Re: what follows from denying an axiom

On 17 tammi, 00:14, Gc <Gcut...@xxxxxxxxxxx> wrote:
On 16 tammi, 23:57, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

But suppose that somebody introduced some other concept of
the universe of sets, maybe inspired by Quine's New Foundations,
or some other alternative set theory. Then if this new conception
of sets became standard, then I could certainly make sense of the
claim that "The completeness theorem is false, but con(ZFC) is true".
That implication may in fact be a theorem of this alternative set
theory.

It might make sense, but I think the "completeness theorem" must be
then formulated in this new theory somehow differently, it would not
be anymore exactly the same theorem.

I maybe not should have said anything :) It is just so weird to think
that the completesness fails, it just feels it would bring down the
whole meaning of FOL.
.

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