On 19 Jul 2009, at 04:43, Rex Allen wrote:
> > On Sat, Jul 18, 2009 at 11:55 AM, Bruno Marchal<marc...@ulb.ac.be> > wrote: >> >> I am OK with all this. It has to be like this if we take the comp hyp > > So what are your thoughts on my question as to whether abstract > concepts other than numbers also exist in a platonic sense? For > example, the idea of "red"? Numbers are not enough. Even assuming first order logic. Then assuming "we" are digitalizable machine, this can be proved: Numbers are not enough. Numbers together with addition and multiplication are enough, and it is "absolutely" undecidable (for us, and us = any universal machine/ number) if there is any richer ontology. Numbers and addition + multiplication is a structure already "Turing universal". With addition and multiplication (and logic) you can already define the computational states and the pieces of histories going through them. You can understand that if you assume comp, all the computations going through the state of self-introspecting agent imagining "red" already exists as much as numbers. All the proposition of the shape "the machine i goes through states S" are, when true, elementary theorem of arithmetic, and they are accompagnying by "dense sets of proofs or relative realisations"). In the arithmetical Platonia, you already have all universal machines, and all their computations, which makes already place for big amount of "abstract concept" existing "platonically" (= like the numbers). And then you can define the modalities or point of view of those machines, by realizing that they will be aware (they have access too) the gap between platonist truth and what they can prove, and ... You may read the paper on Plotinus here, i.e. click on "pdf" on the right of "A purely arithmetical, yet empirically falsifiable, intepretation of Plotinus" on my url http://iridia.ulb.ac.be/~marchal/ You can see, well, not my thought on the subject, but the thought of the universal platonist machine. A machine is platonist when she believes, proves, asserts, the instanciations of the principle of excluded middle principle. > > > So obviously we can cast everything as numbers and say, "In this > program, 0xff000000 represents red". But RED is what we're really > talking about here, and 0xff000000 is just a place holder...a symbol > for what actually exists. Probably so. > > > In your view, Bruno (or David, or anyone else who has an opinion), > what kinds of things actually "exist"? What does it mean to say that > something "exists"? Assuming comp, something S exists ontologically when you can prove that S exists in Robinson Arithmetic (a very weak, yet universal, theory), And something S exists epistemologically when, let us say, you can prove in Robinson Arithmetic that there is a universal machine mentioning S. Technically it is far more elegant and sophisticate. See the eight hypostases (points of view) in the plotinus paper (or look for Plotinus or hypostases in the archive of the list). Instead of Robinson Arithmetic, you can take any first order specification of any universal system, machine or lnaguage (be it Conway's Game of Life, FORTRAN, LISP, prolog, Basic, c++, ... up to modular functor from quantum topology or knot theory, or number theory itself. > > > It seems to me that maybe consciousness is actually very simple. It > is just a group of platonic ideals, like red, that are related to each > other by a point of view: "I like red", or "I see a red sphere." Yes. > > > Maybe what is complicated is constructing or identifying a causal > structure (e.g., a machine, a brain, a program, etc) whose evolving > state can be interpreted as representing a series of "connected" or > "related" instances of consciousness. Yes. The difficulty is that consciousness, from its internal view, can only be related to an infinity of states belonging to high infinities of infinite computations. Third person consciousness, like the consciousness of my friend, is locally attachable (by guess) to a brain. "My consciousness" is not "attachable to a brain, only to an enumerable infinity of brains/machines/numbers weighted by non enumerable infinite histories. > But the machine (physical or > otherwise) is NOT that consciousness, the machine just represents that > consciousness. Indeed. The machine can represent 3-consciousness, like my identity cart can represent myself. 1-consciousness is related to a continuum of machines. This follows form the UDA. 1-consciousness is ignorant which "places" it occupies among continuum of histories. > > > In this view, consciousness itself consists directly of the abstract > platonic ideals that form the contents of a given moment of > consciousness. Not directly. It needs a self-reference, that is no more than two diagonalisations. Computer science suggests, and arguably forces entities to relate to themselves relatively to most probable local universal history. This needs already virtual substitutions. Purely arithmetical one do the job very well. > > > >> It remains to explain the relative stability of that illusion. How >> and >> why some dreams glue, in a way sufficiently precise for making >> predictions about them. > > Maybe unstable illusions exist, but, being unstable, don't ponder such > questions? > > Obviously we have such conscious beings here in this world, with > schizophrenics and the like. > > So your questions about "why are my perceptions so orderly", would NOT > be universally valid questions, because there are conscious entities > whose perceptions are NOT orderly. Nice try! See UDA for making this precise in term of relative probabilities. And we have to recover the "observable probabilities". We can come back on this, but I cannot explain all this is any shorter way than what is in the papers. (Your intuition is correct, and I am perhaps playing with the flexibility of "NOT orderly". > > > And I would say that even my perceptions are not consistently orderly, > as when I dream I often experience strange scenarios. > > To say that dreaming and hallucinating are special cases I think is to > make an unfounded assumption. It would seem to me that orderly > perceptions are the special case, and dream-logic realities would be > the norm. At first sight! This is akin to the white rabbit problem. So we have to justify the "norm" from the structure of Platonia. > > > If consciousness is in some way a result of computation, then a > program that generates all possible mind-simulations will surely > result in the vast majority of resulting minds experiencing > dream-logic realities, not "law-and-order" realities like ours. You are close to the UDA, which we discuss since years here ... All the problem is there. But once you look closely, you can see the beginning of the reason why "law-and-order" realities win against "dream-logic" realities. This is eventually coming from the fact that numbers TOGETHER with addition and multiplication give already a very rich, complex (even non axiomatizable) reality, with a strong tendency to repeat itself in an universal dovetailing way. Look at the youtube videos on the Mandelbrot set (M) to see a "platonic simple sequence of arithmetical objects illustrating a similar (perhaps equivalent) multiplication of itself and variants. It is a simple object because the definition of M is not much longer than the definition of the circle. The sequences are simple too, because their are just successive enlargements (zooms) in different places) Examples: http://www.youtube.com/watch?v=eCUFiFuUj00&feature=channel_page http://www.youtube.com/watch?v=BUhFLpC2EfU http://www.youtube.com/watch?v=YSQCpBN8QuA&feature=channel_page > > > I think Sean Carroll (who I'm reasonably sure would disagree with > everything I've proposed above, but still) had a pretty good point on > such "counter-intuitive" predictions: > > "The same logic applies, for example, to the highly contentious case > of the multiverse. The multiverse isn’t, by itself, a theory; it’s a > prediction of a certain class of theories. If the idea were simply > “Hey, we don’t know what happens outside our observable universe, so > maybe all sorts of crazy things happen,” it would be laughably > uninteresting. By scientific standards, it would fall woefully short. > But the point is that various theoretical attempts to explain > phenomena that we directly observe right in front of us — like > gravity, and quantum field theory — lead us to predict that our > universe should be one of many, and subsequently suggest that we take > that situation seriously when we talk about the “naturalness” of > various features of our local environment. The point, at the moment, > is not whether there really is or is not a multiverse; it’s that the > way we think about it and reach conclusions about its plausibility is > through exactly the same kind of scientific reasoning we’ve been using > for a long time now. Science doesn’t pass judgment on phenomena; it > passes judgment on theories." Well, yeah, OK. It is already true for the theory saying: there is 0 physical universes, 1, 2, ..., infinity, bigger infinities ... of physical universes. Comp seems to go in the direction 0 physical universes, 1 local (apparent) multiverses. It is too early to really say. Scientist don't commit themselves ontologically, and many theories does the same, yet most assume numbers, or any universal frame. > > > So, I could continue further and go into a lengthy defense of why I > think this supports what I'm saying, BUT maybe you'll come to the same > conclusion I have and I can save myself a lot of typing! So, I'll > just try that approach first. I basically agree with all what you say, and I hope you will take as good news that the classical (platonist) universal machine agrees too, and even can justify all this, and makes those things sufficiently precise so that we can test it. And retrospectively, the quantum facts, as understood by Everett & Al. in Physics, saves the Classical Machine discourses from a too easy refutation (given that comp predicts huge self-multiplication indirectly observable when we look at ourself below our common substitution level). I will be a bit slowed down this week, due to work, but I intend to be able to explain what is a universal function, what are universal numbers, and what are computations, and how they exist in the tiniest part of math where actually classical (platonist) mathematicans and intuitionist (non classical) mathematicians understand themselves very well. I did not comment your other post because I rarely comment post where I tend to agree completely. 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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