Re: The relative point of view
On 09 Feb 2011, at 20:29, Brent Meeker wrote: snip On 2/9/2011 8:02 AM, Bruno Marchal wrote: I define then knowledge, following Theaetetus by the true opinion (Bp p), You've never said what your answer is to Gettier's example. I did it, the saturday 29 Jan 2011, according to my computer. Let me paste it again. It is probably too short. I have a full chapter on this in Conscience et Mécanisme. Tell me if you see the point, or if I should make it clearer: quote: Apes fetus can dream climbing trees but they do that with ancestors climbing the most probable trees of their most probable neighborhoods since a long period. With classical mechanism, I would say, that to know is to believe p when luckily p is true, So what is your response to Gettier's problem? [Brent Meeker] The answer is that, with comp, we cannot distinguish reality from dream. We can know that we are dreaming (sometimes), but we cannot ever know for sure in a public way that we are awaken. Another fact related to this is that knowledge, consciousness and truth are not machine-definable. If we are machine, we can use those notion in theoretical context only. In practice, as real life illustrates very often, we never know as such that we know. We belief we know, until we know better. The SAGrz logics is a logical tour de force. Here Gödel's theorem gives sense to Theaetetus. S4Grz, the logic of (Bp p) formalizes a notion which is not even nameable by the machine, unless she postulates comp and relies explicitly on that postulate, or better, relies on the study of a simpler than herself machine. In science, or in public, we never know, as such. Knowing is a pure first person notion. But this does not mean that we cannot make 3-theory on such pure first person notion, as S4Grz illustrates particularly well. Same remarks for feelings (Bp Dt p). Bruno http://iridia.ulb.ac.be/~marchal/ Hmmm? I guess I thought you hadn't answered because I don't grasp the relevance of your answer. Gettier points out that one can believe a true statement for reasons that have nothing to do with what makes the statement true. It is a very old argument. It is usually presented with dreams. In Conscience et mécanisme (CM), I give this version: a person is asleep in a flying plane, and dreams that he is flying. The Theaetetical definition of knowledge forces us to say that he knows that he is flying, despite the wrong reason. The answer is that this is an intrinsic defect of the notion of knowledge, and unless you believe that you can distinguish I am awaken from dreaming, there is no means to ever develop a notion of knowledge not having that problem. So the critics of the Theatetical definition of knowledge is based on the (admittedly strong feeling) that we can know that we are not dreaming. But I show that both comp, and experimental neurophysiology entails the existence of contralucid dreams (as I define them in CM). Some drugs can also lead to contralucidity, apparently. In his example Bob buys a new car which is blue, but while waiting for the car to be delivered he borrows a car which also happens to be blue. Jim sees Bob driving this car and believes that Bob has bought a new car which is blue. It is a true belief, but only by accident. So it seems that there is a difference between true belief and knowledge. It seems, only. Gettier proposes that the true belief must be causally connected to the fact that makes it true in order to count as knowledge. If such causal connection exist, then comp has to be false. The analogy in arithmetic would be to believe something, like Goldbach's conjecture, which may be true but is unprovable. I guess you mean: might be unprovable. OK. To sum up: those, like Gettier, who criticizes the true-belief as knowledge, does believe in a magical (non Turing emulable) connection between mind and some reality. My point is that such connection is incompatible with comp, and is hard to sustain with the idea of dreams, perfect video-game, and many things made possible in the comp theory. There is always a part of serendipity in the knowing phenomenon, if comp is correct. The only thing which can be known and known as such is consciousness here and now. All the rest are beliefs, well or badly justified, and sometimes true, but we can never be sure on them. It is almost obvious if you realize that with comp, knowledge in a constructed mental state. 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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: The relative point of view
On 08 Feb 2011, at 21:08, Brent Meeker wrote: On 2/8/2011 8:47 AM, Bruno Marchal wrote: On 07 Feb 2011, at 20:52, Andrew Soltau wrote: (Is the 'intensional' referred to here the 'attach' you used in another email?) Not really, although it is related. Intensional refers to the fact that if you define a provable(x) by beweisbar(x) and x', where x' denote the proposition which has x as Gôdel number, you define a probability predicate, You mean provability predicate don't you? Yes I mean provability. It is unfortunate that the v and b are so close on my keyboard. I also apologies for my many spelling mistakes and my style which can go very bad when I have to answer many posts, at time where time is a bit missing ... Given that you are defining 8 basic points of view in the abstract, applied to intensional variants of the current provability predicate of the machine with or without some oracle, it sounds a bit, well, abstract. Could you be a bit more specific? I try to be more specific in sane04. May be we should start from that. Or search hypostasis or hypostases in the archive, or guardian angel, etc. Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993). Read perhaps the Theaetetus by Plato. In short you can say that I model belief or opinion by formal probability (Bp). You mean formal provability? Mind your ps and vs. :-) You mean my bs and vs, I guess :-) Yes, again I meant formal provability. That error is annoying because, if Bp, is a shorthand for provability(p), Bp Dp plays the role of a formal probability (yes, with a b), indeed probability 1, or maximal credibility. I'm really sorry. I define then knowledge, following Theaetetus by the true opinion (Bp p), You've never said what your answer is to Gettier's example. I did it, the saturday 29 Jan 2011, according to my computer. Let me paste it again. It is probably too short. I have a full chapter on this in Conscience et Mécanisme. Tell me if you see the point, or if I should make it clearer: quote: Apes fetus can dream climbing trees but they do that with ancestors climbing the most probable trees of their most probable neighborhoods since a long period. With classical mechanism, I would say, that to know is to believe p when luckily p is true, So what is your response to Gettier's problem? [Brent Meeker] The answer is that, with comp, we cannot distinguish reality from dream. We can know that we are dreaming (sometimes), but we cannot ever know for sure in a public way that we are awaken. Another fact related to this is that knowledge, consciousness and truth are not machine-definable. If we are machine, we can use those notion in theoretical context only. In practice, as real life illustrates very often, we never know as such that we know. We belief we know, until we know better. The SAGrz logics is a logical tour de force. Here Gödel's theorem gives sense to Theaetetus. S4Grz, the logic of (Bp p) formalizes a notion which is not even nameable by the machine, unless she postulates comp and relies explicitly on that postulate, or better, relies on the study of a simpler than herself machine. In science, or in public, we never know, as such. Knowing is a pure first person notion. But this does not mean that we cannot make 3- theory on such pure first person notion, as S4Grz illustrates particularly well. Same remarks for feelings (Bp Dt p). 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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: The relative point of view
On 2/9/2011 8:02 AM, Bruno Marchal wrote: On 08 Feb 2011, at 21:08, Brent Meeker wrote: On 2/8/2011 8:47 AM, Bruno Marchal wrote: On 07 Feb 2011, at 20:52, Andrew Soltau wrote: (Is the 'intensional' referred to here the 'attach' you used in another email?) Not really, although it is related. Intensional refers to the fact that if you define a provable(x) by beweisbar(x) and x', where x' denote the proposition which has x as Gôdel number, you define a probability predicate, You mean provability predicate don't you? Yes I mean provability. It is unfortunate that the v and b are so close on my keyboard. I also apologies for my many spelling mistakes and my style which can go very bad when I have to answer many posts, at time where time is a bit missing ... Given that you are defining 8 basic points of view in the abstract, applied to intensional variants of the current provability predicate of the machine with or without some oracle, it sounds a bit, well, abstract. Could you be a bit more specific? I try to be more specific in sane04. May be we should start from that. Or search hypostasis or hypostases in the archive, or guardian angel, etc. Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993). Read perhaps the Theaetetus by Plato. In short you can say that I model belief or opinion by formal probability (Bp). You mean formal provability? Mind your ps and vs. :-) You mean my bs and vs, I guess :-) Yes, again I meant formal provability. That error is annoying because, if Bp, is a shorthand for provability(p), Bp Dp plays the role of a formal probability (yes, with a b), indeed probability 1, or maximal credibility. I'm really sorry. I define then knowledge, following Theaetetus by the true opinion (Bp p), You've never said what your answer is to Gettier's example. I did it, the saturday 29 Jan 2011, according to my computer. Let me paste it again. It is probably too short. I have a full chapter on this in Conscience et Mécanisme. Tell me if you see the point, or if I should make it clearer: quote: Apes fetus can dream climbing trees but they do that with ancestors climbing the most probable trees of their most probable neighborhoods since a long period. With classical mechanism, I would say, that to know is to believe p when luckily p is true, So what is your response to Gettier's problem? [Brent Meeker] The answer is that, with comp, we cannot distinguish reality from dream. We can know that we are dreaming (sometimes), but we cannot ever know for sure in a public way that we are awaken. Another fact related to this is that knowledge, consciousness and truth are not machine-definable. If we are machine, we can use those notion in theoretical context only. In practice, as real life illustrates very often, we never know as such that we know. We belief we know, until we know better. The SAGrz logics is a logical tour de force. Here Gödel's theorem gives sense to Theaetetus. S4Grz, the logic of (Bp p) formalizes a notion which is not even nameable by the machine, unless she postulates comp and relies explicitly on that postulate, or better, relies on the study of a simpler than herself machine. In science, or in public, we never know, as such. Knowing is a pure first person notion. But this does not mean that we cannot make 3-theory on such pure first person notion, as S4Grz illustrates particularly well. Same remarks for feelings (Bp Dt p). Bruno http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/ Hmmm? I guess I thought you hadn't answered because I don't grasp the relevance of your answer. Gettier points out that one can believe a true statement for reasons that have nothing to do with what makes the statement true. In his example Bob buys a new car which is blue, but while waiting for the car to be delivered he borrows a car which also happens to be blue. Jim sees Bob driving this car and believes that Bob has bought a new car which is blue. It is a true belief, but only by accident. So it seems that there is a difference between true belief and knowledge. Gettier proposes that the true belief must be causally connected to the fact that makes it true in order to count as knowledge. The analogy in arithmetic would be to believe something, like Goldbach's conjecture, which may be true but is unprovable. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: The relative point of view
On 07 Feb 2011, at 20:52, Andrew Soltau wrote: How do you define the relative point of view? Do you know Gödel's provability predicate? The points of view are defined by intensional variants of the current provability predicate of the machine with or without some oracle. There are 8 basic points of view p (truth), Bp (provability/believability), Bp p (knowability), Bp Dp (observability), Bp Dp p (sensibility/feelability). Three of them inherits the G/G* splitting, making a total of 8. It is really 4 + 4*infinity, because the 'material points of view' (with Dp) admits themselves graded variants. I know *about* Gödel's provability predicate! Good. (Is the 'intensional' referred to here the 'attach' you used in another email?) Not really, although it is related. Intensional refers to the fact that if you define a provable(x) by beweisbar(x) and x', where x' denote the proposition which has x as Gôdel number, you define a probability predicate, which is not definable by the machine, or in arithmetic, yet proves exactly the same proposition of arithmetic than the one provable. Provable(x) and beweisbar(x) are intensional variant of provability. They are extensionnally equivalent, but intensionnally different, a bit like different algorithm can have the same behavior. More simple beweisbar(x) ~beweisbar(~x) is an intensional variant of beweisbar(x). Intensional variant of bewesibar(x) have been introduced by Rosser in his elimination of Gödel's assumption of omega-completeness in the proof of incompleteness of formal systems. I am still no clearer about how you define the machine, with or without some oracle, and what defines the relative point of view. Oracle have been introduced by Turing for the study of the degree of unsolvability. It is a package of usually infinite information, typically not computable. The halting oracle provides the halting information, that no computer can generate. The goal consisted in showing that some problem remains non solvable, and that some function remains uncomputable, even when powerful oracle are added, and this has been used to study the degrees of unsolvability of arithmetical and mathematical problems. The UD generate all the oracles, like it dovetails on all the reals (trivial exercise; yet people are often wrong on this because they confuse the impossibility of enumerating the reals, with the impossibility of generating them). Think about the iterated self- duplication experiment. Given that you are defining 8 basic points of view in the abstract, applied to intensional variants of the current provability predicate of the machine with or without some oracle, it sounds a bit, well, abstract. Could you be a bit more specific? I try to be more specific in sane04. May be we should start from that. Or search hypostasis or hypostases in the archive, or guardian angel, etc. Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993). Read perhaps the Theaetetus by Plato. In short you can say that I model belief or opinion by formal probability (Bp). I define then knowledge, following Theaetetus by the true opinion (Bp p), observation by the consistent opinion (Bp Dp), and sensibility by the true consistent opinion (Bp Dp p). Incompleteness motivates the initial model, even if it leads to a restriction on the ideally correct machine. The whole thing provides an arithmetical interpretation of Plotinus theory of the one, the intellect and the soul + his double (intelligible and sensible) matter theory. The arithmetical matter theory has been compared to the current inferred theory of matter, and it looks, up to now, that Nature is correct :) (correct with respect to comp and its neoplatonist rendering, for sure). 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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: The relative point of view
On 2/8/2011 8:47 AM, Bruno Marchal wrote: On 07 Feb 2011, at 20:52, Andrew Soltau wrote: How do you define the relative point of view? Do you know Gödel's provability predicate? The points of view are defined by intensional variants of the current provability predicate of the machine with or without some oracle. There are 8 basic points of view p (truth), Bp (provability/believability), Bp p (knowability), Bp Dp (observability), Bp Dp p (sensibility/feelability). Three of them inherits the G/G* splitting, making a total of 8. It is really 4 + 4*infinity, because the 'material points of view' (with Dp) admits themselves graded variants. I know *about* Gödel's provability predicate! Good. (Is the 'intensional' referred to here the 'attach' you used in another email?) Not really, although it is related. Intensional refers to the fact that if you define a provable(x) by beweisbar(x) and x', where x' denote the proposition which has x as Gôdel number, you define a probability predicate, You mean provability predicate don't you? which is not definable by the machine, or in arithmetic, yet proves exactly the same proposition of arithmetic than the one provable. Provable(x) and beweisbar(x) are intensional variant of provability. They are extensionnally equivalent, but intensionnally different, a bit like different algorithm can have the same behavior. More simple beweisbar(x) ~beweisbar(~x) is an intensional variant of beweisbar(x). Intensional variant of bewesibar(x) have been introduced by Rosser in his elimination of Gödel's assumption of omega-completeness in the proof of incompleteness of formal systems. I am still no clearer about how you define the machine, with or without some oracle, and what defines the relative point of view. Oracle have been introduced by Turing for the study of the degree of unsolvability. It is a package of usually infinite information, typically not computable. The halting oracle provides the halting information, that no computer can generate. The goal consisted in showing that some problem remains non solvable, and that some function remains uncomputable, even when powerful oracle are added, and this has been used to study the degrees of unsolvability of arithmetical and mathematical problems. The UD generate all the oracles, like it dovetails on all the reals (trivial exercise; yet people are often wrong on this because they confuse the impossibility of enumerating the reals, with the impossibility of generating them). Think about the iterated self-duplication experiment. Given that you are defining 8 basic points of view in the abstract, applied to intensional variants of the current provability predicate of the machine with or without some oracle, it sounds a bit, well, abstract. Could you be a bit more specific? I try to be more specific in sane04. May be we should start from that. Or search hypostasis or hypostases in the archive, or guardian angel, etc. Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993). Read perhaps the Theaetetus by Plato. In short you can say that I model belief or opinion by formal probability (Bp). You mean formal provability? Mind your ps and vs. :-) I define then knowledge, following Theaetetus by the true opinion (Bp p), You've never said what your answer is to Gettier's example. Brent observation by the consistent opinion (Bp Dp), and sensibility by the true consistent opinion (Bp Dp p). Incompleteness motivates the initial model, even if it leads to a restriction on the ideally correct machine. The whole thing provides an arithmetical interpretation of Plotinus theory of the one, the intellect and the soul + his double (intelligible and sensible) matter theory. The arithmetical matter theory has been compared to the current inferred theory of matter, and it looks, up to now, that Nature is correct :) (correct with respect to comp and its neoplatonist rendering, for sure). 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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
The relative point of view
How do you define the relative point of view? Do you know Gödel's provability predicate? The points of view are defined by intensional variants of the current provability predicate of the machine with or without some oracle. There are 8 basic points of view p (truth), Bp (provability/believability), Bp p (knowability), Bp Dp (observability), Bp Dp p (sensibility/feelability). Three of them inherits the G/G* splitting, making a total of 8. It is really 4 + 4*infinity, because the 'material points of view' (with Dp) admits themselves graded variants. I know *about* Gödel's provability predicate! (Is the 'intensional' referred to here the 'attach' you used in another email?) I am still no clearer about how you define the machine, with or without some oracle, and what defines the relative point of view. Given that you are defining 8 basic points of view in the abstract, applied to intensional variants of the current provability predicate of the machine with or without some oracle, it sounds a bit, well, abstract. Could you be a bit more specific? -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
