[SPK] So <>p is "it is not provable that not p"? This is a double negative implying that your logic follows the law of the excluded middle. That is ok, but I was hoping that you would see that as being a logicwise subset of Intuitionistic logic, ala Topos and Heyting Algebras...
BM: I use the classical boolean logic for the third person discourse by machine. I get the Heytingian Intuitionist logic for the first person, "modelized" by the thaetetic definition of knowledge apply to classical self-reference. That is the passage from p to p & p. I get the quantum logic by refining that notion of knowledge when I translate the uda in a consistent machine language. A little more below.
BM: Any machine or theory extending classical logic and capable of > proving elementary arithmetical theorems. [SPK] Umm, what are the bounds of this "extension" of classical logic? Any possibility of getting into contectual or modal aspects, such as p iff some x implies p, where x is some context that may vanish in some limit. An example of this is found in solutions of the "grue" paradox.
BM: There are no bounds for the extension. What I prove remains true for any definissable or axiomatizable extension of classical logic + Peano arithmetic (let us say).
snipSPK: > We may note that "machines" are usually defined by some set offunctions>N -> N, where N are the Natural numbers. BM: Read my to diagonalisation post for making this precise. I would saythatcontrolable machine, constructive reals, and total computable function(wheretotal means defined on all N, can be, in our context, identified. But such a set is not *recursively* (mechanically) enumerable!!!! All "my" enterprise, and actually Church thesis, are made consistent bythefact that the set of total computable function is a necessarily fuzzy set include in the set of all computable functions.[SPK] You are avoiding my question! How is this "fuzzyness" defined? Is it some analogy to the boundary of a recursively enumerable set or is it some membership function that can range over [0,1] or some thing else?
BM: There is an analogy with the border of a Recursively Enumerable set (having a non recursively enumerable complement). That is, a RE but non recursive set. It can be arbitrary difficult to decide the belongness for the point near the "frontier". But the precise meaning is given in the diagonalisation posts.
SPK: >I am very skeptical that this >(countable) set of numbers alone is sufficient in itself to cover therange>of all possible systems in Nature (the Totality of possible existential >expressions, including all mathematics). Given this caveat, is thiswithin>your notion of a definition of these words? BM: Please read carefully the diagonalisation post. Church thesis is reallythe"schroedinger equation" of comp. I mean a highly non trivial statement inthefundamentals of mathematics. It is the roots of the incompletenessphenomenon.Before Church thesis you could have believed that "to be a machine" is a simplifying assumption. After Church thesis we know that machines, and universal machines in particular" have unbounded complexity. Universal machines are mostly lucky unpredictable being.[SPK] What is the link to the diagonalization post? It is true that I have a "problem" with the Church thesis, but it is that it seems to be myopic and limited.
BM: Mmmh... OK. I promise coming back on it. I have not the time explaining it now. Perhaps it is the real difficulty. Not only Church Thesis is not a limitation, but with comp, it is even a quasi-constructive vaccine against all form of limitation. It is Church thesis which makes general the incompleteness phenomenon and which transforms any honest machine into a modest machine.
I see no analogy between the Church thesis and SWE other than a mapping function "->" such that Church thesis is about N -> N and SWE can be considered to be about C -> C, but it is obvious that N \subset C and not the otherway around.
BM: Well, that analogy is shallow :( I was just saying that Church thesis introduces non trivial constraints on the "machine psychological states". My comparison with SWE, here, was probably unpedagogical, sorry.
snip>[SPK] > > What I am trying to argue is that we can not abondon eiter sup-physnor>comp except in the very very special case where the distinguishability >between the two vanishes, e.g. a neutal monism that obtains in theinfinite>limit of all possible existential (or ontological) expressions and, >additionally, we must not be so cavalier in our postulations. > As I have tried to argue before, the notion that the mind is UTM >emulable is not a proven fact and at this point should be considered tobe>merely a conjecture. BM: It cannot be taken as a conjecture. It is an hypothesis which has the curious feature that if you add it as an axioms it becomes false![SPK] This is what bothers me about it, it is like the Createan what is honest so long as he never speaks a word and yet you do not seem to allow for a resolution of the Liar paradox other that demanding silence, ala Russell's solution. I hope some day soon we can explore the notion of non well founded sets that Peter Wegner proposed as a means to generalize the notion of computation.
But at the level where my argument proceed Wegner's generalization of computation is not relevant. Non well founded set are very interesting,
but to use them here would simply be premature. I use the less numerous
possible mathematical concept in the proof so that the most people can go
(This is a known feature of modal logics or intensional mathematics). So "the notion that the mind is [consistently] UTM emulable" is not only not a proven fact, but it will never be a proven fact, even in the seemingly trivial sense as being provable in a theory which take it as axioms. I use modal logic because it is so easy to be wrong in intensional (modal) context.[SPK] I wish that you would be more specific on this "modal logic" other than references to books that are impossible for me to buy. :-(
BM: I think you could find them in libraries. Perhaps you could find the Smullyan's "Forever Undecided" in second hand library. If you don't succeed I can lend you my or IRIDIA's exemplary.
SPK: >The thought experiement using classical cloning and or >teleporting of minds has several assumptions that are contrary to known >physical facts, such as the imposibility of simulataneously measuring the >position and momenta of all the required atoms of a brain such that a UTM >could be defined that would emulate its behaviour. This, in itself, leadsme>to reject the entire notion of "brain cloning" and any idea that dependson>it as simple idealistic. It is as fantastic as a pink unicorn. I see notway>in which the classical teleportation is possible in the "real world". BM: I use brain cloning (and the neuro hypothesis) to make my argument simpler. Then I explicitely eliminate that hypothesis. The elimination is based on the fact that the UD will generate all your digital quantum state.[SPK] How is it a "fact" that the UD will generate all "your digital quantum state"? Since when is a quantum state reducible to a finite "digital" sequence? Did you forget about Kochen-Specker already? You wrote that you read the Calude, Svozil et al papers and yet do not seem to understand the very simple notion that they prove: there does not exist a Binary or Boolean valuation for a quamtum sustem whose Hilbert space is greater than 2 dimensional.
BM: We have had that discussion. I understand very well Kochen and Specker. This has nothing to do with the fact that a quantum computer can be simulated by a classical computer (see Deutsch 1985). And non boolean quantum logic appears in the psychological physics as it is made necessary by the Universal Dovetailer Argument (uda).
I could see that one could argue for finite approximations and propose some kind of "superselection" rules that limit the linear superposition of QM states but all of the models that I have seen that did this failed miserably.
BM: I totally agree with you. Note that's the difference between a pseudo-random generator and an iterated self-duplication experience. The first one does not generate a chaitin random numbers, the second generates almost everywhere truly chaitin random numbers, although it is everywhere impossible to prove it. In the same way the boolean simulation of the SWE generates almost everywhere quantum randomness, and justifies the non booleanity of the first person (subjective, says Everett) views.
BM:You can postulate that you are not a quantum digital machine, for example that you are some analogical quantum machine capable of handling in finite time infinite precision. But in that case you are no more in the context of the comp hypothesis. I have no problem with that.[SPK] I am trying not to postulate anything, especially " analogical quantum machine capable of handling in finite time infinite precision"! The closest that I have read about are Malament-Hogarth Machines... It seems that you misunderstand the notion of Qunatum computation in general ... :-(
BM: Surely you are postulating something! I mean my reasoning go through IF we are Turing emulable, at some level. I explicitely eliminate the "clonability" used in the first steps of the argument, at the end of the ud argument.
snip>[SPK] > > Umm, this confuses me! How can we think of UD as "generating" all of >physicality via computational simulations but yet seems to require theprior>existence of the reals (numbers), oracles, etc. This looks like a"chicken>and the egg" problem! BM: You always seem to forget that I don't postulate any form of physicality. For me term like "matter" or "universe" are like the term "phlogistic" or "God". That is very, very, very, ..., very vague term which confuses us on fundamental questions. Those term have local use but we will not progress if we reify them and take their referent for granted. It would be like to finally criticize a molecular biologist because he has not yet explain the vital principle.[SPK] I agree, you do not postulate any for of "physicality", but that is not the point that I am trying to make. Appeals to Platonia are just as "vague" as "phlogistic" and thus I fail to understand your critisism. Notions such as "position", "momentum", "spin", on the other hand, are not vague at all!
BM: 1) They are! If only by Heisenberg principle. And then by the hardness of making unanimous sense of the quantum. 2) You contradict yourself: you say "appeals to Platonia are just as vague ...", but below you say "I have no problem with the "truth" of mathematical objects being atemporal, aspatial, etc. So what?
SPK: Again, We are back to the question of "what is a machine"! Please explain what a "machine" is! I am looking for a direct definition, not a vague reference!
BM: Anything emulable by a Turing Machine. If comp is true, this includes your servitor ;-) (but NOT the "apparent universe"!!!). If you prefer: anything definissable in lambda calculus. Anything definissable in C++. Or in Lisp, or in Forth, or in Fortran, ..., or in a quantum computer, etc. Or anything definissable through \Sigma_1 arithmetical sentences, etc.
SPK: > What is COMP other than N -> N functions? COuld you explain to us how >you can generate SWE using only N -> N functions, or, equivalently, howto>embed complex valued functions in N? BM: Please, comp is PI (Personal Implication: you say "yes doctor" for his proposition of a artificial brain)[SPK] This is pure conjecture. Allow me to be agnostic on this. We need to get a "machine" (whatever that is!) to pass the Turing test and then, maybe, I will say "yes doctor"!
BM: Even after a 10000 years long Turing test I would still say NO to the doctor! "yes doctor" is a way to explain my working hypothesis, that *we* are, whatever *we* are, turing emulable. Of course "I" am agnostic on this. "Of course" because no consistent Lobian machine can have any certainty about this. I would lose consistency, would I pretend being a consistent lobian machine.
TC (Church Thesis, see what I say above on it) RA (the believe that arithmetical truth is atemporal, aspatial, .... and that it does not depend on you,me...)[SPK] I have no problem with the "truth" of mathematical objects being atemporal, aspatial, etc. What I have a problem with is the idea that mathematics is anything more than a "zero information set" unless there exists, just as must ontologically and the "truthfullness", at least the "posibility" of some form of "implementation" of each and every mathematical function. Greg Egan has expressed this idea well in several of his stories...
BM: Yes but mathematics is not a "zero information set". Unless you believe like some physician, including Einstein, that mathematics is just a set of conventions. But why should mathematicians, like Pythagore's disciples, hide their frightening discoveries (the incommensurability of the diagonal and the side of a square) or their paradoxes, if they were just convention? Mathematical truth kicks back, would say David Deutsch (in FOR). The traditional (physicalist) notion of implementation is problematical. (Cf the discussion with Jacques Mallah in this list). I prefer to use relative interpretability or some relative emulablity notion instead.
Real numbers enters the show in two different ways: as constructive real, which can be identified with total computable function from N to N, and as being generated in the limit by the UD. This include the non constructive reals. Complex, quaternion, octonions, should be explained by Z1* (and *that* isaconjecture!).[SPK] I would really like to better understand Z1and Z1*!!!
Search "Z1" and "Z1*" in the archive. Z is the logic of of a new box defined by p & <>p with  corresponding to Godel Beweisbar provability predicate, and <> = -- Z1 is the same with the interpretation of the sentence letters p to \Sigma_1 sentences. Z1*, and any "starred" logic I talk about are given by the interview of, not the machine itself, but of his guardian angel: the miraculous gift of Solovay second completeness theorem (G*). G* is a sort of truth theory for the consistent machine. See my Computation, Consciousness and the Quantum paper which sum up concisely the role of those logics. See my links to the archive for precise definition given in this list.
SPK: >The manual containing an enumeration of all of the brain states of >Einstein is impossible by the Heisenberg Uncertainty principle. BM: Only if you postulate that einstein brain is an infinite *analogical* quantum computing machine.[SPK] Not at all. I am merely being consistent with the basic mathematics of canonically conjugate operator spaces. YOu do not seem to understand this basic aspect of the Heisenberg Uncertainty principle ...
I understand it but I cannot use it giving that the goal (obliged passage by uda) is to retrieve it from machine psychology/number theory). It seems you forget what I do. I just give a reasoning showing that IF we are machine THEN physics is no more the fundamental science, in the sense that matter with its "canonically conjugate operator spaces" must be explained from some, unique but relative, measure on on all our relatively consistent and accessible (by the ud) computational histories. Then I isolate the skeleton of the possible "physical" propositions by interviewing a lobian machine about those consistent extensions. Recall: Lobian machine = self-referentially correct machine having enough introspective ability. Having enough introspective ability = proving p->p for all p being any \Sigma_1 sentence. \Sigma_1 sentence = sentence provably equivalent to sentence with the shape ExP(x), P recursive (algorithmically decidable).
> BM:But that was what I said in my last post to Colin Hales. Remember? I even have compared the first person to the vampire! It is the most striking feature of the first person: it is not a 3-machine![SPK] I missed that post. Could you link it for us?
And, what the heck is a "3-machine"????
It is a machine as seen by a third person. It is recursively equivalent
with a *description* of a machine, or its "godel number", or its plan, etc.
As opposed to a 1-machine which is the personal view of that machine (if any).
1-X always means: X as seen by a first person, and 3-X means: X as seen from
a third person. Reread the main uda post where I explain 1 and 3 person
point of view. It is the duplication experiment which explains the intuitive
gap between 1 and 3 views.
In the interview of the lobian machine, the  is third person communication.
The first person point view is defined by a new box defined by p & p .
This is non trivial thanks to the godelian gap between truth and provability.
This gives the topos, the one I call the solipsist topos in my technical reports.
The marvelous thing is that this new box cannot be defined in the lobian
machine language. Although you can interview a lobian machine *on* the
first person notions, the lobian machine cannot recognized herself in any
machine you will present to her. Even the machine herself.
That is similar to the fact that you will hardly believe you are a
"Stephen Paul King"-copy I would present to you, with the comp. hypothesis.
Precisely G* proves p is equivalent to (p & p)
But G does not prove that!!!
In some sense it means machine's "guardian angel" (G*) is able to recognize
a form of trans-identity of machines among their histories, but machines
cannot. They always feel being different of any machine's presentation.
Is the correct lobian machine computationnalist? Open problem!!
Some result by Serguei Artemov would go rather in the direction that
machine are "instinctively" not computationalist! It is quite possible
that it is infinitely hard for a machine to believe she is a machine.
Still she can correctly bet on it ....
SPK: >Just because for some >finite testing there could be no difference between a Machine's behaviorand>a "human" does NOT necessitate that they have equivalent 1-personcontent.BM: Sure. SPK: > As a matter of fact, I have no way to prove that you are not amachine>and you can not prove that this post is not just the output of a random >letter generator. All we have is likelyhoods and assumptions. ;-) BM: Sure.[SPK] Well, then how can you avoid my conclusion?! If I can prove nothing except, maybe, "cognito ..." ...
bm: You mean "cogito ..."? I avoid the conclusion because I made explicit the fact that the comp hyp is an assumption. I don't care if it is true or false. I have just suggest why it is hard to really believe in comp; would comp be true.
>SPK: I fail to see how notions such as "time", " casuality" and "1-person/>3-person distinctions are shown to be necessary by your model. My pointis>that if our 1-person experience of a world is nothing more that a stringof>symbols existing a priori in Platonia, BM: But it is not! A first person is a person with her feelings, pains, hopes, joys, headache, and many personal memories. Nothing else. Certainly not a 3-string, not a 3-bunch of 3-particles, not a 3-machine, neither a3-brain.The magic of comp, is that you can 3-study the 1-person discourse. The 1-person are much more than the arithmetical platonia, even if that much more is just platonia seen from inside.[SPK] This makes no sense to me, I am sorry. :-(
bm: I hope the explanations above helps. To sum up: "intuitive" or grandmother 1 and 3 person are explained in the begining of uda. In auda: third person = godel-lob provability. (Logics G and G*) first person= intensional variants, that is new boxes defined from and in the godel lob logic, and then their interpretation in term of weak logics (intuitionist, quantum, etc.) The difference between G and G* (search G* or guardian angels in the archive) provides room for an explanation of the gap between communicable quanta and uncommunicable qualia. G* extends G. G* \ G = logic of uncommunicable true propositions. Machine's psychology = G and G* First person = logic of p & p = S4Grz First person plural = logic of <>p & p = Z or p & <>p & p = X For uda in machine language: you restrict the arithmetical interpretation of p with the sigma_1 sentences (that gives the arithmetical representation of the ud). This gives the Z1* and X1* logics.
SPK: >why do we have enless debates about >the notion of a "flow of consciousness"? It can not be "explained" awayas>just an illusion or "intensional stance". Immaterial strings might be >capable of encoding each other as subsets but unless we have some meansto>explain how Nature solves mathematical problems that are both intractibleby>finite TMs and require that we include the means of explaining concurrent >computations, e.g. we have to explain, at least, the appearence of >interactions between a plurality of systems not just a singlecomputational>system. BM: That's exactly what I begin to do in my thesis.[SPK] I look forward to reading more of it!
BM: Be patient. I am near the half of it! Talking in this list motivates me. Thanks. Still I think you could get more info from browsing the archive from my url.
[SPK] I think that Finkelstein is too finitistic, but that's ok. ;-)
BM: Yes. A little too finitistic for an everything list! But who knows? ;-) Bruno -- http://iridia.ulb.ac.be/~marchal/