> On 27 Aug 2019, at 19:19, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 8/27/2019 4:18 AM, Bruno Marchal wrote: >> >>> On 26 Aug 2019, at 21:04, 'Brent Meeker' via Everything List >>> <[email protected] >>> <mailto:[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. > > Yes, I'm familiar with the fantasy that things can be true by definition. > Sadly it only works for fictional things, as "Watson was Holmes > companion...by definition.”
Sadly, there are few application of Sherlock Holmes in physics or in any science different from the Art of the Detectives. But the arithmetical reality, taught in high school, is full of applications in physics and actually in most sciences. You might read the beginning of the book by Torkel Franzen on the use of “truth" in mathematical logic. Truth, in its mathematical sense, is always relative to a model, but that does not eliminate some intuitive standard notion of truth at the metalevel. and in first order arithmetical logic, we do have a notion of standard (intuitive classical) model, whose sigma_ restriction gives mathematical precise meaning to terms like “computable”, “not computable" and “computation”. The string theory of the photon would not work if the prime numbers did not have taught us that it makes sense to say that the sum of all natural numbers converges to -1/12. But with digital mechanism, the role of numbers become obvious, even if all universal system will compete, somehow. Also, keep in mind that for the ontology, we need only the sigma_1 arithmetical reality, which can be defined by PA. Bruno > > Brent > > >> 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] >> <mailto:[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 >> >> <https://groups.google.com/d/msgid/everything-list/9876DC2B-E2B3-4D47-98BA-F6921F8598F8%40ulb.ac.be?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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/c7035306-9254-c0bc-e3bf-0255aeb70eec%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/c7035306-9254-c0bc-e3bf-0255aeb70eec%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/A85C7CB9-E24D-427C-A424-7652A5B288E1%40ulb.ac.be.
