On Tuesday, June 2, 2020 at 12:34:37 PM UTC-5, Brent 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] <javascript:>> 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. > > Brent >
For the most part computers are meant to run various algorithms that solve some restricted set of problems, say business applications. We use them largely as tools. LC > > > 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/97413020-4a73-4ff5-aec8-68cd2893b73c%40googlegroups.com.
