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

## Advertising

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 amùind to a body (code), but we cannot associate a body to a mind, onlyinfinitely many, and they are defined only relatively to a probablecomputation, which is an infinite object together with the infinity ofuniversal 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 usingScott 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.