FOM: Conclusion on Conclusiveness

Moshe' Machover moshe.machover at
Tue Dec 16 05:39:19 EST 1997

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.


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

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.

  %%  Moshe' Machover                 | E-MAIL: moshe.machover at %%
  %%  Department of Philosophy        | FAX (office)*: +44 171 873 2270  %%
  %%  King's College, London          | PHONE (home)*: +44 181 969 5356  %%
  %%  Strand                          |                                  %%
  %%  London WC2R 2LS                 |  * If calling from UK, replace   %%
  %%  England                         |    +44 by 0                      %%

More information about the FOM mailing list