# Mathematical Modelling and Ideology in the Economics Academy: competing explanations of the failings of the modern discipline?

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## Abstract

The widespread and long-lived failings of academic economics are due to an overreliance on largely inappropriate formalistic methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because many economists are committed to a portrayal of the market economy as a (overly) smoothly or efficiently functioning system or some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to any form typically attributed to the mainstream, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally.

Thank you for submitting this article. Your argument is interesting, but I don’t think you have made much of a case that the problem is mathematical formalism per se, rather than the particular mathematical focus of the mainstream neoclassical tradition: the “stupid” (“absurd” would IMO be more accurate, as well as less belligerent) general equilibrium models. I believe this emphasis arose in large measure out of the realization that unlike physics, economics is impossibly too complex to be addressed with the kind of mathematical tools that were available in the late 19th and early 20th centuries, so the economists who created the neoclassical hegemony used the mathematical tool they had — calculus — in the only way they knew how (a case of having a hammer, and consequently assuming everything is made of nails). Perhaps shifting the mathematical focus off equilibrium and onto chaos, off vacuous “proofs” and onto statistics, though making the math less tractable, might make it more relevant and informative.

I would be interested to read your opinion of “econophysics,” which adapts physics tools to economics problems. Though I don’t think it has much theoretical validity, the great advantage I see in it is its thoroughgoing empiricism, asking only, “What are the data trying to tell us?”

Thank you for this article. I am also somewhat unconvinced by this paper that mathematical formalism or mathematics in general is the problem with the economic discipline. In my experience with mathematics, I have found that there are a great number of ways to express relationships of almost any kind. Using some mathematical tools may not be obvious at first. For example, the use of Lie groups in physics, brownian motions in finance, or topology in economics. My main point is that economics may not be using the right mathematical tools, but we should not give up hope. Mathematics can be used for understanding almost anything that exhibits any pattern, however abstract. Therefore, I would ask that economists investigate the alternatives and reconsider the mathematical tools that exist today. I would also suggest further serious investigation into alternative models, perhaps outside of the scope of the current economic paradigm. To be able to use the mass of mathematical tools more proficiently, rather than just a specific set (here Newtonian calculus), we will be much more prepared to handle the challenges of the future. Certainly the use of more appropriate tools may not yield the clean solutions that we have come to love, but it will likely allow us to continue to apply rigorous and exact meaning to the the theories and models that we create. The greatest strength of mathematical formalism is that it forces economists to express their ideas precisely, and then we can evaluate those ideas without further interpretation. The capability of such formalisms is a continuing discussions in the field of metalogic. I encourage economists to continue to look more at alternative mathematics and at the philosophical nature of mathematics in general.

As a mathematician with a strong interest in real-world economics, I agree with the other comments that the problem is more the kind of mathematics used, and the goals pursued, not the mathematical modeling as such. For an accessible overview of the kind of modern mathematics that could be used, read “Economyths – Ten Ways Economics Gets it Wrong” by mathematician David Orrell. Abstractly, think “non-linearity”, “complexity”, “chaos”, “power laws”, etc – the kind of stuff they do at the Santa Fe Institute.

More concretely, I understand that some economists are starting to use agent based models. Also, the best mathematical economics I know of is still the famous “Limits-to-Growth” system dynamics of the early 1970s – see Ugo Bardi’s recent book “The Limits to Growth Revisited” for an overview of how this work was falsely maligned by some prominent economists like William Nordhaus. A related model for doing mathematical economics the right way is given by climate modeling, since the climate is also highly non-linear and interacts with the natural and even human world in myriad ways.

A key point here is to revisit the whole purpose of mathematical modeling. Exact prediction, or even conventional stochastic prediction, is simply not feasible except in highly constrained circumstances (where non-linear effects are heavily damped). Thus the goals must be qualitative and comparative more than quantitative. If the criteria is “Who could predict the crash of 2008 in 2000?” then forget it. Instead, good models would have shown the strongly increased risk of a financial bubble of some sort due to the extraordinary deregulation through the 1990s, both in policy and practice. They would also have shown through a variety of scenarios what sorts of policy and enforcement actions would have been most effective in moderating that risk.

And really good models (the kind requiring super computers and years of development) could have been very convincing. But only if economists were to be thoroughly re-educated to act more like climate modelers or computational physicists, sidelining their unrealistic toy models and working in teams on big real-world problems.

I would define real-world economics as “the science of how to create sustainable well-being for future generations”, with emphasis on the material aspects of that well-being and in the context of the natural world as well as diverse human cultures. This is far from the point of view of mainstream economics, so I see its ideology as rooted in the very concept of what economics is all about. To an outsider it often looks more like astrology or medieval cosmology than modern science in its devotion to, and elaboration of, simplistic concepts that often end up doing more harm than good.

Note that the 5 key variables of the Limits-to-Growth study are Resources, Population, Food, Pollution, and Industrial Output. This kind of real-world language should be at the core of economic theory – no “externalities” here. The ideological blinders are those that block economists from rethinking the core concepts of their profession.

It is going to be difficult to comment on these responses, if only because I lack the precision in language that the topic requires. In defending what I take Tony Lawson’s position to be, I may also merely reveal my unfamiliarity with his position.

Rather than replacing one formalist method with another that is commendably less absurd (as some reviewers appear to advocate), it may be that faith in formalism in the social sciences is the problem. (Isn’t this Lawson’s own argument?) There appears to be an urge beyond rational understanding to cling to the methods employed with such success in the physical sciences. (Whether it is maleness is a separate issue. It may be that people generally crave to feel that they know at least something about what is important to them. There must be some pop evolutionary psychology that can be dragged in as pseudo-corroboration.)

Is the problem too much math or too much of the wrong kind of math? Though Lawson is trained in mathematics, he appears to regard formalism per se as an unreliable means of analysing, explaining or depicting social life. But does Lawson’s “largely inappropriate” in the Abstract carefully leave open the possibility that formalism has some moderately useful though limited role? Is it the faith in formalism –a fetish inevitably resulting in super-saturation – or is it any use of formal methods per se that is the problem? I’d be surprised if it was the latter. A simple Keynesian model is handy to have in mind, so long as one understands why the relationships are modelled in this way rather than in some other. On the other hand, formalism as a professional practice connotes disdain towards the understanding of these hows and whys. So is “formalism” what is done (i.e., writing down a model, which seems fairly harmless in isolation) or is it about how such modelling is conventionally elevated beyond good sense to a near-monopoly ranking in the community of economists? Is the problem with the “ism” rather than with the “formal”?

Complex formalism is still formalism; it still strives to stand outside what we are trying to explain. Social life is lived and understood socially by those who have participated in social life. We hold beliefs and follow rules in common; we evaluate them and sometimes we choose to change our beliefs and the rules under which we live. Can formalist methods explain the genuine choices we make or even properly define what we regard as the relevant possibilities?

Perhaps introspection and debate can do better in revealing and exploring the rules and the narratives we create and internalise. There may be too many dimensions in which change is open-ended; the equations may not be able to cope, and informality may be imposed upon us by reality. I think that this is Lawson’s long-held position.

I wonder whether the supremacy of Santa Fe or the Club of Room would be any more congenial than the regime in charge now.

Also I wonder where Tony Lawson stands on Schumpeter’s views on ideology and on “vision”. The latter would presumably include one’s ontological inclination. There can be suspicious correlations between ontologies and ideologies. But I know nothing of the politics of Tony Lawson or those who have commented on his paper, so I cannot even conjecture that the differences are ideological.

BL, Jan 23 2012

Comment on: Tony Lawson ‘Mathematical Modelling and Ideology in the Economics Academy: competing explanations of the failings of the modern discipline?’ by Donald Gillies, University College London

Having agreed with most of Tony Lawson’s views on the philosophy of economics for many years, I had expected that, when we both submitted a paper to the new journal: Economic Thought [Gillies (2012), Lawson (2012)], our two papers would be largely in harmony. However, it turns out that there are now quite substantial differences in our points of view, and this comment is designed to explore these differences. I will mention in turn 3 differences, but conclude by drawing attention to a point on which we are still in agreement.

(1) In an earlier paper [Gillies (2004)], I put forward a view about the use of mathematics in economics, which largely agreed with that of Lawson. The paper was entitled: ‘Can mathematics be used successfully in economics?’ and it argued that the answer to this question was ‘no’. In reaching this conclusion I was impressed by the fact that Keynes in the General Theory, and the Marxists in a number of works, had provided very successful explanations of important economic phenomena without using mathematics; whereas the neo-classical economists, who used a lot of mathematics, did not appear to have explained any economic phenomenon satisfactorily. The group, which I failed to consider in that paper, was that of Sraffa and his followers. Many Sraffians use a great deal of mathematics, but they strongly criticise and reject mainstream neo-classical economics. One leading Sraffian, Steve Keen used mathematical techniques to predict successfully the financial crisis of 2008, and he defends the use of mathematics in economics in his (2011). Keen’s work therefore shows that, after all, mathematics can be successfully used in economics.

Lawson seems to allude indirectly to Keen’s success (2012, p. 14) when he reproves “The heterodox Real-World Economics Review” for seeing fit “to create a Revere Award for Economics given in large part for success in predicting the Global Financial Collapse.” Keen was of course one of the recipients of this award. However, Lawson (2012, p. 14) sees the award as “a move that may well further encourage the uncritical reliance on formalistic models and the predictive criterion of success.” Now the predictive criterion of success is used in all the natural sciences, and I see no reason why it should be abandoned in economics. Of course qualifications of the criterion are needed in both the natural sciences and economics. A theory may give a correct prediction just by luck, and again, empirical support need not be generated exclusively by predictions, it could be generated by successful explanations as well. However, given 3 theories T1, T2, and T3 , if T1 gives an incorrect prediction, whereas T2 & T3 give correct predictions, it is surely reasonable to say that T2 & T3 are better supported that T1 by the evidence in question. I also think that Lawson is wrong to associate predictions exclusively with formalistic models. In my 2012, pp. 31-32, I analyse another successful prediction of the financial collapse, that of Soros. Soros, like Keen, got the prediction right, but, whereas Keen used mathematical modelling, Soros’ model was qualitative in character and did not use mathematics.

(2) I now turn to my second point of difference with Lawson (2012). I argue in my own paper [Gillies, 2012, pp. 15-17] that each of the major schools of economic theory is associated with a political ideology. Thus Marxist economics is associated with a left-wing ideology, and neo-classical economics with a right-wing ideology. Now I would argue that it is this right-wing ideology, rather than the use of mathematics, which leads the mainstream economists astray. Keen got a correct prediction using mathematical techniques but theoretical postulates completely different from those of neo-classical economists. This surely shows that it is the theoretical postulates of neo-classical economists, rather than their use of mathematics, which has led them into error. Moreover, these theoretical postulates are suggested by their right-wing ideology. In fact, all those who correctly predicted the financial collapse such as Keen, Soros, etc. were harsh critics of neo-classical economics and rejected its theoretical postulates. This is strong evidence that these theoretical postulates are at fault. I cannot therefore agree with Lawson when he says (2012, p. 10): “ … the insistence that methods of mathematical deductive modelling always be employed … is by itself sufficient to explain the mainstream deficiencies …”

(3) My third criticism of Lawson (2012) concerns his explanation of why the mainstream have adopted mathematics. This is contained in the following passage (2012, p. 15): “Certainly a perception that, especially where measurable quantities are involved, all serious research requires a mathematical form has been widely in evidence since the Enlightenment.” This doesn’t seem to me to be true historically. In the 19th century the sciences of chemistry and biology developed very successfully but used very little mathematics. Yet they were regarded as serious research. Indeed much of chemistry and the bio-medical sciences to this day use very little mathematics beyond basic statistics, and yet everyone recognises that they have made most important advances. This is a relevant point for economics, since, as I suggest in my 2004, economics need not model itself on physics but could choose for its model instead other branches of natural science which have been successful without using a great deal of mathematics.

How then are we to explain the prevalence of mathematics in mainstream economics? We can do so by examining the theoretical postulates put forward by neo-classical economists. These concern the maximisation by agents of their utility and profit, and considerations of equilibrium. Now as soon as some process of maximisation leading to equilibrium is postulated, this almost necessitates the use of differential calculus and so some higher mathematics. The theoretical postulates of Keynes in The General Theory or of Marx in Capital Vol. 1 do not involve maximisation or other assumptions, which provide a stimulus to introduce mathematics.

(4) Let me conclude, however, by mentioning a point in Lawson (2012) with which I strongly agree. He writes (p. 10): “I want briefly to indicate an alternative ideology … that I believe does pervade the economics academy … it is precisely that all serious economics must take the form of mathematical modelling.” I think such an ideology (not a political ideology) does indeed pervade the economics academy. It is a special case of the view which Lawson formulates on p. 18 as “the specific meme: ‘mathematics is essential to science’.” This meme is false, since, as we have seen, many natural sciences have been very successful without using much mathematics. Conversely the use of mathematics does not make a theory scientific, since there are perfectly legitimate branches of pure mathematics, which are unrelated to empirical data, and so not scientific. Economists should aim to produce theories, which are confirmed by empirical data. In some cases, these may use mathematics: in others, not. The key question is not whether the theory is mathematised, but whether it is confirmed empirically.

Let me say in conclusion that, although I disagree with some of the views in Lawson (2012), I found the paper immensely stimulating to read. It is vintage Tony Lawson in that it brings to light crucial and controversial issues which need to be debated. It is thus ideally suited for the first issue of Economic Thought.

References

Gillies, Donald (2004) Can mathematics be used successfully in economics? In Edward Fullbrook (ed.) A Guide to What’s Wrong with Economics, London: Anthem Press, pp. 187-197.

Gillies, Donald (2012) Economics and Research Assessment Systems. Submitted to Economic Thought.

Keen, Steve (2011) Debunking Economics – Revised and Expanded Edition. The Naked Emperor Dethroned? London, New York: Zed Books.

Lawson, Tony (2012) Mathematical Modelling and Ideology in the Economics Academy: competing explanations of the failings of the modern discipline? Submitted to Economic Thought.

Tony Lawson seems to me rare amongst economists who are expert in mathematics in that he is concerned equally with the concepts that underlie the maths. The tendency of mathematicians to overlook conceptual issues may lie behind his contention that mainstream theory lacks any strong political-ideological content, but has only a methodological-ideological content. It is surely difficult to escape the idea that mainstream economics tends to sustain an individualist position, as opposed to communal advantage.

Whether the underlying concepts of mainstream economics are political-ideological or not, the marginal model clearly requires a certain type of mathematics – calculus. So the use of mathematics is inextricably bound up with the basic concept of how people choose in an economy. So when Thomas Bowen (in comments above) suggests that it is the kind of mathematics that is applied in economics that is the problem, he is surely also saying that the underlying concepts are at least part of the problem. He recognises that investigation of alternative approaches to economics might generate a different type of mathematics.

Tony Lawson suggests that mainstream economists, following a general cultural disposition (‘…many people appear to suppose that anything stated in mathematics must be correct’), have the idea that because their concepts are expressed in mathematical terms, they must be right. Then, of course, Thomas Bowen’s advocacy of a different kind of mathematics is more directly to the point. Changing the maths might change what must be right. I have always suspected that this idea of ‘mathematical infallibility’ lies behind much neoclassical analysis, and hence make it sustainable against the evidence. But I tell myself that even mathematicians are not so naïve. When a specialist like Tony Lawson asserts it, I begin to think it really is true.

Thomas Bowen writes, ‘I would also suggest further serious investigation into alternative models, perhaps outside of the scope of the current economic paradigm.’ I have been trying over past decades to develop a theory of support-bargaining and money-bargaining as a more satisfactory conceptual foundation for the explanation of economic activity. This involves a situation-related understanding of consumer choice (and of selection in general). In ‘Situation as Determinant of Selection and Valuation’ (Cambridge Journal of Economics, Vol. 35, No. 2, pp. 335-356), I suggested (p. 347) that symmetry is potentially an important factor in determining what ‘fits’ a particular situation. This concept means that the mathematics of symmetry is appropriate to the concept of situation-related selection, in the same way that calculus is appropriate to marginal theory.

The idea of support-bargaining and money-bargaining is elaborated further in Companies and Markets (submitted to WEJ, already posted for review) and Science and Support (submitted to ET). The role of symmetry in society is taken further in the penultimate chapter of Survival of the Sociable (Forthcoming).

Review.

I understand that the first issue requiring a reviewer’s attention is whether or not the article should be considered for publication. I believe it should.

I would expect the readership of Economic Thought to be interested in understanding what the main characteristics underlying mainstream economics are and why and how did mainstream economics reach its current dominant position. The article addresses these two questions and on such grounds is relevant and fits – as I understand it – within the research scope covered by Economic Thought.

The above been said I would like to share some comments which – if deemed applicable – are intended as suggestions and as constructive criticism.

A Clarification Seems Required.

The author uses, interchangeably, the terms formalism and mathematics and suggests further, on few occasions, that these two terms could also be equivalent – within the scope of the discussions – to calculus and deductive modelling. These terms are not equivalent and therefore should not be used as if they were. However, more importantly, by treating those terms as having equivalent meanings the author diverts the reader’s attention from the actual issue being discussed. I shall elaborate on this latter comment as follows.

Initially, in much the same vein as in Thomas Bowen’s comment, I note that the author’s using, interchangeably, the terms mentioned above readily invites the reader to take a critical stance against his article because mathematics can contribute to clarity and can help understand specific phenomena by providing explanations not expressible in natural languages. My point, however, is that the article contains nothing to suggest otherwise. I took the trouble to read previous work by Lawson to confirm that, indeed, the issue of his interest is not related to mathematics providing (or preventing) clarity in economic debates. Particularly, the issue is not about mathematics being an (in)appropriate language for economics but about specific mathematical techniques being considered as the only valid ones in modelling economic phenomena. Therefore, I consider the author’s lack of precision when interchanging the terms formal and mathematics as the cause for diverting the readers’ attention from the real issue of interest.

The British legal system does not rely on fundamental codes (as opposed to the French system, for example). In view thereof, many contracts have a glossary in the opening section. This is a formal requirement to add clarity and to indicate acceptance of a procedure thought necessary in the absence of codes. Thus, being formal simply means that one is abiding by a requirement thought necessary and applicable. It does not relate to mathematics, although by being mathematical one is always formal.

Although the author seems to suggest that economics would benefit from less formal approaches (e.g., when mentioning Stiglitz on page 13, first paragraph) it is clear that in relation to the confusion being noted, the issue must be clarified as I argue below.

By the sole reading of the paper I failed to grasp how the author was taking issue with formalism and mathematics. The introductory paragraphs 3, 4 and 5 are not sufficient as I shall discuss in the next section. I had to check the relevant (for this paper) references consisting of chapters 1, 2 and 10 of Reorienting Economics. As I understand it now, the author develops an ontological argument to oppose the insistence in one’s using calculus when modelling economic phenomena. My current interpretation of his argument is that even the very basic, fundamental procedure of representing economic agents by functions (e.g., utility or production functions) is problematic. Indeed, the concept of function is applicable only when one presupposes what the author calls “closed system” and “atomism”. In their absence (as the author claims is usual in economic reality) using functions – and the consequent deductive developments called for by calculus – imply a misrepresentation which should be expected to limit, severely, the ability of the resulting economic theory to predict outcomes or simply to provide insights on the phenomena under study.

I am not suggesting that the ontological argument should be developed in the paper. All what I am saying is that the author should be clear that the idea underlying this paper’s arguments concerns economists’ (mainstream and some heterodox as well) using functions and calculus to model most types of economic phenomena. It is not about economics going formal (i.e., all sciences must abide by appropriate methodologies), it is not about opposing deductive reasoning (i.e., in the sense that logical arguments are deductive), and it is not about opposing economics’ being expressed mathematically (i.e., in the sense that mathematics comprehends more than calculus; for example, set theory and algebra).

Further, should the author proceed to clarify this idea, I reckon he will find quite appropriate to clarify also the following point. One might think that the shortcomings of (mainstream) economics could be overcome by using more sophisticate techniques of mathematical analysis – typically, by referring to Complexity. This is the point by Roy Langston. It is my understanding, however, that the author would not see Complexity as being particularly helpful. To the contrary, I think he will consider that more sophistication would only further blur our understanding of the economic phenomena. This is so because the problem lies not with the inherent limitations of calculus but rather with the ontological inadequacy of calculus to represent economic reality. It is within the scope of this particular clarification that I would like to see the author responding to the comment by Dick Burkhart, which calls for economists being “re-educated”.

In view of the foregoing I would recommend the author’s avoiding expressions such as “…methods of mathematical deductive modelling…” (paragraph 3), “…formalistic methods…” (paragraph 3) and “…The (mathematical) method…” (paragraph 5). I would recommend that one term be chosen and consistently used throughout the paper to convey the idea – if my reading is correct – that the author is focusing on calculus – i.e., the methods of mathematical analysis concerned with the systematic study of real and complex-valued, possibly stochastic, functions. I also suggest that he make a point – if indeed applicable – that using more sophisticate methods of mathematical analysis (e.g., complexity) would not help economic theorizing and therefore do not qualify as a counter-argument to his ontological argument. I believe these two recommendations and this suggestion would improve the structure of the paper in a way that the reader would no longer divert his attention from the main issue of interest. I note, for example, that the comment by Bruce Littleboy revolves solely around this confusion. And, with this clarification issue behind, I can now proceed to discuss what I understood the main issue to be.

A Structural Problem.

With the view of discussing the main issue being addressed in the paper I must note initially that – as I see it – there seems to be a structural problem in the way the author has organized his article. Indeed, one could make a case for at least three different issues being the main one, namely:

1st – to dismiss the political-economic ideology contention (see abstract);

2nd – to establish “…the assessment that the misplaced emphasis on mathematical deductive reasoning provides the better explanation of the rather unhappy state of modern economics.” (page 10);

3rd – to disseminate in the readership of a newly establish journal the author’s ontological argument and his critique of the related meme: ‘mathematics is essential to science’.

I can appreciate how these three issues relate to each other and how it makes sense to address the three of them in the paper. However, I sincerely believe the author would help the reader if he could structure the paper in a way such that only one issue would appear as the main one – subsidiary issues and complementary ideas clearly presented either in support or in contrast with the argument discussing the main issue.

My particular reading is that the leading issue should be the first one – to dismiss the political-economic ideology contention. I have been exposed to this contention before. I would have liked to dispute it but I lacked any element with which to articulate an argument accordingly. The author provides several elements and constructs a convincing argument. I have benefit from his analysis and I consider it to be relevant for any discussion concerning the current dominance of the mainstream-type of economics.

Therefore, I would start the article with paragraph 7 (“Ideology is a term I have rarely employed…”) because it is good editorial procedure to open the article with its main theme.

Further, more on the substance vein, I would avoid considering the meme ‘mathematics is essential to science’ as an ideology, albeit a methodological one, because it weakens the claim that the political-economic contention should be dismissed. Contrast these two statements:

“I have considered the two conceptions of ideology that are most often associated with modern academic economists and I have argued that, in the political-economy garb in which these ideologies are usually presented by opponents of the mainstream, they do not serve easily to account for the explanatory failings of the discipline.” (page 10)

“My contention, then, is that contemporary academic mainstream economics is indeed often underpinned by ideology.” (conclusion, page 20)

The meaning of the term “ideology” is not the same in both statements. Although the author clearly accounts for this change in meaning I would, nevertheless, not have used the same term to account for two different ideas. By doing so, the author causes the first issue – i.e., to dismiss the ideology contention – to lose importance as the main one in the paper. I would have restricted the term “ideology” – in both instances “ideology1” and “ideology2” – to be used in connection with “…the usual political-economy garb…” and refer to its other meaning simply as methodology.

The choice by the author to refer to methodology as a type of ideology can be explained if one understands the second issue to be the main one – i.e., the misplaced emphasis by economists on mathematics. Should that be the case, however, the article loses most of its original content since the author has developed this idea elsewhere.

The way I see it, this structural problem of what the main issue is supposed to be can only be sorted out by the author’s further developing the discussions in the section entitled “The modern mainstream and the economic system” (page 17). Therein, the author presents an argument consisting of three steps:

(i) “…mathematical modelling [of economics] is somehow neutral at the level of content or form…” and “…is largely irrelevant.”;

(ii) by pursuing a neutral and irrelevant endeavour mainstream-oriented research diverts significant resources from the investigation of the real world and in so doing “…deflect criticism from the nature of the status quo…”;

(iii) it also reinforces the status quo since “…issues of power, discrimination, domination, oppression, and conflict generally, are effectively masked over or hidden, or at best trivialised.”

To me, this three step argument fits perfectly with the author’s definition of ideology2. If so, the author would have explained the “misplaced emphasis on mathematics” (issue 2) to be ideologically motivated “in the political-economy garb in which [ideology is] usually presented” (here ideology2), thus confirming the political-economic ideology contention – not dismissing it.

This view is further reinforced by the comment “For government sponsored funding bodies and the like are actually less likely to withdraw funds from a project that provides no serious criticism of the government’s actions.”

I had to read the article more than once to be able to reconcile this conclusion with the claim made in the abstract that the author dismisses the political-economic ideology contention. The way out is to understand that the bad guys are not the economists – they are well-intended people pursuing their research innocently and it just so happens that their research is mathematical and irrelevant. The bureaucrats, on the other hand, are able to manipulate – by their controlling the available funds – what type of research is pursued and their choices and preferences are such that mainstream-type of research is the one that best suit their interests.

For the purposes of this review it does not matter if I got it right. The fact that this interpretation is possible indicates the nature of the structural problem being pointed to here and suggests that the author should review how he organizes the different arguments being put forth in the paper.

To conclude this section of the review, I would further suggest that the author simply make a reference to his ontological argument and skip, altogether, the discussion of his Darwinian explanation.

A Further Suggestion.

I believe the author should refer to sources other than his previous work when discussing the “misplaced emphasis on mathematics”. The author would strengthen his argument if he could show how his view relates to some ongoing debate.

I am new to this debate and I do not know much. Yet, I can think of Varoufakis & Arnsperger (2009) as a nice complementary source to discuss the issue of economics’ misplaced emphasis on mathematics. For one thing, they try to define mainstream economics. In other words, they acknowledge the view that – at some superficial level – mainstream economics is not a coherent project. This is the view held by the author: “Indeed at the level of substantive theory the project is marked by overall incoherence and lack of cohesion amongst its various strands, and with significant uncertainty even as to what is worth pursuing.” (page 9). However, they try to find the common grounds underlying its various strands such that a definition of mainstream economics can be put forth.

As they develop their argument it becomes clear that mainstream theorists fail at their own game: from a pure formal, mathematical perspective the mainstream project is inconsistent. For example, the very foundational concept of price only applies in equilibrium. Outside equilibrium, prices cannot be defined. To highlight this problem with an analogy, it is like physicists not being able to define the position of a body. It is not about any difficulty in measuring the body’s position it is about the lack of the position concept! I would like to see the author adding to his list of mainstreams’ shortcomings (neutrality, disconnection from reality and irrelevancy) the idea of inconsistency. And possibly, also commenting how the research agencies could provide funds to a project that is mathematically inconsistent (i.e., it does not work even at the pure theoretical level).

Background Discussions.

In what follows I shall discuss two ideas underlying the present article. I do NOT expect the forthcoming discussions to be incorporated in a possible revised version of the article. I do expect, however, that said discussions might provide the author with background ideas to support, in due course, the further development of his research programme within which the present article is embedded.

These two ideas are:

(i) the possibility that economics – as a science – would be better off if economists would refrain from using mathematics and instead turn to using descriptive discourses. This idea is suggested in page 13, first paragraph: “…we might also question the very emphasis on mathematical modelling itself.” It is further elaborated in footnote 11 on this same page.

(ii) the possibility that economics – as a science – would be better off if economists would only use mathematical constructs which fit the ontology of the phenomena they are interested in studying.

An Economic Science Based On Descriptive Discourses.

The author must realize that his idea of economics’ being better off without mathematics is likely to baffle most readers – I included. It is one thing to claim that mainstream economists use inappropriate mathematical methods, but it is a completely different story to say that mathematics does not suit economics. Thus, given the author’ suggesting (as is implicit in this paper) this latter view, I would urge him to articulate his argument further and beyond just claiming a misplaced emphasis on mathematics.

Patrick Spread – in his comments to this paper – suggests the concept of symmetry as an alternative foundation for the explanation of economic activity. I have checked the references provided and I could not find this idea developed mathematically. However, I think I understand his point. Indeed, symmetry is a highly developed mathematical concept which does not require “atomism” or the regularities called for by “closed systems”. Further, symmetry is a concept with which it is possible to analyse how people make choices. It embodies clear aesthetic features. Therefore, with the mathematical concept of symmetry and its related algebraic framework one might be able to model, for example, agents’ choices and in doing so one would provide economic theorists with a highly formal language quite different from the current mainstream one.

The author is invited to comment if he would consider the allocation of funds to pursue this algebraic oriented research programme as an ideological manipulation (by bureaucrats, presumably) to deflect criticism from the nature of the status quo.

Approaching the issue herein from another perspective let me refer to one particular strand of research, which was pursued in the past by James Buchanan. Buchanan edited The LSE Essays on Cost (Buchanan & Thirlby, eds, 1981) and also wrote Cost and Choice (Buchanan 1969). Together, these two books recast economics from a radically original point of view, which takes opportunity cost as its foundational concept. Except that opportunity cost here is subjective opportunity cost. This research programme has faded out and nobody talks about it anymore. Why? It makes sense; it is well articulated and well written; it draws from very basic intuitive ideas underlying the origins of economics; it does not – prima facie – threaten the status quo (although it clearly opposes mainstream, neoclassical economics). Thus, I invite the author to comment if the failure of this programme to thrive would not have come as the result of its complete lack of formalization. The ideas therein are not stated in mathematics, but in plain English. In view thereof the reader – even when he appreciates the theory – is left unsure which way to go and how to proceed along this type of research.

The Ontological Argument

The author refers in the article to his ontological argument. It is clear to me that this argument underlies most of his research. Although I like this argument, I wish to challenge it with the view of improving the scholarship debate around it. Thus, the background oriented question I wish to posit is how appropriate it is as guidance to approaching economics on new grounds (opposing the current mainstream).

Consider that, based upon what we know today, light is composed by photons. If so, the ontology of light would required mathematical models where said photons would have a role to play. It may be so today in advanced physics, but the models of the past and most application models today disregard photons and approach light as vibrating waves. Indeed, since Newton’s time the diffraction effect had been observed, which could not be explained by means of the atomic-like photons. Therefore, a specific mathematical formalism (i.e., vibrating waves) was introduced and proved most appropriate to dealing with light, even though it does not fit with the ontology of the phenomenon it represents.

This argument can be taken a step further. Vibrating waves require a medium, which has been proved not to exist. Therefore, physicists represent light as waves which are assumed to vibrate “nowhere” exactly. They are not concerned with this question. They satisfy themselves with the fact that the equations of vibrating waves give the solution to the problems they are interested in investigating. And all technological applications involving electromagnetic waves follow this same standard of approach.

Thus, the author may appreciate this example as a provocative counter-argument to his ontological argument and based upon it possibly comment if there could not be a possibility that economics would benefit from mathematical modelling not fitting its underlying, ontological characteristics.

Conclusion.

I have been intellectually stimulated by reading the article. I would like to have this article – or a revised version thereof – entered the annals of Economic Thought. I would suggest a structural review to better indicate the main issue being discussed. I think a more careful usage of the terms “formal” and “mathematical” would help the reader not getting diverted from the issues of interest.

As a final note I have noted two typos: the word “either” appears twice in a row on page 9 and on page 14 one can find the word “hezerdox”.

I did not know about the author previously. After reading this paper I obtained a copy of his book Reorienting Economics and I read through chapters 1, 2 and 10. I will keep track of his future publications. I could see in his webpage that he is currently investigating the ontology of money. This is precisely what my Ph.D. dissertation is about – whence, my interest in completing this review.

References.

Buchanan, J.M. [1969]. Cost and Choice: An Inquiry in Economic Theory. Vol. 6 of the Collected Works of James M. Buchanan. Liberty Fund, 1999-2002, Indianapolis. http://files.libertyfund.org (Original 1969).

Buchanan, J.M. & Thirlby G.F., eds. (1981). The L.S.E. Essays on Cost, New York University Press. http://files.libertyfund.org (Original 1937).

Varoufakis, Y. & Arnsperger, C. (2009). A Most Peculiar Failure, downloaded on 9 February 2012 from http://old.econ.uoa.gr/UA/files/1139148722..pdf

Several things occurred to me in terms of finance, forecasting and other issues related to the adequacy of mathematics and thus the ‘problem’, or perhaps, misdirection, that mathematics within economics and of the economy can represent.

1. ‘New’ complex sophisticated mathematics is not new in finance. It may be the case that the basics of many DSGEs and of options pricing derivatives and of the Taylor rule etc are rather primitive in terms of their assumptions about the ‘real world’. However, many financial organizations have been employing mathematics and physics graduates to apply their ‘sophisticated mathematical’ know-how to the economy and, especially to realise profits since the late 1980s – growing in the 1990s and early 2000s. Many of these are reported to be doing modelling and hi-frequency trading based in secretive quant silos within hedge funds, investment banks etc. This raises the issue of: a) where are the benefits in terms of this activity constructing less volatile, consistent and stable markets (completing contracts, reducing contagion, transfering risk etc. to produce net benefits to society in terms of augmenting the economy); b) where are the clear consistent profits from this business (all the main quant hedge funds from Paulson to Einhorn have recently suffered setbacks)? I’m not interested in the profits but rather in why sophisticated mathematics has not translated into widespread profits – what does this tell us about even the most sophisticated mathematics of economy? In turn what does this tell us about the prospects of ‘better maths’ will solve the problems of mathematical approaches rather than thinking that maybe the problem is making the maths primary in the first case. We do not lack ‘good’ mathematicians working in the economy.

2. Those who had some degree of foresight in regard to the GFC did not share a single mathematical approach to the economy. Keen, Roubini, White and others shared a basic contrarian insight that economies are imperfect, include feedback loops, rationales that are collectively irrational or destructuive, races to the bottom etc. They also shared a focus on particular forms of raw data / descriptive statistics – housing prices, debt levels etc. What they did with it thereafter is really not the main point – one could come to the same inferences without the mathematics… This raises the issue of what any particular sophisticated mathematics is adding to our understanding of issues like the GFC and of foresight in particular as regards vulnerabilities in economy. Is the maths simply a medium that was not necessary and that added credibility? Isn’t good sense and raw data / descriptive statistics as good a place to start?

3. What does complexity in mathematical models really represent? Are human systems meteorological? Really? The interesting question here is why such a model might work FOR SOME TIME OVER SOME ways of setting up its dynamics. The basis of dynamics that may change are more interesting than the dynamics of change within the model, unless the range of possible changes is fixed and thus the relations within the whole are complete if ‘chaotic’. Is this humanity?

None of these points indicates that maths is not useful or applicable but does raise the issues of

1. Why are we using it?

2. What is maths doing when we are using it (as a contributor to the economy)?

In short, had been studying this issue myself, I would like to agree with Donald Gillies. Under the risk of repeating what has been said, mathematics is just a language. One can make relationships using mathematics or just explaining them in any other language. Is it possible to reproduce what Marx or Keynes wrote using mathematics? They used some mathematics themselves, that’s why I would say yes. The problem rather is not a problem of language. It is philosophical. All models are based on philosophical presuppositions. These are the result of a subjective notion of the world determined by personal views about reality. The interaction of every person with reality is unique; it is determined by individual views and experiences, as well as personal idiosyncrasies, and it results in a particular concept of the real. As mathematics is only a language, although a very logic one, the mathematization of individual convictions and world-views turned into economic models does not make them to be scientific. Modern mainstream economic theory is constructed over the past works of Jevons, Marshall, etc, who adopted Bentham’s utilitarism. Neoclassical/Mainstream economic theory is constructed over very fragile, to not say flawed, presuppositions. The problem is with them, not with mathematics that, in the end, is just a language.

Tony Lawson’s contribution evokes an intense déjà-vu:

“A remarkable discussion has been lately going on in the revues and journals concerning the logical method of the science, touching even the question whether there exists such a science at all. Attention was drawn to the matter by Mr. T. E. Cliffe Leslie’s remarkable article “On the Philosophical Method of Political Economy,” in which he endeavours to dissipate the deductive science of Ricardo. Mr. W. T. Thornton’s writings have a somewhat similar tendency. … Many would be glad if the supposed science collapsed altogether, and became a matter of history, like astrology, alchemy, and the occult sciences generally. … But as regards the fate of the deductive method, I disagree altogether with my friend Mr. Leslie; he is in favor of simple deletion; I am for thorough reform and reconstruction.” (Jevons, 1911, pp. xv-xvi)

Jevons’s reconstruction was taken up and elaborated on by Walras — with scant success among Euclid’s aboriginal disciples:

“Walras approached Poincaré for his approval. … But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude. … He also wondered about the premises of Walras’s mathematics: It might be reasonable, as a first approximation, to regard men as completely self-interested, but the assumption of perfect foreknowledge “perhaps requires a certain reserve.”” (Porter, 1994, p. 154)

What, then, is at issue: (a) the deductive method is mistaken, or (b), there is nothing wrong with the method but the foundational assumptions concerning human behavior are beside the point?

Lawson obfuscates the question somewhat by identifying the deductive method with mathematical model building tout court. He presents the neoclassical approach as methodological failure, taking the current crisis as an empirical proof. He quotes Hahn and other spokesmen of the economics academy to the effect that general equilibrium theory had no intended real world application in the first place.

And here is where the flimsy logic of the critics of the neoclassical approach comes in. From the widely accepted premise that standard economics is unsatisfactory and the correct observation that it applies the deductive method and produces an abundance of vacuous mathematical models the conclusion is drawn that the method must be wrong. The simple fact is — as already noticed by Poincaré — that the foundational assumptions of standard economics are inadmissible.

Each theory (heterodox approaches are no exception) starts from ‘hypotheses or axioms or postulates or assumptions or even principles’ (Schumpeter, 1994, p. 15). Therefore, the crucial question is:

“What are the propositions which may reasonably be received without proof? That there must be some such propositions all are agreed, since there cannot be an infinite series of proof, a chain suspended from nothing. But to determine what these propositions are, is the opus magnum of the more recondite mental philosophy.” (Mill, 2006, p. 746)

No theory whatever can dodge this question. Emphasizing that standard economics is unconvincing is neither new nor helpful. Mathematics is not the problem either. It allows us to express the wrong idea that the planets move in circles or the right idea that they move in ellipses. By the same token, it allows us to express the wrong idea that the economy is a closed system and the right idea that it is an open system. Now, take the mathematics away and what is left?

“To Plato’s question, “Granted that there are means of reasoning from premises to conclusions, who has the privilege of choosing the premises?” the correct answer, I presume, is that anyone has this privilege who wishes to exercise it, but that everyone else has the privilege of deciding for himself what significance to attach to the conclusions, and that somewhere there lies the responsibility, through the choice of the appropriate premises, to see to it that judgment, information, and perhaps even faith, hope and charity, wield their due influence on the nature of economic thought.” (Viner, 1963)

This is a fair appraisal of the deductive method. What could be the objections against it? No methodologist ever maintained that it automatically produces ‘true’ theories. This may appear as a serious drawback, but neither exaggerated claims nor disappointed expectations provide a valid argument against the method. Hence:

“We should also like to underline Debreu’s effective reference to Bacon when he says that “citius emergit veritas ex errore quam ex confusione.” It would be a mistake to lower the level of analysis and clarification. The only way possible is a thorough reexamination of the theory’s basic hypotheses, i.e., a true paradigmatic revolution.” (Ingrao und Israel, 1990, p. 362)

References:

Ingrao, B., and Israel, G. (1990). The Invisible Hand. Cambridge, MA, London: MIT Press.

Jevons, W. S. (1911). The Theory of Political Economy. London, Bombay, etc.: Macmillan, 4th edition.

Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications to Social Philosophy, volume 3, Books III-V of Collected Works of John Stuart Mill. Indianapolis, IN: Liberty Fund. (1866).

Porter, T. M. (1994). Rigor and Practicality: Rival Ideals of Quantification in Nineteenth-Century Economics. In P. Mirowski (Ed.), Natural Images in Economic Thought, pages 128–170. Cambridge: Cambridge University Press.

Schumpeter, J. A. (1994). History of Economic Analysis. New York, NY: Oxford University Press.