Re: Incompleteness and Knowledge
Bruno Marchal wrote: provable(p)does not entailprovable(p) and true(p) This should be astonishing, because we have restricted ourself to correct machine, so obviously provable(p) entails the truth of p, and thus provable(p) entails "provable(p) and p"; so what What happens is incompleteness; although provable(p) entails true(p), the machine is unable to prove that. That is the correct machine cannot prove its own correctness. By Tarski (or Kaplan &Montague 1961) such correctness is not even expressible by the machine (unlike provability and consistency). But, (and that's what the "meta" shift of level makes it possible); we can define, for each proposition p, a modal connective knowable(p) by "provable(p) and p". Accepting the idea that the first person is the knower, this trick makes it necessary for any correct machine to have a different logic for something which is strictly equivalent for any omniscient outsider. In some sense this explains why there is necessarily a gap between (3-person) communicable proof and (1-person) non-communicable (as such) knowledge. Why can't the machine just assume that it is correct, until proven otherwise? If its deductions continue to work ( to correspond to its oberved reality), and it gains an ever growing set of larger and larger and more and more explanatory theories through induction and abduction, what's wrong with the machine just assuming without deductive evidence (but rather through a sort of induction about its own meta-level) that it is logically sound and a reliable observer, individuator, conceptualizer etc. I think the incompleteness issue is a limitation of the meaning of the concept of truth. Just like "speed" and "time" are concepts of limited range (speed is no use at lightspeed, time is no use (ill-defined) at the big bang) so truth itself, as a relationship between representative symbols and that which is (possibly) represented, is probably a limited concept, and the limitation has to do with limits on the information that can be conveyed about one structure about another structure. Clearly an embedded structure cannot convey all information about both itself and the rest of reality which is not itself. There is not enough information in the embedded structure to do this. So we should just live with incompleteness of formal systems of representation, and not worry excessively about an absolute all-encompassing complete notion of truth. I don't think such a grand notion of truth is a well-formed concept. This is so important that not only the knower appears to be variant of the prover, but the observables, that is: physics, too. But that could lead me too far now and I prefer to stop. Yes, ok. And indeed evolutionnary theory and game theory and even logic are sometimes used to just put that difference under the rug making consciousness a sort of epiphenomenon, which it is not, for incompleteness is inescapable, and introspective machines can only build their realities from it. All this can be felt as highly counter-intuitive, but the logic of self-reference *is* counter-intuitive. What is one PRACTICAL consequence of a machine only building its reality-representation using incomplete representation? Only that the machine can never know everything? Well come on, no machine is going to have time or space to know anywhere near everything anyway, so what's the big fat hairy deal? Eric
Re: meta-ethics or ethology
If you believe that humans are 98+% identical genetically to the bonobo monkeys then you must believe that it is today's genetics - period. The reductionistic biological sciences found a number of observational results and explained them within the boundaries so far drawn around (this) science - believeing that "that's all to it". Well, compare the epistemic cognitive invetory of 1000 AD with ours at 2000 AD and extrapolate 3000 AD (Oho!) whether it will be more than ours today? (This is not a criticism towards today's TOE, it is only a remark on the (genetical) identiy as many people take it from biology. I also skip connotations to the very debatable 'ethix' or 'morality' fictions). Planet of the apes? Regards John Mikes - Original Message - From: "CMR" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, January 30, 2004 11:15 AM Subject: meta-ethics or ethology > Greetings, > > > > Some previous posts in the current thread have attacked this idea by, > > > for example, explaining ethics in terms of evolutionary theory or game > > > theory, but this is like explaining a statement about the properties > > > of sodium chloride in terms of the evolutionary or game theoretic > > > advantages of the study of chemistry. Yes, you can legitimately talk > > > about ethics or chemistry in these terms, but in so doing you are > > > talking meta-ethics or meta-chemistry, which I think is what Bruno > > > means by "level shift". > > > > > Perhaps, but this view speaks to the rift between those that approach human > behavior as being different in kind from other animals and those that see it > as instead different in degree. The latter, myself included, find the study > of ethology (animal behavior) and animal ecology as directly applicable to > humans and in those very real fields of study, interpretiing behavior in > the context of fitness is standard procedure. So in that sense examining > human behavior in that same context can be seen as a legitimate extension of > ethology and/or animal ecology, as opposed to some form of meta-psychology, > ..anthropology, ..sociology etc.. > > We share 98%+ of our genetic heritage with bonobo chimps. Many researchers > credit our cousins with primitive language capacity, tool usage, and even > self-awareness. I doubt, though, that many would find interpreting chimp > behavior in the context of fitness to be un-orthodox in anyway. Indeed it is > the norm. > > Cheers > CMR >
Re: Is the universe computable
Dear Stephen, [SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a support that was stronger than the one that you propose ... [BM] Where do I give a support to comp? I don't remember. No doubt that I am fascinated by its consequences, and that I appreciate the so deep modesty and silence of the Wise Machine. But the reason why I work on comp is just that it makes mathematical logic a tool to proceed some fundamental question I'm interested in. and that in addition to your 1 and 3-determinacy that there would be a way to shift from the Dovetailer view (the "from the outside" view) to the "inside" view such that some predictiveness would obtain when we are trying to predict, say the dynamics of some physical system. Otherwise, I claim, your theory is merely an excursion into computational Scholasticism. The whole point of my work consists to show (thanks to math) that comp is indeed popper falsifiable. It is just a matter of work and time to see if the logic of observable proposition which has been derived from comp gives a genuine quantum logic and ascribes the correct probability distribution to the verifiable facts. The weakness of the approach is that it leads to hard mathematical question. I am sanguine about QM's "weirdness"! I see it as implying that there is much more to "Existence" than what we can experience with our senses. ;-) I agree with you. Now comp shows much more easily that it *must* be so. You know Bohr said that someone pretending to understand QM really does not understand it. The same with comp, it can even be justified. If a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences until she realizes that indeed if (apology for this infinite sentence). [BM] > comp = > 1) there is level of description of me such that I cannot be aware of functional digital substitution made at > that level. [SPK] Here we differ as I do not believe that "digital substitution" is possible, IF such is restricted to UTMs or equivalents. No consistent machine can really "believe" that indeed. But this does not mean a consistent machine will believe not-comp. The point is: are you willing to accept it for the sake of the reasoning. > 2) Church thesis [SPK] I have problems with Churches thesis because it, when taken to its logical conclusion, explicitly requires that all of the world to be enumerable and a priori specifiable. Peter Wegner, and others, have argued persuasively, at least for me, that this is simply is not the case. Church thesis entails that the partial (uncontrolable a priori) processes are mechanically enumerable. AND Church thesis entails that the total (controlable) processes are NOT mechanically enumerable. In each case we face either uncontrolability or non enumerability. It is Church thesis which really protects comp from reductionnism. That was the subject of one thesis I propose in the seventies. Since then Judson Webb has written a deep book on that point. (Webb 1980, ref in my thesis, url below). See my everything-list posts "diagonalisation" for the proof of those facts. > 3) Arithmetical Realism) > makes the physical science eventually secondary with respect to number theory/computer science/machine > psychology/theology whatever we decide to call that fundamental field ... [SPK] I have no problem with AR, per say, but see it as insufficient, since it does not address the "act" of counting, it merely denotes the list of rules for doing so. Certainly not. AR is the doctrine that even in a case of absolute catastrophe killing all living form in the multiverse, the statement that there is no biggest prime will remain true. It has nothing to do with axioms and rules of formal system. Indeed by Godel's incompleteness theorem Arithmetical truth extends itself well beyond any set of theorem provable in any axiomatizable theory. Now, what do you mean by AR is insufficient? AR just say that arithmetical truth does not depend on us. It does not say that some other truth does not exist as well (although as a *consequence* of comp plus occam they do indeed vanish). Don't confuse AR with "Pythagorean AR" which asserts explicitely "AR and no more". We got P.AR as a consequence of comp, but we do not postulate it in the comp hyp. I will go through your thesis step by step again and see if I can wrestle my prejudices down into some reasonableness. ;-) OK. Be sure to go to step n only if you manage to go to step n-1 before. Don't hesitate to ask question if something is unclear. Be sure you accept the hypotheses (if only for the sake of the argument). Best Regards, Bruno http://irid
Re: Modern Physical theory as a basis for Ethical and Existential Nihilism
Greetings, > > Some previous posts in the current thread have attacked this idea by, > > for example, explaining ethics in terms of evolutionary theory or game > > theory, but this is like explaining a statement about the properties > > of sodium chloride in terms of the evolutionary or game theoretic > > advantages of the study of chemistry. Yes, you can legitimately talk > > about ethics or chemistry in these terms, but in so doing you are > > talking meta-ethics or meta-chemistry, which I think is what Bruno > > means by "level shift". > > Perhaps, but this view speaks to the rift between those that approach human behavior as being different in kind from other animals and those that see it as instead different in degree. The latter, myself included, find the study of ethology (animal behavior) and animal ecology as directly applicable to humans and in those very real fields of study, interpretiing behavior in the context of fitness is standard procedure. So in that sense examining human behavior in that same context can be seen as a legitimate extension of ethology and/or animal ecology, as opposed to some form of meta-psychology, ..anthropology, ..sociology etc.. We share 98%+ of our genetic heritage with bonobo chimps. Many researchers credit our cousins with primitive language capacity, tool usage, and even self-awareness. I doubt, though, that many would find interpreting chimp behavior in the context of fitness to be un-orthodox in anyway. Indeed it is the norm. Cheers CMR <-- insert gratuitous quotation that implies my profundity here -->
Re: Modern Physical theory as a basis for Ethical and Existential Nihilism
At 13:53 30/01/04 +1100, Stathis Papaioannou wrote: fact vs. value; formal vs. informal; precise vs. vague; objective vs. subjective; third person vs. first person; computation vs. thought; brain vs. mind; David Chalmer's easy problem vs. hard problem of consciousness: To me, this dichotomy remains the biggest mystery in science and philosophy. I have very reluctantly settled on the idea that there is a fundamental (=irreducible=axiomatic) difference here, which I know is something of a copout. I really would like to have one "scientific" theory that at least potentially explains "everything". As it is, even finding a clear way of stating the dichotomy is proving elusive. Actually that *difference* is not *really* fundamental. Although I could have taken it as axiom, it appears that the mechanist hypothesis literally forces us to introduce that difference. It is hard to explain this without being a little bit technical. The main fact. is that, in the apparently crisp domain of formal provability by correct machine or correct theorem prover, once the machine are sufficiently powerful, we get this provable(p)does not entailprovable(p) and true(p) This should be astonishing, because we have restricted ourself to correct machine, so obviously provable(p) entails the truth of p, and thus provable(p) entails "provable(p) and p"; so what What happens is incompleteness; although provable(p) entails true(p), the machine is unable to prove that. That is the correct machine cannot prove its own correctness. By Tarski (or Kaplan &Montague 1961) such correctness is not even expressible by the machine (unlike provability and consistency). But, (and that's what the "meta" shift of level makes it possible); we can define, for each proposition p, a modal connective knowable(p) by "provable(p) and p". Accepting the idea that the first person is the knower, this trick makes it necessary for any correct machine to have a different logic for something which is strictly equivalent for any omniscient outsider. In some sense this explains why there is necessarily a gap between (3-person) communicable proof and (1-person) non-communicable (as such) knowledge. This is so important that not only the knower appears to be variant of the prover, but the observables, that is: physics, too. But that could lead me too far now and I prefer to stop. Some previous posts in the current thread have attacked this idea by, for example, explaining ethics in terms of evolutionary theory or game theory, but this is like explaining a statement about the properties of sodium chloride in terms of the evolutionary or game theoretic advantages of the study of chemistry. Yes, you can legitimately talk about ethics or chemistry in these terms, but in so doing you are talking meta-ethics or meta-chemistry, which I think is what Bruno means by "level shift". Yes, ok. And indeed evolutionnary theory and game theory and even logic are sometimes used to just put that difference under the rug making consciousness a sort of epiphenomenon, which it is not, for incompleteness is inescapable, and introspective machines can only build their realities from it. All this can be felt as highly counter-intuitive, but the logic of self-reference *is* counter-intuitive. Bruno
meta-ethics or ethology
Greetings, > > Some previous posts in the current thread have attacked this idea by, > > for example, explaining ethics in terms of evolutionary theory or game > > theory, but this is like explaining a statement about the properties > > of sodium chloride in terms of the evolutionary or game theoretic > > advantages of the study of chemistry. Yes, you can legitimately talk > > about ethics or chemistry in these terms, but in so doing you are > > talking meta-ethics or meta-chemistry, which I think is what Bruno > > means by "level shift". > > Perhaps, but this view speaks to the rift between those that approach human behavior as being different in kind from other animals and those that see it as instead different in degree. The latter, myself included, find the study of ethology (animal behavior) and animal ecology as directly applicable to humans and in those very real fields of study, interpretiing behavior in the context of fitness is standard procedure. So in that sense examining human behavior in that same context can be seen as a legitimate extension of ethology and/or animal ecology, as opposed to some form of meta-psychology, ..anthropology, ..sociology etc.. We share 98%+ of our genetic heritage with bonobo chimps. Many researchers credit our cousins with primitive language capacity, tool usage, and even self-awareness. I doubt, though, that many would find interpreting chimp behavior in the context of fitness to be un-orthodox in anyway. Indeed it is the norm. Cheers CMR <-- insert gratuitous quotation that implies my profundity
Re: Modern Physical theory as a basis for Ethical and Existential Nihilism
Stathis Papaioannou wrote: fact vs. value; formal vs. informal; precise vs. vague; objective vs. subjective; third person vs. first person; computation vs. thought; brain vs. mind; David Chalmer's easy problem vs. hard problem of consciousness: To me, this dichotomy remains the biggest mystery in science and philosophy. I have very reluctantly settled on the idea that there is a fundamental (=irreducible=axiomatic) difference here, which I know is something of a copout. I really would like to have one "scientific" theory that at least potentially explains "everything". As it is, even finding a clear way of stating the dichotomy is proving elusive. Some previous posts in the current thread have attacked this idea by, for example, explaining ethics in terms of evolutionary theory or game theory, but this is like explaining a statement about the properties of sodium chloride in terms of the evolutionary or game theoretic advantages of the study of chemistry. Yes, you can legitimately talk about ethics or chemistry in these terms, but in so doing you are talking meta-ethics or meta-chemistry, which I think is what Bruno means by "level shift". I really think that to get a good grasp on this kind of issue, one has to "get over ones-self". Step outside for a moment and consider whether you "feeling conscious" is as amazing or inexplicable as you think. Consciousness may very well just be an epi-phenomenon of a self-reflection-capable world-modelling representer and reasoner such as our brains. Minsky's society of mind idea isn't fully adequate as a consciousness explanation, but it makes inroads. Some of the most exciting work in this area IMHO is being done by the neurologist Antonio Damasio. Here is a review of his book on the topic of the feeling of consciousness: http://homepage.ntlworld.com/anthony.campbell1/bookreviews/r/damasio-2.html One of his key idea is that the lowest level of consciousness is just the brain's representation of the sensor data about what our body is doing (how it is positioned and moving, if it aches anywhere, and what we're seeing, hearing in each instant etc). He says this is the brain's representation for the purpose of "homeostasis" i.e. the instantaneous "status" of the body. This homeostatis awareness (reflection of sensor data in the brain) he calls the proto-self. Then comes a level (he calls core consciousness) at which those low-level sense data are integrated into a conceptual (or object-modelling) level to form a continuous "stream of consciousness feeling". This is the "watching a movie but you are in the movie" sense. Finally, at the high level, is added (or filled in) ideas from the memory and planning facilities of the higher brain. So what we are doing here is adding in ideas about things which take time. We are adding in (to help explain the "stream of consciousness "object-movie that we're in") a whole bunch of remembered specific episodes and facts and generalized space-time-world-situation-model concepts that we produced by processing experience after experience after experience. And we are adding in hypotheses about how things could go if (i.e. object-movie-that-we're-in-explorations of counterfactuals and hypotheticals and desired future states and plan run-throughs for getting there.) This is just using the same "watching-object-movie-that-I'm-in" capability but to daydream (remember, or wish, or plan) alternative scenarios rather than the sense-data direct movie of the core-self. This highest level self, he calls the "autobiographical self" because the highest level sense of consciousness is in effect, us "writing the story of ourselves (that we're in)" as well as "reading the story of ourself (that we're in)" at the same time. It is a story, and not just a stream-of-consciousness, because it has added in memories and experiences from the past, to provide a meaningful causal narrative to ourself about what is going on now, and what is going to happen next. So highest-level consciousness IS an autobiographical story of ourself and our doings and present-time but past-experientially interpreted experiences. And that is just the back-and-forth-in-time (or sideways to hypotheticals/counterfactuals) extension of the core-self "movie that I'm both watching AND sensing that I'm in it" sense, which itself is the CONCEPTUAL-OBJECT-INTERPRETATION of the continuous stream of homeostasis raw sense-data that the brain is continually receiving and processing in real-time to know what the state of the body is and what it senses to be around it. This makes PERFECT sense (and feels almost adequate, as an explanation of the "feeling of consciousness") to me. Eric p.s. before someone jumps in about how off-topic this is, I think that's narrow minded because understanding consciousness is integral to understanding observers and their role in physics.
Has math landed?
Logician Bruno Marchal ended an email like this Sep 2002 "PS I have found a way to explain with knot theory what "logic" is,as a branch of math, by comparing propositions with knots, proofs withcontinuous deformation, and semantics with knot's invariants. As I saidbefore one of the difficulty for writing a paper is the misunderstandingbetween logicians and physicist ..." I recalled that when I read the following in the article "Dancing the quantum dream" from New Scientist 24th of January 2004: "performing measurements on a braided system of quantum particles can be equivalent to performing the computation that a particular knot encodes." Then I came to the part where the article says: "Freedman and Kitaev (who is now also at Microsoft Research), together with Michael Larson and Zhenghan Wang, both at Indiana University in Bloomington, have now shown how to build a "topological quantum computer" using technology that is available today (www.arxiv.org/quant-ph/0101025). It seems to be the one machine that could get useful quantum computers off the drawing board." And now I wonder: Is this the beginning of math as an empirical science? Lennart
