[OPE-L:1389] Re: Math, methodology and political economy

Gilbert Skillman (gskillman@mail.wesleyan.edu)
Fri, 8 Mar 1996 17:49:06 -0800

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Jerry raises difficult and important questions. I wonder, though,
about the way in which he's posed these questions:

> 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).

This is not an indictment of mathematical reasoning per se; it's an
indictment of any one-sided or unskilled use of given analytical
tools. One could say similar things about the inappropriate or
one-sided application of dialectical reasoning, for example.

> *Dialectical thinking*, on the other hand, is concerned with real,

This is not a question of "real" vs "unreal". Formal analysis can
address real, and for that matter dynamic, and up to a point, contradictory
phenomena as well.

> 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.

If this "social content" concerns consistent possibility or
necessity, then I do not see how dialectical reasoning can assess
such concerns. If it's claimed that it can, I'd like to see how.

>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,

How do you determine the tendencies and counter-tendencies of a
system? What would be an example of this?

> 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?

I believe that this representation is true as far as it goes, which
is only halfway. There are also important modes of inquiry within
political economy which cannot be "replicated by dialectical means."

> 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?

Using formal method in social science does not imply that one is
using "the same methods as physics or chemistry."

> 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?

Yes. And one could pose a parallel question, yielding the same
affirmative answer, by substituting "dialectical method" into the
foregoing question.

> 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"?

Whether it is or not need not be our concern, as long as *we* are not
biased by in this way. Informed dialecticians need not be abashed by
the way the dialectical method was abused by certain Soviet Marxists,
for example.

> Isn't this a rather large
> concession to non-Marxist, especially marginalist, schools of thought?

In a word, no. Marx, for example, issues claims of logical
possibility and necessity throughout capital which are the proper
ground of formal method. And as far as I can see marginalism has
nothing to do with any of this

> 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?

I'm not sure about this imagery (biting on a can of worms? Yuch),
but there it is.

In OPE-L Solidarity,