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*To*: fom@math.psu.edu, ablass@math.lsa.umich.edu*Subject*: FOM: mathematical certainty*From*: Stephen Cook <sacook@cs.toronto.edu>*Date*: Wed, 9 Dec 1998 17:46:51 -0500*Cc*: sacook@cs.toronto.edu*Sender*: owner-fom@math.psu.edu

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. It seems to me that any attempt at a formal definition of mathematical certainty is subject to the kind of attack made by Andreas. My intention was to give a simple operational definition that seems to apply to current mathematical practice. For example, when a mathematician finds a "mistake" in someone's proof, he is pointing out that the proof exposition cannot be translated into a formal ZFC proof in any obvious way. Conversely, all theorems which are currently considered as "established" by the mathematical community have proofs that can be formalized in ZFC. Of course if ZFC is found to be inconsistent, then this definition of mathematical certainty would have to be revised. Steve Cook

**Follow-Ups**:**Vladimir Sazonov**- Re: FOM: mathematical certainty

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