Hi Stephen,

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On 12 May 2009, at 19:53, Stephen Paul King wrote: > > Falsifiable bets. ;) Not all. You bet the number zero makes sense, but you can hardly refute this. You bet there is a reality, but you can't falsify this. Falsifiability just accelerate the evolution of theories. Works by John Case and its students make this a sort of law in theoretical inductive inference: in a sense the Popper falsifiability theory has been falsified :) I agree it is a fundamental criterion of interestingness. It is not by chance that I worked on showing digital mechanism to be an experimentally refutable theory. > > Leibniz' Monadology is difficult to comprehend because he starts > off with an inversion of the usual way of thinking about the world. > By assuming that the observer's point of view is the primitive, it > follows that the notions of space and time are secondary, > "orderings", and not some independent substance or container. That would be too nice to be true. Leibniz would be captured by the 3h and 5th arithmetical "hypostases". I have already tried, but I fail, and I cannot conclude. > >> A synchronization of many such 1PoV, given some simple consistensy >> requirements, would in the large number limit lead to a notion of a >> "common world of experience". > > Don't you need some "common world of experience" to have a notion of > synchronization? > > [spk] > > No, not if all of the structure that one might attribute to a > "commn world of experience" is already within the notion of a monad. > A Monad, considered in isolation, is exactly like an infinite > quantum mechanical system. ? > It has no definite set of particular properties, it has *all > properties* as possibilities. > What I am considering is to replace Leibniz' notion of a "pre- > ordained harmony", his version of a a priori existing measure, I > propose a notion of local ongoing process. A generalized notion of > information processing or computation, for example. We see this idea > expressed by David Deutsch in his book, The Fabric of Reality": > "...think of all of our knowledge-generating processes, ...., and > indeed the entire evolving biosphere as well, as being a gigantic > computation. The whole thing is executiong a self-motivated, self- > generating computer program. ... it is a virtual-reality program in > the process of rendering, with ever increasing accuracy, the whole > of existence." pg. 317-318 > When we consider an infinity of Monads, each, unless it is > identical to some other, is at least infinitesimably different. All > of the aspects of a collections of Monads that are identical > collapse into a single state, a notion of a background emerges from > this. This idea is not different from the notion of a "collective > unconsciousness" that some thinkers like Karl Jung have proposed. > This leave us with finite distinctions between monads. Finite > distictions leads us to notions of distinguishing finite processes, > etc. > The notion of "synchronization" is a figure of speach, a stand > in, for that is called "decoherence" in QM theory. By seeing that > the phase relations of many small QM systems tend to become > entangled and no longed localizable, we get the notion of a > classical finite world. This is a "bottom up" explanation. Remember that with comp we just cannot take physics for granted. It is the whole point. > > > BTW: Notions, such as finitism, might be explained by > intensionally neglecting any continuance of thought that takes one > to the conclusion that infinities might actually exist! Comp is the most finitist theory possible in which you can still give a name to the natural numbers. It is not ultrafinitist in the sense that it shows machines can speed-up relatively to each other by giving name to infinities. But the infinities are epistemological, yet fundamental (physics is also epistemological here!). > > But here is the problem I have, merely "agreeing" that "all > dynamics are contained in the "block-arithmatic truth" will require > me to neglect the computational complexity of that "Block Truth". It is not so much a question of "agreement" than of "seeing the point". I don't see either why accepting that the dynamics are just emerging from some statistical relations between numbers (as treated by numbers) would in any way require you to neglect the computational complexity. On the contrary the realities are explicitly emerging from that complexity, but not ONLY from that complexity, it arises from the topologies of each "self-referencial" modalities and other mathematical constraints. Of course this makes the work technic. > > > The idea of a Platonic Universe of Arithmetical truth is a > notion that is only coherent given the tacit assumption to some non- > static process, such as that implicit in thought, also co-exists. A > What requires a To Whom. Being is the Fixed-Point of Becoming. To avoid confusion I would like to insist that what I call "Arithmetical Realism or Platonism" is just the very common belief that the principle of the excluded middle applies on the closed arithmetical sentences. (And I truly need only this on the Sigma_1 sentences, so it works in Intuitionist Mathematics too). > > > [spk] > > The problem is that all notions such as "substitute", > "misunderstood", "understanding", "emerge", etc. all require some > form of non-staticness. I need the Robinson Axioms of Arithmetic for the ontology. I need the Peano Arithmetic induction axioms and/or infinitely others for the (internal and relative) epistemologies. I treat the case of the ideally self-referentially correct machines. If you understand UDA, you can understand that, except once for the "yes doctor", I never go out of arithmetic. Indeed, that is what is made explicit in AUDA. The appearance of dynamics in the machines' discourse is given by computations, and they have purely arithmetical representations. > Simple existence, "necessary possibility", is not enough. The comp > model is wonderfull, but it requires an engine of implementation. I give it. Robinson Arithmetic is the engine of implementation. Although I could have taken any first order logical specification of any universal system. I could have taken a Diophantine equation, or a base of combinators, or the game of life of Conway. Physics emerge internally in a way not depending on the ontological basic implementation system, and in a manner enough precise so that we can compare the comp-physics and nature. Quantum physics, up to now, confirms some weird aspect of comp (symmetry, many-worlds below the substitution level, non locality, indeterminacies, non boolean logics fro yes/no experiment, etc.). 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 -~----------~----~----~----~------~----~------~--~---