FOM: CH and 2nd-order validity

[Matt Insall]

Professor Black,
You said:
``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 
actually
carried out is a proof that Inacc --> Cons(ZFC) ?  (I take here Inacc to be 
the formula
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)?


Matt Insall
htttp://www.umr.edu/~insall