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

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Thu Sep 15 2005 - 04:48:13 EDT



I may well be. I was trying to use it in the Hegelian sense, although,
as I mentioned, I'm no expert on Hegel, so I'm happy to be corrected. As
far as I can understand Hegel, "dialectical" describes the nature of
"being". Being is dialectical. I interpret this in a similar way to the
claims of, say, "atomism", that being is ultimately composed of
corpuscles, or such like, that interact. According to atomism, being is
atomistic, according to Hegel being is dialectical. Hegel's categories,
are, I think, a deduction of some necessary properties of being, but
using the innovative methodology that valid inferences, the logical
moves, must themselves be derived, organically so to speak, from the
prior categories. Unlike formal logic, which takes a collection of rules
of valid inference as independent variables, Hegel starts at an earlier
point, and tries to self-referentially infer the valid rules of
inference in an incremental fashion. In this sense, Hegel's categories
are dependent variables, necessary consequences of his simple and
abstract starting point. His aim, I suppose, to find the abstract
necessary features of both nature and mind, and unify natural and
logical necessity. So I think "dialectical" refers to both the method of
derivation and the results of derivation.

I too am not a Hegel expert, I read some of his books as an
undergraduate but have not looked at them

for 30 years. But what I recall thinking when I read the Science of
Logic, was the his inferences were not

at all self supporting. They have all sorts of hidden assumptions, or
are simple assertions. At this level

the starting inferences should be treated as a process of introduction
of additional axioms.


One should bear in mind Chaitin's point that one can not get 2 kilos of
theorems from 1 kilo of axioms.


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