[FOM] Truth and set theory

Allen Hazen allenph at unimelb.edu.au
Wed Dec 5 04:51:19 EST 2007

Panu asks
> Now apparently Wang (1952) showed that it is possible to give a (materially
> adequate) truth-definition for the infinitary Z in finitistic set theory
> NBG-. This is interesting enough.
> But is there some reason why one could not also give a truth definition for
> ZF, again in NBG- ? (Z and ZF have, after all, the same language)
> Is anyone here familiar with this stuff?
------David De Vidi (of Philosophy Department, University of Waterloo,
Canada) and Graham Solomon discuss Wang's truth definitions in a paper in
"Journal of Philosophical Logic" vol. 28 (1999), so De Vidi (Solomon died a
few years ago) might be the best person to ask.
I don't trust myself to get the technical details right from memory.  As I
recall, Wang's claim was that he could give definitions of truth for
sentences in the languages of the theories in question, NOT that he could
prove that the axioms of the theories were, in the defined sense, true.  In
many models of the definING theory the set of sentences true, in the defined
sense, would NOT include all the axioms of the "object theory."  The actual
results are quite weak.
Allen Hazen
Philosophy Department
University of Melbourne

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