Dear Bruno, I agree with your assessment of that Wiki article. In most universities the prevalent ontological doctrine is “dialectical materialism” and such has no allowance for any competition in the realm of ideas. I have pointed out that your result is similar to solipsism but never as an insult. It was just that I do not see a means to extend it to being able to consider the appearance of interactions between many minds. As far as I have studied, it seems only to be able to make statements about itself. Until you can show how it can be individuated for many minds this problem will remains, with or without a solution to the measure problem. The difficulty is that the numbers, alone, do not have any of the properties that we would associate with a mind with the notable exception of self-referential logical structure. If we might extend comp with the idea of the isomorphism with topological spaces (via the representation theorem) then we might have a notion of concrete persistence over transitions that allows for a notion of memory – since a single logical algebra is isomorphic to an entire class of stone spaces when we consider the relation of diffeomorphism. The inclusion of topological spaces allows us a coherent notion of “inside” and “outside” that can be used to distinguish multiple minds from each other, if only by having the possibility of differing positions in space. The self-awareness that you mention would, in turn, allow for the expansion of the group of symmetries that can be considered as “internal” that they can be broken and mapped (via fiber bundles) onto the set complement of the stone spaces, that yields field theories. The “glue” that binds them all together is a combination of bisimulation chaining ( a form of homomorphism) on the abstract side and various other morphisms on the concrete “physical” side, all woven together by the wonderful natural contravariance of the stone duality.

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Onward! Stephen From: Bruno Marchal Sent: Tuesday, June 07, 2011 12:31 PM To: everything-list@googlegroups.com Subject: Re: Mathematical closure of consciousness and computation On 07 Jun 2011, at 16:32, Jason Resch wrote: On Tue, Jun 7, 2011 at 5:22 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: On 07 Jun 2011, at 04:00, Jason Resch wrote: I guess you mean some sort of "spiritualism" for immaterialism, which is a consequence of comp (+ some Occam). Especially that you already defend the idea that the computations are in (arithmetical) platonia. Note that AR is part of comp. And the UD is the Universal dovetailer. (UDA is the argument that comp makes elementary arithmetic, or any sigma_1 complete theory, the theory of everything. Quanta and qualia are justified from inside, including their incommunicability. By immaterialism I mean the type espoused by George Berkeley, which is more accurately described as subjective idealism: http://en.wikipedia.org/wiki/Immaterialism I think it is accurate to call it is a form of spiritualism. Well I am not even sure. Frankly, this is wikipedia's worst article. It represents well the current Aristotelian reconsideration or non-consideration of immaterialism. Among the Platonists were the Mathematicians, the ideal platonic worlds for them was either mathematics, or what is just beyond mathematics (like neoplatonist will distinguish the intelligible (the nous) from the ONE behind (and like all self-referentially correct machine will eventually approximate by the notion of theories and the (possible) truth behind). The "enemy" of "immaterialism" try to mock it by reducing it to solipsism (which is typically "childish), or to the naive believe in angels and fairy tales. But immaterialism is not a believe in an immaterial realm, it is before all a skepticism with respect to the physical realm, or to the primacy of the physical realm. It is the idea that there is something behind our observations. The early academical debate was more to decide if mathematics or physics was the fundamental science. Aristotelian's successors take primitive materiality as a fact, where the honest scientist should accept that scientists have not yet decide that fundamental question. Today physics relates observable to measurable numbers, and avoid cautiously any notion of matter, which is an already undefined vague term. The nature of matter and of reality makes only a re-apparition in discussion through the quantum weirdness. I argue that if we assume that there is a level of description of ourselves which is Turing emulable, then, to be short and clear (albeit not diplomatical) Plato is right, and physics becomes a modality: it emerges from self-observation by relative universal numbers. The quantum weirdness becomes quasi- trivial, the existence of Hamiltonians also, the precise form and simplicity of those Hamiltonians becomes the hard question. Comp does not yet explain the notion of space, although it paves the way in sequence of precise (mathematical) questions. Unfortunately, the computationalist philosophers of mind, as reflected at least in wiki, seems to ignore everything of theoretical computer science, including the key fact that it is a branch of math, even of number theory (or combinator theory, of creative sets, Sigma_1 complete finite systems, ...). Now I see they have a simplistic (and aristotelian) view on immaterialism. Okay, this makes sense given your solipism/immaterialism. I would like to insist that comp leads to immaterialism, but that this is very different from solipsism. Both are idealism, but solipsism is "I am dreaming", where comp immaterialism is "all numbers are dreaming", and a real sharable physical reality emerges from gluing properties of those dreams/computations. You are right, I should find a less general term. It is the missing of the glue I think that differentiates the immaterialism of comp from the immaterialism of Berkeley. Don't worry too much on the terms once you get the idea. We can always decide on vocabulary issue later. You sum very well the problem. The glue is really provably missing only in solipsism. There is just no reason to believe that numbers could miss the glue, that is more than quarks and waves. At least before we solve the (measure) problem. Math is there to see what happens. People seems to have the same reluctance to let math enter the subject than the old naturalists. Now, the only way for the numbers to win the measure problem is by self-multiplication, and coherent multiplication of populations, that is sharing stories/computations. The only reason why I can dialog with you must be that we share a 'big number' of similar histories, and those have to be observable below our substitution levels. If those did not exist, keeping comp could lead to solipsism. But then QM, or the MW understanding of QM, shows that we do share indeed big sets, if not a continuum of similar histories, saving comp, empirically, of solipsism. Gödel-Church-Tarski saves mechanism from diagonalization, and QM saves comp from solipsism. Formally, incompleteness will give many possibilities for the glue to form, with the risky one based on lies (shit happens in Platonia too, that is the bad news, but it is there at the start: G* prove DBf (it is consistent to prove the false). Comp's message is not "we got the theory of everything". It is more "Oh, even if physicists unify all laws of nature, the task is NOT yet finished". Taking comp seriously, we *have to* justify those laws from the numbers self-observations. My work translate the classical mind body problem into a body problem mathematically expressed in computer science and in arithmetic. Thanks to computer science (insolubilities and incompleteness), (accepting the classical theory of knowledge), we get a gift: we are able to separate (in the self-referentially correct way) the quanta from the qualia, and to relate the two. When you said that computation are in math, or in arithmetic, are you aware that this is explicitly proved in (good) textbook in logic or computer science? This is not easy to show. It is tedious and long, and there are always subtle points. But it is akin to define a high level programming language in a low level language. Matiyasevitch has gone farer than anyone in showing that diophantine polynomials are already enough (but that is much more complex to prove). This leads to a crazy proposition, which is that all sigma_1 truth can be verified in less than 100 operations, that is addition and multiplication of numbers. It means that all stopping computations can be given in the form of a short sequence of addition and multiplication (on numbers which might be great of course(*)). Bruno (*) I can resist to show a version by Jones of that result. If you remember the RE set W_i, the set analog of partial computable functions (which are also the domain of the phi_i) Matiyasevitch' result can take the shape below. Nu and X are the two parameters, and the other letters, and the two characters "letters" are variables. Unknowns range on the non negative integers. By adding enough variable, you could arrive at a degree four unique polynomial, but here we allow high degree. Look at that B^(5^60). X is in W_Nu iff Nu = ((ZUY)^2 + U)^2 + Y ELG^2 + Al = (B - XY)Q^2 Qu = B^(5^60) La + Qu^4 = 1 + LaB^5 Th + 2Z = B^5 L = U + TTh E = Y + MTh N = Q^16 R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + + LaB^5Q^4)Q^4](N^2 -N) + [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1) P = 2W(S^2)(R^2)N^2 (P^2)K^2 - K^2 + 1 = Ta^2 4(c - KSN^2)^2 + Et = K^2 K = R + 1 + HP - H A = (WN^2 + 1)RSN^2 C = 2R + 1 Ph D = BW + CA -2C + 4AGa -5Ga D^2 = (A^2 - 1)C^2 + 1 F^2 = (A^2 - 1)(I^2)C^4 + 1 (D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1 > > If by representation you mean the representation of consciousness, then this > is the functionalist/computationalist philosophy in a nutshell. Computationalism says that representation *is* something you are. I say the opposite. Representation is something you do, which is so natural to you and so useful to you that you’ve mistaken it as the explanation for everything. You should read this http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind) Functionalism is the idea that it is what the parts do, not what they are that is important in a mind. Computatalism is a more specific form of functionalism (it assumes the functions are Turing emulable) I disagree with this. Putnam' functionalism is at the start a fuzzy form of computationalism (the wiki is rather bad on those subjects). It is fuzzy because it is not aware that IF we are machine, then we cannot know which machine we are. That is why it is a theology, you need an act of faith beyond just trusting the 'doctor'. In a sense functionalism is a specific form of computationalism because functionalist assumes by default some high level of comp. They are just fuzzy on the term "function", and seems unaware of the tremendous progress made on this by logicians and theoretical computer scientists. Note also that comp makes *1-you* different from any representation, from you first person perspective. So, the owner of the soul is the (immaterial) person, not the body. A body is already a representation of you, relatively to some universal numbers. In a sense we can sum up comp's consequence by: If 3-I is a machine, then 1-I is not. The soul is not a machine *from its point of view". He has to bet on its own G* to say 'yes' to the doctor. Of course, once we accept comp, we can retrospectively imagine that "nature" has already bet on it, given that the genome is digital relatively to chemistry, and given the evidences for evolution, and our very deep history. 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 mailto:everything-list%2bunsubscr...@googlegroups.com. 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