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*To*: FOM <fom@math.psu.edu>*Subject*: Re: FOM: mathematical certainty*From*: Vladimir Sazonov <sazonov@logic.botik.ru>*Date*: Thu, 10 Dec 1998 20:13:13 +0300*CC*: "Sazonov, Vladimir" <sazonov@logic.botik.ru>*Organization*: Program Systems Institute, RAS*References*: <98Dec9.174651edt.15567-28300@dvp.cs.toronto.edu>*Reply-To*: sazonov@logic.botik.ru*Sender*: owner-fom@math.psu.edu

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

**References**:**Stephen Cook**- FOM: mathematical certainty

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