[FOM] A proof that ZFC has no any omega-models
Timothy Y. Chow
tchow at alum.mit.edu
Sun Feb 24 18:12:36 EST 2013
On Sat, 23 Feb 2013, Monroe Eskew wrote:
> To me this picture looks like nothing has really changed. Some people
> with philosophical worries forced the mathematicians to put little
> ornaments around their work, but mathematical practice did not actually
> change. The mathematicians went on to assume the same assumptions, A,
> and all they had to do to show good citizenship was to first say,
> "Suppose A," and at the end say, "Therefore A implies...." The
> government didn't actually change how mathematics is done. So what was
> their supposed conservative vision all about?
O.K., so in your scenario nothing really changes. Is that supposed to be
a bad thing?
I mean, the whole point of Hilbert's program, as I understood it, was to
enable us to stay in Cantor's paradise while easing ontological concerns
that the "government" might have. Although we now know that Hilbert's
program can't succeed in its original form, it seems to me that you would
have challenged Hilbert at the outset, asking him what the point of his
program was all about if it wasn't going to lead to any change in
mathematical practice. But surely it's clear that the whole point of the
program was to find good reasons *not* to change mathematical practice.
The vision isn't to force people to adopt more conservative practices, but
to convince skeptics that current practices don't really offend their
metaphysical sensibilities after all.
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