In our book Laws of Chaos, published by Verso in 1983, we advocate a fundamental methodological shift in the foundations of political economy. footnote1 Economists and economic philosophers have often pointed out the essentially indeterminate and statistical nature of economic categories such as price and rate of profit. footnote2 Marxists, in particular, have recognized that this indeterminacy is rooted in the disorderly, uncoordinated and chaotic nature of capitalist market relations. footnote3 Yet, in (theoretical) practice, the approach taken by all economic schools, Marxist and non-Marxist alike, is predominantly determinist: basic economic categories are theorized as determinate numerical quantities, interrelated by means of determinist laws. In loc we advocate the abandonment of this methodology in favour of a thoroughly probabilist conceptual framework, which does not merely pay lip-service to the statistical nature of basic economic categories, but actually builds it into its theoretical models. These categories, we argue, should be theorized as probabilistic ‘random variables’, interconnected by statistical laws.

We also attempt to show in loc how such a methodology, applied to Marxist economic theory, can produce a reconstructed, modern probabilist version of the labour theory of value, capable of overcoming the profound theoretical crisis of traditional Marxist political economy. In our view, this crisis is largely due to the erroneous determinist mediation which the traditional theory posits between values and market-prices; the mediating link being the so-called prices of production. This mediation has given rise not only to the notorious impasse of the ‘transformation problem’—which has afflicted the theory for almost a century, but which melts away under probabilist scrutiny—but also to a more general malaise. In Marxist theory, the underlying deep-level socio-economic reality of capitalism, the nature of capitalist exploitation, is analysed in terms of value categories. But the application of these categories to the analysis of observable economic phenomena (which are directly described in terms of price categories) has remained problematic. Quite apart from the mathematical difficulties posed by the ‘transformation problem’, the crisis in Marxist economics is betrayed by the inability of the ‘traditionalist’ adherents of the labour theory of value to make much use of it in a down-to-earth analysis of the concrete observable reality of capitalism. footnote4 We believe that this crisis is an outcome of the imposition of a determinist model on a ‘chaotic’ reality. In loc we demonstrate that the introduction of a probabilist methodology into the foundations of political economy allows value categories to be integrated as a useful and necessary tool in the analysis of concrete capitalist reality.

The present article is not intended to be a summary of loc; rather, its aim is to put our project in perspective and explain its context in two interconnected respects. We shall discuss the need for a probabilist methodology in political economy, while also making some observations on the history of its application in other sciences. Then we shall sketch how a probabilist approach can help to bridge the rift, in current Marxist political economy, between the deep-level system of value categories and the concrete analysis of the living reality of capitalism.

The methodological shift we are advocating in the foundations of political economy should be viewed in a more general philosophical and historical perspective. In this article we are obviously unable to undertake a systematic survey of the history of the application of probabilist methods in the various sciences, or a comprehensive discussion of the general philosophical problems to which these methods give rise. We shall confine ourselves to making a few remarks that seem to us particularly germane to our thesis. We shall start neither at the nebulous beginning of the story, nor at its non-existent end, but right in the middle.

On 3 October 1848, at a meeting of the Manchester Literary and Philosophical Society, the famous local industrialist and man of science James Prescott Joule presented a paper in which he showed how to calculate the speed of the molecules of hydrogen gas at a given temperature. footnote5 Several interesting points may be raised regarding this celebrated paper, not least of which is that from a more modern point of view the (determinist) theoretical model used by Joule in his calculation is quite inappropriate, and the quantity he calculates (‘the’ speed of the gas molecules) does not exist in reality but is a figment of that model.

Let us describe briefly the background to Joule’s calculation and explain in what way he went wrong. During the 1840s, the view that heat is a special kind of substance, an indestructible fluid (called ‘caloric’), was becoming discredited and replaced by the kinetic theory of heat, a revival of an idea which had in fact been proposed long before. According to this theory—which is still upheld by present-day science—heat is a particular form of energy, inter-convertible with other forms, such as mechanical or electrical energy. It consists in the energy of motion of tiny particles (molecules) of which matter is made up; the more vigorous this molecular motion, the hotter the body of matter made up from them. Thus, for example, when a moving macroscopic body encounters resistance (friction), the mechanical energy of its motion is not destroyed but is ‘distributed’ among the molecules, speeding them up and so producing heat. Indeed, in an exemplary series of experiments, during the five years up to 1848, Joule himself had determined the ‘rate of exchange’ between mechanical and thermal energy. (This won him lasting fame. A unit of energy, the joule, has been named after him. Roughly 4.2 joules are needed to raise the temperature of one gram of water by one degree centigrade.)

This theory also explains the pressure exerted by a gas on the walls of a container in which it is held: the pressure results from the thermal motion of the gas molecules, as they in their millions incessantly bombard the walls and bounce off them. Clearly, if a gas in a closed container is heated, the increased speed of the molecules will result in increased pressure. (This is part of the explanation of how a steam engine works—a topic of some interest to a Manchester industrialist of the mid-19th century.)