THE MERCHANT OF VENICE, OR MARXISM IN THE MATHEMATICAL MODE 19
originally borrowed and developed by neoclassical economists—are used to rethink traditional concerns and to pose new sets of questions. The 'mathematizers* of Marxian theory include writers as diverse as Nobuo Okishio (1963, 1977), Meghnad Desai (1979), Shinzaburo Koshimura (1975), Andras Brody (1970), Michio Morishima (1973), Donald Harris (1972,1978), John Roomer (1986b), Duncan Foley (1982, 1986), Alain Lipietz (1982), lan Steedman (1975), and Anwar Shaikh (1978). The topics of their mathematical contributions range from the logical status of the Marxian theory of value and the problem of price-value transformation to the law of the tendential fall in the rate of profit, economic crisis, and long-run capital accumulation. In some instances, traditional Marxian concepts and propositions are upheld; in many others, mathematical models are used to demonstrate the incorrectness of and to argue against ideas long associated with Marx and the Marxian tradition. In both cases, mathematics is considered central to the task of investigating and presenting Marxian theory.
At the same time that Marxian theory is being rewritten in mathematics, the modernism of social scientific inquiry is being rethought and, in many cases, called into question. There is, for example, increasing attention to the critique of social scientific philosophy and methodology (Hindess 1977), to the problems of traditional epistemology (Rorty 1979), and to the role of rhetoric in economics (McCloskey 1986 and Klamer 1984) and the other human sciences (Nelson et al. 1987).
There is also an important current within the Marxian tradition which has argued that Marxian theory constitutes a fundamental break with other social theories. This notion of break or rupture, long associated with the work of Althusser (1977; and Balibar 1977), is related not only to the kinds of statements Marxists make about the nature of capitalism and other societies; it also involves the methodology and epistemology which condition the manner in which those statements are produced.
These general concerns lead to a questioning of the status and effects of the use of mathematics in Marxian theory. The problem is that the path to be followed in such an inquiry is virtually nonexistent There is little, if any, discussion of the use of mathematics in the social sciences—and still less in Marxism. What does it mean to formalize, quantify, or matheniatize social theory? General endorsements are common; mathematical models are presented as part of normal science, the handmaiden of modern scientific methods. Mathematics is presented as a set of neutral, rigorous, logical tools to develop theories and to test them against reality.
My own experience in teaching mathematics to first-year graduate students in economics is probably typical: since they all believe in science—in the singular—then those who are adept at mathematics tend to accept it and use it with enthusiasm. Those with less