> On 26 Aug 2019, at 03:54, Jason Resch <[email protected]> wrote: > > > > On Sunday, August 25, 2019, Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: > On Mon, Aug 26, 2019 at 11:03 AM Jason Resch <[email protected] > <mailto:[email protected]>> wrote: > On Sunday, August 25, 2019, Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: > On Sun, Aug 25, 2019 at 11:03 PM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > On 25 Aug 2019, at 14:01, Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: >> On Sun, Aug 25, 2019 at 9:39 PM Bruno Marchal <[email protected] >> <mailto:[email protected]>> wrote: >> On 25 Aug 2019, at 10:10, Bruce Kellett <[email protected] >> <mailto:[email protected]>> wrote: >>> The mathematical structure might describe these things, but descriptions >>> are not the things they describe. >> >> I think you confuse the mathematical structure, and the theory describing >> that mathematical structure. Those are very different things. >> >> I think that is exactly the mistake that you make all the time. > > Where? I don’t remind you ever show this. > > I have said it many times. A mathematical structure is an abstract human > construct. Such a structure might go some way towards describing physical > reality, but the map is not the territory. > > > Bruno is talking about the territory and I think you are confusing it with > Bruno talking about the map. To be clear, axioms in math are just theories > to explain the mathematical reality, > > Using the word "reality" here just begs the question. Arithmetic (or > mathematics) is nothing more than the product of its axioms. Proofs from the > axioms may not capture all that one might regard as "truth", but that is > really beside the point. Using the word "truth" is just as fraught as using > the term "reality" -- question begging. > > Any system of axioms can only prove a finite number if bits of Chaitin's > constant. More powerful systems can prove more bits of it, but no system is > capable of proving endless bits of it. So where does this number belong? > It's complete set of digits are not decidable under any system of axioms. > It's not the product of any system if axioms.
Calude mentions an interesting theorem by Solovay. There is a universal machine U such that ZFC cannot compute *any* bit of its Chaitin-Omega number. Not even the first bit. I guess this used ZFC + some strong axiom (Hmm… like the arithmetical soundness of ZF probably). That Universal machine U is not predictible at all by ZFC, yet, its behaviour is arithmetically deterministic. Assuming ZFC arithmetically sound (which I find very plausible). Bruno > > > > in the same sense as physical theories do. Since you presume there is no > mathematical reality all you can imagine are maps. > > Maybe the physical reality actually is the territory that we are talking > about. > > There's no escaping it. The question of whether or not a light will ever turn > during by the evolution of a physical system is a physical problem. > > If the physical system under consideration is a computer running some program > and the light turns on only when the computation finishes, then physical > theories are no longer enough to answer the question. > > If mathematical theories are necessary to answer the question, why aren't > they as much about the reality as the other physical theories? > > Jason > > -- > 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/CA%2BBCJUhivfL_HBydB4rFWbGw%2B_pwYGm2xL8UQcY5w-0J21NLwA%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUhivfL_HBydB4rFWbGw%2B_pwYGm2xL8UQcY5w-0J21NLwA%40mail.gmail.com?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/37BE19E8-07A4-4CD4-ACE1-83D2DAEA55C1%40ulb.ac.be.
