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

## Advertising

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 isat least a Gödel number.) A plurality of 1p is a mapping functionfrom some domain to some co-domain (or range). So if there is nodistinction between the domain and co-domain, what kind of map isit? Maybe it is an automorphism, but it is not something that allowsus to extract a plurality over which variation can occur. You aretalking as if the variation was present but not allowing the meansfor that variation to occur! The use of the word "plurality" is thusmeaningless as you are using it: "first person plural view ofphysical reality".You must show first how it is that the plurality obtainswithout the use of a space if you are going to make claims thatthere is no space and yet plurality (of 1p) is possible. In theexplanation that you give there is discussion of Moscow, Helsinkiand Washington. These are locations that exists and have meaning ina wider context. At least there is assumed to be a set of possiblelocations and that the set is not a singleton (such as {0}) nor doesit collapse into a singleton.Dear Bruno and Friends,I would like to add more to this portion of a previous post ofmine (that I have revised and edited a bit).Let us stipulate that contra my argument above that the "many" ofa plurality is "just a number". What kind of number does it have tobe? It cannot be any ordinary integer because it must be able to mapsome other pair of numbers to each other, ala a Gödel numberingscheme. But this presents a problem because it naturally partitionsGödel numbering schemes into separate languages, one for each Gödelnumbering code that is chosen. This was pointed out in the Wikiarticle about"Lack of uniquenessA Gödel numbering is not unique, in that for any proof using Gödelnumbers, there are infinitely many ways in which these numbers couldbe defined.For example, supposing there are K basic symbols, an alternative Gödelnumbering could be constructed by invertibly mapping this set ofsymbols (through, say, an invertible function h) to the set of digitsof abijective base-K numeral system. A formula consisting of a stringof n symbols <inconnu.png> would then be mapped to the number<inconnu.png>In other words, by placing the set of K basic symbols insome fixed order, such that the ith symbol corresponds uniquely tothe ith digit of a bijective base-K numeral system, each formula mayserve just as the very numeral of its own Gödel number." "This lack of uniqueness is a huge weakness! What it does is thatit implies that ultimately any pair of sufficiently long strings ofnumbers will be equivalent to computations that are bisimilar andthis isomorphic under functional equivalence. I do not know what kindof 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 tothis idea? What axioms are we assuming for this arithmetic?

Bruno http://iridia.ulb.ac.be/~marchal/ -- 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.