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I admire you, Stephen, for writing with such ease about Gödel etc. - in my
agnosticism I would say:
"many' MAY refer to a wider cumulative complexity of similar coomplexities
(like the machine Bruno would call "us") and I never tried to identify
myself (us? humans?) for Bruno's view).
Since I do not stand on the restricted arithmetic base-line, I feel
comfortable NOT to count the 'many'.
*To: 'plurality':* I do not take a "mapping" fundamental. I feel that would
be restrictive into a sectional view.

*Physical reality *is similar. Since I cannot exceed my own domain(s) I
have no way to identify "reality". Bruno's restriction helps.
 John M

On Wed, Jul 25, 2012 at 1:01 AM, Stephen P. King <>wrote:

>  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<,or.r_gc.r_pw.r_qf.,cf.osb&fp=d0885a1bd80304c5&biw=1680&bih=894>)
> *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<,or.r_gc.r_pw.r_qf.,cf.osb&fp=d0885a1bd80304c5&biw=1680&bih=894>,
> but it is not something that allows us to extract a plurality over which
> variation can occur. You are talking as if the 
> variation<,or.r_gc.r_pw.r_qf.,cf.osb&fp=d0885a1bd80304c5&biw=1680&bih=894>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 [image: s_1 s_2 s_3 \dots
> s_n] would then be mapped to the number
>  [image: h(s_1) \times K^{(n-1)} + h(s_2) \times K^{(n-2)} + \cdots +
> h(s_{n-1}) \times K^1 + h(s_n) \times K^0 .]
> 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.
>     So is a N -> NxN map identical to N? Did not Russell Standish make
> some comments that where proximate to this idea? What axioms are we
> assuming for this arithmetic?
> --
> Onward!
> Stephen
> "Nature, to be commanded, must be obeyed."
> ~ Francis Bacon
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