[OPE-L:1380] Re: Math, methodology and political economy

glevy@acnet.pratt.edu (glevy@acnet.pratt.edu)
Fri, 8 Mar 1996 11:04:50 -0800

[ show plain text ]

Some possible issues for discussion:

1) Dialectical and mathematical thought

What do Paul C, Allin, Gil and others make out of the following from Mino
(a person who could hardly be said to be anti-quantitative)?:

"The issue is not whether mathematics can be used in economic analysis
(of course it can) and to what extent (a question to be answered for
each question separately). The issue is one of mathematical
thinking versus dialectical thinking in economics. *Mathematical
thinking* is exclusively concerned with those economic phenomena
which can be expressed mathematically, with the casting of those
phenomena in the form of mathematical models, and with the formal
consistency of those models. Those aspects of economic life which
cannot be expressed mathematically are either ignored or forced
into a theoretical straightjacket which reduces dynamic and
multifaceted processes to a static and one-dimensional picture of
them. Ultimately, one engages in the solution of mathematical
problems and loses sight of the economic, or social, content of
those models (if they ever had any).

*Dialectical thinking*, on the other hand, is concerned with real,
that is, dynamic and contradictory, phenomena -- whether they can
be expressed mathematically or not -- with the analysis of of the
real processes of their reproduction or supersession, and with the
social content of those phenomena and processes. Ultimately, one
engages in the solution of theoretical problems through a
dialectical analysis of social reality. From this (the dialectical)
point of view, reality is seen both in its potential and in its
realized existence, both in its tendencies and its counter-tendencies,
both in its process of reproduction and in its process of radical
change (supersession)." [_Frontiers of Political Economy_, London,
Verso, 1991, p. 303, emphasis in original].

2) Dialectics as a mode of inquiry

Independent of identifying examples of dialectical relations, there is
also the question of whether the Hegelian method of inquiry should be used
in political economy. What this means concretely, we can discuss. In
part, I believe it concerns the systematic ordering of topics and their
analytical inter-relationship. Can this mode of inquiry be replicated by
mathematical means? I don't think it can, although, mathematics has a
role in such a form of investigation. What do others believe?

3) Is political economy a "science"?

If so, what does such an expression mean? Does it mean, for instance,
that the methods of investigation in the "natural sciences" are suitable
for research in political economy (this is the sense I get from Paul C's
understanding, although I will let him speak for himself). I don't
believe that social reality and history can be analyzed using the same
methods as physics or chemistry, for instance. Do other agree?

I will grant the claim that there are passages from Marx and Engels that
support the concept that political economy is a "science." Does that mean
that we should accept that claim, though?

4) Empirical and Theoretical Research

Under what conditions can we say that empirical research either validates
or invalidates theoretical propositions? Can we even make such a claim,
one way or the other, before we have developed an analysis that takes
into consideration all of the variables that affect the phenomena in
question? Do we have such an analysis yet? I have my doubts.

This does not suggest that empirical research isn't necessary or that it
doesn't have a complementary role. What it suggests, though, is that
claims relating empirical research to theoretical questions have to be
guarded and conditional.

5) "Algebraic Marxism" and the "New Math"

The tendency to view political economy as a science has a tradition that
at least dates back to Engels and was popularized, I believe, by Kautsky.
The tradition to express questions relating to political economy with
formal algebraic models is more recent. Are there not inherent problems
and limitations with such a method that stem from the nature of the
algebra used?

In terms of the history of thought, what are the origins of "algebraic
Marxism" (a term that Alain Lipietz used with disdain in _The Enchanted
World_)? To raise a contentious issue: wasn't the development of this
mode of thought a reflection of the conditions that we find ourselves in
academia whereby *only* those arguments couched in formal mathematical
terms are considered to be "serious"? Isn't this a rather large
concession to non-Marxist, especially marginalist, schools of thought?

What about the "new math", e.g. chaos theory? Although chaos theory has
the potential of being used to analyze non-linear dynamics in a more
suitable and realistic manner than matrix algebra, are there not
limitations of that form of mathematics as well? If so, what are they?
Also, there are different forms of chaotic analysis (something that Steve
K knows well). Which forms are best used for the study of particular
non-linear topics and why?

I guess that's enough for now for us to discuss. Would anyone care to
take a bite on the can of worms that I have re-opened above?

In OPE-L Solidarity,