# The Ideology of Mathematical Economics – a Reply to Tony Lawson

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## Abstract

This paper challenges Tony Lawson’s account of the relationship between mainstream economics and ideology along two key axes. First off, we argue that Newtonian physics has been the primary version of pro-science ideology within mainstream economics, rather than mathematics *per se*. Secondly, we argue that the particular uses of mathematics within mainstream economics have always been ideological in the pro-capitalist sense of the term. In order to defend these claims we engage in two procedures that Lawson has thus far strategically avoided. Namely, we view mainstream economic theory as an integrated theoretical paradigm with intrinsic links to the capitalist economy. Viewed in this way, it becomes obvious that Lawson’s (trans) historical analysis is too general to capture the complexity of the relationship between natural science, mathematics and mainstream methods. Having briefly outlined Lawson’s central argument, we highlight the non-mathematical methods underpinning Classical Political Economy. Thereafter, we assess the nature of the mathematics associated with the Marginal Revolution of the 1870s and the Formalist Revolution of the 1950s.

Great paper. Well argued. Lots of insights and good analysis. Of course, I think that in their main thrust the authors are wrong. But great paper. Deserves to be published

Review of Brian O’Boyle and Terrence McDonough “The Ideology of Mathematical Economics: a Reply to Tony Lawson” for Economic Thought

by

Dimitris Milonakis

University of Crete

O’Boyle and McDonough’s paper offers a direct challenge to one of Lawson’s main contentions, that ideology has nothing to do with the formalistic tendency in modern economics and that the latter can be accounted for mainly by the awe of mathematics in western culture which Lawson elevates to a form of ideology. They offer two main arguments against Lawson’s thesis. First, that although Newtonianism was very influential in developments in economic science from its inception, the same does not apply to the use of mathematics, which had to wait until the marginalist revolution in order to have any impact whatsoever (section 3). Second, they show that the use of mathematics in neoclassical economics ever since the marginalist revolution, has been ideological. Indeed, for them, it is not the use of mathematics per se that is the main issue but the (mis)use of Newtonian science as the scientific prototype (p. 3). As far as the marginalists are concerned, this misusage involves two basic elements: first, although in theory both Jevons and Walras preached Newtonianism, in practice they failed to apply one of its basic principles which is the anchorage of theory to reality in the form of empirical investigation, opting instead for a more Platonic, a priori mode of analysis (pp. 21-22). Second is the fact that neoclassicists stuck to their Newtonian cosmology even after the latter was abandoned by the physical sciences following the Einsteinian revolution in physics at the turn of the twentieth century, by taking refuge in the Bourbakian, axiomatic conception of mathematics during the formalist revolution of the 1950s (pp. 6, 25). In both cases, as O’Boyle and McDonough show, the specific (mis)use of Newtonianism had important ideological (pro-capitalist) connotations.

Overall, I think this is an important and innovative approach to the problem of the formalisation of economic science and deserves to be published as it is.

As chance would have it, I have been working on the same theme for some time now as part of a book project (a first version of my paper on this theme was presented at a conference in September 2013 under the title “Mathematics and Formalism in Economic Discourse: a Potted History with Some Partial Explanation”), and I have reached very similar conclusions, although the scope of my paper is wider, including a whole historiographical tradition in economics which includes the work of Ingrao and Israel, Mirowski and Weintraub as well as Lawson. At the same time, the type of argumentation used in the two cases is also very different. O’Boyle and McDonough’s paper uses a more conceptual/analytical type of argument, whereas my paper offers a more historical type of narrative. As such, the two papers are complementary, reinforcing our common challenge to Lawson’s thesis. The title of the current version of my paper is “Formalising Economics: Social Change, Ideology and Mathematics in Economic Discourse” and an abbreviated form under the same title is currently under review in another journal. I have discussed the issue with the authors of the paper (who have also read my piece), as well as with the editors of both “Economic Thought” and the special issue of the journal to which I have submitted my paper, and we have all reached the conclusion that this is a case of parallel or “simultaneous discovery”.

Brian O’Boyle and Terrence McDonough “The Ideology of Mathematical Economics: a Reply to Tony Lawson”: A comment, by Josef Mensik, Masaryk University Brno

I consider the research programme of relating ideology to economics interesting and purposeful. There are two main tacit theses behind it. First, any investigation is done by actual people whose mindsets determine both the questions they ask, and the answers they accept as correct. Second, if people believe their ideas may be of some consequence to the world they live in, they are bound to consider influencing the word by their ideas. This is why many economists must be tempted to spread their political ideas through their academic output.

Although I am, I suppose, in general agreement with the authors on the above, I am with Tony Lawson as what regards the relation of ideology and mathematical economics. If you asked Tony Lawson whether using regression to explore social reality is politically left or right, the answer would be, I believe, “it is not political, it is plainly wrong”. Regression, game theory, function optimization on convex sets — all of mathematics — is in itself apolitical.

Using mathematics in economics has nothing pro-capitalist about itself. After all, it was the pro-socialist authors (Lange, Lerner) who argued for central planning using mathematical economics while their pro-capitalist opponents (Mises, Hayek) were strictly against any use of mathematics in economics. Or take the Sraffa’s model: it is both explicitly contra-capitalist and completely mathematical.

Neither is resistance against using mathematics in economics pro- or contra-capitalist on its own. Current heterodox economics covers schools with both pro- and contra-capitalist positions which disagree completely about what should the preferred economic system look like, yet most of them agree on one thing: mathematical modelling is not an appropriate method for economics.

If the claim stands that “the particular uses of mathematics within mainstream economics have always been ideological in the pro-capitalist sense of the term,” it is the “use” rather than “mathematics” which is the culprit here of any political bias being introduced into economics. But since anyone uses all means available to attain their ends, this does not explain much. If some people find it convenient to advance their political views using mathematics, they might choose to do so whether the views in question were pro-capitalist or contra-capitalist. The claim as such does not say us much about the relation of mathematical economics and pro-capitalist views. Rather, it can be translated as a prevalence of pro-capitalist views within the present mainstream coupled with the growth of mathematical modelling in economics.

We would like to begin by thanking Tony Lawson, Dimitris Milonakis and Josef Mensik for taking the time to read and comment on our paper.

Special thanks go to Tony who, although he not unexpectedly disagrees with the thrust of the argument, was good enough to argue for publication on the strength on what he sees as interesting insights and good argumentation.

Overall, our thesis is developed around two key arguments.

The first is that we must explore the development of mainstream economics, including the rise of mathematics, within its historical and socio-economic context. The second is that we must see economic theory as a totalising research programme, linking key concepts and methodological devices – including mathematics – to a foundational vision of free market capitalism.

In our estimation, Lawson’s analysis is insufficiently historical and insufficiently conceptual.

To see this, we argued that a detailed history of economic theory does not bear out the assessment that mathematics have always been the source of ideological attachment within mainstream economics. In fact, prior to the 1870’s the dominant school of economic theory – British Classical Political Economy – was expressly non-mathematical. This causes problems for Lawson’s transhistorical pronouncements.

Our second key argument is that the particular development of mathematics within economic theory took place within a conceptual system that prioritised utilitarian metaphysics rather than empirical investigation. The use of mathematics was, moreover, part of a conceptual framework built to deduce the superiority of free market capitalism.

At this point we can take up the criticism of Josef. His first argument seems to be that because mathematics have been used to both defend and attack the system, there is no inherent bias towards capitalism in the use of mathematics. We would largely accept this claim with the proviso that it doesn’t speak to the argument we are making. Our argument is about the historical development of mainstream economics, with its particular blend of utilitarian metaphysics and Newtonian mathematics. There are important differences between Sraffa’s technical use of an input – output model and the paradigm shift away from real world empirical analysis into a mathematicised –utilitarian utopia constitutive of the Marginal Revolution.

This necessitates engaging with the historical analysis and agreeing or disagreeing – something that Josef unfortunately doesn’t do.

He then states that it must be the use of mathematics that is key rather than mathematics itself. This is precisely our case, argued with an analysis of the three key turning points in the actual development of mainstream mathematical economics. Yet instead of engaging with the strengths or otherwise of our argument, Josef falls back onto the current subjective intentions of practicing economists. This is one of the longstanding problems in Tony’s analysis reproduced by Josef.

It completely misses the point of our analysis which is to link mainstream mathematics to a particular research programme that has a pro-capitalist bias. It is not about subjective intentions and neutral methods – it is about a framework built to ask certain (pro-capitalist) questions with mathematics used to help answer them.

Josef’s final sentence about the prevalence of pro-capitalist views and an independent rise of mathematics is basically restating the Lawsonian case without explaining why we are wrong and he is right. In the end his review has not engaged with our ideas on their own terms.

This brings us to Dimitris’ comments. Having read his paper “Mathematics and Formalism in Economic Discourse: a Potted History with Some Partial Explanation” after submitting our own one, we are extremely gratified that an almost identical assessment of the problems in Tony’s work from a Marxist perspective is beginning to emerge. As Dimitris rightly suggests, this is a case of parallel or “simultaneous discovery” on the basis of a similar assessment of the historical record. Hopefully this will spark further debate and reflection on what is clearly an extremely important topic.