[FOM] Disproving Godel's explanation of incompleteness

[praatika@mappi.helsinki.fi]

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 
Loeb's Theorem).  

-Panu



Panu Raatikainen
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
P.O. Box 9
FIN-00014 University of Helsinki
Finland

E-mail: panu.raatikainen at helsinki.fi

http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm