> On 4 Jun 2020, at 20:28, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 6/4/2020 4:07 AM, Bruno Marchal wrote: >>> On 2 Jun 2020, at 19:34, 'Brent Meeker' via Everything List >>> <everything-list@googlegroups.com> wrote: >>> >>> >>> >>> On 6/2/2020 2:49 AM, Bruno Marchal wrote: >>>>> On 1 Jun 2020, at 22:43, 'Brent Meeker' via Everything List >>>>> <everything-list@googlegroups.com> wrote: >>>>> >>>>> >>>>> >>>>> On 6/1/2020 2:08 AM, Bruno Marchal wrote: >>>>>> Brent suggest that we might recover completeness by restricting N to a >>>>>> finite domain. That is correct, because all finite function are >>>>>> computable, but then, we have incompleteness directly with respect to >>>>>> the computable functions, even limited on finite but arbitrary domain. >>>>>> In fact, that moves makes the computer simply vanishing, and it makes >>>>>> Mechanism not even definable or expressible. >>>>> That's going to come as a big shock to IBM stockholders. >>>> Why? On the contrary. IBM bets on universal machine >>> No, they bet only on finite machines, and they will be very surprised to >>> hear that they have vanished. >> They bet on finite machines … including the universal machine, which I >> insist is a finite machine. That is even the reason why I called it from >> times to times universal number. >> >> I recall that once we get the phi_i, > > i = 1 to inf.
That is the potential infinite, that you already need for a concept like the square root of 2, used all the time in elementary quantum mechanics. Without it, neither CT, nor YD makes any sense. We could aswell stop doing any math, if not stop thinking. The axioms that I use are just Kxy = x, and Sxyz = xz(yz). There is no axiom of infinity, nor even induction axiom. That belongs only to the observers, and the proof of their existence requires only the two axiom above, or the arithmetic one, or anything Turing equivalent. With less than that, there is no computer, nor laptop … The universal machinery is potentially infinite. The universal machine is finite. Bruno > >> which can be defined in elementary arithmetic, we get all the universal >> numbers, that is all u such that there phi_u(x, y) = phi_x(y), and such u >> can be used to define all the recursive enumeration of all digital machines. >> >> The implementation of this fine but universal machines are called (physical) >> computer, and is the domain of expertise of IBM. >> >> Bruno >> >> >> >>> Brent >>> >>>> and know well what is a computer: a finite arithmetical being in touch >>>> with the infinite, and indeed, always asking for more memory, which is the >>>> typical symptom of liberty/universality. IBM might be finitist, like >>>> Mechanism, but is not ultrafinist at all. Anyway, mathematically, >>>> Mechanism is consistent with ulrafinitsim, even if to prove this, you need >>>> to go beyond finitism, (but then that’s the case for all consistent >>>> theory: none can prove its own consistency once “rich enough” (= just >>>> Turing universal, not “Löbian”). >>>> >>>> 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/3068f558-7f61-56cb-61fe-44832ec28a91%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/87582a17-b101-aa86-0c27-cf21a663c828%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/42703C5F-F8E7-47BA-AF8C-E962FADF8553%40ulb.ac.be.
