[FOM] Truth and set theory

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Fri Dec 7 06:57:09 EST 2007

Thanks for all the responses to my request. Here are few comments.

Thomas Forster <T.Forster at dpmms.cam.ac.uk> wrote:

> Are you quite sure
> that it is NBG- that he gives the truth-definition in?  Not the version
> with the impredicative class existence scheme..?

If I understand him correctly, Wang first shows how to give a truth
definition for Z in an inpredicative theory of finite sets S1, but then also
shows how it can be done even in a predicative theory of finite sets S2.
(Theorem II, on page 253)

Quoting Richard Heck <rgheck at brown.edu>:

> I'm somewhat puzzled by this question, for reasons close to ones you 
> mention here in passing. Namely: A theory (or definition) of truth is a 
> theory (or definition) of truth for a /language/. I don't know what one 
> would mean by saying that one had defined truth for a /theory/.

Yes, this puzzles me too. (Though, Tarski allowed that a "language" may
contain some non-logical axioms). I just wonder why Wang's result is always
stated for Z, and not for ZFC. Just an historical accident?

I would expect that if one can give in NGB- a materially adequate truth
definition for  ZF-, this would automatically be a truth definition for Z,
ZFC and whathever shares the same language. Right?  

All the Best,


Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki

E-mail: panu.raatikainen at helsinki.fi


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