> On 27 Oct 2019, at 02:25, 'Brent Meeker' via Everything List > <[email protected]> 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)))…).
That is used to denote the natural numbers. Peano arithmetic is not finitely many axiomatisable due to the necessary presence of the scheme of inductions axioms. But that is why the ontology is ,to given by Peano arithmetic, but by Robinson arithmetic, which is indeed a finitely axiomatisble theory. It has seven axioms (sides the axioms of classical logic). > 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? Of course not. But the st of all finite things is not a number, nor even a thing. That is the oldest problem in theology: is god a possible object of the reality. Neoplatonists, but also Vimalarty and many Indian schools, got the opinion that it cannot. That is why the ONE is neither a part, nor an element of the set of beings. The whole is not even definable from inside. Quine New foundations allows a universal set, though. So it might makes sense that God can be in the universe, but it cannot make sense once we assume mechanism, where the numbers of numbers is not a number, as Plotonius foresaw. 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/e5d91183-8b6f-f92e-b22f-700f7c4c095f%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/E649DB6C-EC58-4B75-8316-A1C6AB30E3B7%40ulb.ac.be.
