**From:** Paul Cockshott (*wpc@dcs.gla.ac.uk*)

**Date:** Wed Apr 02 2008 - 18:33:20 EDT

**Next message:**dogangoecmen@aol.com: "[OPE] How to read Capital"**Previous message:**Paul Cockshott: "RE: [OPE] Dialectics for the New Century"**In reply to:**GERALD LEVY: "RE: [OPE] Dialectics for the New Century"**Next in thread:**Dave Zachariah: "Re: [OPE] Dialectics for the New Century"**Reply:**Dave Zachariah: "Re: [OPE] Dialectics for the New Century"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Jerry ----- Computation refers to "any type of information processing that can be represented mathematically." Formal logic is synonymous with mathematical logic: http://en.wikipedia.org/wiki/Formal_logic Computation is not "more abstract than" mathematics: rather, it is a a subject which _is_ mathematics and, hence, utilizes formal logic. Also, the very architecture of the computer is dependent on the binary system - by definition, an expression of mathematical / formal logic. Paul I think you are verging on Platonic idealism here, in which the ideal mathematics underpins the physical reality of the computational system. Computation is always everywhere a material process governed by material laws, it is these material laws, the laws of physics, that give rise to the possibility of mathematics. "Calculi are rules for the manipulation of strings of symbols and these rules will not do any calculations unless there is some material apparatus to interpret them. Leave a book on the l-calculus on a shelf along with a sheet of paper containing a formula in the l-calculus and nothing will happen. Bring along a mathematician, give them the book and the formula and, given enough paper and pencil the ensemble can compute. Alternatively, feed the l-calculus formula into a computer with a lisp interpreter and it will evaluate." (Are There New Models of Computation? Reply to Wegner and Eberbach, Paul Cockshott and Greg Michaelson,, The Computer Journal 2007 50(2):232-247; doi:10.1093/comjnl/bxl062) "And conversely, when we interpret Turing's theorem as a statement about what can and cannot be computed in physical fact, we are adopting some of his tacit assumptions about physical reality or equivalently about the laws of physics. So where does mathematical effectiveness come from? It is not simply a miracle, "a wonderful gift which we neither understand nor deserve" [17] - at least, no more so than our ability to discover empirical knowledge, for our knowledge of mathematics and logic is inextricably entangled with our knowledge of physical reality: every mathematical proof depends for its acceptance upon our agreement about the rules that govern the behavior of physical objects such as computers or our brains. Hence when we im- prove our knowledge about physical reality, we may also gain new means of improving our knowledge of logic, mathematics and formal constructs. It seems that we have no choice but to recognize the dependence of our math- ematical knowledge (though not, we stress, of mathematical truth itself) on physics, and that being so, it is time to abandon the classical view of com- putation as a purely logical notion independent of that of computation as a physical process. In the following we discuss how the discovery of quantum mechanics in particular has changed our understanding of the nature of computation."( MACHINES, LOGIC AND QUANTUM PHYSICS DAVID DEUTSCH, ARTUR EKERT, AND ROSSELLA LUPACCHINI) _______________________________________________ ope mailing list ope@lists.csuchico.edu https://lists.csuchico.edu/mailman/listinfo/ope

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