On 06 Mar 2009, at 18:06, Günther Greindl wrote:
> The idea was that the numbers encode moments which don't have > successors > (the guy who transports), that's why there exist alien-OMs encoded in > numbers which destroy all the machines (if we assume that arithmetic > is > consistent). Hmmm.... (Not to clear for me, I guess I miss something. I can build to much scenario from you say here). Of course we are in complex matter. It is good to recall that UDA is essentially a question. It is an rgument of the kind; "did you see that taking comp seriously the mind-body problem is two times more complex that in the usual Aristotelian version of it. We have not only to find a theory of mind/consciousness/psyche:soul/first-person; but we have to extract the physical laws (laws of the observable), if there exists any, from that theory of mind. But now it happens that the theory of mind already exists, if we continue to take the comp hyp seriously. Indeed, it is computer science, alias intensional and extensional number theory (or combinators ...). here there are the "bombs" (creative bomb) of Post Turing ... discover of the mathemaical concept of "universal machine", and of Gödel' Bernay Hilbert Löb's discovery of the formal probability predicate, expressible in arithmetic, and some of its key and stable properties, leter capture completely (at some level) by Solovay. Roughly speaking Universal Machine + induction axioms gives Löbian Machine, and this is the treshold she remains Lobian in all its correct extension. It is the ultimate modest machine. The discovery if the universal machine is a discovery is one of the very rare "absolute" notion. It makes "computable" an absolute notion. Now, is the universal machine really universal? That is the content, in the digital realm, of Church Thesis. Gödel discovery is that there is no corresponding notion of provability. If you are interested in just arithmetical truth, truth concerning relations between natural numbers, you cannot have a theory or a machine enumerating all the true propositions. You will have with chance a succession of theories: like Robinson Arithmetic, Peano Arithmetic, Zermelo-Fraenkel set theory, ZF+there is an inaccessible cardinal, whatever ... Each of them will prove vaster and vaster portion of arithmetical truth, but none will get the complete picture; like us, obviously today at least. > > > >> If a successor state requires something impossible, *that* successor >> state will be impossible, but it does not mean there will not be >> other >> successor states, indeed, for mind corresponding on machine's >> state, a >> continuum of successor states exists. > > This is the issue at stake: from what do you gather that all machine > states have a continuum of successor states (the aleph_0/aleph_1 is > not > at issue now; it suffices to say: at least one successor state)? > > After all, there are halting computations. By step seven. A machine halt only relatively to a universal machine which executes it. The whole problem for *us* is that we cannot not know which univerrsal machine we are, nor really which universal machine supports us. The UD generates your state S again, and again, and again an infinity of time (UD-step time) in many similar and less similar computational histories. The first person expectations have to be defined (by UDA(1-6) on *all* computational histories. If only due to those stupid histories dovetailing on the reals while generating your state S, makes the cardinal of the set of all (infinite) computational histories going through that state S a continuum. That the "UDA" informal view. In AUDA, the first person view is given by the conjunction of provability with truth. We lose kripke accessibility, but we get a richer topology, close to histories with continuous angles in between; but it is heavily technical. Each hypostases has its own mathematics. Surely more later, 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-l...@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 -~----------~----~----~----~------~----~------~--~---
