On Sat, Oct 26, 2019 at 05:25:39PM -0700, 'Brent Meeker' via Everything List wrote: > > > On 10/26/2019 5:05 PM, Russell Standish wrote: > > On Sat, Oct 26, 2019 at 12:50:10PM -0700, 'Brent Meeker' via Everything > > List wrote: > > > I'm glad you recognize there's a difference between "potential" and > > > "real"; > > > a distinction this list is founded to obfuscate. > > > > > > Brent > > I don't know about that. The everything is "all finite things" is a > > perfectly rational starting point for an ensemble theory. > > > > Even though Max's original "all mathematical objects" theory is > > ambivalent on the point, I've always interpreted that as "all finite > > axiomatic systems", even in my first paper on the subject: "Why Occams > > Razor". > > Peano arithmetic is not a finite axiomatic system. It has infinitely many > axioms of the form (s...(s(s(s)))...). > So I'm not sure what your refer to. I doubt that "all finite things" is > well defined. Is the set of all finite things finite? >
It was a way of characterising a type of theory, such as "all finite axiomatic systems", or "all turing machines". Peano arithmetic is a finite axiomatic system. However, the integers is not - as shown by Goedel's incompleteness theorem. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University 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/20191027003338.GI12720%40zen.
