Euclid and economic methodology
We are therefore justified in saying that with Euclid's Elements the causa materialis of geometry underwent a radical transformation; from a more or less amorphous aggregate of propositions it acquired an anatomic structure. Geometry itself emerged as a living organism with its own physiology and teleology, .... And this true mutation represents not only the most valuable contribution of the Greek civilization to human thought but also a momentous landmark in the evolution of mankind comparable only to the discovery of speech or writing. (Georgescu-Roegen, 1966, p. 9), original emphasis
In political economy, Ricardo and James Mill compared the certainty of the propositions they were advancing to the certainty of the propositions of Euclid. (Halévy, 1960, p. 494)
In the definition which we have attempted to frame of the science of Political Economy, we have characterized it as essentially an abstract science, and its method as the method à priori. Such is undoubtedly its character as it has been understood and taught by all its most distinguished teachers. It reasons, and, as we contend, must necessarily reason, from assumptions, not from facts. It is built upon hypotheses, strictly analogous to those which, under the name of definitions, are the foundations of other abstract sciences. (Mill, 2004, p. 110)
To Senior belongs the signal honor of having been the first to make the attempt to state, consciously and explicitly, the postulates that are necessary and sufficient in order to build up … that little analytic apparatus commonly known as economic theory, or to put it differently, to provide for it an axiomatic basis. (Schumpeter, 1994, p. 575)
... the theory here given may be described as the mechanics of utility and self-interest. Oversights may have been committed in tracing out its details, but in its main features this theory must be the true one. Its method is as sure and demonstrative as that of kinematics or statics, nay, almost as self-evident as are the elements of Euclid, when the real meaning of the formulæ is fully seized. (Jevons, 1911, p. 21)
Holbach put it thus: 'Morality is the science of the relations which exist between the minds, wills and actions of men, in the same manner as geometry is the science of the relations that are found between bodies. What is the geometry of ethics? What is the geometry of politics? How are we to reduce these sciences to the same degree of certainty and clarity as physics and geometry?' (Berlin, 2002, pp. 12-13)
The impression that one could build price theory up from basics in the image of Euclid was much more important than commitment to any particular proposed formalization. (Mirowski, 2004, pp. 348-349)
These economists were implicitly treating microeconomics as a pure axiomatic system, whose terms may or may not be instantiated in the real world, but which is of great interest, like Euclidean geometry, whether or not its objects actually exist. (Rosenberg, 1994, p. 229)
The essence of neoclassical economic theory is its exclusive use of a deductivist Euclidean methodology. A methodology – which Arnsperger & Varoufakis calls the neoclassical meta-axioms of “methodological individualism, methodological instrumentalism and methodological equilibration” – that is more or less imposed as constituting economics, and, usually, without a smack of argument. (Pålsson Syll, 2010, p. 24)
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight – as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required to-day in economics. (Keynes, 1973, p. 16)
The discipline of economics has so far successfully resisted all efforts to alter its character as an exercise in how to reason deductively from axiomatic principles. That is, it has insisted on remaining the Euclidean geometry of the social sciences. (Eichner, 1979, p. 172)
Like mathematics and physics, economics is proud of having an axiomatic foundation, and rightly so. (Helbing, 2013, p. 4)
The core problem is: conventional economics is based on behavioral axioms and that cannot work. This, clearly, is not a fault of the axiomatic method. Orthodoxy misuses Euclid and Heterodoxy refuses him for the wrong reasons. Ultimately, this is why conventional economics lacks the 'intellectual miracle of a logical system' (Einstein) with an identifiable counterpart in reality.
It is silly to be proud of behavioral axioms.
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, ... (Viner, 1963, p. 12)
The criteria are material and logical consistency. Ultimately, these criteria drive out all arbitrariness in the selection and acceptance of axioms. However, ...
... we cannot over-emphasize the fundamental role played in his research by a special intuition, which is not the popular sense-intuition, but rather a kind of direct divination (ahead of all reasoning) ... (Bourbaki, 2005, p. 1272)
Divination is quite different from the green cheese assumptionism of conventional economics. Subjective-behavioral axiomatization is a deterrent example of popular sense-intuition. Conventional economists, though, have been perfectly satisfied with this Euclidean look-alike.
Berlin, I. (2002). Freedom and Its Betrayal. London: Chatto Windus.
Bourbaki, N. (2005). The Architecture of Mathematics. In W. Ewald (Ed.), From Kant to Hilbert. A Source Book in the Foundations of Mathematics, volume II, pages 1265–1276. Oxford, New York, Ny: Oxford University Press.
Eichner, A. S. (1979). A Look Ahead. In A. S. Eichner (Ed.), A Guide to Post- Keynesian Economics, pages 165–184. London, Basingstoke: Macmillan.
Georgescu-Roegen, N. (1966). Analytical Economics, chapter General Conclusions for the Economist, pages 92–129. Cambridge, MA: Harvard University Press.
Halévy, E. (1960). The Growth of Philosophic Radicalism. Boston, MA: Beacon Press.
Helbing, D. (2013). Economics 2.0: The Natural Step towards A Self-Regulating, Participatory Market Society. EconoPhysics Forum, pages 1–29. URL
Jevons, W. S. (1911). The Theory of Political Economy. London, Bombay, etc.: Macmillan, 4th edition.
Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London: Macmillan.
Mill, J. S. (2004). Essays on Some Unsettled Questions of Political Economy, chapter On the Definition of Political Economy; and the Method of Investigation Proper to It., pages 93–125. Electronic Classic Series PA 18202: Pennsylvania State University. URL (1844).
Mirowski, P. (2004). The Effortless Economy of Science?, chapter Smooth Operator: How Marshall’s Demand and Supply Curves Made Neoclassicism Safe for Public Consumption but Unfit for Science. Durnham, London: Duke University Press.
Pålsson Syll, L. (2010). What is (Wrong With) Economic Theory? real-world economics review, (55): 23–57. URL
Rosenberg, A. (1994). What is the Cognitive Status of Economic Theory? In R. E. Backhouse (Ed.), New Directions in Economic Methodology, pages 216–235.
London, New York, Ny: Routledge.
Schumpeter, J. A. (1994). History of Economic Analysis. New York, Ny: Oxford University Press.
Viner, J. (1963). The Economist in History. American Economic Review, 53(2): pp. 1–22. URL
The icon above represents the special case of the golden ratio consumption economy with market clearing and budget balancing. The market clearing price is in this case equal to phi, the wage rate is equal to phi times the productivity. The three coloured rays from the origin represent the first three structural axioms for the simplest case DN=0. The three angles represent wage rate, price and productivity. With the real variables employment and productivity given all other variables are then determined by the golden ratio condition which can be read off from the segments on the x-axis. This geometrical condition, though, has no specific economic content. Economically it is one feasible configuration among others. For the general case see Geometrical Exposition of Structural Axiomatic Economics URL. The relevant aspect of Euclid with regard to economics is methodological and relates to axiomatization and not to geometry. The latter is here applied for the visualization of elementary economic relations.
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