> On 16 May 2019, at 01:40, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 5/15/2019 9:01 AM, Bruno Marchal wrote: >>> On 13 May 2019, at 23:46, 'Brent Meeker' via Everything List >>> <[email protected]> wrote: >>> >>> >>> >>> On 5/13/2019 8:50 AM, Jason Resch wrote: >>>> But then what is arithmetical truth? We have no label for it. It cannot be >>>> derived from or defined by labels. >>> And it depends on the model. Which is why it's undefinable within the >>> system. And also why it's not the same as the "true" in "It is true that >>> snow is white.” >> ? >> >> I don’t see the difference. The standard model of arithmetic is given by the >> intersection between all models. > > Isn't the intersection of all models just the provable part?
By incompleteness that is not the case. The provable part is much smaller than the true part. The true undecidable sentences are true in the standard sense, just possibly false in the non start sense. Typical example: the consistency of PA. Everyone familiar with natural numbers believe that PA is consistent, but PA cannot prove this, and thus there is a model of PA where “PA is inconsistent” is true. It means that some “omega” (see my preceding posts) is a proof of “0=1”; but as omega is not accessible by the successor relation, that they is still consistent. PA + (PA is inconsistent) is a consistent theory of natural numbers, but it is not a sound theory. It is false in the standard model. Bruno > > Brent > >> See my other recent explanations. >> >> 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/816e0c3c-76cc-82c8-a3b3-18f6af30b042%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/ab8bbe0f-a236-9628-c030-4de2928ca181%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/614D86A6-0E19-4C7F-A515-21D19A6A8E92%40ulb.ac.be.
