> On 5 Jun 2020, at 21:10, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 6/5/2020 2:32 AM, Bruno Marchal wrote: >>> On 4 Jun 2020, at 20:28, 'Brent Meeker' via Everything List >>> <[email protected]> wrote: >>> >>> >>> >>> On 6/4/2020 4:07 AM, Bruno Marchal wrote: >>>>> On 2 Jun 2020, at 19:34, 'Brent Meeker' via Everything List >>>>> <[email protected]> wrote: >>>>> >>>>> >>>>> >>>>> On 6/2/2020 2:49 AM, Bruno Marchal wrote: >>>>>>> On 1 Jun 2020, at 22:43, 'Brent Meeker' via Everything List >>>>>>> <[email protected]> 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, > > No, you can't diagonalize on an infinity that is only potential.
That is not true. Cantor’s diagonal cannot be done, but Kleene’s diagonal (the one I have explained) does not require any actual infinities. You might reread it. > >> that you already need for a concept like the square root of 2, used all the >> time in elementary quantum mechanics. > > And in every computer...which uses on finitely many bits. At each moment, but with question like will a machine stop or not, you need potential infinity. > >> Without it, neither CT, nor YD makes any sense. > > CT doesn't. So much the worse for CT. OK. But that’s says something. CT is the most solid non trivial facts in modern science, I would say. > YD makes better sense since the doctor can now be sure he only needs to > reproduce finitely many functions. YD is a far more stronger principle that CT. I have never met someone doubting CT, actually. It is not so for YD, which requires some sort of faith. > >> We could aswell stop doing any math, if not stop thinking. > > At least stop imagining the supernatural. Better to stop imagining the “natural”, to begin with. > >> >> The axioms that I use are just Kxy = x, and Sxyz = xz(yz). > > But you allow rules of inference that permit inferences about the enumerated > array of all functions. Right. Here is the complete set of ontological assumptions: AXIOMS KAB = A SABC = AC(BC) RULES: If A = B and A = C, then B = C If A = B then AC = BC If A = B then CA = CB For the phenomenology, we can use as much as we want, like in physics. It is provably never enough. Bruno > > Brent >> >> 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 [email protected]. >>>>> 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 [email protected]. >>> 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/633e265d-a2d6-a08a-4dbf-5e8de7aaa100%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/3401EFC6-4041-431A-8257-2F69A9F5CFFE%40ulb.ac.be.
