FOM: Conclusion on Conclusiveness

[Moshe' Machover]

J Shipman writes:

>The fact of the matter is (to use a favorite FOM phrase) that we never have
>absolute certainty that a proof is valid.

*Never*?

Does `a proof' in the above sentence mean *any* proof?

Are you claiming, eg, that we do not (yet?) have an
absolutely-certainly-valid proof that for any natural n there is a prime p
> n?

Only such a very strong claim would suffice to answer the original query,
whose underlying intent was to argue for the social-constructivist view of
mathematics.

My feeling is that the case of `absolutely-certainly-valid proof' is
somwhat like that of `elephant': it may be difficult (or even impossible)
to give a satisfactory definition; but we can bloody well tell one when we
see one.



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