[FOM] Disproving Godel's explanation of incompleteness
praatika at mappi.helsinki.fi
Mon Oct 24 08:55:20 EDT 2005
Roger Bishop Jones keeps on insisting that Tarski's theorem (of the
undefinability of truth) is false. I doubt I can convince him, but for
others, here are some further explanations.
Goedel refers in the relevant passage to Tarski. Tarski required that
any "materially adequate" truth-definition must satify what he called
Convention T, that is, it must entail as its consequences all instances of
the following schema:
(T) True([p]) <-> p.
He then showed that for any sufficiently rich theory T, there is no formula
P(x) in the language of T such that T proves P([S]) <-> S, for every
sentence S of L(T).
The alleged counter-example of Jones, which equates truth with provability,
is completely irrelevant, for Prov(x) does not satisfy Convention T (apply
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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