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

From: Allin Cottrell (cottrell@wfu.edu)
Date: Thu Sep 15 2005 - 20:12:58 EDT 

Brief response on "what does dialecticaal mean anway?"

In my understanding, there's a general, pre-Hegelian sense of this
term which simply means, "proceeding by means of argument."  Thus,
one might contrast a dialectical approach, which contends that truth
is best attained by means of the contest of opposed views, with a
more linear rationalist approach which maintains that one should
start from the "best" axioms and proceed with deduction, without the
distraction of opposed views.

In that sense, I guess I am in favour of dialectics.

With Hegel, this rather vague notion is given a (spuriously?)
precise sense: the notion of "argument" (a human category) is
transposed onto the Real, which then supposedly "argues with itself"
(the famous Thesis-Antithesis-Synthesis) in its own process of
Becoming.  Despite Engels' best efforts to force the scientific
advances of his day into this mold, I find this rather foreign to
the understanding offered by modern science.  But if some people
find this perspective a fruitful source of ideas, fine.

On Wed, 14 Sep 2005, Ian Wright wrote:

> When dialectical materialists, of whatever stripe, argue that
> dialectics surpasses the limitations of formal logic, they will
> find support and clarification for that point of view from the
> work of Turing and Godel etc. The theory of computation, or at
> least the mathematical strand of it, grew out of a critique of
> formal logic.

I'm not going to accuse Ian of obscurantism -- far from it -- yet I
have to say that just about all the invocations I have seen to date
of dialectics as "surpassing formal logic" have been instances of
the purest obscurantism from writers who apparently know very little
of formal logic.

Both the propositional calculus and the predicate calculus are known
to be complete (Bernays, Post, Henkin, Godel).  The Godel
incompleteness theorem refers to formal systems "strong" enough to
generate elementary arithmetic.

Allin Cottrell

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