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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