On 7/27/2012 6:03 AM, Bruno Marchal wrote:



Le 25-juil.-12, à 07:01, Stephen P. King a écrit :

    On 7/24/2012 1:07 PM, Stephen P. King wrote:

        On 7/22/2012 2:41 PM, Stephen P. King wrote:

               Many (as implied by the word plural) is not just a
            number. (It is at least a Gödel number.) A plurality of 1p
            is a mapping function from some domain to some co-domain
            (or range). So if there is no distinction between the
            domain and co-domain, what kind of map is it? Maybe it is
            an automorphism, but it is not something that allows us to
            extract a plurality over which variation can occur. You
            are talking as if the variation was present but not
            allowing the means for that variation to occur! The use of
            the word "plurality" is thus meaningless as you are using
            it: "first person plural view of physical reality".
                You must show first how it is that the plurality
            obtains without the use of a space if you are going to
            make claims that there is no space and yet plurality (of
            1p) is possible. In the explanation that you give there is
            discussion of Moscow, Helsinki and Washington. These are
            locations that exists and have meaning in a wider context.
            At least there is assumed to be a set of possible
            locations and that the set is not a singleton (such as
            {0}) nor does it collapse into a singleton.

    Dear Bruno and Friends,

        I would like to add more to this portion of a previous post of
    mine (that I have revised and edited a bit).

        Let us stipulate that contra my argument above that the "many"
    of a plurality is "just a number". What kind of number does it
    have to be? It cannot be any ordinary integer because it must be
    able to map some other pair of numbers to each other, ala a  Gödel
    numbering scheme. But this presents a problem because it naturally
    partitions Gödel numbering schemes into separate languages, one
    for each Gödel numbering code that is chosen. This was pointed out
    in the Wiki article about

    "Lack of uniqueness
    A Gödel numbering is not unique, in that for any proof using Gödel
    numbers, there are infinitely many ways in which these numbers
    could be defined.
    For example, supposing there are /K/ basic symbols, an alternative
    Gödel numbering could be constructed by invertibly mapping this
    set of symbols (through, say, an invertible function /h/) to the
    set of digits of abijective base-/K/ numeral system. A formula
    consisting of a string of /n/ symbols <inconnu.png> would then be
    mapped to the number
    <inconnu.png>In other words, by placing the set of /K/ basic
    symbols in some fixed order, such that the /i/

    th

     symbol corresponds uniquely to the /i/

    th

     digit of a bijective base-/K/ numeral system, /each formula may
    serve just as the very numeral of its own Gödel number." "/
    //
      This lack of uniqueness is a huge weakness! What it does is that
    it implies that ultimately any pair of sufficiently long strings
    of numbers will be equivalent to computations that are bisimilar
    and this isomorphic under functional equivalence. I do not know
    what kind of isomorphism this is or if it is already known.


It is part of the 1person indeterminacy point. We can associate a mùind to a body (code), but we cannot associate a body to a mind, only infinitely many, and they are defined only relatively to a probable computation, which is an infinite object together with the infinity of universal numbers realizing it.

 Dear Bruno,

Can you see how this association of a body to an infinite sheaf of minds has a dual situation, the association of a mind to an infinity of bodies? There is a problem in this. An infinite set is degenerate in that is is isomorphic with any and all of its proper subsets. This degeneracy must be broken by the selection of a finite set of minds(bodies) so that we can get any form of definiteness.





        So is a N -> NxN map identical to N?


Better to compare N and N^N. They can be made isomorphic by using Scott semantics, or, as I do, by using recursion theory.


    Did not Russell Standish make some comments that where proximate
    to this idea? What axioms are we assuming for this arithmetic?


    Russell will have to answer this question himself.


--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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