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
> > 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.

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