Re: Penrose and algorithms
Le 05-juil.-07, à 22:14, Jesse Mazer a écrit : His [Penrose] whole Godelian argument is based on the idea that for any computational theorem-proving machine, by examining its construction we can use this understanding to find a mathematical statement which *we* know must be true, but which the machine can never output--that we understand something it doesn't. But I think my argument shows that if you were really to build a simulated mathematician or community of mathematicians in a computer, the Godel statement for this system would only be true *if* they never made a mistake in reasoning or chose to output a false statement to be perverse, and that therefore there is no way for us on the outside to have any more confidence about whether they will ever output this statement than they do (and thus neither of us can know whether the statement is actually a true or false theorem of arithmetic). I think I agree with your line of argumentation, but you way of talking could be misleading. Especially if people interpret arithmetic by If we are in front of a machine that we know to be sound, then we can indeed know that the Godelian proposition associated to the machine is true. For example, nobody (serious) doubt that PA (Peano Arithmetic, the first order formal arithmetic theory/machine) is sound. So we know that all the godelian sentences are true, and PA cannot know that. But this just proves that I am not PA, and that I have actually stronger ability than PA. I could have taken ZF instead (ZF is Zermelo Fraenkel formal theory/machine of sets), although I must say that if I have entire confidence in PA, I have only 99,9998% confidence in ZF (and thus I can already be only 99,9998% sure of the ZF godelian sentences). About NF (Quine's New Foundation formal theory machine) I have only 50% confidence!!! Now all (sufficiently rich) theories/machine can prove their own Godel's theorem. PA can prove that if PA is consistent then PA cannot prove its consitency. A somehow weak (compared to ZF) theory like PA can even prove the corresponding theorem for the richer ZF: PA can prove that if ZF is consistent then ZF can prove its own consistency. So, in general a machine can find its own godelian sentences, and can even infer their truth in some abductive way from very minimal inference inductive abilities, or from assumptions. No sound (or just consistent) machine can ever prove its own godelian sentences, in particular no machine can prove its own consistency, but then machine can bet on them or know them serendipitously). This is comparable with consciousness. Indeed it is easy to manufacture thought experiements illustrating that no conscious being can prove it is conscious, except that consciousness is more truth related, so that machine cannot even define their own consciousness (by Tarski undefinability of truth theorem). 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 PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Penrose and algorithms
On Jul 5, 2:14 pm, LauLuna [EMAIL PROTECTED] wrote: I don't see how to reconcile free will with computationalism either. It seems like you are an incompatibilist concerning free will. Freewill can be reconciled with computationalism (or any deterministic system) if one accepts compatabilism ( http://en.wikipedia.org/wiki/Free_will#Compatibilism ). More worrisome than determinism's affect on freewill, however, is many-worlds (or other everything/ultimate ensemble theories). Whereas determinism says the future is written in stone, many-worlds would say all futures are written in stone. Jason --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Some thoughts from Grandma
Le 05-juil.-07, à 17:31, David Nyman a écrit : On 05/07/07, Bruno Marchal [EMAIL PROTECTED] wrote: BM: OK. I would insist that the comp project (extract physics from comp) is really just a comp obligation. This is what is supposed to be shown by the UDA (+ MOVIE-GRAPH). Are you OK with this. It *is* counterintuitive. DN: I believe so - it's what the reductio ad absurdum of the 'physical' computation in the 'grandma' post was meant to show. This was not so clear, but OK. My version of the 'comp obligation' would then run as follows. Essentially, if comp and number relations are held to be 'real in the sense that I am real', I am not sure that numbers are real in the sense that I am real, unless you are talking of the third person I. Then you are as real as your (unknown) Godel-number. In general, when people use the word I they refer to their first person, or to first person plural feature of their physical body. It is a unexpected (by me) discovery that quanta belongs to that sharable first person view (making the comp-QM a bit more psychological than some Many-Worlder would perhaps appreciate. So that Fuch-Pauli could be right ... (if you know the work of Fuchs). then to use Plato's metaphor, it is numbers that represent the forms outside the cave. OK, but not only (there are also the relations between numbers, the relation between the relations between the numbers, etc.) If that's so, then physics is represented by the shadows the observers see on the wall of the cave. This is what I mean by 'independent' existence in my current dialogue with Torgny: i.e the 'arithmetical realism' of numbers and their relations in the comp frame equates to their 'independence' or self-relativity. And the existence of 'arithmetical observers' then derives from subsequent processes of 'individuation' intrinsic to such fundamental self-relation. Actually, I find the equation of existence with self-relativity highly intuitive. OK. (Technically it is not obvious how to define in arithmetic such self-relation: the basic tool is given by the recursion or fixed point theorems). BM: Then, the interview of the universal machine is just a way to do the extraction of physics in a constructive way. It is really the subtleties of the incompleteness phenomena which makes this interview highly non trivial. DN: This is the technical part. But at this stage grandma has some feeling for how both classical and QM narratives should be what we expect to emerge from constructing physics in this way. I am not sure how could grandma have a feeling about that, except if grandma get Church Thesis and the UDA. BM: There is no direct (still less one-one) correlation between the mental and the physical, that is the physical supervenience thesis is incompatible with the comp hyp. [A quale of a pain] felt at time t in place x, is not a product of the physical activity of a machine, at time t in place x. Rather, it is the whole quale of [a pain felt at time t in place x] which is associated with an (immaterial and necessarily unknown) computational state, itself related to its normal consistent computational continuations. snip Comp makes the yes doctor a gamble, necessarily. That is: assuming the theory comp you have to understand that, by saying yes to the doctor, you are gambling on a level of substitution. At the same time you make a gamble on the theory comp itself. There is double gamble here. Now, the first gamble, IF DONE AT THE RIGHT COMP SUBSTITUTION LEVEL, is comp-equivalent with the natural gamble everybody do when going to sleep, or just when waiting a nanosecond. In some sense nature do that gamble in our place all the time ... But this is somethjng we cannot know, still less assert in any scientific way, and that is why I insist so much on the theological aspect of comp. This is important in practice. It really justify that the truth of the yes doctor entails the absolute fundamental right to say NO to the doctor. The doctor has to admit he is gambling on a substitution level. If comp is true we cannot be sure on the choice of the subst. level. DN: ISTM that a consequence of the above is that the issue of 'substitution level' can in principle be 'gambled' on by cloning, or by evolution (because presumably it has been, even though we can't say how). But by engineering or design??? Would there ever be any justification, in your view, for taking a gamble on being uploaded to an AI program - and if so, on the basis of what theory? Well, if you are willing to believe in neurophilosophy, you can bet on some high level description. If you bet on Hammerof's theory, you have to duplicate the qunatum state of the brain (and this is of courese not possible). I don't think we are concerned with those practical matter. The point is just that physics appears as a sort of sum on your
Re: Penrose and algorithms
Le 06-juil.-07, à 14:00, Jason a écrit : On Jul 5, 2:14 pm, LauLuna [EMAIL PROTECTED] wrote: I don't see how to reconcile free will with computationalism either. It seems like you are an incompatibilist concerning free will. Freewill can be reconciled with computationalism (or any deterministic system) if one accepts compatabilism ( http://en.wikipedia.org/wiki/Free_will#Compatibilism ). More worrisome than determinism's affect on freewill, however, is many-worlds (or other everything/ultimate ensemble theories). Whereas determinism says the future is written in stone, many-worlds would say all futures are written in stone. Like comp already say. At least with QM we know that the future are weighted and free-will will correspond to choosing among normal worlds. With comp, there is only promising results in that direction, (which could lead to a refutation of comp). John Bell (the physicist, not the quantum logician) has also crticized the MWI with respect to free-will, but this does not follow from the SWE. The SWE does not say all future are equal. It says that all future are realized, but some have negligible probability, and this left room for genuine free-will. For example I can choose the stairs, the lift or the windows to go outside, but only with the stairs and lift can I stay in relatively normal worlds. By going outside by jumping through the windows, I take the risk of surviving in a white rabbit world and then to remain in the relatively normal world with respect to that not normal world. This is why I think quantum immortality is a form of terrifying thinking ... if you think twice and take it seriously. Of course reality (with or without QM or comp) is more complex in any case, so it is much plausibly premature to panic from so theoretical elaborations. Actually computer science predicts possible unexpectable jump ... Is it worth exploring the possible comp-hell, to search the limit of the unbearable? Well, news indicate humans have some incline to point on such direction. That could be the price of free-will. Have you read the delicious texts by Smullyan (in Mind'sI I think) about the guy who asks God to take away his free-will (and its associated guilt feeling) ? 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 PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Some thoughts from Grandma
On 06/07/07, Bruno Marchal [EMAIL PROTECTED] wrote: I am not sure that numbers are real in the sense that I am real, unless you are talking of the third person I. Then you are as real as your (unknown) Godel-number. In general, when people use the word I they refer to their first person, or to first person plural feature of their physical body. It is a unexpected (by me) discovery that quanta belongs to that sharable first person view (making the comp-QM a bit more psychological than some Many-Worlder would perhaps appreciate. So that Fuch-Pauli could be right ... (if you know the work of Fuchs). What I meant was something looser, a tautology perhaps. That is, whatever we postulate as giving rise to our personal 'reality' must thereby be 'real' in just this sense: it 'underpins' that reality. I recall your various debates with Peter on this issue, and whatever else was at issue, I just felt that at least implicitly this must be entailed by the 'realism' part of AR. OK, but not only (there are also the relations between numbers, the relation between the relations between the numbers, etc.) You are more precise (and correct!) OK. (Technically it is not obvious how to define in arithmetic such self-relation: the basic tool is given by the recursion or fixed point theorems). My basic notion of self-relative existence equates I think to Plotinus' One as you describe it in the Sienna paper. I postulate it to stand for 'existence' independent of other causality. I see the big One as 'self-differentiating' through spontaneous symmetry breaking, as the basis for all subsequent categorisation whatsoever, except the original - and unique - ontic category of self-relative existence. This entails that all such subsequent categorisation is in some fundamental sense epistemic: i.e. how the One 'gets to know' itself. So I agree with Plotinus that the One can't be said to 'know' anything without such differentiation. I am not sure how could grandma have a feeling about that, except if grandma get Church Thesis and the UDA. Well, I'm working on the technicalities. But the 'feeling' comes from what I've said above. If all categories of 'process' or 'structure' are epistemic - i.e. forms of self-relative 'coming to know' - this entails that everything arises as an interpretation from a 'point of view'. So what is revealed in any given context and - at least as importantly - what is obscured, must then be characteristic of that specific point of view, in no sense 'absolute reality' (whatever that could mean). The point is just that physics appears as a sort of sum on your lobian ignorance. I think this is what I mean by 'obscured'. As I said this is a point where I would like to disagree with the lobian machine. The fact is that even the lobian machine warns us on the possibility of zombie. Certainly the current artificial cops on the road are zombie. Tomorrow we will be able to build artificial skin for androids capable of making us believe they are normal humans citizens, ... We should distinguish local zombie which are capable to fail you during some finite time, and theoretical global zombie which are capable to fail you, in principle, for ever (like Torgny try to make us believe he belongs too: nobody can prove him wrong). You're right, we must distinguish zombies. The kind I have in mind are the kind that Torgny proposes, where 'everything is the same' as for a human, except that 'there's nothing it is like' to be such a person. My key point is that this must become incoherent in the face of self-relativity. My reasoning is that a claim for the 'existence' of something like Torgny's B-Universe is implicitly a claim for self-relative existence: i.e. independent of other causality, like the One. When Torgny proposed the Game of Life as an example of 'another universe', I pointed out that GoL clearly doesn't possess independent existence: it's just a part of the A-Universe. If one is to postulate a universe suitable for the thought experiment, one must in effect propose 'another One' - i.e. an independently self-relative 'B-Universe'. It follows that, given the other assumptions of 'sameness', conversations with machines in such a B-Universe must then proceed exactly as they do in the A-Universe, because they depend on self-relation in the same ways. Now, it may seem that - beyond all relativity - the question still remains of the 'absolute' quality of 'what it's like' to be 'One' in the context of such self-individuation. I leave it for you to judge whether - if a machine can report just as we do on what it's like to be itself, with exactly the same self-relative justification - it can then remain coherent to claim that 'it's not like anything' to be that machine. Before a long time (despite Kurzweyl) we just can do it, even at a high level. A brain is *very* complex, for any theory. In the future people will just bet on the available theory through some Pascal wag.
Re: Penrose and algorithms
Bruno Marchal wrote: ... Now all (sufficiently rich) theories/machine can prove their own Godel's theorem. PA can prove that if PA is consistent then PA cannot prove its consitency. A somehow weak (compared to ZF) theory like PA can even prove the corresponding theorem for the richer ZF: PA can prove that if ZF is consistent then ZF can prove its own consistency. Of course you meant ..then ZF cannot prove its own consistency. Brent Meeker So, in general a machine can find its own godelian sentences, and can even infer their truth in some abductive way from very minimal inference inductive abilities, or from assumptions. No sound (or just consistent) machine can ever prove its own godelian sentences, in particular no machine can prove its own consistency, but then machine can bet on them or know them serendipitously). This is comparable with consciousness. Indeed it is easy to manufacture thought experiements illustrating that no conscious being can prove it is conscious, except that consciousness is more truth related, so that machine cannot even define their own consciousness (by Tarski undefinability of truth theorem). But this is within an axiomatic system - whose reliability already depends on knowing the truth of the axioms. ISTM that concepts of consciousness, knowledge, and truth that are relative to formal axiomatic systems are already to weak to provide fundamental explanations. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Some thoughts from Grandma
David Nyman skrev: You're right, we must distinguish zombies. The kind I have in mind are the kind that Torgny proposes, where 'everything is the same' as for a human, except that 'there's nothing it is like' to be such a person. My key point is that this must become incoherent in the face of self-relativity. My reasoning is that a claim for the 'existence' of something like Torgny's B-Universe is implicitly a claim for self-relative existence: i.e. independent of other causality, like the One. When Torgny proposed the Game of Life as an example of 'another universe', I pointed out that GoL clearly doesn't possess independent existence: it's just a part of the A-Universe. It is intresting to study the GoL-universe we can see on the Wikipedia page. What will happen if we stop the program that shows this GoL-universe? Will the GoL-universe stop to exist then? No, the GoL-universe will not stop, it will continue for ever. The rules for this GoL-universe makes it possible to compute all future situations. It is this that is important. This GoL-universe is not dependent of the A-Universe. What we see when we look at the Wikipedia page is just a picture of a part of this GoL-universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Some thoughts from Grandma
On 06/07/07, Torgny Tholerus [EMAIL PROTECTED] wrote: No, the GoL-universe will not stop, it will continue for ever. The rules for this GoL-universe makes it possible to compute all future situations. It is this that is important. This GoL-universe is not dependent of the A-Universe. What we see when we look at the Wikipedia page is just a picture of a part of this GoL-universe. Torgny, I'm really confused now. In your original post, you postulated: Imagine that we have a second Universe, that looks exactly the same as the materialistic parts of our Universe. We may call this second Universe B-Universe. (Our Universe is A-Universe.) This B-Universe looks exactly the same as A-Universe. Where there is a hydrogen atom in A-Universe, there will also be a hydrogen atom in B-Universe, and everywhere that there is an oxygen atom in A-Universe, there will be an oxygen atom i B-universe. The only difference between A-Universe and B-Universe is that B-Universe is totally free from consciousness, feelings, minds, souls, and all that kind of stuff. The only things that exist in B-Universe are atoms reacting with eachother. All objects in B-Universe behave in exactly the same way as the objects in A-Universe. Now, surely you're not claiming that GoL is fully equivalent to your specification for the B-Universe? 'GoL' may exist in the plenitude, but it doesn't look exactly the same as the A-Universe. And if it should turn out to be capable of evolving to this stage, it will by then have acquired the full characteristics of self-relativity, just like the A-Universe. This list is devoted to the idea that all possible universes exist. There is a trap contained in this proposition. You, I think, read this as any describable state of affairs, but what is describable may not be possible, and what is not possible cannot exist. GoL is in fact possible in this sense, as you haven't postulated any self-contradictory properties for it. But B-Universe? Sure, you can describe a 'universe' that looks exactly the same but doesn't have all that kind of stuff. But this comes from imagining all that kind of stuff as a sort of optional extra that you can decide not to pay for but still retain a 'possible' universe. But the error is that there is no such stuff to dispense with: all the characteristics of the A-Universe, whether 'mental' or 'physical', arise necessarily from self-relativity (i.e. independent existence). The 'split personality' of the B-Universe is therefore self-contradictory. As such, it can't exist self-relatively, and consequently exists only relative to the A-Universe, in the form of a misconception. David David Nyman skrev: You're right, we must distinguish zombies. The kind I have in mind are the kind that Torgny proposes, where 'everything is the same' as for a human, except that 'there's nothing it is like' to be such a person. My key point is that this must become incoherent in the face of self-relativity. My reasoning is that a claim for the 'existence' of something like Torgny's B-Universe is implicitly a claim for self-relative existence: i.e. independent of other causality, like the One. When Torgny proposed the Game of Life as an example of 'another universe', I pointed out that GoL clearly doesn't possess independent existence: it's just a part of the A-Universe. It is intresting to study the GoL-universe we can see on the Wikipedia page. What will happen if we stop the program that shows this GoL-universe? Will the GoL-universe stop to exist then? No, the GoL-universe will not stop, it will continue for ever. The rules for this GoL-universe makes it possible to compute all future situations. It is this that is important. This GoL-universe is not dependent of the A-Universe. What we see when we look at the Wikipedia page is just a picture of a part of this GoL-universe. -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
