Posted to 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 <stephe...@charter.net>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<http://www.google.com/#hl=en&gs_nf=1&pq=domain%20range%20map&cp=10&gs_id=l&xhr=t&q=plural+definition&pf=p&sclient=psy-ab&oq=plural+def&gs_l=&pbx=1&bav=on.2,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<http://www.google.com/#hl=en&sclient=psy-ab&q=automorphism+definition&oq=automorphism+definition&gs_l=serp.1.0.0j0i5i30.43772.43772.2.44960.1.1.0.0.0.0.63.63.1.1.0...0.0...1c.vfE317HvrJQ&pbx=1&bav=on.2,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<http://www.google.com/#hl=en&gs_nf=1&gs_mss=automorphism%20definition&pq=automorphism%20definition&cp=10&gs_id=1d&xhr=t&q=variation+definition&pf=p&sclient=psy-ab&oq=variation+definition&gs_l=&pbx=1&bav=on.2,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<http://en.wikipedia.org/wiki/Invertible_function> > *h*) to the set of digits of abijective base-*K* numeral > system<http://en.wikipedia.org/wiki/Bijective_numeration>. > 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 > > -- > 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. > -- 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.
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