On 5/17/2019 3:35 AM, Bruno Marchal wrote:
It's a matter of equivocating on "the natural numbers". If you
regard them as a theory of things, the way you learn them at your
mother's knee, then there are objective truths "Two garbanzo beans
plus two chick peas make four beans." the way "Snow is white." But
if you want to evaluate the truth of "2+2=4" that's a proposition in
arithmetic. If it's PA then it's true in every model because it's a
theorem. But when you say there are true statements of arithmetic
that aren't provable in PA, what they are depends on the model.
Hmm… No.
Are you saying that non-standard models of arithmetic don't assign
different truth values to some propositions?
Brent
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