> 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, 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/A0BB4342-6D1A-41E9-833A-BCBC9C3CBDF6%40ulb.ac.be.
