----- Mensaje original ----- Message from Bruno Marchal--------------------------------------Hi Jerry, hi List, > On 06 Jun 2012, at 17:43, Jerry LR Chandler wrote: > but offhand it seems to me to depedn on a sort of idealism that I do not > accept. > "It does not. It does rely on Church thesis, which relies on arithmetical > realism, that is the idea that elementary arithmetical truth are NOT a > creation of the mind, which is a form of > anti-idealism."------------------------------- > I am utterly confused by this post. > It seems to intermingle mathematics, logic, philosophy and personal beliefs > without any apparent connection to the history of the subjects or science. > My post was a pointer to a (technical) paper which proves that digital > mechanism, or computationalism, is incompatible with physicalism. The paper > is > here:http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html > In my url, you can find longer and more detailed versions (the longer one are > in french, alas). > > > I have not any idea what "elementary arithmetics truths" means. It is a > standard expression for logicians. It means all first order arithmetical > statements true in the usual structure (N, +, *). > A first order logical sentence is a sentence build with the logic symbols (&, > V, ->, "for all", "it exists" ...) and the arithmetical symbols s, 0, +, and > *. For example "6 is even" abbreviates the true arithmetical sentences: > "It exists x such that s(s(s(s(s(s(0)))))= s(s(0)) * x". (or > Ex(s(s(s(s(s(s(0)))))= s(s(0))*x) > Elementary arithmetical truth can be seen as the collection of such > sentences. That set is well defined, even if it is not axiomatizable, nor > constructively definable. Technically, only a tiny subset has to be supposed > true independently of me. > > Do you wish to include or exclude logs?Log is not among the primitive > notions. But you can already defined the ceiling of log just with addition > and multiplication. Thanks to the work of Matiyasevich, it is not to > difficult to prove that addition and multiplication of natural numbers are > Turing universal. We can define all computable functions with "s" > (successor), "(", ")", and "+" and "*", and "0". > > > Either way, are you including or excluding arithmetic and/or geometric > progressions from "arithmetic realism"?Could you be specific and point out > the exact relations between "truths" as used in this context and your > philosophy of physics? Or the nature of physics?Truth means "satisfied by > the model (N,+, *). (in the logician's sense, quite akin to our intuitive > idea of truth in arithmetic). > The reasoning detailed in the paper mentioned above is hard to sum up. I hope > you agree that "science" has not yet decide between the Aristotelian > conception of reality and the Platonist conception of reality. > Basically, for the Aristotelian, the physical reality (what we observe and > measure) is real.For the Platonist, the physical reality is only the > "shadow", or the border of something vaster. > What I explain in the paper is that IF we assume that there is a level of > description of my brain (even in a very large sense of the word) such that I > would survive with a digital substitution respecting functionality at that > level, then the Aristotelian picture of reality is no more consistent, and > the Platonic one is correct. The proof is constructive and explain how to > derive physics from arithmetic. It makes comp testable. > > > > "a creation of the mind" ?? What does this possibly mean in this context? > In particular, do you wish to imply or infer or illate that the human mind > before the social creation of arithmetic symbol systems was somehow > "non-creative"?? VERY CONFUSING from a historical perspective. > We must distinguish the arithmetical propositions and their content, with the > shape of the sentences used by humans to communicate and think about those > propositions. Comp needs Church's thesis, and Church's thesis need > arithmetical realism to make sense. But we need only to be realist on a tiny > fragment of arithmetic, usually accepted by both classical and intuitionist > mathematicians. Such tiny part of arithmetic is also needed to define what is > a formal system, and is accepted by formalist. It is equivalent with the > admission that all programs/machine stop or don't stop. This can be > translated into an arithmetical sentence. > > > > "a form of anti-idealism"??? Perhaps you mean something to do with > representation or symbolization of your beliefs? Why introduce "form" as a > concept related to a personal view of "anti-idealism" Makes no sense to > me.Your point is not clear. Idealists believe that reality is a creation of > the mind, and I explained that computationalism (my working hypothesis), just > to make sense, needs to assume that the arithmetical truth (actually a tiny > part of it) is independent of me (and you, and the physical universe if that > exists). > For example I accept that the table of addition and multiplication does not > depend on me, I accept that the non existence of a biggest prime number is > independent of me. That is why I am saying that comp is not based on an > idealist conception of the arithmetical reality, even if in fine, it leads to > an idealist conception of the *physical* reality, which appears to emerge > from the interference of "machine's dreams". But you have to study the > argument in detail to see what is meant by that. The key ingredient is the > notion of first person indeterminacy. Look at the sane04 paper for the suite > simple definition I am using for the first and third person points of view. > > Does your view reject the polar opposites / electricity of Schelling?I > assume some mundane reality (like brain, doctors, etc.) to develop the > argument. I don't assume them to be primitively material, nor non primitively > material at the beginning of the reasoning. At the end of the reasoning, they > can no more be primitive, and for the primitive we need only one Turing > universal system. > The argument eventually shows that physics is independent of the choice of > the universal system used to describe the computable functions, and I use > arithmetic because everyone know it (even if few people knows that it is > Turing universal). So I do not assume any physical theory in the reasoning, > nor in the "TOE" isolated through the reasoning. The "TOE" being a tiny (but > Turing universal) part of arithmetic. > > > Finally, I would note that Dalton's Law of ratio of small whole numbers, an > established physical principle based on the atomic numbers and fundamental to > quantum chemistry, contradicts the essence of your post as I understand > it.Yes, you have to backtrack to Plato. Most people today believe > "religiously" that physical reality is primitive. Some pseudo-scientists > makes it into a dogma. I think we are ignorant on such matter. > My point is logical: if we are Turing emulable, then physics is an emergent > pattern. With comp the physical laws have an arithmetical origin. The > Aristotelian "dogma" just doesn't fit with the logical consequences of > computationalism. > If we found an evidence for primitive matter (Aristotle primary matter), then > we get evidence against comp. But such evidence does not exist. We have of > course a lot of evidence that there is an important physical reality, but > that is not an evidence that it is primary. > > > > Frankly, I can not find any immediate coherence between this article and > either electro-mechanical or electro-chemical principles that are essential > to physical and chemical information theory.That is interesting, and you > might elaborate. With respect to my argument, this would show that > electro-mechanical or electro-chemical principles would contradict the comp > hypothesis. That would be a big discovery. > I am not defending at all the comp hypothesis. I am just saying that IF comp > is true, then we have to backtrack to Plato's (and Plotinus') notion of > reality, where the physical reality is no more primitive, but an emergent > pattern of the number's or machine's mind. > My main point is that comp is testable, because the argument is constructive. > It explains how to derive physics from arithmetic. So, to test comp, we can > compare the physics extracted from comp, and the physics inferred from > observation. Up to now, it fits remarkably. I have already extract the logic > of the observable, and get a quantum logic. It is still an open question if > that quantum logic makes quantum computing necessary in our most probable > neighborhoods, like it looks to be the case with nature. > Best, > Bruno > http://iridia.ulb.ac.be/~marchal/-------------------------------------------------------------------- > http://iridia.ulb.ac.be/~marchal/ >
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