> On 20 Feb 2020, at 00:44, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 2/19/2020 4:36 AM, Bruno Marchal wrote: >>> On 18 Feb 2020, at 23:07, 'Brent Meeker' via Everything List >>> <everything-list@googlegroups.com> wrote: >>> >>> >>> >>> On 2/18/2020 5:05 AM, Bruno Marchal wrote: >>>> It is simply a fact that all computational (and thus all conscious state, >>>> with mechanism) are executed by an infinity of universal machine/number in >>>> arithmetic >>> That's about as much a fact as "Jehovah did it.” >> >> It is as much a fact that Euclid’s theorem asserting that there is no >> greatest prime number, or equivalently, that there is an infinity of prime >> numbers. > > Only because you assume every number has a successor.
We agreed on classical predicate logic + 1) 0 ≠ s(x) 2) x ≠ y -> s(x) ≠ s(y) 3) x ≠ 0 -> Ey(x = s(y)) 4) x+0 = x 5) x+s(y) = s(x+y) 6) x*0=0 7) x*s(y)=(x*y)+x But any Turing-universal theory would do, even without classical logic, or any logic, we could use only: 1) If A = B and A = C, then B = C 2) If A = B then AC = BC 3) If A = B then CA = CB 4) KAB = A 5) SABC = AC(BC) Even ultrafinitist agrees with those theories (but disagrees on some of their interpretation, but that does not concern us). Bruno > > >> I can prove it to you, when you want. Or you can read Gödel’s 1931 paper, or >> Davis’s Dover Book “Computability and Unsolvability”, which proves this by >> the usual method (using Kleene’s predicate( instead of Gödel "prove(x,y)”), >> and the Turing machine formalism. > > And I can prove anything if I'm allowed to choose the axioms and rules of > inference. > > Brent > >> >> 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 everything-list+unsubscr...@googlegroups.com. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/a23cd212-eaa3-68bb-0cee-ba95ab31d6e2%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/90c8ac74-90b2-2add-330c-d68d70c7b3c1%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/1D4C8B1F-5E41-4C89-ABC9-28712EB4D257%40ulb.ac.be.
