On Sunday, August 25, 2019, Bruce Kellett <[email protected]> wrote:
> On Mon, Aug 26, 2019 at 11:03 AM Jason Resch <[email protected]> wrote: > >> On Sunday, August 25, 2019, Bruce Kellett <[email protected]> wrote: >> >>> On Sun, Aug 25, 2019 at 11:03 PM Bruno Marchal <[email protected]> >>> wrote: >>> >>>> On 25 Aug 2019, at 14:01, Bruce Kellett <[email protected]> wrote: >>>> >>>> On Sun, Aug 25, 2019 at 9:39 PM Bruno Marchal <[email protected]> >>>> wrote: >>>> >>>>> On 25 Aug 2019, at 10:10, Bruce Kellett <[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. > > 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]. 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.
