Dear Günther,

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Le 06-mai-08, à 21:19, Günther Greindl a écrit : > - CRH implies COMP > - COMP implies the negation of CRH > >> Universality, Sigma_1 completeness, m-completness, creativity >> (in Post sense), all those equivalent notion makes sense only through >> complementary notion which are strictly sepaking more complex (non RE, > productive, ...). >> The self-introspecting universal machine can hardly miss the inference > of such "realities", >> and once she distinguishes the 1, 1-plural, 3-person points of view, > she has to bet on >> the role of the non computable realities (even too much getting not > just randomness, >> like QM, but an hard to compute set of anomalous stories >> (white rabbits, coherent but inconsistent dreams). > > Why does the machine have to bet on these complementary non-RE > histories? I do not quite see how this arises from 1 and 1-plural POV; > after all, it could be just rec. enumerable continuations? Hmmm.... The UDA should just show that, and I am not sure which points you are missing. Suppose there is a physical concrete universe and that a UD is running in it without ever stopping (like in step seven of http://iridia.ulb.ac.be/~marchal/publications/SANE2004Slide.pdf). Now, if you agree with the preceding steps, it should be clear that your personal immediate future first person experience is determined by the set of all computations going through your actual state. I agree it is reasonable to consider such computations as equivalent with recursively enumerable sets, but this does not mean that the set of such continuations/computations is recursively enumerable. Actually, such set is not even enumerable, because the UD, stupidly enough, dovetails on some product of each computation with the real (oracle), even the non computable reals. And, given that from a first person point of view we cannot be aware of the infinitely many delays, we have to take into account, to eliminate white rabbits (or to refute comp) all the possible computations at once, including those dovetailing on the reals or on any non enumerable structure. I have discussed this with Schmidhuber on the list some time ago. The non enumerability of the reals cannot prevent the UD to dovetail on all the reals. From a third person point of view, everything is and remains enumerable, but from the first person point of view, the subjective indeterminacy has as domain something vastly bigger. > > Schmidhuber's/Tegmarks Computable Universe Hypothesis seems very > attractive: it gives rise to structure, _evolves_ self-aware > sub-structures, and gives reasonable (?) measure, for instance > Schmidhuber's speed prior. > > This also takes care of the white rabbit. Any constructive version of Feynman Integral will take care of the third person white rabbits, but not of the first person white rabbits. When we dream, although we loose soundness (depart from truth) we remain consistent. The problem with comp is that there are a priori to many dreams, too many consistent extensions ... unless *physical reality* emerges from some gluing of *all* the dreams. I am just arguing that for comp to be true, you have to extract a theory of matter/body from first person coherence notions, eventually reducible to notions from computer science/mathematical logic. > >> It's a bit like "understanding" (putting in a RE set) the (code of) >> the total computable >> functions, forces us to accept the existence of only partially > computable functions, >> which sometimes (most of the time, see the thesis by Terwijn) have a > non recursive domain. > >> OK, the ontic part of a comp TOE can be no *more* than Sigma_1 >> complete, >> but a non self-computable part of Arithmetical truth and analytical > truth, >> is needed to get the *internal* measure, we can't even give a name >> to our first person plenitude and things like that. > > I think this answers part of my question above. The ontic part is only > the Sigma_1 complete stuff; we assume the others for our measure ... We don't assume the others, we are just confronted to them, like we are confronted to the non stopping programs when we try to capture all stopping programs (successfully, with Church thesis). The very notion of Sigma_1 completeness forces us to accept machine Pi_1 incompleteness (and then machine Sigma_2 incompleteness, etc...). And then the UDA shows that our 1-indeterminacy domain (hopefully plural) is determined by all that non computable stuff. In the Whashington-Moscow self-duplication experiment, everything is computable from a third person view, yet you cannot give an algorithm predicting with certainty what precise experience you will feel to have in your immediate future when you undergo it. Why do you expect a computable reality when confronted with the whole deployment of the UD, where you are reconstituted infinitely often in all consistent extensions? > ... but > my claim is that they do not give rise to first person experience. By assumption (comp), first person experiences rise from some amount of computations. But then the UD shows that you cannot know in any way which computations generate your mind, and that your 1-expectations is determined by all such computations. Now, empirically our expectations are given by "physical laws". But if that is true, and if comp is true too, those two ways to infer realities have to fit, so we have to derive the physical laws from a sort of sum/mean/average-calculation on *all* computations (even those with non computable oracle). What I try to explain is that to solve the mind body problem, with comp you have to justify the apparent computability of the observable reality. You have to reduce somehow the body (physics) to the mind (which, assuming comp is more easy: it is mainly computer science/mathematical logic). > > I think the central question is this: _what_ does the Arithemetic Truth > of whatever simulate? Reality at a granular level (like in the CA > approach, Zuse's Rechnender Raum) - that is what I would assume - that > reality at the lowest level is a number-relation; but that awareness > only arises in these domains as a higher oder abstraction. I can agree with this. The devil is in the details. Well, things get more complex when you realize that the ontic has to be universal, and that the physical (first person plural) has to emerge from all computations. Each computation is computable (of course), but the problem is in the *all*. Even between two discrete steps of any computation going through your actual experience, there will be infinitely many computations going through those steps. > > I think you assume that the Sigma_1 sentences give the OMs directly, > .... Yes, in the sense that the UD generates succesively all 3-OMs. No, in the sense that, by being unaware of any delays raised by the UD, our 1-OM are never generated. We can only experience them, personnally, and they depends on the whole structure bearing on *all* 1- OMs. > is > that correct? So in your view there is no underlying reality; QM and > stuff like that is only an "illusion". Am I correct in how I interpret > your theory? Well yes ok, with the proviso repeated just above. And then a vocabulary remark. In general "illusion" is a bit a pejorative. I would prefer to say that QM and stuff like that are "emerging" . Given that dreams and illusions are related to complex (uncomputable) sets of computations, they obey rational principles, and, from a deep and important perspective, they kick back and are not all illusionary. But you are right, physics emerge from dream multiplication in the universal deployment. > >> Perhaps this is why the Intelligible has been discovered (Plato) >> before the "ONE" >> (Plotin). It is far bigger. With comp you can restrict the ontic to > the Universal Machine >> (the baby ONE), > > Ok, I'm with you this far. > >> but its intelligible realm is well beyond its grasp. > > For me, the intelligible can be only a (proper?) subset of the ontic. Ok, this is a bit subtle. I have been wrong myself often on things like that. I mention one example: the set of total computable functions is a proper part of the set of all (strictly partial and strictly total) computable functions. But the set of total computable functions (TOT) is far more complex than the set of partial computable functions (PFC). PFC is Sigma_0, TOT is Pi_2. A simpler example: nothing is more simple than a dense rectangle. The Mandelbrot set if far more complex. yet, the Mandelbrot set is a proper part of that rectangle. A subset can be more complex that a superset. Another example; Everett universal wave is very simple (not only computable but linear!), yet it generates branches with observers confronted to the ten thousand non linear and even non computable (1)-stories. Yet another example: there is no program capable of generating Chaïtin Omega number, and generating *only* Chaïtin Omega number; yet, the UD, or even simpler programs, generates it easily ... *among* all the binary sequences. > How could something that does not exist (ontic) be intelligible? James Watson, a reductionist, says that only atoms exist. For him molecules are already a construct of the mind. Yet molecules are certainly intelligible for him (given that he has discovered the double helix DNA). Does a Bridge Play exist? Does a nation exist? I prefer to say, contra Watson, that molecules, Bridge Plays, and Nations, and People exist. The doubt is about the bottom, and I need no more than numbers with addition and multiplication to explain how stable and lawful illusions *exist* in the emerging and epistemic sense. But then this move predicts that if I look at the bottom, and if I want to say precise things about it (with all "decimals" correct), then I have to take into account almost everything, both ontic and epistemic (to be short). > Or > would you say that this is mathematical imagination? If you agree that imagination exist, or at least follows laws. > >> All this is related to the fact, already understood by Judson Webb, >> that comp is truly a vaccine against reductionist theories of the >> mind. > > I have the Webb book on my desk and have glanced occasionally inside, > it > looks like a wonderful book, but I have not yet had the time to study > it in detail. > > But I wonder - why do you say that comp is not reductionist? In Philosophy of mind the term "reductionist" is often used for the reduction of mind to matter. Comp forbids this (assuming com, assuming I am correct, etc.). Of course you are left over with a reduction of matter (physics) to mind (computer science/mathematical logic). Comp is also non reductionist in insisting that "saying yes to the doctor" has to be an act of faith, which eventually has to be a purely personal decision. If you bet on comp, and if you "understand" comp, you know you cannot be proselyte about it. It *is* a personal "religion", despite its pure scientific consequences which can only be used to refute it, never to make it a definitive statement. (I know we will be in trouble when we will practice comp because some of us will take their own survival as some kind of proof of comp, but personal survival is (scientifically) never communcable. > For me comp > is reductionist - mind as the working of computation (I am pro > reductionist, that is not a negative word in my view). No problem as far as you see that computation has to be used in a mathematical sense, contra Landauer and Deutsch who believes that computation has to be reduced to the natural science. > > So, two questions: > > 1) At what level do your Sigma_1 sentence operate? OM's directly (I > would interpret your paper in this way) or low level (more like a > classical physical/digital physics view)? This is a bit ambiguous. The true (and thus provable by universal theorem prover machine (universal for computability, not provability, but Sigma_1-provability universal) Sigma_1 sentences can correspond to the 3-OMs, or to the "mental state" generated by the UD. But their relative uncertainty first person measure (cf RSSA) are given by the density (for some topology I try to derive with the lobian interview) of their proofs-computation (those things are isomorphic because we restrict ourselves to the Sigma_1 sentences). > > 2) You say that the ontic part is computable (in this sense, I would > say > COMP does _not_ refute CRH?) Because what "is" that is not ontic? > That > would be contradiction in terms? Well, this is related to the (rather hot) debate on "emergence". I have a Pythagorean-Kroneckerian slogan. All what exist "ontically" are the natural numbers, together with their additive and multiplicative structures. All the rest, including physics, exists as well, but not ontically. It emerges epistemically from the way the intrinsical ignorance of numbers about numbers (and sequences of numbers, etc.) structure itself. Now, that "intrinsical ignorance" is (with comp) what Godel has discovered, and others (Lob, Solovay, + Post, Church, Turing ...) have seen its structure; rather well captured by the modal logic G and G*, and especially G* \minus G. That led to the Lobian interview ... Please ask any questions. Be sure you have completely grasp the first person comp indeterminacy before anything else (but the 1-3 distinction of course). I do not pretend that all this is easy stuff, nor that I am always clear about it. The problem is that what is simple for some is difficult for others and vice versa. Best, Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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