FOM: mathematical certainty
Vladimir Sazonov
sazonov at logic.botik.ru
Thu Dec 10 12:13:13 EST 1998
Stephen Cook wrote:
>
> Here is a reply to Andreas Blass's comments on my working definition
> of mathematical certainty as provability in an appropriate formal
> system such as ZFC.
>
...
>
> Of course if ZFC is found to be inconsistent, then this definition
> of mathematical certainty would have to be revised.
I agree with the omitted part (...); cf. the original message of
Stephen Cook. But I would like to comment on the last two lines.
I think that in the case of inconsistency of ZFC this theory,
but *not* the above general and sufficiently clear "definition"
of mathematical certainty will be revised (may be very
radically!). Actually, ZFC itself was obtained by such a
correction of set theory with unrestricted comprehension axiom.
Mathematical certainty (relative to or irrespective to any version
of set theory) will be again understood in exactly the *same* way,
as "provability in ANY [VS.] appropriate formal system".
Vladimir Sazonov
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