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 ith symbol corresponds uniquely to
the ith 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.
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?
Bruno
http://iridia.ulb.ac.be/~marchal/
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