[FOM] Truth and set theory
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,
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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