I’ve been trying to grasp why mainstream economics considers itself the superior approach over heterodox disciplines like Post-Keynesianism or Marxism. After reading a couple of papers, and articles, a constant argument that appears is the one of rigour. Mainstream economics is mathematically axiomatic, that is, it begins from a set of primitive assumptions and then derives a whole system through self-consistent mathematical formalism. Usually this is contrasted with heterodox approaches like Post-Keynesianism, which are seen as less coherent and ad-hoc, with some writers referring Post-Keynesianism as “babylonian babble” and not superior to a pamphlet. Even if some heterodox economists use mathematical modelling, they do not follow from some axiomatic method, but are ad-hoc implementations.

What interests me about this argument is its definition of science. According to many mainstream economists, heterodox economics isn’t a science. The main reason given for the unscientific status of heterodox economics is that the latter lacks internal coherence, that it is not rigourous. As mentioned above, mainstream economics claims rigour by deriving its propositions from mathematical inference that begins with a set of axioms. It is by the usage of this rigour, that mainstream economics defines itself as a science.

If a field claims to be scientific, it must justify its own status. For better or worse, in the west, the status of science is epistemically privileged. In other words, an activity can assert more legitimacy than other modes of producing knowledge by claiming the mantle of science. Therefore mainstream economics by arguing for its scientific status due to an axiomatic coherence, while denying that same mantle to heterodox economics, is implicitly arguing that heterodox economics is an inferior epistemological approach and unscientific.

A common retort against the mathematical rigour of economics is that its coherent mathematical frameworks don’t necessarily correlate with empirical reality, which calls the scientific status into question. However this argument has been done to death, probably by people much smarter than me. What I find interesting is the idea that inferential coherence is a necessary condition for science. In fact the argument being made by mainstream economists is that even if heterodox economics may arguably be able to explain some empirical phenomena mainstream economics cannot, heterodox economics is less scientific because it lacks internal coherence. Therefore, mainstream economics claim a necessary condition for science is rigorous logical coherence.

Where does this definition of science as rigorous logical inference comes from? There is only one natural science, which is physics, that approximates this sort of rigorous coherence, that is, that there is a set of primitive axioms that lead to a whole system of knowledge by the application of rules of mathematical inference. Even then, the mathematical rigour in physics is often inferior than in economics, given that physicists don’t do mathematical proofs as much as economists. The rest of the natural sciences are less rigorously formulated – many of them are a “bag of tricks” that are heuristically unified. This is because anything more complex than a system of two interacting particles is mathematically intractable due to nonlinearities. A good example is psychology. Although psychologists assume that certain personality traits are a manifestation of chemical processes in the brain, there is no rigorous mathematical inference that connects psychology to brain chemistry – these scales are unified heuristically and qualitatively. There are similar examples in biology, where in theory, morphological evolution is coupled to chemical evolution of genes, but the rigorous, mathematical linkage of both scales is close to impossible.

How did the definition of science as mathematical inference came into being? It is certainly not the normative self-consciousness of scientists, who see themselves as Popperian. Popper’s theory treats the evolution of science as a process where propositions are falsified by empirical evidence only to be replaced by better explanations – it does not say anything about “logical rigour”. Nor this definition is descriptive, as shown in the previous paragraph, because most natural sciences aren’t as rigorously self-coherent as mainstream economics. Weintraub argues that the current axiomatic approach to mainstream economics can be traced back to Gerard Debreu, an important french-american economists of the 20th century. In the first half of the 20th century, David Hilbert and Bourbaki (a pseudonym used by a group of french mathematicians) attempted to axiomatize mathematics, given the discovery of non-euclidian geometry in the 19th century. Before non-euclidian geometry, geometry was thought to derive its axioms intuitively from the world – the truth-value of the axioms were self-evident. An example of an “intuitive” axiom in euclidian geometry is that parallel lines don’t meet. However 19th century mathematicians realized that they could create self-consistent, alternate geometries where parallel lines could meet. An alternative geometry that starts from non-euclidian axioms was self-consistent if rigorously inferred through mathematical rules. This led Hilbert and Bourbaki to develop a more axiomatic approach to the study of mathematics. Debreu, who learnt mathematics from the Bourbaki school, brought this axiomatic way of thinking to economics.

Today this axiomatic approach is very obvious in the average graduate economics curriculum. For example some of the classes emphasize writing mathematical proofs! I am very close to competing a PhD in physics and I only experienced very basic proofs at my undergraduate level in a linear algebra class. After that I never wrote a single proof ever again. Yet, economics, which arguably has had less empirical success from its mathematics, requires more mathematical rigour than the average paper in physics. This tells me that the economist’s emphasis on rigour is not inspired in the example of the successful, natural sciences, but it’s endogenous – from within. If anything, it shows that mainstream economics is at most a bizarre synthesis of philosophy and mathematics, owing more to these abstract fields, than to any of the existing natural sciences. Therefore, mainstream economics should be described as more of a mathematical philosophy than a science.

The case of the arbitrary rigour of economics has interesting implications in academia at large. An uncharitable person would say that the spurious mathematical rigour of economics is simply gate-keeping for a professional guild. The extremely technical skills required to master mainstream economics limit the supply of would-be economists, generating a manageable number of rent-seekers that can be paid handsomely. But this probably extends to much of academia as well. Academia is peppered with examples where “rigour” and “method” are elevated with no obvious epistemic justification. One has to wonder if appeals to rigour are more often than not guild building in order to justify large pay-checks by limiting the supply of the participants. The trope of “how many angels can dance on the tip of a pin” is a famous example of this spurious rigour. Medieval theologians were accused of developing beautiful, often rigorous and coherent systems, that deal with questions of no intellectual consequence. Similarly, the same phenomenon probably emerges in some sector of academia, given that rigour and opacity are a cheap way of signalling expertise to institutions in order to justify large salaries.

Finally, I think the unjustified emphasis on rigour when not warranted is unhealthy for democracies. Often, many problems that are meaningful to humanity at large, such as issues of political and economic nature, require the mass participation of society in order to build an engaged citizenship. Spurious rigour and credentialism are ways to build a technocratic hierarchy that is not necessarily justified. In the absence of authentic knowledge, rigour becomes simply a guild-like mechanism for confining meaningful problems to a set of fake experts that decide the fate of whole nations, often in the interests of a reduced elite. A socialist, democratic society would require a more egalitarian epistemology than the one that exists today.

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