> On 27 Jul 2019, at 20:42, Lawrence Crowell <goldenfieldquaterni...@gmail.com> > wrote: > > On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote: > All that assumes that infinity exists for any meaningful use of the word > “exists” and as far as I know nobody has ever found a infinite number of > anything. Mathematics can write stories about the infinite in the language of > mathematics but are they fiction or nonfiction? > > John k Clark > > > Infinity is not a number in the usual sense, but more a cardinality of a set. > Infinity has been a source of trouble for some. I work with Hilbert spaces > that have a form of construction that is finite, but where the finite upper > limit is not bounded ---- it can always be increased. This is because of > entropy bounds, such as the Bekenstein bound for black holes and Bousso > bounds on AdS, that demands a finite state space for local physics. George > Cantor made some set theoretic sense out of infinities, even a hierarchy of > them. This avoids some difficulties. However, I think that mathematics in > general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo > set theory even has an axiom of infinity. The main point is with axiomatic > completeness, and mathematics with infinity is more complete.
Mechanism provides an ontological finitism (what exists are only 0, s(0), s(s(0)), …), but it explains why those finite objects will believe correctly in some phenomenological infinite (already needed to get an idea of what “finite” could mean. The infinite is phenomenologically real, but has no ontology. No first order logical theories can really define the difference between finite and infinite. Even ZF, despite its axiom of infinity is not able to do that, in the sense that it too has non standard model, in which we can have a finite number greater than all the “standard” natural numbers 0, s(0) … I am not sure why you say that adding an axiom of infinity makes a theory more complete. There are sense it which it only aggravate incompleteness. Once a theory is rich enough to define and prove the existence of a universal machine, that theory becomes essentially undecidable (which means that not only it is undecidable, but it is un-completable: all the effective consistent extensions are undecidable. Bruno > > Richard Feynman talked about Greek mathematics, the axiomatic formal systems > of mathematics, and Babylonian mathematics that is set up for practical > matters. I have no particular preference for either, and think it is > interesting to switch hats. > > LC > > > On Sat, Jul 27, 2019 at 7:36 AM Lawrence Crowell <goldenfield...@gmail.com > <javascript:>> wrote: > On Thursday, July 25, 2019 at 10:02:39 PM UTC-5, Bruce wrote: > On Fri, Jul 26, 2019 at 12:48 PM John Clark <johnk...@gmail.com <>> wrote: > When I was younger I read a lot of science fiction, I don't do it so much > anymore and technically I didn't do it this time either but I did listen to a > audio book called "We Are Legion We Are Bob" it's the first book of the > Bobiverse trilogy and I really enjoyed it. You can get a free 5 minute sample > of the book here: > > We Are Legion (We Are Bob): Bobiverse, Book 1 > <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8&qid=&sr=> > > It tells the story of Bob, a young man who has just sold his software company > for a crazy amount of money and decides that after a decade of hard work he's > going to spent the rest of his life just goofing off. On a whim he signs with > a Cryonics company to have his head frozen after his death and then just > hours later while crossing the street to go to a science fiction convention > is hit by a car and dies. Five subjective seconds later he wakes up and finds > that a century has passed and he's been uploaded into a computer. This is all > in the opening chapter. > > Parts of the story are unrealistic but parts of it are not, I think it was > Isaac Asimov who said it's OK for a science fiction writer to violate the > known laws of physics but only if he knows he's doing it, and when Dennis > Taylor, the creator of Bob universe, does it at one point with faster than > light communication it's obvious that he knowns it. And I can't deny it makes > for a story that is more fun to read. I have now read (well listened) to all > 3 Bob books and, although parts are a little corny and parts a little too > Star Trek for my taste, on the whole I greatly enjoyed them all. They're a > lot of fun. > > The only other novel I can think of that treats the subject of uploading with > equal intelligence is "The Silicon Man". > > The Silicon Man by Charles Platt > <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/1888869143> > > John K Clark > > Consider any of the earlier novels by Greg Egan, the Australian hard science > fiction write based in Perth, WA: particularly "Permutation City" (1994). > > Bruce > > I had this idea of a science fiction story of where minds are stored in > machines in order to "eternally" punish them. The idea is that if a million > seconds in the simulated world is a second in the outer world then one can in > effect construct a near version of eternal hell-fire. The setting is a world > governed by complete terror. Then Egan came out with Permutation city, which > explores a similar set of ideas. > > The problem with the idea of putting minds into machines is that machines can > run recursive functions or algorithms, but in a number system such as Peano's > we make the inductive leap that the successor of any number can't be the same > number or zero in all (infinite number) cases. We can make an inference from > a recursively enumerable set. I would then think that the idea of putting > minds into machines, or robotic consciousness, is at this time an unknown, > maybe an unknowable, proposition. > > LC > > -- > 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 everyth...@googlegroups.com <javascript:>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/44ed303e-5650-430b-b255-bc28392194ae%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/44ed303e-5650-430b-b255-bc28392194ae%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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/1c518015-9dc2-47a8-968c-3b6c8eed1594%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/1c518015-9dc2-47a8-968c-3b6c8eed1594%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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