[FOM] Intuitionists and excluded-middle
praatika at mappi.helsinki.fi
Fri Oct 14 04:12:41 EDT 2005
Ritwik Bhattacharya <ritwik at cs.utah.edu>:
> Ah, but the argument being made was that the *proof* might be useless,
> not that the theorem itself was useless. So nobody is suggesting that
> mathematics/mathematical "facts" need to have use, but a proof, by
> definition, must have the "use" of convincing the reader of the proof.
> > Moreover, it is not clear exactly how the possession of a particular
> > solution is so much more useful...
> Quite simply because it is far more convincing, in this case, to have in
> hand a number of the type that the theorem claims there exists, than to
> have a purported 'proof' of the existence of such a number.
So, the question was: what is the argument against the reliability of LEM,
that is, why should we not be convinced by a proof using LEM ? Lew Gordeew
suggested that such proofs may be "useless". I then argued that this is
not sufficiently clear. But now we are told that it means that they are
not convincing. Surely we haven't made much progress here.
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
P.O. Box 9
FIN-00014 University of Helsinki
E-mail: panu.raatikainen at helsinki.fi
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