FOM: geometrical reasoning, logic and proof
Colin McLarty
cxm7 at po.cwru.edu
Thu Feb 25 14:51:25 EST 1999
kanovei at wmfiz1.math.uni-wuppertal.de (Kanovei)
wrote:
>There is apparently no any example of a
>mathematical statement commonly accepted as a
>true theorem but not deducible logically from
>some (also commonly accepted) list of axioms,
>say ZFC.
Obviously every commonly accepted mathematical statement can be
deduced from commonly accepted mathematical statements. It can be deduced
from itself, for example.
On the other hand, as soon as any recursive set of mathematical
statements becomes commonly accepted, we find further statements which are
not logically (i.e. first order) deducible from them and yet are commonly
accepted.
Peronally, I believe ZFC is consistent, and I believe most people
who understand the issue agree. But I do not derive this belief (in the
consistency of ZFC) from deduction in any formal theory.
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