> On 5 Jun 2020, at 13:34, Philip Thrift <[email protected]> wrote: > > > > On Friday, June 5, 2020 at 4:47:14 AM UTC-5, Bruno Marchal wrote: > >> On 4 Jun 2020, at 22:33, Philip Thrift <[email protected] <javascript:>> >> wrote: >> >> >> Years ago I wrote about the Zetans >> >> >> http://poesophicalbits.blogspot.com/2012/04/persons-without-infinities.html >> <http://poesophicalbits.blogspot.com/2012/04/persons-without-infinities.html> >> >> who never imagined infinities, nor found any reason to either think of them, >> or invent them. >> >> They have a fine definition of computers and computing, and have found no >> need for anything more than finite mechanism in any of their theory of >> computing. >> >> That we came to think "infinity" plays a role in computing (or in computing >> theory, or in mathematics in general) is just an aspect of our own peculiar >> psychology and history, but it is not needed. > > > That makes some sense. You can compute without axiom of infinity, and indeed > you can define what is a computer just by using the two axioms Kxy = x, and > Sxyz = xz(yz), as I have explicitly shown on this list. Similarly you can > define a computer using only elementary arithmetic, like Gödel did implicitly > and Kleene did explicitly. But to prove anything non trivial, you need > induction, and to get semantics treated mathematically, you need actual > infinity axioms, like with the notion of real numbers, etc. > > To *understand* Kxy = x …, you need an axiom of infinity at the meta-level, > and this is required by all scientist-numbers in arithmetic, so “infinity” is > more than welcome to define the notion of observer, and for the notion of > physical *laws*. > > Bruno > > > > > As my old post shows, the Zetans do have their Axiom of Infinity - called the > Axiom of Zillions.
? > > They are happy with their finite set of numbers, but sometimes they construct > bigger numbers to add to the set. But they do not think there are numbers > between the bigger numbers. There are gaps. > > There is no potential infinity since they don't think their galaxy will last > forever. The notion of “forever” and/ or “not forever” needs potential infinity. Like the notion of (natural) law. Anyway, you are free to interpreted Kxy = x, or arithmetic, … ultrafinitaitsically. That does not change the Mechanist phenomenological predictions. Bruno > > ( All this follows from https://www.jstor.org/stable/2273942 ) > > @philipthrift > > > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/dbe74497-12f7-4743-bfbb-079602af43a6o%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/dbe74497-12f7-4743-bfbb-079602af43a6o%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/58BB3018-122B-420C-9F1D-7A77E559ADB2%40ulb.ac.be.
