FOM: con ZFC
Randall Holmes
holmes at catseye.idbsu.edu
Fri Mar 19 11:05:31 EST 1999
Kanovei said:
Con ZFC is believed to be true
not as a formal statement of any sort
but rather as a prediction that any
contradiction in ZFC will never be found in
the practical activity of mathematicians.
For instance if you succeed to prove
some A assuming Con ZFC this will
mathemtically mean that you have proved
Con ZFC --> A, but not that you have proved A.
Holmes replies:
This is the attitude of some. On the other hand, some probably think
that it is clear that there is an inaccessible cardinal (by an
extension of the same intuition that makes causes most of us to think
ZFC is OK in the first place) and so Con(ZFC) is simply true.
I'm of several minds about ZFC being "true" (in the sense that there
is any model of second-order ZFC) but I'm quite sure that it is
consistent; I believe Con(ZFC) as a statement of arithmetic to be true
as a formal statement, and I think that there are many who are of this
opinion.
I think that there are a wide variety of "informal" beliefs held
by mathematicians.
And God posted an angel with a flaming sword at | Sincerely, M. Randall Holmes
the gates of Cantor's paradise, that the | Boise State U. (disavows all)
slow-witted and the deliberately obtuse might | holmes at math.idbsu.edu
not glimpse the wonders therein. | http://math.idbsu.edu/~holmes
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