[OPE-L:1447] more on math and dialectics

Michael A. Lebowitz (mlebowit@sfu.ca)
Tue, 12 Mar 1996 00:45:42 -0800

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In message Mon, 11 Mar 1996 04:54:15 -0800, glevy@acnet.pratt.edu writes:

> To Mike L (responding to #1408): I didn't say that you were someone who
> is an example of one who is not doing mathematical work or who is opposed
> to the use of math in political economy. I said that your *book* was an
> example of a *subject* that was treated in a non-formal and
> non-mathematical manner.

No problem. I didn't take offence nor did I misunderstand you. You didn't
say that I was such an example and it is true that my book is.

> Since you are a proponent of the use of calculus
> for certain topics in political economy, let me ask you the following
> question: do you think that the theories presented in your book *can* be
> formalized in mathematical terms?
Could be. Much of the book [Beyond *Capital*: Marx's Political Economy
of the Working Class] is an attempt at developing from Marx the side of the
worker which is not explored in CAPITAL (given its limited object) and, as
such, is intended more to raise questions about the one-sided Marxism which
limits itself to CAPITAL than to generate directly such theories.
*However*, I think some of the implications of the arguments developed
can be formalized in mathematical terms. Eg., in Ch. 4 ("The Political
Economy of Wage-Labour"), I draw from Marx the proposition that "in any
society, separation and division in social relations among producers allow
those who mediate among the producers to capture the fruits of co-operation
in production" (69). Implicit here is a variable which is nowhere explicit
in Marx--- the "degree of separation among workers". I make the argument
somewhat more explicit in Ch. 5 ("One-Sided Marxism"),eg, by noting, with
respect to specific innovations within production, that "one which weakens
workers by increasing their separation and their competition among themselves
will increase the rate of surplus value by acting not only upon productivity
*but also upon the work-day (its length and intensity) and the real wage*"
(86). In the book (which is not directed specifically to economists), I
didn't try to formalize this, but when I explore these issues in my class,
I explicitly identify the degree of separation among workers as a variable
(positively related to the workday and inversely to the real wage). Once we
acknowledge that variable (or its opposite, the degree of unity among
workers) as an object of struggle on the part of both capitalists and
workers, then the course of the rate of surplus value and the rate of profit
seems rather less determined than in the usual (one-sided) Marxist
Mathematical formalization is also possible in exploring the
implications of removing Marx's CAPITAL assumption that the standard of
necessity is given and fixed (the assumption he intended to remove in the
book on wage-labour). In Ch. 5, I note:

"Effectively, insofar as it posits real wages constant when productivity
increases (that is, that money-wages fall at the same rate as money prices),
CAPITAL assumes that the degree of competition among workers is (and
remains) such as to prevent any 'quantitative participation in the general
growth of wealth'. Once that assumption is dropped, however, what becomes
obvious is the significance of differing degrees of competition among
workers. As noted earlier, where workers have successfully organised trade
unions, they will be able to prevent the price of labour-power from being
driven down at the same rate that money-prices fall; where they are separate
and unorganised, on the other hand, all the gains from productivity
increases will be captured by capital" (95).
So, I would say that, yes, there's lots there to mine, Jerry. I've never
gotten around to doing it myself (having presumably gone on to greater
things), but keep saying "one of these days..." In any event, having set out
the general framework, the arguments in the book are now common property.
in solidarity,
Michael A. Lebowitz
Economics Department, Simon Fraser University
Burnaby, B.C., Canada V5A 1S6
Office: (604) 291-4669; Office fax: (604) 291-5944
Home: (604) 255-0382
Lasqueti Island: (604) 333-8810
e-mail: mlebowit@sfu.ca