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 CT thesis is strictly false in such a case, but could possibly apply in an approximate sense. > 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.
