> On 26 Aug 2019, at 21:04, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 8/26/2019 4:19 AM, Bruno Marchal wrote: >> >>> On 26 Aug 2019, at 02:28, 'Brent Meeker' via Everything List >>> <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> >>> >>> On 8/25/2019 12:50 PM, Jason Resch wrote: >>>> What's the difference between abstract and concrete? I think it's only a >>>> matter of relative perspective. Other universes to us seem abstract. >>>> While to people in other universes ours would seem abstract. Do you agree? >>> >>> No. The difference is one of completeness. A abstract something is >>> incomplete. >> >> It is the finite construction, like a theory, which can be incomplete. The >> arithmetical reality is complete. The theories are incomplete. > > That arithmetical reality is complete is a theory.
No, it is true by definition of the arithmetical reality, which here has been defined by the set of all true sentences in the standard model of PA. I “model” it by the set of the Gödel’s number of those true sentences. No theories can axiomatise that set, but by definition, that set is complete. The definition of that set can be done informally, and does not ask much that we we need to understand real number or analysis. 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/912ef024-038f-c308-9608-b08eb5d560e7%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/912ef024-038f-c308-9608-b08eb5d560e7%40verizon.net?utm_medium=email&utm_source=footer>. -- 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/9876DC2B-E2B3-4D47-98BA-F6921F8598F8%40ulb.ac.be.
