> 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 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 > > 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/b030815d-789a-a63d-8848-0c59dcc5b4ad%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/F684BF1E-CE03-4F22-A6A0-6FD16912E389%40ulb.ac.be.
