I hope to communicate today to my students an idea that they
may find rather difficult to grasp, or so I fear. Perhaps if I have a go at explaining it here,
the effort will help me to clarify my exposition. Let me say, by way of setting the scene,
that today I shall try to bring together into a single integrated account the
four strains of argument I have been developing in my course: Marx's economic analysis of capitalism,
Marx's historical account of the development of capitalism, the modern
mathematical formalization of the classical and Marxian tradition of Political
Economy, and my literary critical explanation of the extraordinary language of
the first six or seven chapters of

*Capital*. The reading assigned for today is my 1981 essay, "A Critique and Reinterpretation of Marx's Labor Theory of Value." That essay, which so far as I can determine, in David Hume's words, fell stillborn from the presses, is a rather difficult read for philosophers, containing as it does a good deal of linear algebra. [Linear Algebra, which is mother's milk to economists, is actually quite elementary undergraduate math for a math major, but as C. P. Snow observed many decades ago, we live in a society of two cultures, and philosophers whose intellectual sophistication knows no bounds confront a page of mathematics as though it were Linear B.]
The idea, in a sentence, is this: The narrative accompanying a mathematical
model frequently contains a good deal of information that finds no formal
representation in the model, and it is a mistake to think that the deductions
from the model constitute a proof or endorsement of those elements present only
in the narrative. In the case of Marx's
theory, the distinction between labor power and labor, which Marx claims is the
key to understanding the origin of profit in a capitalist system, actually
finds no representation in the formalism
implicit in Marx's argument and made explicit by the modern mathematical formalization
of that argument. The goal of my essay
is two-fold: First, to demonstrate that
the labor/labor-power distinction plays no formal role in Marx's argument, and
that all of his results can be reproduced for any arbitrarily chosen commodity
as "substance of value;" and
Second, to find an alternative formalization of what I believe to be Marx's
correct analysis and critique of capitalism.

There are a number of examples of this sort of mismatch
between a formal argument and the accompanying narrative. My favorite is the narrative that has grown
up around the so-called Prisoner's Dilemma.
I shan't reproduce here my analysis of that familiar example, from Game
Theory, of a two-person non-zero-sum game in which each player has two pure
strategies. Those who are interested
will find it in the book-length tutorial I wrote on The Use and Abuse of Formal
Methods in Political Philosophy, archived at box.net. Other examples, considerably more important
at one time in U. S. military affairs, are the mismatches between the narratives
of deterrence and nuclear war and the game theoretic analyses accompanying
them. [To be found in my unpublished
book,

*The Rhetoric of Deterrence*, also archived.]
If one prefers a more light-hearted example, one can consider
the practice adopted by some Grade School teachers of drawing circles as happy
faces and squares as Sponge Bob Square Pants when introducing little children
to Geometry. Sooner or later, the
children must learn that the mathematical properties of a circle are
independent of whether a happy or sad face is drawn in it.

## 2 comments:

my 1981 essay, "A Critique and Reinterpretation of Marx's Labor Theory of Value." That essay, which so far as I can determine, in David Hume's words, fell stillborn from the pressesWell, it has, apparently, but cited 26 times, which is significantly above-average. It's hard to know how many of those cites actually deal with it, as opposed to just mentioning it in passing, but at least a couple of them purport to directly address the essay. It may not be the recognition one wants, but it's certainly more than most people get! (Especially so insofar as many of the people citing it are really smart scholars.) See here:

http://scholar.google.com/scholar?cites=7879254250754083804&as_sdt=5,39&sciodt=1,39&hl=en

Is it that the distinction has no formal representation whereupon it is unique or special, or no formal representation whatsoever?

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