From: Ian Wright (ian_paul_wright@HOTMAIL.COM)
Date: Tue Jan 20 2004 - 18:01:20 EST
Hello Andy >I would have thought that dialectical logic is precisely a sublation of >formal logic which means that it can never be 'formalised': it cannot >be captured in a formal system. The failure of logicism, the >reduction of maths to logic, (a failure I take Godel to have proved) >can be viewed in this light. I am not an expert on this only knowledgeable. Before answering your question I would just like to reflect on the following. The development of the theory of universal computation and the construction of the first computers has profoundly affected almost all scientific disciplines. Mathematics has become more experimental, the first proofs relying on automated deduction have appeared, and constructive approaches to philosophical foundations have experienced a renaissance. Psychology has been transformed by computation, and mutated into cognitive science, which takes information processing as its core paradigm, and almost all philosophy of mind is now conducted either explicitly for or against computational theories. Entirely new fields of science have appeared, such as artificial intelligence and theoretical computer science. More recently the theory of computation has seen to be fundamental and important in physical theories, for example arguments over whether computational laws are more fundamental then physical laws, the idea of "it" from "bit", particularly via the emerging interest in digital physics, and the possibility of quantum computation. Economics has not been immune from the influence of computation, as masterfully explored in Philip Mirowski's "Machine Dreams", which I thoroughly recommend. The picture I am trying to paint is one of slow but seemingly unstoppable colonisation of almost all aspects of scientific knowledge by what can roughly be described as computational theories, or at least computational metaphors and talk. I'd say we've had about fifty years of this process, which is not very long. There is something about the computational approach that is not only very useful, for researchers of different disciplines don't use new tools unless they help, but also very universal, given the pervasive and broad influence of this new set of ideas. What is surprising is that the origin of this revolution in thought and practice derived from highly abstract and esoteric problems in logic and mathematics (there needed to be a parallel development in mechanical machinery, also, but nonetheless). My guess is that the set of scientific preconceptions about the nature of the fundamental "stuff" of the world we live in, labelled "materialism", is gradually being replaced by a new set of preconceptions, which could be called "computationalism", which performs a very similar job, but with new content. This is almost certain to occur if it is shown that the laws of computation are fundamental to even micro-scale physical laws, and constrain them. For example, Stephen Wolfram's recent book, "A New Kind of Science", which I also recommend, makes a very brave claim that universal computation is fundamental even to physics. I think this kind of intellectual risk-taking and boldness should be commended. (It is ok to be wrong, but it is not ok to not hypothesise.) So empircally at least it appears there is an emerging computational universalism. The question I have been asking myself, and asking one or two people who have knowledge of the ins and outs of dialectical materialism, such as yourself, is: What is the relation between the theory of computation and the theory of dialectical materialism? One property they have in common -- although please correct me if I am mistaken -- is, perhaps to use a pejorative label, "pan-logicism", the idea that logical laws are somehow identical with physical laws. Although I tried to read Hegel, and given up because it reads like nonsense to me, I do think there is pan-logicism there, and I see an emerging pan-logicism in the growing influence of computation in the sciences. Maybe it was in Turing that being truly become conscious of itself, rather than Hegel. Only questions, no answers. Returning to your question. Godel showed that no single axiomatic system could generate all the true statements of mathematics. Gregory Chaitin, who has an alternative proof of Godel's Theorem that uses information theory, interprets this to mean that purely deductive approaches are inherently limited. But this doesn't stop us from employing induction to understand new parts of mathematics, for example experimenting with new axiomatic starting points. But Godel's result doesn't imply that formalism, by which I mean theories with very precise semantics, should be abandoned. Formalism in that sense is always a good thing, which is why I think that a theory of dialectical logic, if there can be one, should aspire to formalism, rather than remaining in the form of natural language statements, often with unclear semantics. Please note that I said "aspire". I don't mean that all natural language theorising is no good, otherwise I wouldn't have bothered writing! Your thoughts would be much appreciated on all this speculation. ATB, -Ian. _________________________________________________________________ STOP MORE SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail
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