Concluding Remarks

Neoclassical economics did not maintain Marshall’s realist approach throughout the twentieth century, not even within the Economics Faculty that Marshall founded at Cambridge, as Harcourt (2003) noted 100 years after its foundation. The emphasis on the use of mathematico-deductivist methods, which had been criticised by Keynes early on, is now the central characteristic of mainstream economics, as Lawson (2003) notes.

Economics was always shaped by the mathematical methods used. The classical political economists, from Petty to Ricardo, used only arithmetic (as Marx and Sraffa also did later). The marginalists relied on differential calculus, and Marshall even found in it a justification for his partial equilibrium method, a justification which Sraffa and Keynes criticised. The twentieth century witnessed the further development of calculus, and the appearance of econometrics (criticised by Keynes), and of fixed-point theorems which shaped two central mathematical developments within mainstream economics, namely general equilibrium theory and game theory. The use of the mathematical methods developed during the twentieth century presupposes, of course, independence of the factors involved, that is, the absence of internal relations, which is the same thing as presupposing atomism, as Keynes realised.

Keynes’s critique of the use of mathematical methods that presuppose atomism has been developed at Cambridge, especially by Tony Lawson (1997, 2003).

In so doing, Lawson recovers the fundamental notion of the philosophy of the Cambridge tradition, namely the notion of internal relations. Effectively, it is the recognition that economic reality is internally related that leads Lawson to the development of a realist perspective, and of a critique of mainstream economics. Although Lawson started his analysis of these themes through a study of Keynes’s Treatise on Probability, the method of study developed by Lawson is quite in line with Sraffas own approach. Just as Sraffa focused on the conditions of possibility for the reproduction of economic structures as a whole, so Lawson focuses on the conditions of possibility for the reproduction of social structures as a whole. The need of focusing on conditions of possibility for the reproduction of a whole stems from the recognition that reality is internally related, so much so that we cannot focus on the analysis of a given component while assuming that everything else remains constant, as Marshall did when addressing the problem of internal relations.

Lawson (ibid.) notes that in the natural sciences, we often can insulate and thereby identify a given mechanism through laboratory experimentation, in turn allowing for the application of mathematical methods. But in the social realm, we are in an open system, where mathematical methods that presuppose closed systems are not effective. In the social realm, the best methodological procedure available consists in finding partial r egularities that persist through time. Kaldor misleadingly labelled these as ‘stylized facts’, and they were subsequently more appropriately reformulated as demi-regularities (or partial regularities) by Lawson. The closest analogue to a mathematical constant which can be found in economics are those persistent demi-regularities. However, most often the only mathematics that we need to possess in order to study them is arithmetic, used by classical economists since Petty.

The method of focusing on enduring regularities, that persist through time as a centre of gravitation, and can be observed as such in the real world, was the classical method, as Garegnani (1984) notes. Harcourt (1981) explains that it was also the method used by different Cambridge economists who shaped the Cambridge economic tradition, like Marshall, Keynes, and Sraffa. But at the level of economic theory, those economists had conflicting interpretations of classical theory: the Marshallian one, which is the dominant interpretation (which Keynes also followed, leading him to criticise classical theory), and the Sraffian one, which is simply Marx’s original interpretation. The Cambridge contribution to the revival of classical political economy followed those two divergent interpretations, which remain today the most influential.