On 20 Aug 2009, at 02:07, David Nyman wrote:

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> > 2009/8/19 Jesse Mazer <laserma...@hotmail.com>: > >>>>> I completely agree that **assuming primary matter** computation >>>>> is "a >>>>> physical process taking place in brains and computer hardware". >>>>> The >>>>> paraphrase argument - the one you said you agreed with - asserts >>>>> that >>>>> *any* human concept is *eliminable* >>>> >>>> No, reducible, not eliminable. That is an important distinction. >>> >>> Not in this instance. The whole thrust of the paraphrase argument is >>> precisely to show - in principle at least - that the reduced concept >>> can be *eliminated* from the explanation. You can do this with >>> 'life', so you should be prepared to do it with 'computation'. >> Well, not if you believe there are objective truths about >> computations that >> are never actually carried out in the physical world, like whether >> some >> program with an input string a googolplex digits long ever halts or >> not. > > Yes, but here - in connection with Peter's apparent support for the > Quinean concept-reduction argument - I was specifically commenting on > the status of 'computation' **if** you assume primitive matter. In > that case, I'm not sure what "never actually carried out in the > physical world" would mean. On the contrary. If you assume there is a primitive material reality, a primitive physical universe, then it makes sense to talk about the computations which are carried out in the physical universe, like the one done by this or that computer or brains, and the computations which are not done in that universe, like some possible counterfactuals (the computations carried out by Julius Caesar meeting Napoleon), or some extravagant computations like the computation of the 10^(10^1000) digit of the square root of two. Of course in the special case of a large multiverse, or in the concrete ever expanding universe assumed in step seven, the universal dovetailing is integrally executed so that in such a universe all the computations are carried out. > I don't have a problem with step 8 on the basis of the Olympia > argument, as I've tried to demonstrate - is there some other aspect of > computational supervenience that you feel I'm missing? > >> >> May be you don't want to do the math? The math for UDA are really >> basic compared to the math needed for AUDA. >> > > I'm trying to follow the math as you go through it, although I still > haven't really fathomed where it's leading. Your second sentence answers the first one. Your paragraph above also. The current "seventh step series" is leading to the understanding of what is a computation, and a machine, for a mathematician. With or without assuming PM (primitive matter) there is an mathematical notion of computation and of computability. This is amazing, because Cantor discovered a technic which is capable of demolishing most attempt to define a real universal thing in math, but as Gödel will eventually realize, the set of computable functions remains closed for that technic. Gödel described this as a kind of miracle, and was very skeptical about it. That "miracle" is Church thesis. Gödel, on its own saying, missed it, despite he invented one of the candidate for a definition of what are computations, and what means computable. The notion of computation does not rely on anything physical. Computation and computability theory are branch of mathematics, and in my youth those branches were taught in the "pure mathematics courses"., not in "applied mathematics course". And in some universities this remains so. In informatics "applied computer science", such course on the mathematical computation are not taught: you have to do pure math to study it, and if you dare to pretend there could be relations between them, you are consider as a betrayer of pure math! I think that what remains unclear in step seven is due to the lack of knowledge of that "purely mathematical" notion of computation. You need it to justify why Universal Machine and Universal Dovetailer" exist and in what sense they are truly universal. The notion of physical computation *today* is quantum computation, and this is a priori something else, except it can be shown defining the same class of computable functions. A big problem for the comp hyp. consists in explaining why apparently everything we can touch and smell is described only by quantum computation. Why in UD* (the infinite execution of the UD, or of any UD) does the quantum computation wins the "measure battle", at least from the first person (plural) points of view. Of course the first person plural indeterminacy explains why, but we have to recover the detail. The apparent "primitive matter" that we recover from comp is a priori "too much powerful, and leads to too much "white rabbits". Only pure mathematical computer science explains why this is not trivial at all. 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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