[OPE-L:1373] (Fwd) Re: Math, methodology and political economy

Gilbert Skillman (gskillman@mail.wesleyan.edu)
Fri, 8 Mar 1996 06:46:54 -0800

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For some reason the first version of this didn't go through.
Apologies for any resulting repetition. Gil

------- Forwarded Message Follows -------
From: Self <FS1/GSkillman.ECON.WU>
To: ope-l@anthrax.ecst.csuchico.edu
Subject: Re: [OPE-L:1353] Math, methodology and political economy
Reply-to: gskillman@wesleyan.edu
Date: Thu, 7 Mar 1996 12:44:40

Jerry responds to the following passage from Paul C.:
> > The two processes can go hand in hand. Casting
> > things in a mathematical form forces one to be
> > precise about what one means, in a way that does
> > not occur if one just thinks about things
> > qualitatively.
> > I dont accept that there is anything that is
> > unsuited to mathematical modeling. If something
> > is declared 'unsuited' that just indicates the
> > depth of our ingnorance and confusion in the field
> > in question.

Jerry's response:

> I guess Hegel and Marx (as well as many Marxists, including Rubin and
> Mattick) could be said, therefore, to be ignorant and confused since they
> frequently did not frame their analysis in quantitative terms. Mike L's
> and Tony's books must also be examples of fuzzy thinking since they are
> not very mathematical. I, for instance, don't think that Mike's work can
> be quantified with any degree of precision. IMHO, this is not a
> weakness on Mike's part but stems from the nature of the subject being
> investigated.
> * On what basis do you claim that a mathematical form of inquiry is more
> suitable for investigation in political economy than a systematic
> dialectical [and primarily non-mathematical] method of inquiry?
> * Mathematics *by definition* is an expression of formal logic. Are there
> instances in which dialectical logic can not be expressed in
> mathematical terms? If so, does that mean we formalize and linearize what we
> are studying in order to produce mathematical "results" or do we accept
> that some topics are more suited than others for expression in
> mathematical terms?
> I don't think we've ever tackled these questions on this list head-on
> before. Who wants to take a bite?

I guess I'd like to. I believe there is more of a middle ground here
than is suggested by Paul's or Jerry's posts. To begin with, I think
the appropriate distinction is not qualitative vs. quantitative, but
formal vs. informal (or perhaps more suitably, non-formal) analysis.
Mathematical analysis need not involve numbers. Indeed, what I have
in mind when I speak of formal analysis can be seen in George
Spencer-Brown's LAWS OF FORM, in which he develops a non-numerical
calculus of indications with respect to---here's the key
phrase--continent distinctions, that is, distinctions that can be
taken as given with respect to a given analytical project.

[An aside: contrary to Jerry's representation, Spencer-Brown shows
that formal logic is but an "expression" of mathematics, specifically
just one possible application of his calculus of indications, which
yet transcends formal logic by allowing for the possibility of an
"imaginary" truth value, just as there are "imaginary" numbers.]

Dialectical analysis, on the other hand, deals with processes in
which given structures of distinctions negate themselves, i.e. give
rise to new sets of distinctions. This is akin to changing the
postulate set underlying a given formal analysis. My favorite cheap
example of a dialectical process is the historical development of
jazz. Its history has been characterized by a series of mini-revolutions, in
which accepted canons are overturned by new forms. The unvarying
response of critics--keepers of the old forms--to these musical
innovations? "That's not jazz!" [E.g., in response to be-bop, "free
jazz", and fusion.] But then the new form is fused with the old form
to create a new totality, and the process goes on from there.

Now clearly dialectical analysis and formal analysis are not
addressing the same aspect of reality, so there is no inconsistency
in asserting the potential relevance of both forms of analysis.
But they are suited to very different concerns. Formal
analysis whenever one want to investigate the possible or necessary
implications of a *given* form--for example, the nature of social
relations in a given historical moment. Dialectical analysis, in
contrast, would instead concern itself with the process by which
given historical structures negate themselves.

I don't know much about the "logic" of dialectical analysis, and I'd
be presumptuous to attempt any description of such on this list,
especially when we have people like Tony Smith who have worked in
depth on dialectics and their application in Marx. [Tony, if you're
reading, and willing, I'd love to hear you comments on the issue raised by
Jerry and Paul].

But I do know that claims of possiblity and necessity are well-nigh
unavoidable in political economic analysis. Marx, for example, makes
such claims all the time, claims which dialectical methods are
intrinsically unsuited to assess, and which are instead the proper ground
of formal analysis. CAPITAL is peppered with phrases like
"It follows from this that...", "...must therefore...",
"If...then...", and the like, which amply indicate that Marx is
working in vineyards suitable for the application of formal analysis.

In solidarity, Gil