Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/15/05 

Date: 15 Jan 2005 10:54:25 +0100

poopdeville@gmail.com writes:

> Paraphrasing, amongst other things, Tim Chow asked if AC and the other
> axioms of ZF are true. Unless he was using a non-model-theoretic use
> of the term "true," the ZFC is just as true as the group axioms, since
> we can exhibit models for both sets of axioms.

  If by a "model-theoretic use of 'true'" you mean a use whereby the
axioms of a theory are called "true" if they have a model, there is
no such usage in logic or mathematics. So obviously Tim was using a
"non-model-theoretic" sense of "true". You are reluctant to speak of
the axioms of ZFC as true (except in your Pickwickian sense), but why
is this? Would you say that since we can exhibit a model of
PA+"PA is inconsistent", the axioms of this theory are "just as true
as the group axioms"?

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