Hi Bruno: As I see it, to hold that numbers are the precursor existence of all else is a selection. That is information. In my approach universe states with numbers as the precursor existence are surely divisions of my list [which are descriptions of objects] but so are all other sorts of states. No selection - no information. I have frequently held that your comp "("yes doctor" + "Church thesis + Arithmetical realism)" seemed to be an element permissible within mine.

Hal Ruhl At 11:27 AM 3/7/2006, you wrote: >Le 06-mars-06, à 22:33, Georges Quénot a écrit : > > > Norman Samish wrote: > >> > >> Thanks to all who replied to my question. This question has > >> bothered me for years, and I have hopes that some progress can > >> be made towards an answer. > >> > >> I've heard some interesting concepts, including: > >> (1) "Numbers must exist, therefore 'something' must exist." > >> (2) "Something exists because Nothingness cannot non-Exist." > >> > >> Perhaps the above two are equivalent. > >> > >> With respect to (1) above, why must numbers exist? > > > > I am not sure that any definitive answer can be given to this > > question. A possible argument is that the existence of numbers > > by themselves is much easier to accept than the existence of > > "usual material things" in a classical sense. Of course, even > > if it was really a weakest assumption, it is not granted. > > >What can be said about numbers is that it is impossible to explain what >numbers are to someone who does not already knows what they are. >If a TOE does not implicitly or explicitly presupposes the existetnce >of natural numbers, then the natural numbers will not be definable in >that TOE, and for this reason that TOE will not be a plausible TOE, >although Hartree Field, if I remember correctly, makes a case for a >science without number. (Of course such a science will be aristotelian >and un-platonist automatically). >That is why I put "arithmetical realism" explicitly in the definition >of comp ("yes doctor" + "Church thesis + Arithmetical realism). > >Once you accept the existence of natural numbers, and of addition, >multiplication; you get freely universal dovetailing, and thus you get >enough for comp-like kind of TOE. >For the notion of observer or lobian entities, you need the belief in >numbers, addition and multiplication; but also of some amount of >induction, that is, the axioms saying, for any formula A(x) already >definable, that : > >{A(0) and for all n [A(n) -> A(n+1)]} implies that for all n A(n). > >(In english, the induction axioms say that if some property is true for >the number 0, and remains true when going from any number n to the >successor of n, then the property will be true for all number n. Think >about an infinite range of dominoes). > >Those induction axioms are enough to explain why lobian machine will >have enough introspection ability to discover their ignorance and to >reflect about. > >So numbers are needed. Are numbers enough? Ontologically: perhaps (and >even surely with some Occam razor in case comp is accepted). >Epistemologically: No. By incompleteness a lot of apparently simple >problems needs theories far more powerful than Peano Arithmetic (say) >to find solution. The use of analytical tools (complex analysis) in >number theory is a symptom of that phenomenon. > >Just to explain the behavior of natural numbers you need the whole >mathematics. > > > > > The idea behind "numbers must exist" is that "God Himself > > cannot make that two plus two equates something different of > > four". Another way to say it is that "even if there were nothing > > (or no thing) there would remain that whenever/wherever there > > would be something in which natural numbers could be thought of, > > the Fermat conjecture should be true". If natural numbers did > > not exist, this necessity would immediately apply to them > > whenever and wherever they appear. I would say that the set of > > such necessities is not different from natural numbers themselves. > >I agree. > > > Of course, it is too strong to claim that natural numbers exist > > individually and one independently of another. The arguement is > > that "arithmetics" as a whole exists by itself (and as something). > >Yes. It would be ridiculous and actually inconsistent to believe that >the number 13 can be suppressed. > > > > > Yes. It should even forbid the existence of a "Fermat theorem > > constraint" and it is hard to imagine (at leat for me) that such > > a constraint could not exist. So it is not so puzzling (at least > > to me) that something exist. > >Mmmhhh... By accepting the numbers I would agree. Nevertheless, our >very ability to "understand" numbers is, for me, as mysterious as the >understanding of a word like "consciousness" itself. >I feel a little bit like Colin McGuin and tend to feel that numbers are >sort of a necessary mystery. > > >Bruno > > > >http://iridia.ulb.ac.be/~marchal/ > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---