Hal Ruhl wrote: >>In what sense "4+1=" is a proof chain ? A proof must be a sequence of >>formula each of which are either axiom instance or theorems. > >IMO it is ...

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Definitions are not matter of opinion, but of conventional consensus. > ... a sequence of: >1) A formula which in this case is of the form ("data string" + ), it is a >rule of inference acting on a initializing theorem. "data string " + can hardly be considered as a formula. You should decribe the formal system you are using (if any ?). Then you tell us it is a rule of inference as if it was possible for a formula to *be* a rule of inference. I don't understand. >2) The initializing theorem is "data string". Let us ignore the fact that >the strings above are so short as to be individual alphabet elements. Not an a priori problem, but not very helpful without a presentation of your formal system. >The next step in the sequence is the axiom "1". "1" is not an axiom. It is a symbol denoting the number 1. It is neither an axiom, nor a formula. >The value of this formula is designated by "=". I see what you mean. This will not help us. >>If you interpret the theorem "4+1=5" as 5 is a number, how will you >>interpret 3+2=5 ? > >It is another proof the theorem "string "5" is a number or WFF" [ Again >ignoring that this string is so short as to be a single alphabet >element.] There can be more than one proof of a theorem. Of course you can build a FAS such that the number will be considered as theorem. But then it is a very ad hoc special fas which has nothing to do with number theory, and Juergen's remark remains valid. In another post Hal Ruhl wrote: >Ok so "computation" is more than "prove" but prove is computation is that >the idea? If you consider an axiomatisable theory, you can consider proof as a (partial) computable function defined on a set of sentences and with value in {0,1}. If the theory is decidable then the function is total. Even a theory as weak as Robinson Arithmetic can be use to compute all partial recursive function (programmable function): in that sense "proving" is more than computation. Well, you can compare proof and computation in a lot of manner, and depending of the criteria you choose, proof or computation will be more or less than computation or proof. A good book is "Introduction to Mathematical Logic" by Eliott Mendelson (third edition), Wadsworth & Brooks, California, 1987. >Here it is in one line: > > ....N - N -> S; S + N -> N; N - N -> S.... > >N is the Nothing and S is the Superverse. >All information = no information >N is no information. >N - N is the smallest possible computable perturbation brought on by a need >of N to test its own stability. >S is all information absent the N. It is as close to the N as can be. >S also needs to respond to the stability question via test because it >contains almost all information which is almost no information. Like the >UD it can not prove anything it just generates stuff. The smallest >perturbation is to add back the N which results in all information and S >becomes N. Both events destroy history. > >It is your scanner-duplicator acting at the lowest level. > >My difference is that when S is manifest it is not a UD but is like a vast >collection of individual computers running in parallel. A great "dove >tailed" structure. Each is isomorphic to a universe. > >I also introduce two additional arguments re each computer as to why >determinism does not apply. 1) Deterministic cascades hit a complexity >wall, 2) The random oracle is in S anyway - it gets used or it is a >selection - it would be information unused by an exception. These plus the >lowest level scanner-duplicator mean there is some degree of random oracle >present in each one including those that have SAS or attempt deterministic >cascades. There is an even distribution of universes since each computer >is present an infinite number of times again to avoid any absolute or >relative information in S. > >Since N and S can not prove anything it is good that they can nevertheless >compute the respective perturbations that run the scanner-duplicator >alternation. I"m willing to believe you try to say something, but I don't understand a bit. I'm sorry. >After looking at all of your recent posts re my questions I conclude that >my Superverse idea and your UDA idea are cousins. See also my just >previous post re "Some progress I think". The UDA is used to prove something, mainly that physics is ultimately a branch of machine psychology. >My argument carries a rationale for a lowest level repeating >scanner-duplicator type of behavior [i.e. stability], my Superverse is >generated immediately and repeatedly at one end of that behavior, the >Superverse acts as "data food" for all my parallel computers which are >actually comparators orchestrating isomorphic link shifts between all the >patterns in the Superverse [link shifts = evolving universes], and it takes >no selected information to construct all these computers since they are >self contained in each link but such information though small seems >necessary to construct the UD. ? Bruno