post-autistic economics review
Issue no. 24, 21 March 2005
article 1



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A Response to King’s Argument for Pluralism

Paul Davidson   (Editor of the Journal of Post Keynesian Economics)

© Copyright 2004 Paul Davidson

In an article in the last issue of this journal, John King presented “Three Arguments for Pluralism in Economics.1  In his paper, King misrepresents my view in this matter.  More importantly I disagree with the arguments put forth by King.  Accordingly, the following presents my  responses (in the form of a dialog) to King’s PAER statements:


King: Is there a single correct alternative to neoclassical economics? The purpose of this short paper is to suggest that there is not, and to show that this fact is increasingly recognized by eminent practitioners of several varieties of heterodox economic theory.


Davidson: If one wishes to explain (describe) the production, exchange and financial features and operations of a market-oriented, money using,  entrepreneurial economy, then Keynes’s  “General Theory” is the sole “correct” alternative to neoclassical economics.  Neoclassical theory is, as Keynes specifically noted (on page 3 of his 1936 book) merely a “special case” of his general theory2 Moreover I would argue that Sraffian, Kaleckian, and other heterodox theories that try to explain the operation of a market economy are other special cases obtained by adding additional restrictive axioms to Keynes’s basic general theory.


King: Heinz Kurz and Neri Salvadori . . . surprisingly, [come] to the defence of pluralism. Economic reality, they note, is widely believed to be very complicated. The questions that economists ask are therefore inherently difficult, and it is unlikely that they have simple answers. Since no theory can consider all relevant factors in any particular economic context, there is a strong prima facie case for theoretical pluralism.


Davidson: All reality is complicated. But that is not a sufficient defense for pluralism. For example, it is said that an equation that takes account of all the gravitational forces that affect the tides on any place on Earth, can run to several pages. This does not stop weathermen from using a simplification of the law of gravity to provide a useful approximation of the time of high tide at any specific place on the ocean shore  by relating the tides solely to the gravitational forces of the Earth and the Moon. Complications per se do not require plural alternative explanations for observed phenomena.


King:  Geoff Hodgson argues that the notion of a single, ‘‘general’’ theory applicable to human behaviour in all societies, at all points in time, is a dangerous delusion that has led astray not only neoclassical economists but also many heterodox theorists. Failure to appreciate the need for historical specificity in economic theorising has not only blighted the work of several generations of general equilibrium theorists, but also reduced the analytical achievements of some of their most vocal opponents, including Clarence Ayres, John Maynard Keynes and Joan Robinson.


Davidson: Keynes’s General Theory is meant to explain a modern, money using, market economy.  If one wishes to analyze (explain, discuss) feudalism, or the economies of biblical times, one must add additional restrictive axioms to Keynes’s general theory to obtain a special case theory of feudalism, or of biblical economics, etc.  Nevertheless, a common general theory will underlay all these specific cases of historical economies.


King: One does not have to agree with all [of] Hodgson... to accept the truth of his contention that ‘‘there are several problems with general theorizing in the social sciences. One is of analytical and computational intractability. Facing such computational limits, general theorists typically simplify their models, thus abandoning the generality of the theory. Another related problem with a general theory is that we are confined to broad principles governing all possible structures within the domain of analysis. In practice, a manageable theory has to confine itself to a relatively tiny subset of all possible structures. Furthermore, the cost of excessive generality is to miss out on key features common to a subset of phenomena’’.


Davidson: Hodgson, as well as King and many others, have confused the concept of a general theory with that of Debreu’s concept of general equilibrium as the mother of all economic theory! Unlike Debreu’s general equilibrium theory, Keynes’s general theory analysis is an axiomatic based approach that required fewer restrictive axioms than any other economic theory. Moreover, in defending his fewer axiomatic approach as a realistic general economic theory,  Keynes noted  “It is for those who make a highly special assumption to justify it rather than for those who dispense with it to prove a general negative”. In that sense Keynes was not only a developer of economics as a mathematical (axiom-oriented) logical analysis, but his theory had a pragmatic vision of a physical real world  process in mind.


Roy Weintraub in his recent book How Economics Became a Mathematical Science3 noted that a new image of mathematics emerged in the early decades of the 20th century, and this image shaped the development of mainstream mathematical economics. “To preserve the relationship between rigor and truth, economists began to associate rigor with axiomatic development of economic theories, since axiomatization was seen as the path to discovery of new scientific truths” (Weintraub, 2002,p.98)


But this mathematical approach leads to the question of whether “truth” is discovered by having sufficient axioms to obtain the “right” level of generality or by an axiomatic theory based on the least number of assumptions (“a general theory of employment, interest and money”) that is descriptive and applicable to reality? The right level of generality was Debreu’s vision of discovering truth.  On the other hand, using the least number of assumptions descriptive of the real world was Keynes’s approach to the “truth”  -- as suggested in his analogy of comparing classical economists with Euclidean geometers in a non-Euclidean world who continued to use the restrictive axiom of parallels to explain why lines apparently parallel often crash. This is also the belief that underlies Sidney Weintraub and my vision of a Post Keynesian economic theory where the axiomatic base of a general theory should not only be a small as possible – but these axioms should be applicable to the real world.


The restrictive bigger axiomatic foundation of Debreu’s general equilibrium theory, in my view,  is not applicable to the real world market economy that we live in..  The onus is therefore on those who, like Debreu, would add such restrictive axioms to obtain a general theory to demonstrate the relevance to the real world of their additional postulates of specific case analysis.


In economics, the school of Bourbaki mathematical philosophy was transplanted into post-war American economics by Debreu. The seed bed that encouraged the domination of this non-real world view of economic theory was the Cowles Commission of the early 1950s (Weintraub, 2002, p. 104). The Bourbaki method argued that economists developing special cases had to build on the foundation of  general (Walrasian-Debreu) equilibrium case.  The general structure of this equilibrium foundation was obtained by developing chains of syllogisms from what Debreu considered fundamental axioms that might be buried under accumulated debris of real world details. In this Bourbaki approach “good general theory does not search for the maximum generality, but for the right generality” (Weintraub, 2002, p. 113). In other words, Bourbaki did not accept Keynes’s search for the “maximum” general theory, i.e., a general theory that had the smallest axiomatic foundation that still provides a readily recognizable description of a real world economy. (Keynes’s general theory threw out three classical restrictive axioms4.)  According to Bourbaki, Keynes’s general theory -- based on fewer axioms than Debreu’s general equilibrium theory -- is  not “good” theory.  Instead, Debreu’s general equilibrium theory of value which expresses itself in terms that few, if any, would readily recognize as an apt description of a real world economy (Weintraub, 2002, p. 114) provides the Bourbakian  “right” level of generality. In other words, in a Bourbaki view of economics, theories that are readily recognizable as descriptions of reality are not necessarily important.  As Weintraub (2002, p.  120) notes, Debreu’s 1959 monograph “The Theory of Value . . . still stands as the benchmark axiomatization of  the Walrasian General Equilibrium model . . . the 1959 book wore its Bourbakist credentials on its sleeve, though there may have been few economists at this juncture who would have understood the implications of” Debreu’s statement on p. x of the preface:

The theory of value is treated here with the standards of rigor of the contemporary formalist school of mathematics. The effort towards rigor substitutes correct reasoning and results for incorrect ones......leads to a deeper understanding of the problems to which it is applied...also lead to a radical change of mathematical tools.... Alliance to rigor determines the axiomatic form of analysis where the theory, in the strict sense, is logically disconnected from its interpretation.


Here is a declaration of independence indicating there is no need for the elements of a rigorous economic theory to have counterparts in the real world. Debreu considered that “the model of Walrasian equilibrium was the root structure [the right level of generality] from which all further work in economics would eventuate” and he showed disdain for attempts (like that of Kenneth Arrow and Frank Hahn) to forge explicit links between the Walrasian model and contemporary theoretical concerns in macroeconomics” (Weintraub, 2002, p. 121)


In his bold leap of faith, Debreu believed his work to be “the definitive mother-structure from which all further work in economics would start, primarily by weakening its assumptions or else superimposing new interpretations upon the existing formalism. This stance, however, requires one very crucial manoeuver that was never explicitly stated by Debreu, namely that the Walrasian general equilibrium approach was the root structure from which all further scientific work in economics must be developed (Weintraub, 2002, p. 122).


Just as Jefferson’s declaration of independence liberated the thirteen colonies from fat King George, Debreu’s declaration of what constituted the mother-structure “liberated” economics from its dependence on real world analogies. Weintraub (2002, p, 122) states that Debreu’sBourbaki program marked a definitive break with physical metaphors”. Successes in the natural sciences may depend upon “bold conjectures and experimental refutation, but economics had nothing else to fall back upon but mathematical rigor”.


It is this Bourbakian view that, I believe, the proponents of “pluralism” are protesting against -- even though they do not know it.


King: The Post Keynesians Victoria Chick and Sheila Dow make an equally powerful, if largely implicit, case for pluralism in their penetrating analysis of what is implied by mathematical modeling in economics. Formalising an argument is not, they suggest, an unambiguous improvement, as neoclassicals believe. On the contrary, it is a matter of costs and benefits. Formalism entails a particular view of the world, namely that it displays event regularities strong enough for it to approximate to a closed system.


Davidson: Formalism can be consistent with “open models” as I (Davidson5) demonstrated in my development of the use of nonergodic systems in economic theory.  It is the importance of nonergodic processes that makes refutation in economics difficult if not impossible. In my view most (but not necessarily all) important economic stochastic processes are nonergodic and hence a permanent rejection of any conjecture about important economic phenomena such as employment, economic growth, etc. are linked to specific historical events, culture, and an uncertain, not statistically reliably (even in principle) predictable future.


Although Debreu’s expresses “enthusiasm” for the way he  incorporates “uncertainty” into his axiomatic model, his concept of uncertainty has nothing to do with the concept of an unpredictable future.  Debreu introduces “uncertainty” by merely redefining the interpretation of a commodity to take account of contingencies (or expressed different states of the world) and a complete set of contingency markets for every date in the foreseeable future. Thus for Debreu uncertainty does not require an open  model.


Weintraub (2002, p. 125) notes that the “Bourbakism propagated by Cowles had identified neo-Walrasianism and good economic theory . . . . neo-Walrasian theory had become conflated with the very standard of mathematical rigor in economic thought . . . .why precisely should the Walrasian framework be taken as the sole ‘structure’ from which all mathematical work should depart? . . . was it not better to make a case for the right level of generality, then claim one had the maximum level? The Bourbaki answer is that rigor was a matter “of style...and politics...and taste”.


Similarly, when  King notes that “ Hodgson’’s own proposal for the reconstruction of economic theory, putting the history back, is innately and profoundly pluralistic” I believe that Hodgson’s view of what is good economics is a matter style, politics and taste on Hodgson’s part.


King: Chick and Dow do not completely deny the legitimacy of formalism in economics, in all circumstances, for all purposes. On the contrary: some problems lend themselves to closed-system thinking and cry out for precise, formal solutions.   They argue only that it is a serious mistake to suppose that all economic problems are of this type.


Davidson:  I believe that Chick and Dow are confusing Debreu’s Bourbakian variant of formalism with the use of formal logic. In Chick’s and Dow’s view what problems are susceptible to Debreu’s formalism is, I think, a matter of taste, style, and politics.


King: If pluralism does not (quite) rule out formalism, what does it exclude? Unqualified relativism, for one thing; logical incoherence, for another. Hodgson is the most outspoken in denying that ‘‘anything goes’’, and the most sternly critical of postmodernist claims in this regard. “An acceptable policy of pluralism’’, he suggests, ‘‘concerns the policy of institutions towards the funding and nurturing of science. Such a policy involves ‘pluralism in the academy’. But it would not extend to the individual practices of science itself. This confusion, between encouraging contradictory ideas in the academy and encouraging them in our own heads, is widespread in post-modernism . . . There is much to be said for tolerance of many and even antagonistic scientific research programmes within an academic discipline or university. But we should not tolerate the existence of inconsistent ideas within our own heads.”


Davidson: But how can we assure that different models are not logically inconsistent unless we have a benchmark “general” model with a minimum number of well-specified axioms that acts as the foundation of all other models?


King:, King notes that Hodgson states “the policy towards science must be pluralistic and tolerant, but science itself must be intolerant of what it regards as falsehood . . . Any failure of social science to erect an adequate and coherent general theory is not rectified by applauding incoherence’’ Horses for courses, as Geoff Harcourt has always put it, but they must each have four legs and a jockey and proceed anti-clockwise around the course.


Davidson: The horses for courses analogy is misleading. In my view the legs of any economic model (horse) must be the same basic axioms underlying Keynes’s general theory.  Those who wish to add additional restrictive axioms must, as Keynes notes, specifically justify the use of these additional postulates as realistically applicable to the real world.  Only if all the horses shares the same basic axiomatic legs can we let them race on different courses


King: Kurz and Salvadori also insist on the need for logical consistency in economic theorising. For them this criterion is enough to rule neoclassical analysis out of the race, since its conception of capital is fundamentally flawed. If the ‘‘principle of substitution’’ is central to mainstream theory, they argue, it should be applied in a logically consistent manner. In the long period, this means that an increase in the price of one input induces a decrease in the quantity of that input per unit of output. ‘‘All propositions of the theory can be traced back to this basic idea. If it is not true in general, the theory appears to be in trouble’’ (Kurz and Salvadori, 2000:238). But it has been known since the mid-1960s that it is, in general, false when applied to the collection of heterogeneous commodities known as ‘‘capital’’.


Davidson: Unfortunately for Kurz, Salvadori and King, Keynes rejected the axiom of gross substitution long before the 1960s capital controversy. In Keynes’s chapter 17 on the essential properties of interest and money, Keynes specifically rejects the ubiquitous applicability of the axiom of gross substitution. And Arrow and Hahn6 have demonstrated that in the absence of gross substitutability, all existence proofs of a general equilibrium are jeopardized.


King: From a quite different perspective the Post Keynesian Paul Davidson has criticised what he terms the ‘‘babel’’ of New Keynesian economics, in which market imperfections that prevent downward price and wage flexibility are denounced as the fundamental cause of involuntary unemployment while in the same breath a falling price level (‘‘deflation’’) is decried as a serious macroeconomic evil (Davidson, 1999; compare Solow, 1997 and Taylor, 1997 for graphic examples of this incoherence). Horses for courses, once again, but all four legs must be pointing in the same direction.


Davidson: And the horse merely must show that his legs display the essential properties of interest and money– independently of the substitutability of labor and/or capital as factors of production.  In sum, then, I believe that encouraging pluralism in economics without a common general theory foundation merely encourages heterodox economists to erect a modern Tower of Babel, thereby making it easier for Mainstream economists to ignore the resulting incomprehensible babel coming from this heterodox structure.


Instead, heterodox economists who want to affect the development of their discipline as taught in major universities and economic journals must unite behind Keynes’s general theory and demonstrate that what passes as mainstream theory is merely a special logical case requiring additional restrictive axioms that are unrealistic and therefore policies based on this special case will be disastrous if applied to the real world global economy of the 21st century.




1. J. E. King, “Three Arguments for Pluralism in Economics”, post-autistic economics review, issue no. 23, 5 January 2004, article 2,

2. “The characteristics of this special case....happens not to be those of the economic society in which we actually live, with the result that its teaching is misleading and disastrous if we attempt to apply it to the facts of experience”. J. M. Keynes, The General Theory of Employment Interest and Money (Harcourt, Brace, New York, 1936), p. 3.

3. E. R. Weintraub, How Economics Became A Mathematical Science (Duke University Press, Chapel Hill, 2002).

4. These are (1) the ergodic axiom for stochastic models or the ordering axiom for deterministic models, (2) the gross substitution axiom, and (3) the neutrality of money axiom.

5. P. Davidson, Financial Markets, Money and the Real World (Elgar, Cheltenham, 2002), chapter 3.

6. K. Arrow and F. H. Hahn, General Competitive Analysis (Holden Day, San Francisco, 1971),  p. 361.

Paul Davidson,
A  Response To King’s Argument For Pluralism, post-autistic economics review, issue no. 24, 15 March 2004, article 1,