Re: Minds, Machines and Gödel
On Wednesday, December 25, 2013 2:09:07 PM UTC-5, Bruno Marchal wrote: On 25 Dec 2013, at 16:18, Craig Weinberg wrote: On Wednesday, December 25, 2013 5:07:22 AM UTC-5, Bruno Marchal wrote: On 24 Dec 2013, at 17:31, Craig Weinberg wrote: It's straighforward I think. What you are saying is that this semantic trick prevents us from seeing that the truth does not agree with the theory. ? (sorry but I still fail to see the connection). I am just saying that the discovery of the many non computable attribute of machine makes invalid the reasoning against comp invoking non computable aspect of the human mind. What I'm saying is that the reference to non-computable phenomena means that they are not likely to be attributes of machines. Yes, that is what you were saying, and my point is that this is not valid. Most machine's or number's attributes are not computable. Then how do you know that they are attributes of the number? If I count that I have five fingers, I don't assume that the fingers are attributes of the number five. In fact, it is the price of the consistency of Church thesis, as I have often explained in detail. If interested I could show it to you. The consistency may come at the expense of reality. Comp has no right to ever mention non computable attributes of anything and still be comp. ? Comp is I am a machine (3-I). This does not entail that everything is computable. Then how do you know that what you are has anything to do with machines? If some things are not computable, what are they, and why would they have anything to do with computation? Worse, the price of universality entails that many things *about* machine will necessarily be non-computable. A large part of computability theory is really incomputability theory, the studies of the complex hierarchies of non computability and non solvability in arithmetic and computer science. Have you considered that they be non computable and non solvable because they aren't directly related to mathematics? It would have to explain how non-computable phenomena are derived from computation and what that can even mean. I can do that. I can prove that if a universal number exists, then non computable relation between numbers exists. Löbian numbers can actually already prove that about themselves. How do you know that the numbers aren't just the computable relations between experiences instead? For comp to be consistent, it can only ask 'what do you mean 'non-computable?'. For finite to be consistent, it can only ask what do you mean by infinite? Well, OK. But we can do that. We can ask, but if we say that something is infinite, then our theory of finite can't be complete. Even with the intuitive definition, we can do that. A function (from N to N) is computable iff you can explain in a finite numbers of words, in a non ambiguous grammar, to a reasonably dumb fellow, how to compute it, in a finite time, for each of its finite argument. Now, a function is not computable, if you cannot do that, even assuming you are immortal. Church thesis say the number LAMDDA is a universal number. This simplifies non computability. A function is not computable if you cannot program it in LAMBDA. The universal number LAMBDA cannot simulate that function. If LAMBDA is all that you have, how do you know that what it can't program is a number at all? If I had a theory of autovehicularism in which cars drive themselves, I can't then claim that these soft things that sit behind the wheel inside the car are non-vehicular attributes of cars. If there can be non-vehicular attributes of cars then any autovehicular theory of cars is false. It means also that most proposition *about* machine, cannot be found in a mechanical way. The simplest examples are that no machine can decide if some arbitrary machine will stop not, or no machine can decide if two arbitrary machine compute or not the same function, etc. If there is no complete theories for machines and/or numbers, it makes harder to defend non-comp, etc. How can computationalism support the idea of there being a non-mechanical way though? What other way is there? Computation with oracle for non computable arithmetical truth, or just some non computable arithmetical truth. Arithmetic is full of them. You are telling me that arithmetic is full of non-arithmetic, No. Full of non computable relations between number. If they are not computable, how do you know they are part of arithmetic rather than physics or sense? Because I work in arithmetic. I use Gödel's arithmetization of meta-arithmetic. In AUDA, I never leave arithmetic. Then how do you know that you aren't suffering from the fallacy of the instrument? Most of arithmetic is not computable. Truth escapes proof, and many computations do not stop,
Re: Minds, Machines and Gödel
On 25 December 2013 16:51, Craig Weinberg whatsons...@gmail.com wrote: On Saturday, December 21, 2013 5:28:29 PM UTC-5, Edgar L. Owen wrote: Craig, Sorry, but I don't really understand what you are trying to get at. Your terminology is not giving me any clarity of what you are really trying to say... Edgar The condensed version of what I'm trying to say is that computation is less than real, reality combines experience and computation, and experience is greater than reality and does not depend on computation. Computation is less than real? - how so? And what is experience, in your view? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
On 21 Dec 2013, at 21:52, Edgar Owen wrote: Liz, No, that doesn't make Reality subject to the halting problem. The halting problem is when a computer program is trying to reach some independently postulated result and may or may not be able to reach it. Reality doesn't have any problem like this. It just computes the logical results of the evolution of the current information state of the universe. There are no independently postulated states that aren't directly computed by reality which reality then attempts to reach (prove). This contradicts both comp and QM. Bruno Edgar On Dec 21, 2013, at 3:26 PM, LizR wrote: Reality is analogous to a running software program. Godel's Theorem does not apply. A human could speculate as to whether any particular state of Reality could ever arise computationally and it might be impossible to determine that, but again that has nothing to do with the actual operation of Reality,since it is only a particular internal mental model of that reality. Wouldn't that make reality susceptible to the halting problem? ...hello, is anybody there? Why have all the stars gone out? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything- l...@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
On 25 Dec 2013, at 16:18, Craig Weinberg wrote: On Wednesday, December 25, 2013 5:07:22 AM UTC-5, Bruno Marchal wrote: On 24 Dec 2013, at 17:31, Craig Weinberg wrote: It's straighforward I think. What you are saying is that this semantic trick prevents us from seeing that the truth does not agree with the theory. ? (sorry but I still fail to see the connection). I am just saying that the discovery of the many non computable attribute of machine makes invalid the reasoning against comp invoking non computable aspect of the human mind. What I'm saying is that the reference to non-computable phenomena means that they are not likely to be attributes of machines. Yes, that is what you were saying, and my point is that this is not valid. Most machine's or number's attributes are not computable. In fact, it is the price of the consistency of Church thesis, as I have often explained in detail. If interested I could show it to you. Comp has no right to ever mention non computable attributes of anything and still be comp. ? Comp is I am a machine (3-I). This does not entail that everything is computable. Worse, the price of universality entails that many things *about* machine will necessarily be non-computable. A large part of computability theory is really incomputability theory, the studies of the complex hierarchies of non computability and non solvability in arithmetic and computer science. It would have to explain how non-computable phenomena are derived from computation and what that can even mean. I can do that. I can prove that if a universal number exists, then non computable relation between numbers exists. Löbian numbers can actually already prove that about themselves. For comp to be consistent, it can only ask 'what do you mean 'non- computable?'. For finite to be consistent, it can only ask what do you mean by infinite? Well, OK. But we can do that. Even with the intuitive definition, we can do that. A function (from N to N) is computable iff you can explain in a finite numbers of words, in a non ambiguous grammar, to a reasonably dumb fellow, how to compute it, in a finite time, for each of its finite argument. Now, a function is not computable, if you cannot do that, even assuming you are immortal. Church thesis say the number LAMDDA is a universal number. This simplifies non computability. A function is not computable if you cannot program it in LAMBDA. The universal number LAMBDA cannot simulate that function. If I had a theory of autovehicularism in which cars drive themselves, I can't then claim that these soft things that sit behind the wheel inside the car are non-vehicular attributes of cars. If there can be non-vehicular attributes of cars then any autovehicular theory of cars is false. It means also that most proposition *about* machine, cannot be found in a mechanical way. The simplest examples are that no machine can decide if some arbitrary machine will stop not, or no machine can decide if two arbitrary machine compute or not the same function, etc. If there is no complete theories for machines and/or numbers, it makes harder to defend non-comp, etc. How can computationalism support the idea of there being a non- mechanical way though? What other way is there? Computation with oracle for non computable arithmetical truth, or just some non computable arithmetical truth. Arithmetic is full of them. You are telling me that arithmetic is full of non-arithmetic, No. Full of non computable relations between number. If they are not computable, how do you know they are part of arithmetic rather than physics or sense? Because I work in arithmetic. I use Gödel's arithmetization of meta- arithmetic. In AUDA, I never leave arithmetic. Most of arithmetic is not computable. Truth escapes proof, and many computations do not stop, without us able to prove this in advance in any specific way. I'm afraid you are unaware of computer science. I told you to be cautious with machines and numbers, because since Gödel we know that we know about nothing on them. so therefore your computationalism - the idea that consciousness and physics develop from unconscious computation, includes (unspecified, unknowable) non-computationalism too. I don't see what you mean by includes non-computationalism. I can try to make sense. yes, the arithmetical reality is 99,999...% non computable. But computationalism is not the thesis that everything is computable. It is the thesis that the working of my brain can be imitate enough closely by a digital machine so that my first person experience will not see any difference. If only 0.000...1% of arithmetic truth is computable, why would a digital computation be enough to imitate anything other than another digital computation? It can't, indeed. Computation and imitation or simulation, or
Re: Minds, Machines and Gödel
Liz, No, that doesn't make Reality subject to the halting problem. The halting problem is when a computer program is trying to reach some independently postulated result and may or may not be able to reach it. Reality doesn't have any problem like this. It just computes the logical results of the evolution of the current information state of the universe. There are no independently postulated states that aren't directly computed by reality which reality then attempts to reach (prove). Edgar On Dec 21, 2013, at 3:26 PM, LizR wrote: Reality is analogous to a running software program. Godel's Theorem does not apply. A human could speculate as to whether any particular state of Reality could ever arise computationally and it might be impossible to determine that, but again that has nothing to do with the actual operation of Reality,since it is only a particular internal mental model of that reality. Wouldn't that make reality susceptible to the halting problem? ...hello, is anybody there? Why have all the stars gone out? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
I have probably missed this - I don't have time to engage as much as I would like with this list (or any others) - but where or how are these computations taking place? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
On 21 Dec 2013, at 17:32, Craig Weinberg wrote: On Thursday, December 19, 2013 10:13:25 AM UTC-5, Bruno Marchal wrote: On 19 Dec 2013, at 15:07, Craig Weinberg wrote: On Thursday, December 19, 2013 5:23:20 AM UTC-5, Bruno Marchal wrote: Hello Craig, That is the very well known attempt by Lucas to use Gödel's theorem to refute mechanism. He was not the only one. Most people thinking about this have found the argument, and usually found the mistakes in it. To my knowledge Emil Post is the first to develop both that argument, and to understand that not only that argument does not work, but that the machines can already refute that argument, due to the mechanizability of the diagonalization, made very general by Church thesis. In fact either the argument is presented in an effective way, and then machine can refute it precisely, or the argument is based on some fuzziness, and then it proves nothing. If 'proof' is an inappropriate concept for first person physics, then I would expect that fuzziness would be the only symptom we can expect. The criticism of Lucas seems to not really understand the spirit of Gödel's theorem, but only focus on the letter of its application...which in the case of Gödel's theorem is precisely the opposite of its meaning. The link that Stathis provided demonstrates that Gödel himself understood this: So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified . . . (Gödel 1995: 310). To me it's clear that Gödel means that incompleteness reveals that mathematics is not completable OK. Even arithmetic. in the sense that it is not enough to contain the reality of human experience, ? He says the 'human mind', but I say human experience. Mathematics is not enough for the mind and experience of ... the machines. not that it proves that mathematics or arithmetic truth is omniscient and omnipotent beyond our wildest dreams. Arithmetical truth is by definition arithmetically omniscient, but certainly not omniscient in general. Indeed to get the whole arithmetical Noùs, Arithmetical truth is still too much weak. All what Gödel showed is that arithmetical truth (or any richer notion of truth, like set theoretical, group theoretical, etc.) cannot be enumerated by machines or effective sound theories. The issue though is whether that non-enumerablity is a symptom of the inadequacy of Noùs to contain Psyche, or a symptom of Noùs being so undefinable that it can easily contain Psyche as well as Physics. The Noùs is the intelligible reality. It is not computable, but it is definable. Unlike truth and knowledge or first person experience. I think that Gödel interpreted his own work in the former and you are interpreting it in the latter - doesn't mean you're wrong, but I agree with him if he thought the former, because Psyche doesn't make sense as a part of Noùs. That is too much ambiguous. The psyche is not really a part of the Noùs, which is still purely 3p. I see Psyche and Physics as the personal and impersonal presentations of sense, Machine think the same, with sense replaced by arithmetical truth. Except that the machine has to be confused and for her that truth is beyond definability, like sense. and Noùs is the re-presentation of physics (meaning physics is re- personalized as abstract digital concepts). The Noùs has nothing to do with physics a priori. It is the world of the eternal platonic ideas, or God's ideas. keep in mind the 8 hypostases: - p (truth, not definable in arithmetic, but emulable in some trivial sense) - Bp (provable, believable, assumable, communicable). It splits into a communicable and non communicable part (some fact about communication are not communicable) - Bp p (the soul, the knower, ... the psyche is here). It does not split. - Bp Dt (the intelligible matter, ... matter and physics is here). It splits in two. - Bp Dt p (the sensible matter. the physical experience, (pain, pleasure, qualia) are here. It splits also in two parts. Physics is the commercialization of sense. Psyche is residential sense. Noùs is the hotel...commercialized residence. An excellent book has been written on that subject by Judson Webb (mechanism, mentalism and metamathematics, reference in the bibliographies in my URL, or in any of my papers). In conscience and mechanism, I show all the details of why the argument of Lucas is already refuted by Löbian machines, and Lucas main error is reduced to a confusion between Bp and Bp p. It is an implicit assumption, in the
Re: Minds, Machines and Gödel
On 21 Dec 2013, at 19:06, Edgar Owen wrote: Craig, Godel's Theorem applies only to human mathematical systems. provably assuming that humans are arithmetically sound machine (which is a rather strong assumption). It doesn't apply to the logico-mathematical system of reality, of which the computational systems of biological organisms including humans are a part. I agree. Why? The answer is straightforward. Because Reality's logico- mathematical system is entirely computational in the sense that every state at every present moment is directly computed from the prior state. Only in the third person perspective, but with computationalism, all accessible realities are not computation, nor result of computation, but they are the result of infinitely many computations mixed with the first person indeterminacies. Godel's Theorem does not apply to this. Right. Gödel' theorem applies to finite or enumerable machines or theories. Not on their models, even in arithmetic. What Godel's Theorem says is that given some mathematical system it is possible to formulate a correct statement It is correct if we already know that the theory is correct, which is doubtful for rich theories like us, in case of comp. which is not computable from the axioms. But Reality doesn't work that way. It simply computes the next state of itself which is always possible. Reality does not compute. That's the digital physics thesis, which makes no sense. Indeed, as often explained here: if digital physics is correct then comp is correct, BUT if comp is correct then digital physics is incorrect. thus digital physics entails the negation of digital physics, and this makes digital physics incorrect (for a TOE) in all case (with comp or with non comp). The implication is that the logico-mathematical system of reality IS AND IN FACT MUST NECESSARILY BE logically consistent and logically complete in every detail. If it wasn't Reality would tear itself apart at the inconsistencies and pause at the incompletenesses and could not exist. But Reality does exist. OK, but we don't *know* that. We hope that. We know only that we are conscious here-and-now. We don't *know* if there are planets and galaxies. We bet on that. Those are theoretical assumptions. Reality is analogous to a running software program. Read the UDA. Apparent realities have to be much bigger than anything we could emulate on a computer. That is already the case for arithmetic itself. You might confuse proof and computation. Godel's Theorem does not apply. A human could speculate as to whether any particular state of Reality could ever arise computationally and it might be impossible to determine that, but again that has nothing to do with the actual operation of Reality,since it is only a particular internal mental model of that reality. The universal dovetailer get all states of mind, but no states of physical reality at all, which needs the non computable First Person Indeterminacy on all (relative) computations. Then the bigger theological (true) reality is even bigger. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
On Sunday, December 22, 2013 7:21:05 AM UTC-5, Bruno Marchal wrote: On 21 Dec 2013, at 17:32, Craig Weinberg wrote: On Thursday, December 19, 2013 10:13:25 AM UTC-5, Bruno Marchal wrote: On 19 Dec 2013, at 15:07, Craig Weinberg wrote: On Thursday, December 19, 2013 5:23:20 AM UTC-5, Bruno Marchal wrote: Hello Craig, That is the very well known attempt by Lucas to use Gödel's theorem to refute mechanism. He was not the only one. Most people thinking about this have found the argument, and usually found the mistakes in it. To my knowledge Emil Post is the first to develop both that argument, and to understand that not only that argument does not work, but that the machines can already refute that argument, due to the mechanizability of the diagonalization, made very general by Church thesis. In fact either the argument is presented in an effective way, and then machine can refute it precisely, or the argument is based on some fuzziness, and then it proves nothing. If 'proof' is an inappropriate concept for first person physics, then I would expect that fuzziness would be the only symptom we can expect. The criticism of Lucas seems to not really understand the spirit of Gödel's theorem, but only focus on the letter of its application...which in the case of Gödel's theorem is precisely the opposite of its meaning. The link that Stathis provided demonstrates that Gödel himself understood this: So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified . . . (Gödel 1995: 310). To me it's clear that Gödel means that incompleteness reveals that mathematics is not completable OK. Even arithmetic. in the sense that it is not enough to contain the reality of human experience, ? He says the 'human mind', but I say human experience. Mathematics is not enough for the mind and experience of ... the machines. i agree, of course, but how is that view compatible with computationalism? not that it proves that mathematics or arithmetic truth is omniscient and omnipotent beyond our wildest dreams. Arithmetical truth is by definition arithmetically omniscient, but certainly not omniscient in general. Indeed to get the whole arithmetical Noùs, Arithmetical truth is still too much weak. All what Gödel showed is that arithmetical truth (or any richer notion of truth, like set theoretical, group theoretical, etc.) cannot be enumerated by machines or effective sound theories. The issue though is whether that non-enumerablity is a symptom of the inadequacy of Noùs to contain Psyche, or a symptom of Noùs being so undefinable that it can easily contain Psyche as well as Physics. The Noùs is the intelligible reality. It is not computable, but it is definable. Unlike truth and knowledge or first person experience. The Noùs is intelligible, but why is it necessarily reality? I think that Gödel interpreted his own work in the former and you are interpreting it in the latter - doesn't mean you're wrong, but I agree with him if he thought the former, because Psyche doesn't make sense as a part of Noùs. That is too much ambiguous. The psyche is not really a part of the Noùs, which is still purely 3p. Cool, we agree. I see Psyche and Physics as the personal and impersonal presentations of sense, Machine think the same, with sense replaced by arithmetical truth. Except that the machine has to be confused and for her that truth is beyond definability, like sense. I don't think that Psyche can be strongly related to arithmetic truth. There are thematic associations, but I would say that they are by way of reflected Noùs. First person arithmetic truth is intuition of Noùs, and Noùs is alienated sense. The idea that confusion of truth would be necessary to transform quantitative rules into qualitative experiences seems to be a shaky premise at best. It smells like hasty reverse engineering to plug a major hole in comp. It creates an unacknowledged dualism between arithmetic truth/definitions and colorful/magic confusion of definition. and Noùs is the re-presentation of physics (meaning physics is re- personalized as abstract digital concepts). The Noùs has nothing to do with physics a priori. It is the world of the eternal platonic ideas, or God's ideas. I understand, yes. I place it here on the upper left (West) side:
Re: Minds, Machines and Gödel
On 22 Dec 2013, at 14:56, Craig Weinberg wrote: On Sunday, December 22, 2013 7:21:05 AM UTC-5, Bruno Marchal wrote: Mathematics is not enough for the mind and experience of ... the machines. i agree, of course, but how is that view compatible with computationalism? It prevents the use of the idea that mathematics is not enough to circumscribe the human mind, to be applied against mechanism. It means also that most proposition *about* machine, cannot be found in a mechanical way. The simplest examples are that no machine can decide if some arbitrary machine will stop not, or no machine can decide if two arbitrary machine compute or not the same function, etc. If there is no complete theories for machines and/or numbers, it makes harder to defend non-comp, etc. The issue though is whether that non-enumerablity is a symptom of the inadequacy of Noùs to contain Psyche, or a symptom of Noùs being so undefinable that it can easily contain Psyche as well as Physics. The Noùs is the intelligible reality. It is not computable, but it is definable. Unlike truth and knowledge or first person experience. The Noùs is intelligible, but why is it necessarily reality? It is the world of ideas, and with comp it is the world of universal numbers' idea, which rise up as a consequences of addition and multiplication. It splits into G and G* (but you need to study a bit of math for this). I think that Gödel interpreted his own work in the former and you are interpreting it in the latter - doesn't mean you're wrong, but I agree with him if he thought the former, because Psyche doesn't make sense as a part of Noùs. That is too much ambiguous. The psyche is not really a part of the Noùs, which is still purely 3p. Cool, we agree. I see Psyche and Physics as the personal and impersonal presentations of sense, Machine think the same, with sense replaced by arithmetical truth. Except that the machine has to be confused and for her that truth is beyond definability, like sense. I don't think that Psyche can be strongly related to arithmetic truth. There are thematic associations, but I would say that they are by way of reflected Noùs. First person arithmetic truth is intuition of Noùs, and Noùs is alienated sense. No problem. The intuition of truth comes from the fact that sometimes our beliefs are true. The Noùs is alienating us, as anything which is not personal consciousness. The Noùs is a gate to the others. The idea that confusion of truth would be necessary to transform quantitative rules into qualitative experiences seems to be a shaky premise at best. It smells like hasty reverse engineering to plug a major hole in comp. It creates an unacknowledged dualism between arithmetic truth/definitions and colorful/magic confusion of definition. The idea comes from Plato and notably the Theaetetus idea of defining knowledge by true belief. It works well. Socrate refuted the idea, but Gödel's incompleteness refutes Socrate's refutation of Theaetetus. Also, it is the only definition of knowledge which is coherent with the dream metaphysical argument, and thus with comp. This wold be long to be developed. All this is fully developed in conscience et mécanisme. and Noùs is the re-presentation of physics (meaning physics is re- personalized as abstract digital concepts). The Noùs has nothing to do with physics a priori. It is the world of the eternal platonic ideas, or God's ideas. I understand, yes. I place it here on the upper left (West) side: keep in mind the 8 hypostases: - p (truth, not definable in arithmetic, but emulable in some trivial sense) Instead of p being truth, p is just a symbolic way to represent truth. p alone means p is true, when asserted by a machine which is supposed to be correct by definition and choice. I see truth as a narrow intellectual sensitivity, not primordial. Truth encompasses everything. It is provably beyond anything intellectual. In the Plotinus/arithmetic lexicon: Arithmetical truth plays the role of the non nameable God of the machine. The primordial capacity to experience, from which comparisons and discernments can self-diverge *must* be more primitive than the notion of right and wrong or is-ness and may-not-be-ness. Before anything can 'be', there must be a the potential for a difference between being and non-being to be experienced. That difference is a quality, not a logic. The logic of the discernment I think must be second order - the primary quality of discernment is a sense of obstruction, a fork in the road which interrupts peace/solitude. Perhaps. - Bp (provable, believable, assumable, communicable). It splits into a communicable and non communicable part (some fact about communication are not communicable) Instead of belief or proof being primitive or ontological, Belief or proof are not primitive. They are
Re: Minds, Machines and Gödel
On Thursday, December 19, 2013 10:13:25 AM UTC-5, Bruno Marchal wrote: On 19 Dec 2013, at 15:07, Craig Weinberg wrote: On Thursday, December 19, 2013 5:23:20 AM UTC-5, Bruno Marchal wrote: Hello Craig, That is the very well known attempt by Lucas to use Gödel's theorem to refute mechanism. He was not the only one. Most people thinking about this have found the argument, and usually found the mistakes in it. To my knowledge Emil Post is the first to develop both that argument, and to understand that not only that argument does not work, but that the machines can already refute that argument, due to the mechanizability of the diagonalization, made very general by Church thesis. In fact either the argument is presented in an effective way, and then machine can refute it precisely, or the argument is based on some fuzziness, and then it proves nothing. If 'proof' is an inappropriate concept for first person physics, then I would expect that fuzziness would be the only symptom we can expect. The criticism of Lucas seems to not really understand the spirit of Gödel's theorem, but only focus on the letter of its application...which in the case of Gödel's theorem is precisely the opposite of its meaning. The link that Stathis provided demonstrates that Gödel himself understood this: So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified . . . (Gödel 1995: 310). To me it's clear that Gödel means that incompleteness reveals that mathematics is not completable OK. Even arithmetic. in the sense that it is not enough to contain the reality of human experience, ? He says the 'human mind', but I say human experience. not that it proves that mathematics or arithmetic truth is omniscient and omnipotent beyond our wildest dreams. Arithmetical truth is by definition arithmetically omniscient, but certainly not omniscient in general. Indeed to get the whole arithmetical Noùs, Arithmetical truth is still too much weak. All what Gödel showed is that arithmetical truth (or any richer notion of truth, like set theoretical, group theoretical, etc.) cannot be enumerated by machines or effective sound theories. The issue though is whether that non-enumerablity is a symptom of the inadequacy of Noùs to contain Psyche, or a symptom of Noùs being so undefinable that it can easily contain Psyche as well as Physics. I think that Gödel interpreted his own work in the former and you are interpreting it in the latter - doesn't mean you're wrong, but I agree with him if he thought the former, because Psyche doesn't make sense as a part of Noùs. I see Psyche and Physics as the personal and impersonal presentations of sense, and Noùs is the re-presentation of physics (meaning physics is re-personalized as abstract digital concepts). Physics is the commercialization of sense. Psyche is residential sense. Noùs is the hotel...commercialized residence. An excellent book has been written on that subject by Judson Webb (mechanism, mentalism and metamathematics, reference in the bibliographies in my URL, or in any of my papers). In conscience and mechanism, I show all the details of why the argument of Lucas is already refuted by Löbian machines, and Lucas main error is reduced to a confusion between Bp and Bp p. It is an implicit assumption, in the mind of Lucas and Penrose, of self-correctness, or self-consistency. To be sure, I found 49 errors of logic in Lucas' paper, but the main conceptual one is in that self-correctness assertion. Penrose corrected his argument, and understood that it proves only that if we are machine, we cannot know which machine we are, and that gives the math of the 1-indeterminacy, exploited in the arithmetical hypostases. Unfortunately, Penrose did not take that correction into account. Gödel's theorem and Quantum Mechanics could not have been more pleasing for the comp aficionado. Gödel's theorem (+UDA) shows that machine have a rich non trivial theology including physics, and QM confirms the most startling points of the comp physics. As far as QM goes, it would not surprise me in the least that a formal system based on formal measurements is only able to consider itself and fails to locate the sensory experience or the motive 'power on' required to formalize them in the first place. They don't address that question. Formal systems are seen as mathematical object, even number, and they exist independently of us, if you still accept arithmetical realism. I accept the realism of arithmetic representation, and that they
Re: Minds, Machines and Gödel
Reality is analogous to a running software program. Godel's Theorem does not apply. A human could speculate as to whether any particular state of Reality could ever arise computationally and it might be impossible to determine that, but again that has nothing to do with the actual operation of Reality,since it is only a particular internal mental model of that reality. Wouldn't that make reality susceptible to the halting problem? ...hello, is anybody there? Why have all the stars gone out? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
On 20 Dec 2013, at 01:01, LizR wrote: On 20 December 2013 11:40, meekerdb meeke...@verizon.net wrote: On 12/19/2013 1:30 PM, Jesse Mazer wrote: To me it seems like thinking something is true is much more of a fuzzy category that asserting something is true Maybe. But note that Bruno's MGA is couched in terms of a dream, just to avoid any input/output. That seems like a suspicious move to me; one that may lead intuition astray. I seem to recall that Bruno claimed this is a legal move because any possible input/output can be encoded as data within the computation (or something along those lines. Yes. Eventually it comes to decide what is your generalized brain. If you need the entire physical universe, with 10^100 decimals, that will change nothing in the reasoning, because in step seven, your state will still be accessed. Of course, the entire physical universe also has no input nor output (by definition of entire). For the six first steps, it is easier to assume some high substitution (neuronal) for the thought experiment. Then in step 7, this high level assumption is eliminated. No doubt Bruno will be able to explain much better than me). I have tried to talk in English. Now the fact that we can put the input in the code is a fundamental theorem for the universal system, know as the SMN theorems. In terms of the phi_i it means that there is one function S of two arguments with phi_i(x) = phi_S(x, 4)() (S10) or phi_i (4, y, z) = phi_S(x, 4) (y, z) (S32) The meta-program S take the input (4), and put it in the code, and suppress one variable. For example S(4, READ x, READ y, output x + y) = Read Y, output 4 + y. S is really a substitution. S is a program, so it exists a number s such that S = phi_s. You can use this to see that we can write the SMN theorems with quantifying only on numbers. The whole of recursion theory can be based axiomatically on the two axioms: - SMN theorem (here an axiom, provable for all reasonable programming languages, or universal system) - It exists u such that phi_i(x) = phi_u(i, x) (existence of a universal number) (again provable for each individual programming language). The universal function u computes phi_i(x), for any program i and any data x. But I guess that here, I do not explain better than you, as I use notation, which frighten the beginners or the non mathematicians. Yet, we need the SMN theorem to explain the Dx = xx method (to define self-reference in arithmetic) in terms of the phi_i and the w_i (which I promised to do for you!) But we might need to revise a bit those phi_i and w_i perhaps, but then I don't want to annoy you with too much technic either. What do you think? Also we started this on the FOAR list, would you like to continue this, and on which list? Take it easy. I know we are in an end of the year feast period :) Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
A nice exposition, Jesse. But it bothers me that it seems to rely on the idea of output and a kind of isolation like invoking a meta-level. What if instead of Craig Weinberg will never in his lifetime assert that this statement is true we considered Craig Weinberg will never in his lifetime think that this statement is true? Then it seems that one invokes a kind of paraconsistent logic in which one just refuses to draw any inferences from this sentence that one cannot think either true or false. Brent On 12/19/2013 8:08 AM, Jesse Mazer wrote: The argument only works if you assume from the beginning that an A.I. is unconscious or doesn't have the same sort of mind as a human (and given your views you probably do presuppose these things--but if the conclusion *requires* such presuppositions, then it's an exercise in circular reasoning). If you are instead willing to consider that an A.I. mind works basically like a human mind (including things like being able to make mistakes, and being able to understand things it doesn't say out loud), and are willing to put yourself in the place of an A.I. being faced with its own Godel statement, then you can see it's like a more formal equivalent of me asking you to evaluate the statement Craig Weinberg will never in his lifetime assert that this statement is true. You can understand that if you *did* assert that it's true, that would of course make it false, but you can likewise understand that as long as you try to refrain from uttering any false statements including that one, it *will* end up being true. Similarly, an A.I. who is capable of making erroneous statements, and of understanding things distinct from its output to the world outside the program, might well understand that its own Godel statement is true--provided it never outputs a formal judgment that the statement is true, which would mean it's false! So if the A.I. in fact avoided ever giving as output a judgment about that the statement is true, it need not be because it lacks an understanding of what's going on, but rather just because it's caught in a bind similar to the one you're caught in with Craig Weinberg will never in his lifetime assert that this statement is true. To flesh this out a bit, imagine a community of human-like A.I. mathematicians (mind uploads, say), living in a self-contained simulated world with no input from the outside, who have the ability to reflect on various arithmetical propositions. Once there is a consensus in this community that a proposition has been proven true or false, they can go to a special terminal (call it the output terminal) and enter it on the list of proven statements, which will constitute the simulation's output to those of us watching it run in the real world. Suppose also that the simulated world is constantly growing, and that they have an internal simulated supercomputer within their world to help with their mathematical investigations, and this supercomputer is constantly growing in memory too. So if we imagine a string encoding the *initial* state of the simulation along with the rules determining its evolution, although this string may be very large, after some time has passed the memory of the simulated supercomputer will be much larger than that, so it's feasible to have this string appear within the supercomputer's memory (and it's part of the rules of the simulation that the string automatically appears in the supercomputer's memory after some finite time T within the simulation, and all the A.I. mathematicians knew that this was scheduled to happen). Once the A.I. mathematicians have the program's initial conditions and the rules governing subsequent evolution, they can construct their own Godel statement. Of course they can never really be sure that the string they are given correctly describes the true initial conditions of their own simulated universe, but let's say they have a high degree of trust that it is--for example, they might be mind uploads of the humans who designed the original simulation, and they remember having designed it to ensure that the string that would appear in the supercomputer's memory is the correct one. They could even use the growing supercomputer to run a simulation-within-the-simulation of their own history, starting from those initial conditions--the sub-simulation would always lag behind what they were experiencing, but they could continually verify that the events in the sub-simulation matched their historical records and memories up to some point in the past. So, they have a high degree of confidence that the Godel statement they've constructed actually is the correct one for their own simulated universe. They can therefore interpret the conceptual meaning of the statement as something like you guys living in the simulation will never enter into your output terminal a judgment that this statement is true. So they could understand perfectly
Re: Minds, Machines and Gödel
To me it seems like thinking something is true is much more of a fuzzy category that asserting something is true (even assertions can be ambiguous when stated in natural language, but they can be made non-fuzzy by requiring that each assertion be framed in terms of some formal language and entered into a computer, as in my thought-experiment). Is there any exact point where you cross between categories like being completely unsure whether it's true and having a strong hunch it's true and having an argument in mind that it's true but not feeling completely sure there isn't a flaw in the reasoning and being as confident as you can possibly be that it's true? I never really feel *absolute* certainty that anything I think is true, even basic arithmetical statements like 1+1=2, because I'm aware of how I've sometimes made sloppy mistakes in thinking in the past, and because I know intelligent people can seem to come to incorrect conclusions about basic ideas when hypnotized, or when dreaming (like the logic of various characters in Alice in Wonderland). I think of certain truth as being like an asymptote that an individual or community of thinkers can continually get closer to but never quite reach. If I consider the statement Jesse Mazer will never think this statement is true, I may imagine the perspective of someone else and see that from their perspective it must be true if Jesse's thinking is trustworthy, but then I'll catch myself and see that this imaginary perspective is really just a thought in Jesse's head--at that point, have I had the thought that it's true? And at some point in considering it I can't really help thinking some words along the lines of oh, so then it *is* true (it's hard to avoid thinking something you know you are forbidden to think, like when someone tells you don't think of an elephant), but is merely thinking the magic words enough to count as having thought it's true, and therefore having made it false once and for all? Jesse On Thu, Dec 19, 2013 at 3:46 PM, meekerdb meeke...@verizon.net wrote: A nice exposition, Jesse. But it bothers me that it seems to rely on the idea of output and a kind of isolation like invoking a meta-level. What if instead of Craig Weinberg will never in his lifetime assert that this statement is true we considered Craig Weinberg will never in his lifetime think that this statement is true? Then it seems that one invokes a kind of paraconsistent logic in which one just refuses to draw any inferences from this sentence that one cannot think either true or false. Brent On 12/19/2013 8:08 AM, Jesse Mazer wrote: The argument only works if you assume from the beginning that an A.I. is unconscious or doesn't have the same sort of mind as a human (and given your views you probably do presuppose these things--but if the conclusion *requires* such presuppositions, then it's an exercise in circular reasoning). If you are instead willing to consider that an A.I. mind works basically like a human mind (including things like being able to make mistakes, and being able to understand things it doesn't say out loud), and are willing to put yourself in the place of an A.I. being faced with its own Godel statement, then you can see it's like a more formal equivalent of me asking you to evaluate the statement Craig Weinberg will never in his lifetime assert that this statement is true. You can understand that if you *did* assert that it's true, that would of course make it false, but you can likewise understand that as long as you try to refrain from uttering any false statements including that one, it *will* end up being true. Similarly, an A.I. who is capable of making erroneous statements, and of understanding things distinct from its output to the world outside the program, might well understand that its own Godel statement is true--provided it never outputs a formal judgment that the statement is true, which would mean it's false! So if the A.I. in fact avoided ever giving as output a judgment about that the statement is true, it need not be because it lacks an understanding of what's going on, but rather just because it's caught in a bind similar to the one you're caught in with Craig Weinberg will never in his lifetime assert that this statement is true. To flesh this out a bit, imagine a community of human-like A.I. mathematicians (mind uploads, say), living in a self-contained simulated world with no input from the outside, who have the ability to reflect on various arithmetical propositions. Once there is a consensus in this community that a proposition has been proven true or false, they can go to a special terminal (call it the output terminal) and enter it on the list of proven statements, which will constitute the simulation's output to those of us watching it run in the real world. Suppose also that the simulated world is constantly growing, and that they have an internal simulated supercomputer
Re: Minds, Machines and Gödel
On 12/19/2013 1:30 PM, Jesse Mazer wrote: To me it seems like thinking something is true is much more of a fuzzy category that asserting something is true Maybe. But note that Bruno's MGA is couched in terms of a dream, just to avoid any input/output. That seems like a suspicious move to me; one that may lead intuition astray. Brent (even assertions can be ambiguous when stated in natural language, but they can be made non-fuzzy by requiring that each assertion be framed in terms of some formal language and entered into a computer, as in my thought-experiment). Is there any exact point where you cross between categories like being completely unsure whether it's true and having a strong hunch it's true and having an argument in mind that it's true but not feeling completely sure there isn't a flaw in the reasoning and being as confident as you can possibly be that it's true? I never really feel *absolute* certainty that anything I think is true, even basic arithmetical statements like 1+1=2, because I'm aware of how I've sometimes made sloppy mistakes in thinking in the past, and because I know intelligent people can seem to come to incorrect conclusions about basic ideas when hypnotized, or when dreaming (like the logic of various characters in Alice in Wonderland). I think of certain truth as being like an asymptote that an individual or community of thinkers can continually get closer to but never quite reach. If I consider the statement Jesse Mazer will never think this statement is true, I may imagine the perspective of someone else and see that from their perspective it must be true if Jesse's thinking is trustworthy, but then I'll catch myself and see that this imaginary perspective is really just a thought in Jesse's head--at that point, have I had the thought that it's true? And at some point in considering it I can't really help thinking some words along the lines of oh, so then it *is* true (it's hard to avoid thinking something you know you are forbidden to think, like when someone tells you don't think of an elephant), but is merely thinking the magic words enough to count as having thought it's true, and therefore having made it false once and for all? Jesse On Thu, Dec 19, 2013 at 3:46 PM, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: A nice exposition, Jesse. But it bothers me that it seems to rely on the idea of output and a kind of isolation like invoking a meta-level. What if instead of Craig Weinberg will never in his lifetime assert that this statement is true we considered Craig Weinberg will never in his lifetime think that this statement is true? Then it seems that one invokes a kind of paraconsistent logic in which one just refuses to draw any inferences from this sentence that one cannot think either true or false. Brent On 12/19/2013 8:08 AM, Jesse Mazer wrote: The argument only works if you assume from the beginning that an A.I. is unconscious or doesn't have the same sort of mind as a human (and given your views you probably do presuppose these things--but if the conclusion *requires* such presuppositions, then it's an exercise in circular reasoning). If you are instead willing to consider that an A.I. mind works basically like a human mind (including things like being able to make mistakes, and being able to understand things it doesn't say out loud), and are willing to put yourself in the place of an A.I. being faced with its own Godel statement, then you can see it's like a more formal equivalent of me asking you to evaluate the statement Craig Weinberg will never in his lifetime assert that this statement is true. You can understand that if you *did* assert that it's true, that would of course make it false, but you can likewise understand that as long as you try to refrain from uttering any false statements including that one, it *will* end up being true. Similarly, an A.I. who is capable of making erroneous statements, and of understanding things distinct from its output to the world outside the program, might well understand that its own Godel statement is true--provided it never outputs a formal judgment that the statement is true, which would mean it's false! So if the A.I. in fact avoided ever giving as output a judgment about that the statement is true, it need not be because it lacks an understanding of what's going on, but rather just because it's caught in a bind similar to the one you're caught in with Craig Weinberg will never in his lifetime assert that this statement is true. To flesh this out a bit, imagine a community of human-like A.I. mathematicians (mind uploads, say), living in a self-contained simulated world with no input
Re: Minds, Machines and Gödel
On 20 December 2013 11:40, meekerdb meeke...@verizon.net wrote: On 12/19/2013 1:30 PM, Jesse Mazer wrote: To me it seems like thinking something is true is much more of a fuzzy category that asserting something is true Maybe. But note that Bruno's MGA is couched in terms of a dream, just to avoid any input/output. That seems like a suspicious move to me; one that may lead intuition astray. I seem to recall that Bruno claimed this is a legal move because any possible input/output can be encoded as data within the computation (or something along those lines. No doubt Bruno will be able to explain much better than me). -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
If this is a proof of the falsity of mechanism, is there any chance of a precis? :-) -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: Minds, Machines and Gödel
On 19 December 2013 08:32, LizR lizj...@gmail.com wrote: If this is a proof of the falsity of mechanism, is there any chance of a precis? :-) The argument has been restated with elaboration by Penrose, and has been extensively criticised. http://www.iep.utm.edu/lp-argue/ -- Stathis Papaioannou -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
