Hi Stephen, > > > Ok, Robinson Arithmatic is " ... or Q, is a finitely axiomatized > fragment of Peano arithmetic (PA). ...Q is essentially PA without > the axiom schema of induction. Even though Q is much weaker than PA, > it is still incomplete in the sense of Gödel." > http://en.wikipedia.org/wiki/Robinson_arithmetic_Q > > It does not tell me where the assumption of implementation of > the addition and multiplication obtain.
I don't use the assumption of implementation of the addition and multiplication. I use only the fact that some relations among numbers are true or false. You could as well ask a physical realist in what he implements the physical laws ... > Just because one can define X does not mean that one has produced X; > unless we are assuming that the act of defining a representational > system is co-creative of its objects. I think you are confusing numbers and their representations. Arithmetical truth is independent of the representation used for numbers. > Are we to consider that an object, physical or platonic, is one and > the same as its representations? Of course not. And that is why I don't need, at the ontological level, any representation. Of course I need some to talk with you, but that's different. > > Oh, I forgot, it has been proposed that a book containing a > symbolic representation of Einstein's Brain is equal/equivalent to > Einstein's Mind. OK! ... Moving on. Where? In the book Mind's I, Hofstadter just argues that if comp is true then you can converse with Einstein through the manipulation of a book describing (at the right level) the brain of Einstein at some moment. To proceed we have to be careful in all those little nuances. The devil is in the details. > [BM] > You can entirely define in arithmetic statements of the kind "The > machine x on input y has not yet stop after z steps". The notion of > "time" used here through the notion of computational steps can be > deined entirely from the notion of natural numbers successor (which > can be taken as primitive or defined through addition and > multiplication). > > [SPK] > > Ok, time (pun intended!) for a thought experiment. I go the > Library of Babel and pull out the "Einstein's Brain" and bring it > home with me. > > I sit down and ask it: "what are your latest thoughts on the > nature of Unified Fields?". How long am I going to wait before I > realize that I will never get an answer? > > You might say:"Stephen, you are going about it all wrong! You > have to first create a well-formed question in the language of > "Eintein's Brain" and then look up the appropriate responce inthe > book." > > I answer, "Ah, So "Einstein's Brain" can answer my question > after all; it can only sit there on the table until I opening and > use my own computational implementation to get my answer." Of course, if you want that Einstein answers relatively to you, you have to implement it relatively to you. Either with a Mac, or a PC, or an IBM, or with your hands, whatever. Come on Stephen ... > > So where is "Einstein's Mind"? Nowhere... The 3-OMs of Einstein are distributed in the whole of Arithmetic (assuming comp this is quasi trivial to show, yet tedious. The 1-OMs of Einstein appears from inside arithmetic (only Einstein knows them) and their relative statistics are defined by a relative measure (which has to exist or comp is false) pertaining on the 2^aleph_zero computations going through its states. Ask any precise question on this if you have any difficulties. > > > What is it that distinguishes a random sequence of scratches on > a plane of sand from the sequence of symbols of the equation > representing the Grand Unified Theory of Everything? Well, one > person might say: " I can read the one that is an equation..." > Meaningfullness necessitates a subject to whom meaning obtains. Sure. > Computational states, symbolic scratches or patterns of concurrent > neuron firings or distributions of voltage potentials, mean > something because their existance is such that situations would be > different otherwise for some system other than that of the states, > scratches, patterns, etc.. Sure. > Remember the notion of Causation? There are plenty notion of causation derivable from inside arithmetic when you assume comp. Most would collapse to classical logic if the incompleteness did not exist. But machines are incomplete and reflect that incompleteness. This entails not only causation, but also responsibility and I would even argue it implies a form of strong, but partial, (free)-will. > > X is the Cause of Y if and only if X would not occur without the > occurence of Y. David Deutsch defines it more pointedly: "...an > event X causes an event Y in our universe if both X and Y occur in > our universe, but in most variants of our universe in which X does > not happen, Y does not happen either." The trouble is that unless > there exists a unique measure on the "space" where in events are > coded in the Universe of possible statements or sentences of > Robinson Arithmatic, it is undecidable if X happens or Y happens > because one can not distinguish between actual computational steps > that would generate a means to distinguish X from Y or strings that > code some other computational string. Could you explain? This is not clear too me. > Remember how Goedel numbering works... Only if the number of > possible statements that can be coded with the same string are > computationally isomorphic (generate the same output per input) can > one obtain a means to distinguish X from Y, but if we require this > it will be no longer possible to code any variants of our universe. > Variants would not be allowed. Without the possibility of variants, > how does one obtain a notion of contrafactuality? I'm afraid you will have to revise your comp basic, if you allow me to be frank. Up to now, the real (mathematical) problem with comp is that it allows too much variants, including many consistent but unsound variants like the white rabbits. And we have the counterfactuals, where any particular physical activity miss them ... In comp fact and counterfacts are relative notions, and all exist, in the usual sense that prime number exist. And then we can explain how very different and layered notions of existence emerge from that. Don't confuse platonia before Gödel and after Gödel: we know now that in Platonia everything move and shit happens. But we (the old Löbian machine) do have partial control on our probable realities. We partially define them in a sense. > > To claim that the ordering of natural numbers from the notion of > succession allow for us to obtain a coherent notion of the ordering > of events time is fine, but only if there is one and only one > possible successor per any given number. This is used to measure only the "time" of the UD works, not possible internal times of its "subcomputations", and still less subjective times of entities, etc. Any decidable predicate pertaining on the proof of sentence of the shape "ExP(x)" with P decidable would have work for the UD-time. In complexity theory this is called a Blum Measure. It has nothing to do neither with physical times nor with subjective duration, which emerge statistically and from an inside epistemological machine point of view. Like in Borgess the UD generates a labyrinthine web of times. Symmetries and relatively broken symmetries, in many (too much a priori yet) directions. > The notion of Causation, inherent in the notion of "time" requires > there to be more than one possible successor or else there would be > no notion of "variants", ala Deutsch's statement above or any > contrafactuals. In a Mathematical Set, one can is not free to have > uniqueness or excluded middle rules apply only when convinient for > the theorists. Axioms and Rules are Universal or Nothing. > The identification of Time as a "dimension", usually represented > as the Real number line does not allow for anything like the > variants that we obtain in QM theory. You are a bit unfair here. All your critics bears on QM as on COMP (which if my work is correct are really equivalent). The UD already execute all evolution of all Heisenberg matrices or Schroedinger Wave. It even dovetails on its real and complex approximations. My point is that this is not enough to solve the body problem, we have to explain why such matrices, and exactly which one, wins the histories measure competition. > As a matter of fact, events prior to the specification of 1) a > basis and 2) a specific experimental condition exists as quantities > that have a complex number value. We cannot invoke QM, before we have justify it. You are changing the topic. The point is that with classical comp we have to justify the quantum, even as a first person plural sharable qualia ... We have to explain why the time is illusion, and why the illusion of time is NOT an illusion. > Complex numbers DO NOT have a natural ordering. Thus the notion of > Time as a Real number Lines is Not an a priori defined notion, it is > strictly a posteriori and thus not available as a means to assing > successional overing to events. I can agree, but I don't see the relevance here. > > > > [BM] > If you prefer, I could tell you that in arithmetic we have a very > notion of time: the natural number sequence. Then we can define in > arithmetic the notion of computation, and the notion of next step > for a computation made by such or such machine. And from that, we > can explain how the subjective appearance of physical times and > spaces occur. > [SPK > > That would make sense only if we could show how numeric > succession, which is a form of "x is less than y, thus y succeds x", > is equivalent in all situations for sequential stepping in a > computational string. If we have to allow for some form of process > for our notion to be coherent then we have not eliminated some > primitive form of change from our theory; we have merely pushed it > into a corner and hope that no one notices. Again, we can not derive > any form of change from a system that does not allow for its > existence. Computer science can provide an infinity of counter-examples here. Of course, from the point of view of the ontology, there is no change, but from the point of view of the observer we can justify the dynamics. many physicist agree on this. Not Prigogine, nor those who want to make time primitive, but then my argument is that they should say no to the doctor. That's all. I am not saying they are wrong. > I would like to better understand tyhe notion of a > Theaetetical Knower. Could you link to a discussion of it? The best discussion is the original Theaetetus by Plato. Myles Burnyeat wrote a nice book "The Theaetetus of Plato". It is the idea of defining knowledge by true belief, or by true and justified belief, and variations of this type. > I do not wish for any one to abandon Comp, I wish only to show > that it is a key fragment in a larger system. Then you should point on what exactly you don't follow in UDA, because the whole point of UDA is that comp (yes doctor + Church thesis) does not allow for more than comp. The mind body problem in the cognitive/ physical science is reduced to the body problem in number theory/ combinator/computer science. > We can easily show how "static" systems emerge from dynamics ones. > The converse is difficult at best. No, it is simple. really. What *is* difficult is to derive the appearance of particles ... without too much white rabbits. The appearance of first person time *is* already explained (in a sense), like the appearance of many worlds, and many times indeed. > When we assume that "Becoming" is fundamental, If you assume this, either UDA is incorrect or you are yourself an actual infinite. You should say no to the doctor. You cannot keep comp, and make time or becoming fundamental at the ontological level. You can make it fundamental at the epistemological level. I could agree that Becoming is fundamental from the inside points of view. UDA does not conclude by "matter does not exist": it concludes that "substantial matter" has to be replaced by "a measure on computational histories". The comp hypothesis is made testable, or better the degree of falsity of comp can be measured in the dialog with nature. Up to now, nature fits well with the comp "internal universal machine facts". I can understand the shock you can have when grasping how the usual ontology is transformed with comp. What is admittedly "diabolical" with comp is that comp predicts that universal machine cannot believe that they are machine, but they can bet and reason to learn the consequence of comp. But with reasonable definition the machine cannot believe it and still less know it. She can reason with and from it. She can bet it, like with those who try artificial hypo-campus on rats ... > "Being" is show to be identical to the automorphisms. A change in a > system that leaves it invariant is identical to a non-change, but to > neglect the fact that a change is possible is to nullify the entire > notion of meaningfulness. Many change are possible ... from inside. It is the same with any block interpretation of physics. You are almost arguing that if the laws does not change themselves, then no change will ever occur. I am not proposing a theory, Stephen, I show an argument showing that if we say yes to the doctor, then we have to change the current paradigm, because it does not work or it eliminates person, consciousness and meaningfulness. The difference between the betting-on-comp approach and the physicist one, is that it starts from the person. It disallows person and consciousness elimination. It works very well apparently, it can save the appearance of space and time ... and it save consciousness and meaningfullness, even sort of "gods" in the process. OK, the ontology seems so little and unattractive at first sight, but the point if that comp leads to this or similar. Comp defines a realm, and is not a theories per se. The arithmetical hypostases are derived theories from the comp hyp. After Gödel we have good reason (comp) to know that we will never have a complete theory about either numbers, and machines. What I have done, or try to do, is to show that the comp hyp transforms the mind body problem into the body problem. The mind part is the easiest part, because it is, assuming comp, "just" computer science (and computer's computer sciences), or number theory thanks to Godel-Matiyasevitch translations/embedding. The body part is difficult and counterintuitive, but it is mainly reduce to a problem of relative measure on computationnal histories, as seen from internal point of views (which, in AUDA, are translated in term of intensional variant of the self-reference logics). If you keep comp in the cognitive science, you have to accept the consequences it has everywhere (physics, theology, whatever). I follow Deutsch dicto: it is only by taking our theory seriously that we can find them false, and correct them or abandon them. If you have a problem with UDA, don't hesitate to let me know where and why. UDA1-6 is judged easy. UDA-7 is falsely easy (you need a few amount of computer science to not been abuse by the apparent easyness). UDA-8 is notoriously difficult. And AUDA is easy ... relatively to mathematical logic, and even a bit of quantum mechanics to have a sort of concrete illustration of the comp weirdness (alas QM is still even more weirder than it has been possible to prove for comp ...). I hope this helps, but to play serious, you really should investigate each step of UDA. In all case; me or you (or both) will learn in that process. 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 email@example.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 -~----------~----~----~----~------~----~------~--~---