Here I use the word "true" in its internal sense within PA. But to be clearer (and to avoid using a confusing word like "true"), I should have written
You could have a number m that's defined to equal 1 if P and 2 if not-P, for some particular proposition P in PA.
That isn't problematical, is it? PA lacks a truth-predicate, but it doesn't need to have one for my purpose. Jim Propp On Tue, Sep 3, 2013 at 8:51 PM, Dan Asimov <dasimov@earthlink.net> wrote:
What does "true" mean here? Provable within PA?
Because if it's undecidable in PA, there's disagreement over whether "true" (independent of any axiom system) has a well-defined meaning.
--Dan
Jim wrote:
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