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

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Tue Sep 13 2005 - 05:55:49 EDT

I have now looked briefly at the rest of the website that Gerry
mentions, and there may be something

in it, I would now not necessarily reject it all out of hand.

On Ian's points

I am no expert in Hegel, unlike others on the list. Reasons why
computation may be the modern form of dialectics:
(i) Computation is logic in motion. At each instant a computer program
conforms to the laws of ordinary logic (the value of a variable cannot
both be 0 and 1), yet it can instantiate processes that are in real
contradiction to each other.


Negation of the Negation

If you have ever built a computer from scratch the first practical
hurdle in getting the damned

thing to do anything is to get the oscillator going.

A computer relies on a clock signal that sequences all other operations,
and such a clock

signal is a wire that alternates between the values true and false very

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.


I suspect that this is the sort of thing that the Byelorussian web site
is talking about

in the context of wave equations.

(ii) The Church-Turing thesis is a structurally similar claim to the
Hegelian identity of thought and being. (Both, unsurprisingly,


Do you mean the Church-Turing thesis, or Deutsch's extended form of the
Church-Turing principle whereby

any finite physical system can be emulated to an arbitrary degree of
precision by a universal computer?

This latter form is the one which has the strongest analogy with


I believe that there is a possible political/ideological component in
the debate over the

extent of the CT principle. Hayekian economists like Boetke use the
argument by Penrose

against the CT thesis as arguments against the possibility of planned


See some of the discussions on


which is run by Witold Marciszewski who also argues that
Hyper-computation has outdated the

concept of the CT thesis and uses this as an argument against Lange's
ideas of  the feasibility

of running a socialist economy.


I thus consider that it is ideologically important to defend the work of

on this see the paper Greg Michaelson and I have just posted

(iii) Computation is a general theory of causation, and can be used to
model both objective and subjective phenomena, similar to the claims of
dialectical logic.
(iv) The causal sequences of a computer program unfold with logical
necessity, despite being natural processes. I believe that Hegel argued
that natural necessity was identical to logical necessity in order to
refute Hume.

There is also, I think, a great similarity between the analysis of the
commodity in Capital 1 and the 

analysis of the signature of a datatype in systems like the type
theories of Lof  or Milner.

The exhange of commodities for money is a strictly formal or
computational system

and as such is eminently suitable for the application of formal
analysis. Given the

intellectual background of his education, Marx used Hegelian Logic.
Today one

might use type theory.



The problem is, not many experts in Hegel know about computation, and
vice-versa. A further problem is that many people think computation is
about crunching numbers, rather than a very general theory of dynamic


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