Re: [OPE-L] is algebra dialectical and vice versa?

From: Allin Cottrell (
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

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

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