> On 26 Aug 2019, at 03:28, Bruce Kellett <[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.
I use the term “reality” to avoid “model” which is often used in the sense of theory in physics. > Arithmetic (or mathematics) is nothing more than the product of its axioms. That is simply false. We do have a reasonable intuition of what the arithmetical reality is. It does not ask us much more than the usual belief in analysis. But it escapes essentially *all* effective theory. Even ZF = a giant cardinal cannot prove all the true proposition of the standard model of arithmetic. Arithmetic is essentially undecidable (Tarski). All its finite or recursively enumerable extensions miss some truth. > 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. Arithmetical truth does admit a purely mathematical definition (cf Tarski). Like the notion of “reality” used here. All theories needs more than themselves to define their models or semantics. No effective theories can prove the existence of a reality staying its axioms, by incompleteness. That is why the study by a machine, of its own semantics, will be a theology. It will requires an irrational, or better surrational, act of faith. The set of such possible faith is axiomatised by the modal logic G* (that is why I call it theology, for the machine who begin to guess the presence of that something above itself). > > 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. With mechanism, that territory appearance is explained by the statistic on all (relative) computations. Let us do the test to see if we get some discrepancy with Nature. Bruno > > Bruce > > -- > 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/CAFxXSLQ%3D2UEXJc1X3s6A6A%2B-LAd6gOT1dGfTkf5WsqQHBkZuXg%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLQ%3D2UEXJc1X3s6A6A%2B-LAd6gOT1dGfTkf5WsqQHBkZuXg%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/C3247E82-AD63-4467-B2AC-70FE4A79A949%40ulb.ac.be.
