> On 31 May 2020, at 09:50, Russell Standish <[email protected]> wrote: > > On Sun, May 24, 2020 at 01:21:38PM +0200, Bruno Marchal wrote: >> >>> On 24 May 2020, at 01:37, Russell Standish <[email protected]> wrote: >>> >>> However, I would think that ultrafinitism would change COMP's >>> predictions, and in a sense be incompatibe with it. Some programs will >>> not exist, because one would need to wait too long >> >> “Too long” is still finite. >> >> The biggest natural number is of course “infinite”, but the ultrafinitist >> cannot know that. >> >> That is why a “real ultrafinitiste” will never say that he is ultrafinitist. >> He has no means to explains why ultra-finitism means. Only a finitists can >> prove that ultra-finitsime is consistent (indeed PA can prove that RA is >> consistent). >> >> >> >>> for them to be >>> executed by the UD. In fact, the choice of reference universal machine >>> would be significant in ultrafinitism, IIUC. >> >> Why? As long as the theory is Turing complete, all programs are run (in all >> interpretation of the theory), including all finite segment of the >> executions of all non terminating programs, and this with the usual >> redundancy. >> > > For an ultrafinitist, there is a biggest number (perhaps unknowable), > and consequently computer programs that don't get run (because they > take more steps than that biggest number.
The biggest number is a non-standard number, meaning that a genuine ultra-finest machine will be, in the eye of a non ultra-finitist, be a “non standard machine”, making a non-standard computations (quite out of the one defined by CT) > > The CT thesis is strictly false in such a case, Indeed. > but could possibly > apply in an approximate sense. That remains to be made more precise, but will require non finitism, … It is the general problem of the ultrafinitist, which is that they cannot define “ultrafinitist”. An ultrafinitst cannot say “I am an ultrafinitist” ! Bruno > > >> Bruno >> >> >> >>> >>> >>> -- >>> >>> ---------------------------------------------------------------------------- >>> Dr Russell Standish Phone 0425 253119 (mobile) >>> Principal, High Performance Coders [email protected] >>> http://www.hpcoders.com.au >>> ---------------------------------------------------------------------------- >>> >>> -- >>> 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/20200523233705.GC27696%40zen. >> >> -- >> 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/596AD8C2-0628-4F05-926E-0BDEF0767A46%40ulb.ac.be. > > -- > > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders [email protected] > http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > -- > 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/20200531075033.GB25940%40zen. -- 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/BB7D2A30-2A19-4347-BAE1-FE4C56A15C14%40ulb.ac.be.
