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

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Fri Sep 16 2005 - 11:25:55 EDT

Allin Cottrell wrote:
> On Tue Sep 13
> 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.

In the context in which I was describing it is not an assignment.
I was talking about the context of computer hardware not software. Here
logical variables are represented by wires, and logical operators
by chips or gates that perform logic operations.

The line
A = Not A
means take a wire and connect the output of a Not chip to
its input.

What results is a system that is dynamically unstable but
has no external synchronisation ( which is entailed in any
logical system with assignment ).

One can certainly argue as you have, that it is just mystification
to call this dynamic instability 'dialectics', since one could
re-express it in terms of differential equations and electrodynamics.

However, the representation of the electronics as logic is a useful
level of abstraction, and the mark of a dynamically unstable logical
circuit is that it has no assignment of truth values to the variables
that is consistent. I think that this comes close to the idea
of contradiction driving a time varying process.

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