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 > 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 knowledge. Kp makes both > truth and provability participating in the knower, like in Plotinus. In > fact, quite amazing things appears here. First "Bp & p" cannot be > directly defined in the language of the lobian machine, making the > "soul" or the first person unnamable, like the big ONE. Secondly the > logic of Kp (which *is* completely *defined* in G and G*) appears to be > a temporal logic of a self-extending self, and it can be related the > brouwer "creative subject" philosophy in intuitionistic logic. This is > confirmed also by the fact that G and G* completely agree on Kp. G* > does not add anything: the soul of the machine is bound up to confuse > proof and truth, the Kp logic (already known in the logician literature > as S4Grz) does not split into two like the intellect. > In the arithmetical interpretation of Plotinus' "TOE", it corresponds > to the "ALL SOUL" or "universal SOUL". It is a good candidate for a > simple form of first person pov. > > The 1-person plural pov. This is the consistent believer. It is defined > by Cp = Bp & ~B~p. Or equivalently Bp & ~B~t. (with t = any tautology) > Again by incompleteness, although it is equivalent with both Bp and Bp > & p at the G* level, it obeys different logic, and here the G and G* > difference does again split it into two. In the arithmetical > interpretation of Plotinus' "TOE", it corresponds to the "INTELLIGIBLE > MATTER". It is here that a logic of counterfactual, or a quantum logic > appears. It is the logic of probability on observable proposition. > Actually the quantum appears only at the G* level, and this can be used > to show that "we" (the first person plural) share the quantum > splitting: here we recover Everett. The price of that is that the > "quanta" have to be just a case of sharable qualia. Note that it is the > difference between the 1-person and the 1-plural person which prevents > comp from solipsism. I call its modal logic Z. > > The incorrigible 1-person plural pov. This one is again an "intensional > (modal) variant" of G. It is defined by Op = Cp & p = Bp & ~B~p & p. It > is also split into two by G and G*. In the arithmetical interpretation > of Plotinus' "TOE", I would say it corresponds to the "SENSIBLE > MATTER", its G* part gives an astonishing non trivial notion of > "correct qualia" (showing the existence of possible non correct qualia > in the intelligible matter, this can be used to explain phantom limb, > phantom body, phantom universe). > > To sum up, and to relate this with RITSIAR, I would say that the > unnamable reality (of the lobian machines PA, (resp. ZF ...)) is > arithmetical truth, (resp. set-theoretical truth, ...) which is somehow > beyond existence, and all form of existence are internal modalities of > arithmetical (set theoretical, ...) truth. > Does this help a bit? I have long thought that if you are not assuming traditional Platonism (numbers exist), you must be assuming some thesis that along the lines that existence is somehow subsumed by truth.(" which is somehow > beyond existence, and all form of existence are internal modalities of > arithmetical (set theoretical, ...) truth"). Either claim in highly metaphysical, and the argument is therefore not pinned solely on the scientific-sounding COMP premiss. > To be short I have not mentionned that the quantum appears only when I > translate the comp hypothesis in the language of the machine. Now comp > can be translated in G (and G*) into the formula "p -> Bp", so what I > say above is true with G1 = G + "p -> Bp". To explain why comp is > "p-> Bp", we should dig deeper in recursion theory/computer science (cf > the Wi and the Fi for those who remembers those posts). Of course you > can also interview non computationalist machine, if you desire (good > subject for a PhD thesis!). > > Perhaps I could compare this with Spinoza Neutral Monism. The big > 0-person view (cf Nagel's view from nowhere) is truth, and all the form > of existence (quanta, qualia, space, time, taxes, death ...) emerges > from relatively canonical views from inside. Incompleteness makes this > approach consistent, and comp makes it provable by any lobian machine > M1 for any machine M2 when M1 is sufficiently stronger than M2. Then > M1, by postulating comp, can lift abductively (and thus > interrogatively) the M2 theology to itself. > > Bruno > > > > > > > > > > > > > > http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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