# Lawson’s Mathematics Ideology

Tony Lawson *Mathematical Modelling and Ideology in the Economics Academy: competing explanations of the failings of the modern discipline? *Economic Thought 1:3-22, 2012.

## Abstract

The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. …

## Introduction

[The] fundamental problem of modern economics is that methods are repeatedly applied in conditions for which they are not appropriate. …

The specific conditions required for the sorts of mathematical methods that economists continually wield to be generally applicable, I have shown, are a ubiquity of (deterministic or stochastic) closed systems. A closed system is simply one in which an event regularity occurs. Notice that these closures are as much presupposed or required by the ‘newer’ approaches to mathematical economics, those often referred to as non-linear modelling, complexity modelling, agent-based modelling, model simulations, and so on (including those developed under the head of behavioural or neuro- economics), as they are by the more traditional forms of micro, macro and econometric modelling.

The most obvious scenario in which a prevalence of such closures would be expected is a world 1) populated by sets of atomistic individuals or entities (an atom here being an entity that exercises its own separate, independent, and invariable effect, whatever the context); where 2) the atoms of interest exist in relative isolation (so allowing the effects of the atoms of interest to be deducible/predictable by barring the effects of potentially interfering factors). Not surprisingly the latter two (ontological) presuppositions are easily shown to be implicit in almost all contemporary economic modelling contributions.

However, explicit, systemic and sustained (ontological) analysis of the nature of social reality reveals the social domain not to be everywhere composed of closed systems of sets of isolated atoms. Rather social reality is found to be an open, structured realm of emergent phenomena that, amongst other things, are processual (being constantly reproduced and transformed through the human practices on which they depend), highly internally related (meaning constituted though [and not merely linked by] their relations with each other – e.g., employer/employee or teacher/ student relations), value-laden and meaningful, amongst much else.Employing the term

deductivismto denote the thesis that closed systems are essential to social scientific explanation (whether the event regularities, correlations, uniformities, laws, etc., are either a prior constructions or a posterior observations), I conclude that the fundamental source of the discipline’s numerous, widespread and long lived problems and failings is precisely the emphasis placed upon forms of mathematical deductivist reasoning1.

### An assessment of the political-economic ideology explanations

My own view is that neither of these explanations of the state of modern economics is sustainable. [That ideology renders economists blind to reality, or that economists seek to support a laissez-faire view.]

Rather it

is precisely the doctrine that all serious economics must takethe form of mathematical modelling.… the problems of modern economics stem first and foremost from the misplaced attachment to mathematical reasoning despite the record of failure so far ..

… Let me emphasise that I am quite aware that there are forms of mathematical systems, methods and techniques beyond those currently and/or traditionally prosecuted by economists. Deductivist forms, presupposing closures of the sort defined above, just happen to be those that economists (so far) find easiest to wield or otherwise most convenient. I do not argue that all forms of mathematical method (including those yet to be invented) must necessarily be inappropriate to social analysis – though I strongly doubt that any will ever prove of general use for addressing/illuminating the sort of capitalist social system in which we currently live.

[The] reliance on mathematical modelling and on criteria like predictive accuracy, goes almost unquestioned throughout much of the economics academy, certainly within the mainstream and sometimes even beyond. ..

[The] belief/conviction that ‘the only proper economics is a mathematical economics’ is a prevailing form of ideology.

… A large part of the explanation, I suggest, is simply that mathematics has been so successful in the history of human endeavour, and especially within (non-social) natural science, that its centrality to all science and serious and systematic investigation is, throughout wide sections of society, taken as an article of faith.

So my contention, in sum, is that the modelling emphasis of modern mainstream economics is explained by a largely unquestioning society-wide conviction (a form of ideology) that mathematics is fundamental to all science, a conviction or ideology that itself is in large part explained by the successes of mathematics in so many other domains.

… Parenthetically, I believe this inability of the mathematical modelling project to challenge anything seriously or convincingly is a major factor in understanding how the project has survived as long as it has in the economics academy, and even how it originally came to dominate.

## Conclusion

[The] primary explanation of the numerous, long lived and continuing failings of modern academic economics is the (misplaced) emphasis on mathematical modelling. It is an emphasis underpinned by the cultural belief that a reliance on mathematical technique in science is somehow so normal or neutral or natural that any questioning of this emphasis can be ignored or swiftly dismissed as obviously far too radical if not nonsensical.

## Comments

The abstract is moderate and reasonable, blaming ‘an over reliance on largely inappropriate … methods … ‘ for various economic problems. I would go further and discuss the social welfare impact of such methods. But the conclusion, it seems to me, goes beyond this, to criticise mathematical modelling and mathematical technique on the whole, not just those models and techniques that have been used so far.

I think that the paper is reasonable in calling the mind-set that has led to the (largely inappropriate) use of mathematics an ‘ideology’, and in this respect would make common cause with the author. But in my blog I attempt to draw a distinction between the (mis)use of mathematical models and techniques as tools in the service of some ideology, and what I would recognize as a properly mathematically-minded use.

Lawson notes that the mathematical methods used by contemporary mainstream academic economists all assume ‘event regularity’, by which he presumably means something like ergodicity. He overlooks Keynes’ use of mathematical methods for economies without such regularities.

He notes that it is common to assume interacting agents behaving like relatively independent classical ‘atoms’ that have an ‘invariable effect, whatever the context’. Again, this overlooks Keynes’ approach, in which agents are more like atoms in physics.

The paper uses the term ‘deductivism’ in a confusing way, akin to a reductionist viewpoint. I would agree with the author (and Keynes) that reductionism is not appropriate, but disagree with the author that deductions of the kind that Keynes proposed are ‘a bad thing’. Indeed, the reductionist mathematical approach has been a failure in many areas, having been replaced by a more nuanced yet still mathematical approach. If economics is to follow the example of the sciences, it should abandon its inappropriate reductionism and embrace more appropriate mathematics. In doing so it would be taking an approach that could challenge many of those policies impacted by the current ideologies.