Methodology

Although a book in mathematical Marxian economics is no longer a unique phenomenon, its author must still confront the opinion held in many circles, both Marxian and non-Marxian, that such an endeavor is a contradiction in terms. Two lines of defense are available: (1) that Marx himself was not against the use of mathematical methods; (2) that regardless of Marx's position, these methods are appropriate to aid in understanding the social phenomena with which Marx was concerned. Although what Marx believed on this question should not settle the issue, if we consider Marxism to be a science and not a religion, it nevertheless appears that Marx was a supporter of the use of mathematical methods in economics. This is shown by the work of Leon Smolinski (1973), who studied Marx's unpublished as well as published manuscripts for his views on the matter. Smolinski reports there was “not a single injunction against mathematical economics [in] Marx's published or unpublished writings.” Moreover, Lafargue attributes to Marx the statement: “A science becomes developed only when it has reached the point where it can make use of mathematics” (Smolinski, p. 1201). Still, the opposing circumstantial evidence remains that Marx made very little use of formal mathematics (beyond arithmetic) in his work. As Marx studied algebra and calculus quite extensively in his later years, why did he not use these tools?