From: Allin Cottrell (cottrell@wfu.edu)
Date: Fri Sep 16 2005 - 10:42:06 EDT
On Tue Sep 13 Paul Cockshott wrote: "In order to drive the clock signal one typically constructs an electrical circuit consisting of a NOT gate coupled back on itself. This has the logical form: clock = NOT clock This is obviously a contradiction, and the contradiction expresses itself in practice in the clock wire oscillating between true and false. This is straight out of chapter I of Hegel's Science of Logic, where double negation gives rise to 'becoming' or in this case continuous change." Allin responds: I see what you're saying, but I would register some qualifications. Is "A = NOT-A" a contradiction? I'd say this idea relies on a pun on the meaning of '=', between its use in mathematical or logical equations and its use in computer programming. If "A = NOT-A" is interpreted as a Boolean equation, then it's simply a false statement. A genuine contradiction in that system is the statement "A and NOT-A". When a programmer writes "A = NOT-A" (or "A = !A") this (as of course Paul knows well) is not an equation, it's an assignment. It translates as "If the variable A had a non-zero value prior to this statement, give it value 0; and if it had value 0 prior to this statement, give it value 1." It might be expressed more transparently as A <- !A A "genuine contradiction" is also expressible in computer code, for example "A && !A" (where "&&" represents Boolean AND). But note that (so far I know) nobody ever writes this. "A && !A" always evaluates to 0 (FALSE): why type "A && !A" when you can just type "0"? So my point is: assignments that flip the values of variables (and that _look like_ contradictions because the symbol '=' happens to be used in many computer languages to represent the assignment operator) are very useful in computing. But to my knowledge, actual contradictions are useless. Allin Cottrell
This archive was generated by hypermail 2.1.5 : Sat Sep 17 2005 - 00:00:01 EDT