> On 20 Feb 2020, at 00:44, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 2/19/2020 4:36 AM, Bruno Marchal wrote: >>> On 18 Feb 2020, at 23:07, 'Brent Meeker' via Everything List >>> <[email protected]> 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 [email protected]. >>> 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 [email protected]. > 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/1D4C8B1F-5E41-4C89-ABC9-28712EB4D257%40ulb.ac.be.
