> On 2 Dec 2019, at 19:10, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 12/2/2019 12:41 AM, Bruno Marchal wrote: >> In First Order Logic, Real Numbers are the one which simplifies. The first >> order theory of the real is decidable, unlike the first order theory of the >> natural numbers. The digital, or discrete, reality is more complex than the >> reals, which fits all holes, and provides (in the complex extensions) all >> roots for the polynomials. > > Do you know whether Gisin's "random" numbers produce a decidable structure?
It certainly does not. Real numbers are logically much simpler than Natural Numbers (think about x^n + y^n = z^n in integer structure and with real numbers for example), but Gisin use QM, which adds the trigonometrical functions, or complex numbers, and this re-intrdouces the discrete structure and the integers in the picture (sin(2pi*x) = 0). Trigonometry, or waves, is what makes the continuum able to imitate the digital. Whatever physics can appear from arithmetic, it is described by a continuum, and it needs to be able to imitate the digital machines (or we would not be there (assuming Mechanism of course). Bruno > > Brent > >> Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” by >> “physical”), which requires a non Mechanist theory of mind. >> With Mechanism, real number are phenomenological constructs by digital >> entities. It is real, but not ontologically real. >> >> Bruno > > > -- > 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 everything-list+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/5cdc993a-d81f-2508-a970-6c62bcaba4b4%40verizon.net. -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/C75466E0-4953-418A-8B0E-972AB1113D21%40ulb.ac.be.
