> On 17 May 2019, at 20:58, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > 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?
Indeed. All what you prove in PA is true in all Models, standard and non standard alike. This follows from completeness (also proved by Gödel). The non standard models assign just “false” truth value to UNDECIDABLE sentences. Like assigning true to “provable(false)”. Bruno > > Brent > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/382aedaf-a8bb-a63b-dcfa-01ef7534dab1%40verizon.net. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/E26427AF-7B6D-40E9-9B98-DA41508A766F%40ulb.ac.be.
