RITSIAR (was Numbers, Machine and Father Ted)
Le 02-nov.-06, à 17:34, David Nyman a écrit : Bruno Marchal wrote: I don't understand really what you mean by AUDA is not RITSIAR. AUDA is just the lobian interview, or if you prefer the complete mathematical formalization of the UDA reasoning. In some sense you can interpret it as the eventual elimination of the yes doctor hypothesis in the UDA argument (but here I do simplify a little bit). Yes, sorry, perhaps I should have said 'if number is not RITSIAR, is anything?' The intention behind the question is to find out how and where you would apply RITSIAR in your schema - if at all - because Peter has been willing to do this but you haven't. I just want to know why. I recall RITSIAR = Real In The Same Sense That I Am Real (introduced by Peter). Now, the notion of existence is very difficult, and the notion of personal existence is still more difficult, and was the object of the debate. Take the expression I am real. Does it mean I am real and this is something I cannot doubt about, in which case I refer to the first person, or is it my physical body is real, in which case it refers to a third person description of I based on some theory (for example physics, or comp, etc.). So RITSIAR is an highly ambiguous which presuppose many points we were arguing about. Let me try shortly to make it less ambiguous in the frame of the AUDA. Now I cannot be 100% rigorous without being long and boring, so I ask you some indulgence, and I am just trying to convey the idea. As you know I am realist or platonist about numbers and their arithmetical relations. For example I believe in theorem like all numbers can be written as a sum of four square (Lagrange theorem). I take such a truth as being completely independent of me, you, time, place. I take such truth as being primitive and beyond time and space, a-physical if you want. Now I also believe in 1-persons, or souls, etc. I am not a solipsist, and I really believe in my own current experience, but also in yours even if I am currently feeling them differently. I don't believe at all that a first person experience is a number, nor do I believe any first person can believe to be a number. Still, I assume comp, so there must be a relation between 1-person experience and numbers. Indeed persons can manifest themselves relatively to me when they are related to some computations (brain activity with comp and some high substitution level for making things simple). Those computations define or are defined by complex set of counterfactuals, and UDA shows that physics emerge or should emerge (with comp) from their structure. It is plausible because quantum logic can already be seen as a logic of counterfactuals. How to get them, and what the results will say for RITSIAR ? Let me give you all the person point of views (pov), that is the complete science and theology of a simple lobian machine like PA (Peano Arithmetic). It is a fact that if M1 and M2 are lobian machine, and if M2 has stronger provability abilities than M1, then M2 can prove both the science and the theology of M1. But NO lobian machine can prove its own theology without becoming inconsistent, they can only abductively infer their own theology: 0-person pov = arithmetical truth. This can be shown ineffable or non definable by the machine (Tarski theorem). In the arithmetical interpretation of Plotinus' TOE, it corresponds to the ONE. It is the big unameable entity at the origin of all forms of existence. 3-person pov = arithmetical provability. It is the self-referential godelian provability predicate. The fundamental thing here is that the incompleteness phenomenon splits it into two parts, each of which are captured by a modal logic: G and G* respectively. G captures what the machine can prove about herself, and G* captures in addition what is true about the machine but unprovable by the machine (like self-consistency for example). G axiomatizes the self-referentially correct science of the machine, and G* minus G axiomatizes the correct theology that the machine can infer without proving (its hope-space if you want). In the arithmetical interpretation of Plotinus' TOE, it corresponds to the INTELLECT. Terrestrial or discursive = G, divine = G*. Please note that G and G* capture self-referentially correct *3-person* statements, like someone talking about his own brain with his doctor. It is I with I = my 3-description of my body. It is not the I with I = my soul, or my experiences ... The 1-person point of view. I identify him/it/her with the incorrigible knower. By Godel's second incompleteness theorem, no correct machine can prove its own incorrigibility. But that fact makes it possible to define the knower by making the explicit conjunction of truth and provability, for example by defining a new modal connector like Kp = Bp p. This is what actually Theaetetus has proposed to Socrates when Socrates asked him to define
Re: Zuse Symposium: Is the universe a computer? Berlin Nov 6-7
Marc, I do not argue with 'your half' of the 'answer' you gave to the conference announcement of Jürgen Schm , I just ask for the 'other part': what should we call a computer? 'Anything' doing Comp? (meaning: whatever is doing it)? Will the conference be limited to that technically embryonic gadget - maybe even on a binary bases - we use with that limited software-input in 2006? a Turing machine? John M - Original Message - From: [EMAIL PROTECTED] To: Everything List everything-list@googlegroups.com Sent: Thursday, November 02, 2006 10:09 PM Subject: Re: Zuse Symposium: Is the universe a computer? Berlin Nov 6-7 Ah the famous Juergen Schmidhuber! :) Is the universe a computer. Well, if you define 'universe' to mean 'everything which exists' and you're a mathematical platonist and grant reality to infinite sets and uncomputables, the answer must be NO, since if uncomputable numbers are objectively real (strong platonism) they are 'things' and therefore 'part of the universe' which are by definition not computable. But if by 'universe' you just mean 'physical reality' or 'discrete mathematics' or you refuse to grant platonic reality to uncomputables or infinite sets (anti-platonism or weaker platonism) then the answer could be YES, the universe is a computer. Cheers! --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Zuse Symposium: Is the universe a computer? Berlin Nov 6-7
uncompoutable numbers, non countable sets etc. don't exist in first order logic, see here: http://www.earlham.edu/~peters/courses/logsys/low-skol.htm [EMAIL PROTECTED] [EMAIL PROTECTED]: Ah the famous Juergen Schmidhuber! :) Is the universe a computer. Well, if you define 'universe' to mean 'everything which exists' and you're a mathematical platonist and grant reality to infinite sets and uncomputables, the answer must be NO, since if uncomputable numbers are objectively real (strong platonism) they are 'things' and therefore 'part of the universe' which are by definition not computable. But if by 'universe' you just mean 'physical reality' or 'discrete mathematics' or you refuse to grant platonic reality to uncomputables or infinite sets (anti-platonism or weaker platonism) then the answer could be YES, the universe is a computer. Cheers! --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Zuse Symposium: Is the universe a computer? Berlin Nov 6-7
It is not a question of existence but of definability. For example you can define and prove (by Cantor diagonalization) the existence of uncountable sets in ZF which is a first order theory of sets. Now uncountability is not an absolute notion (that is the Lowenheim-Skolem lesson). Careful: uncomputability is absolute. Bruno Le 03-nov.-06, à 13:43, Saibal Mitra a écrit : uncompoutable numbers, non countable sets etc. don't exist in first order logic, see here: http://www.earlham.edu/~peters/courses/logsys/low-skol.htm [EMAIL PROTECTED] [EMAIL PROTECTED]: Ah the famous Juergen Schmidhuber! :) Is the universe a computer. Well, if you define 'universe' to mean 'everything which exists' and you're a mathematical platonist and grant reality to infinite sets and uncomputables, the answer must be NO, since if uncomputable numbers are objectively real (strong platonism) they are 'things' and therefore 'part of the universe' which are by definition not computable. But if by 'universe' you just mean 'physical reality' or 'discrete mathematics' or you refuse to grant platonic reality to uncomputables or infinite sets (anti-platonism or weaker platonism) then the answer could be YES, the universe is a computer. 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: RITSIAR (was Numbers, Machine and Father Ted)
Bruno Marchal wrote: Le 02-nov.-06, à 17:34, David Nyman a écrit : Bruno Marchal wrote: I don't understand really what you mean by AUDA is not RITSIAR. AUDA is just the lobian interview, or if you prefer the complete mathematical formalization of the UDA reasoning. In some sense you can interpret it as the eventual elimination of the yes doctor hypothesis in the UDA argument (but here I do simplify a little bit). Yes, sorry, perhaps I should have said 'if number is not RITSIAR, is anything?' The intention behind the question is to find out how and where you would apply RITSIAR in your schema - if at all - because Peter has been willing to do this but you haven't. I just want to know why. I recall RITSIAR = Real In The Same Sense That I Am Real (introduced by Peter). Now, the notion of existence is very difficult, and the notion of personal existence is still more difficult, and was the object of the debate. Take the expression I am real. Does it mean I am real and this is something I cannot doubt about, in which case I refer to the first person, or is it my physical body is real, in which case it refers to a third person description of I based on some theory (for example physics, or comp, etc.). We don't *have* to assume that there is a gulf between the first personal and third personal. So RITSIAR is an highly ambiguous which presuppose many points we were arguing about. Let me try shortly to make it less ambiguous in the frame of the AUDA. Now I cannot be 100% rigorous without being long and boring, so I ask you some indulgence, and I am just trying to convey the idea. As you know I am realist or platonist about numbers and their arithmetical relations. For example I believe in theorem like all numbers can be written as a sum of four square (Lagrange theorem). I take such a truth as being completely independent of me, you, time, place. I take such truth as being primitive and beyond time and space, a-physical if you want. Now I also believe in 1-persons, or souls, etc. I am not a solipsist, and I really believe in my own current experience, but also in yours even if I am currently feeling them differently. I don't believe at all that a first person experience is a number, nor do I believe any first person can believe to be a number. Still, I assume comp, so there must be a relation between 1-person experience and numbers. Indeed persons can manifest themselves relatively to me when they are related to some computations (brain activity with comp and some high substitution level for making things simple). Those computations define or are defined by complex set of counterfactuals, and UDA shows that physics emerge or should emerge (with comp) from their structure. It is plausible because quantum logic can already be seen as a logic of counterfactuals. How to get them, and what the results will say for RITSIAR ? Let me give you all the person point of views (pov), that is the complete science and theology of a simple lobian machine like PA (Peano Arithmetic). It is a fact that if M1 and M2 are lobian machine, and if M2 has stronger provability abilities than M1, then M2 can prove both the science and the theology of M1. But NO lobian machine can prove its own theology without becoming inconsistent, they can only abductively infer their own theology: 0-person pov = arithmetical truth. This can be shown ineffable or non definable by the machine (Tarski theorem). In the arithmetical interpretation of Plotinus' TOE, it corresponds to the ONE. It is the big unameable entity at the origin of all forms of existence. Don't entities have to exist? 3-person pov = arithmetical provability. It is the self-referential godelian provability predicate. The fundamental thing here is that the incompleteness phenomenon splits it into two parts, each of which are captured by a modal logic: G and G* respectively. G captures what the machine can prove about herself, and G* captures in addition what is true about the machine but unprovable by the machine (like self-consistency for example). G axiomatizes the self-referentially correct science of the machine, and G* minus G axiomatizes the correct theology that the machine can infer without proving (its hope-space if you want). In the arithmetical interpretation of Plotinus' TOE, it corresponds to the INTELLECT. Terrestrial or discursive = G, divine = G*. Please note that G and G* capture self-referentially correct *3-person* statements, like someone talking about his own brain with his doctor. It is I with I = my 3-description of my body. It is not the I with I = my soul, or my experiences ... The 1-person point of view. I identify him/it/her with the incorrigible knower. By Godel's second incompleteness theorem, no correct machine can prove its own incorrigibility. But that fact makes it possible to define the knower by making the explicit conjunction of
Re: Zuse Symposium: Is the universe a computer? Berlin Nov 6-7
In conscience et mécanisme I use Lowenheim Skolem theorem to explain why the first person of PA see uncountable things despite the fact that from the 0 person pov and the 3 person pov there is only countably many things (for PA). I explain it through a comics. See the drawings the page deux-272, 273, 275 in the volume deux (section: Des lois mécanistes de l'esprit). It explains how a machine can eventually infer the existence of other machine/individual). Here: http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume2CC/2%20%203.pdf Note also that the word model (in http://www.earlham.edu/~peters/courses/logsys/low-skol.htm ) refers to a technical notion which is the opposite of a theory. A model is a mathematical reality or structure capable of satisfying (making true) the theorem of a theory. Like a concrete group (like the real R with multiplication) satisfy the formal axioms of some abstract group theory. (Physicists uses model and theory interchangeably, and this makes sometimes interdisciplinary discussion difficult). ZF can prove the existence of non countable sets, and still be satisfied by a countable model. This means that all sets in the model are countable so there is a bijection between each infinite set living in the model and the set N of natural numbers. What is happening? just that the bijection itself does not live in the model, so that the inhabitants of the model cannot see the bijection, and this shows that uncountability is not absolute. It just means that from where I am I cannot enumerate the set. But, contrariwise, uncomputability is absolute for those enough rich theories. Here I am close to a possible answer of a question by Stathis (why comp?), and the answer is that with comp you have robust (absolute, independent of machine, language, etc.) notion of everything. Comp has a Church thesis. few notion of math have such facility. Tegmark's whole math, for example, is highly ambiguous. Thanks to Saibal for Peter Suber web page on Skolem (interesting). Bruno Le 03-nov.-06, à 13:50, Bruno Marchal a écrit : It is not a question of existence but of definability. For example you can define and prove (by Cantor diagonalization) the existence of uncountable sets in ZF which is a first order theory of sets. Now uncountability is not an absolute notion (that is the Lowenheim-Skolem lesson). Careful: uncomputability is absolute. Bruno Le 03-nov.-06, à 13:43, Saibal Mitra a écrit : uncompoutable numbers, non countable sets etc. don't exist in first order logic, see here: http://www.earlham.edu/~peters/courses/logsys/low-skol.htm [EMAIL PROTECTED] [EMAIL PROTECTED]: Ah the famous Juergen Schmidhuber! :) Is the universe a computer. Well, if you define 'universe' to mean 'everything which exists' and you're a mathematical platonist and grant reality to infinite sets and uncomputables, the answer must be NO, since if uncomputable numbers are objectively real (strong platonism) they are 'things' and therefore 'part of the universe' which are by definition not computable. But if by 'universe' you just mean 'physical reality' or 'discrete mathematics' or you refuse to grant platonic reality to uncomputables or infinite sets (anti-platonism or weaker platonism) then the answer could be YES, the universe is a computer. http://iridia.ulb.ac.be/~marchal/ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
