FOM: CH and 2nd-order validity
montez at rollanet.org
Wed Oct 18 17:37:07 EDT 2000
``It *is* of course provable in ZFC plus an inaccessible, and I don't think
it's too unreasonable to say that that proof formalizes the informal
notions that provide the principal basis for our confidence in the
consistency of ZFC. So that would be an example of a rigorous proof which
is not a proof in ZFC. ''
Is it not the case that Professor Kanovei may object that the proof that is
carried out is a proof that Inacc --> Cons(ZFC) ? (I take here Inacc to be
that formalizes the large cardinal axiom ``there is an inaccessible
cardinal''.) May he
not reasonably assert that such a proof is not a proof of Cons(ZFC)?
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