From obscurity to enlightenment

Comment on Lars Syll on 'Axiomatic economics ― total horseshit'

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I came across David Glasner's post of 16 July 2014 'Modern macroeconomics ― obscurantist axiomatization' on this blog.

This post also deserves a comment in the present context. I will ignore the counterproductive resentments (snobbishness, pedantry, etc.) against axiomatization and focus on some pivotal historical facts.

Glasner writes: “Before discussing the situation in economics, I would note that axiomatization did not become a major issue for mathematicians until late in the nineteenth century (though demands ― luckily ignored for the most part ― for logical precision followed immediately upon the invention of the calculus by Newton and Leibniz) and led ultimately to the publication of the great work of Russell and Whitehead, Principia Mathematica whose goal was to show that all of mathematics could be derived from the axioms of pure logic.”

Axiomatization became already a major issue for mathematicians with Euclid around 300 BC. Among heterodox economists, it seems that only Georgescu-Roegen understood the significance of this unique event.

“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.” (1966, p. 9)

Axiomatization then became a major issue for physicists with Newton.

The Principia starts with the famous 'Axioms, or the Laws of motion' and the role of Euclidean geometry for Newtonian physics cannot be overestimated. So impressive were the accomplishments of Newtonian physics that eighteenth-century philosophers, including the founders of political economy, jumped on the bandwagon.

And so it became an issue in the so-called social sciences with Hume. “Like most of his fellow moral philosophers, Hume thought it was worth a try to make all sciences as rigorous as Newtonian physics ...” (Redman, 1997, p. 111)

Finally, this is how axiomatization became a major issue in economics around 1800: “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)

So Glasner got it not quite correct: “The fetish for axiomatization in economics can largely be traced to Gerard Debreu’s great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium.”

The traces go even back before Adam Smith. In fact, the first attempts to axiomatize human behavior can be traced back to Hutcheson, Hume's and Smith's celebrated teacher (Redman, 1997, p. 116).

Glasner got it, again, not quite correct with: “The idea that a good scientific theory must be derived from a formal axiomatic system has little if any foundation in the methodology or history of science.”

Exactly the opposite is true: “But it was a second and more important quality that struck readers of the Principia. … For readers of that day, it was this deductive, mathematical aspect that was the great achievement.” (Truesdell, quoted in Schmiechen, 2009, p. 213)

The rest of Glaser's argumentation is not much better (for the refutation of the awkward Gödel argument see here).

The conclusion is obvious. Heterodoxy is right; the neoclassical axioms have to be rejected. This, though, does not mean that axiomatization has to be rejected. On the contrary, in order to replace neoclassical economics, Heterodoxy has to replace the neoclassical axioms with heterodox axioms. There is no way around this.

“The moral of the story is simply this: it takes a new theory, and not just the destructive exposure of assumptions or the collection of new facts, to beat an old theory.” (Blaug, 1998, p. 703)

And each theory is built upon some foundational premises, as J. S. Mill already made abundantly clear. As a matter of fact, cutting-edge physicists take their inspiration from an economist.

“... but underneath the complexities [of string theory] is a modern version of John Stuart Mill's desideratum of fundamental physics: a unified description of all fundamental interactions.” (Farmelo, 2009, p. 436)

Heterodoxy does not have one good reason to reject axiomatization yet many to apply it. The best reason is indeed that correct axiomatization ends confusion, of which there is plenty among both orthodox and heterodox economists (2013).

The outrageous fact, written in stone for all future methodologists, is that to this day the representative economist cannot tell the difference between income and profit.

Egmont Kakarot-Handtke


References
Blaug, M. (1998). Economic Theory in Retrospect. Cambridge: Cambridge University Press, 5th edition.
Farmelo, G. (2009). The Strangest Man. The Hidden Life of Paul Dirac, Quantum Genius. London: Faber and Faber.
Georgescu-Roegen, N. (1966). Analytical Economics, chapter General Conclusions for the Economist, pages 92–129. Cambridge: Harvard University Press.
Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series, 2207598: 1–16. URL
Redman, D. A. (1997). The Rise of Political Economy as Science. Methodology and the Classical Economists. Cambridge, London: MIT Press.
Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited, volume 1. Norderstedt: Books on Demand, 2nd edition. URL
Schumpeter, J. A. (1994). History of Economic Analysis. New York: Oxford University Press.

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Twitter/X Jul 9, 2026 Newton built on Descartes

Still in the woods

Comment Lars Syll on  'Proper use of math in economics'

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In my post of Dec 22, I introduced the Prophets of Preemptive Vanitization. More often than not, these prophets populate the social sciences, and from all theorems that have ever been developed in mathematics or physics, the impossibility theorems are closest to their hearts because they are equally good for both inhibition and excuse.

So, one cannot mention the word axiom in the social sciences without the Pavlovian reflex: Oh, you know, Gödel has proved that a complete and consistent set of axioms is impossible (see Wikipedia). Yes, and now? Is Newtonian physics wrong because the Euclidean axioms are incomplete? And, by the way, one can always expand a set of axioms if necessary, so Gödel is not of practical concern at all outside mathematics.

For a snail, it is irrelevant that it cannot, in principle, surpass the speed of light. By the same token, are the impossibility theorems from cutting-edge physics and logic irrelevant to economic methodology? By no stretch of the imagination can Gödel's proof be used to argue against axiomatization. Heterodox economists could know this from one of the great heterodox economists.

“Lest this position is misinterpreted again by some casual reader, let me repeat that my point is not that arithmetization [= axiomatization] of science is undesirable. Whenever arithmetization can be worked out, its merits are above all words of praise. My point is that wholesale arithmetization is impossible, that there is valid knowledge even without arithmetization, and that mock arithmetization is dangerous if peddled as genuine.” (Georgescu-Roegen, 1971, p. 15)

We can easily agree on this. Thus, to argue against axiomatization amounts for all practical purposes to the conservation of manifest logical and conceptual defects in the theoretical edifice of economics. And there are many of them. Economists are known as sloppy thinkers.

“The truth is, most persons, not excepting professional economists, are satisfied with very hazy notions.” (Fisher, quoted in Mirowski, 1995, p. 86)

This goes some way in explaining the secular stagnation of economics. “I think it is the lack of quite sharply defined concepts that the main difficulty lies, and not in any intrinsic difference between the fields of economics and other sciences.” (von Neumann, quoted in Mirowski, 2002, p. 146 fn. 49)

The arguments of the Prophets of Preemptive Vanitization against axiomatization have always been far off the mark. Axiomatization is a very effective tool, and the fact that it is not exactly 100 percent effective is no argument against it. How effective is the Verstehen of the so-called social sciences?

This said, my key argument is not so much methodological but indeed very practical. In order to replace the neoclassical approach, which is axiomatized, Heterodoxy must replace the axiomatic foundations of neoclassical theory. Hence, there is no urgent need to discuss axiomatization in the abstract. According to well-established scientific practice, there is no other way.

“The moral of the story is simply this: it takes a new theory, and not just the destructive exposure of assumptions or the collection of new facts, to beat an old theory.” (Blaug, 1998, p. 703)

And each theory is built upon some clearly stated premises. It is as straightforward as this.

“When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” (Resume of Aristotle's Analytica).

It has often been argued that scientists do not proceed axiomatically in their research. This, of course, is well-known in the history of science. But clearly, the moment they apply some piece of mathematics, they do so indirectly. And in the end, the whole theoretical edifice must be logically coherent. This goes without saying.

“I am of the opinion that, certainly, for the purposes of research it is always necessary to combine the intuition with the axioms.” (Felix Klein, quoted in Weintraub, 2002, p. 25), see also (2013, Sec. 6).

From the fact that physics is not completely axiomatized at the moment does not logically follow that economics cannot or should not be axiomatized.

“Some day, when physics is complete and we know all the laws, we may be able to start with some axioms, and no doubt somebody will figure out a particular way of doing it so that everything else can be deduced.” (Feynman, 1992, p. 50)

Asad Zaman correctly remarks that all methodology, in the end, boils down to empirical testing: “For example, Egmont keeps arguing that his axiomatization is better than others, and that others are wrong while his is correct. To me, it seems that this requires demonstration on practical grounds ...”

This, indeed, is the all-decisive argument.

As it happens, this argument has already been answered on this blog and elsewhere. For example, see my comment 'Going beyond error and distortion' of Dec 12.

In this comment, I have refuted the Keynesian I=S and presented the correct formula, which is testable. See also my refutation of Keen's profit theory (2013). The fact of the matter is that all logical implications of the structural axiom set are testable because the axioms contain only measurable variables. And this is why structural axioms are methodologically superior to the behavioral axioms of Orthodoxy.

To answer Asad Zaman's key argument, there are as many testable propositions available as one could wish. See the working papers on SSRN.

See also the comment of Dec 21 above: “If anybody thinks that the structural axiom set is false, he is invited to refute one proposition that follows deductively from it.”

From the structural axioms follows the Profit Law. And this makes it possible to empirically refute other approaches, e.g., (2011).

My claim is that the objective-structural axiom set is superior to the familiar formal starting points of economic analysis. This claim is open to scrutiny according to the criteria of formal and material consistency. One is not obligated to apply the structural axiom set provided one already possesses the correct formal foundations, which is improbable given the unacceptable state of orthodox and heterodox economics.

Axiomatization means clarity. As self-defined social scientists, economists traditionally prefer the twilight zone where “.. nothing is clear and everything is possible.” (Keynes, 1973, p. 292). And after they have muddled everything up to the point of inconclusiveness, they invariably excuse the mess with the complexity of the subject matter. This has already gone on for a while. Here we have Duhem-Quine:
“Knight accuses the positivists of overlooking the complexity and uncertainty of testing in all sciences and argues at length that positivist views of science are particularly inappropriate to economics, which, like all sciences of human action, must concern itself with reasons, motives, values, and errors, not just causes and regularities.” (Hausman, 1989, p. 118)

Concerning methodology, Asad Zaman stands firmly in the neoclassical tradition.

“Post-Kuhnian understanding of science and axiomatics is rather complex, with no obvious and simple theory of knowledge attached.”

After Kuhn's schematic account of a paradigm shift, the Prophets of Preemptive Vanitization tried hard to get back into their natural habitat, the twilight zone of human all too human messiness. However, nobody needs a theory of knowledge to convince themselves that BOTH Orthodoxy and Heterodoxy do not satisfy scientific standards.

It is not a big issue when Asad Zaman does not understand the merits and chances of axiomatization. It is, though, of utmost importance that he refrains from silly statements like: “The failure of economics is due to the use of the axiomatic method,” or, even worse: “Thus, any axiomatization can only make a LIMITED set of claims. For example, Egmont’s axioms may provide an explanation for the role of money, but have nothing to say about the global financial crisis. Indeed, since so far the best explanation come from behavioral finance, while Egmont’s axioms bypass behavior, it would seem that his axiom CANNOT say anything about this crisis.”

This looks pretty much like an impossibility assertion out of thin air. It is obvious that Asad Zaman prefers to stay in the woods of psychology and sociology. This personal decision has to be accepted. But it cannot be accepted that he ignores facts. These are:
(i) From the fact that behavioral assumptions (like utility maximization) are denied the status of an axiom does not logically follow that no behavioral assumptions can be applied. Just the contrary: structural axiomatization is compatible with ANY behavioral assumption, that is, it is fully compatible with behavioral finance.
(ii) From the structural axiom set, indeed, follows quite a lot about financial crises. For those who can read and think, it is all on SSRN.

Asad Zaman is right, axiomatization makes only limited claims ― grandiose vacuousness is left to the so-called social sciences ― yet these claims are as certain as can be. The first important result of structural axiomatization is:

Neither Classicals, nor Walrasians, nor Marshallians, nor Marxians, nor Keynesians, nor Institutionalists, nor Monetary Economists, nor Austrians, nor Sraffaians, nor Evolutionists, nor Game theorists, nor Econophysicists, nor RBCers, nor New Keynesians, nor New Classicals ever came to grips with profit. Hence, they fail to capture the essence of a capitalist market economy.

In its present state, Heterodoxy is unacceptable according to scientific criteria. The options are: move on or move out.

Egmont Kakarot-Handtke


References
Blaug, M. (1998). Economic Theory in Retrospect. Cambridge: Cambridge University Press, 5th edition.
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. Cambridge: Cambridge University Press.
Hausman, D. M. (1989). Economic Methodology in a Nutshell. Journal of Economic Perspectives, 3(2): 115–127. URL
Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–15. URL
Kakarot-Handtke, E. (2013a). Crisis and Methodology: Some Heterodox Misunderstandings. SSRN Working Paper Series, 2083519: 1–25. URL
Kakarot-Handtke, E. (2013b). Debunking Squared. SSRN Working Paper Series, 2357902: 1–5. URL
Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.
Mirowski, P. (2002). Machine Dreams. Cambridge: Cambridge University Press.
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, London: Duke University Press.

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Twitter/X May 7, 2026 Why Gödel is irrelevant for economics

And the answer is NCND ― economics after 200+ years of Glomarization

Comment on Lars Syll on ‘What are axiomatizations good for?’

Blog-Reference

Gilboa, Postlewaite, Samuelson, and Schmeidler ask: “What have these axiomatizations done for us lately?” Wrong question, of course. The right question economists have to ask themselves is: what have WE done for the proper axiomatization of economics lately?

The fact is, to begin with, that economic methodologists do not understand to this day what axiomatization is all about. Lars Syll even maintains that it is a kind of mental body-building: “Studying mathematics and logic is interesting and fun. It sharpens the mind.”

It is not at all a surprise, therefore, that economics is a failed science. Walrasianism, Keynesianism, Marxianism, Austrianism, and their derivatives are mutually contradictory, axiomatically false, and materially/formally inconsistent. As a result, economic policy guidance has NO valid scientific foundations since Adam Smith/Karl Marx.

This pluralism of provably false theories is pretty strange. How could it happen that economics is still at the proto-scientific level while science has made such incredible advances? The answer is that economics had been captured from the very beginning by political agenda pushers. Agenda-pushers, though, have no truck with science except for building Potemkin facades.

Science is binary true/false and NOTHING in between. Non-science is the swamp between true and false where “nothing is clear and everything is possible” (Keynes). Vagueness/ inconclusiveness is what Popper called an immunizing stratagem because: “Another thing I must point out is that you cannot prove a vague theory wrong.” (Feynman) While scientifically this is a bad thing, politically it is a good thing.

Because economists are not scientists but swamp creatures, they see to it that no analysis and no debate ever leave the swamp. This is achieved by the tried and tested method of Glomarization. #1 For example, to the central question, Does a General Economic Equilibrium exist? The answer is: “We can neither confirm nor deny the existence of a General Equilibrium.” And so on with NCND for any other question. #2, #3, #4

Accordingly, if a clear-cut refutation occasionally happens, it is simply filibustered away: “In economics we should strive to proceed, wherever we can, exactly according to the standards of the other, more advanced, sciences, where it is not possible, once an issue has been decided, to continue to write about it as if nothing had happened.” (Morgenstern)

Glomarization is the communicative modus operandi in the political sphere. Science is the exact opposite of the political swamp. Science aims for a clear-cut true/false answer with truth well-defined as material and formal consistency. The methodological tool to achieve this is the axiomatic-deductive method. As Aristotle put it 2000+ years ago: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” This is why axiomatization is of overriding importance.

Neither orthodox nor heterodox economists know how to apply the axiomatic-deductive method correctly. #5 This is why their economic policy proposals have no valid scientific foundation. To the question What have economists ever done for their fellow citizens? The clear-cut answer is nothing but vacuous political blather.

Egmont Kakarot-Handtke


#1 Wikipedia, Glomar response
#2 How the representative economist gets it wrong big-time
#3 Economic recommendations out of the swamp between true and false
#4 Failed economics: The losers’ long list of lame excuses
#5 For details of the big picture, see cross-references Axiomatization

Related 'Clueless about money and profit' and 'Keynesianism ― the economists’ senile dementia' and 'Buridan’s ass economics' and 'Knowledge is attainable ― even in economics' and 'Failed critique of failed economics' and 'Stop knowing nothing, start knowing something' and 'The scientific self-elimination of Heterodoxy' and 'Prophets of Preemptive Vanitizations' and 'Economics as fool’s paradise' and 'A heap of proto-scientific rubbish' and 'Truth by definition? The Profit Theory has been axiomatically false for 200+ years' and 'Real-World Economics: The sanctuary of stupidity and corruption' and 'The inexorable paradigm shift in economics'.

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AXEC121i

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REPLY to John Vertegaal on Jul 15

You say: “Lars and Asad, great minds but still groping after all these years… All reasoning starts from assumptions, but in order to be valid in the real world, those assumptions require empirical confirmation. All economists, as far as I know, assume that the present is complete and we live within our economy. Hence, they come up with assumed points of departure like the accounting identity: Y=C+I, blissfully unaware that accounting itself is based on unprovable assumptions.”

Scientific analysis starts with premises, and these have to be clearly stated. This is the minimum requirement. #1 Otherwise, things end after a few steps in confusion and blather. This happened with economics in general, and this happens every day in the econblogosphere.

The current state of economics is that neither Orthodoxy nor Heterodoxy nor Lars Syll nor Asad Zaman nor Craig nor Dave Marsay nor the rest has gotten the foundational concepts of profit and income right. #2

Economists are swampies. Economics is a failed science. All microfounded (Walrasian) and macrofounded (Keynesian) models are provably false. Economists do not know how the economy works. Economics is a cargo cult science. The “Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel” is a fraud.

“The moral of the story is simply this: it takes a new theory, and not just the destructive exposure of assumptions or the collection of new facts, to beat an old theory.” (Blaug) Economics needs a Paradigm Shift, and the expulsion of the scientifically incompetent or the “throng of superfluous economists” as Joan Robinson called them. #3

#1 United in the social science delusion

#2 Wikipedia and the promotion of economists’ idiotism (II)

#3 Joan Robinson and the ‘throng of superfluous economists’

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REPLY to Asad Zaman on Jul 16

Since Adam Smith/Karl Marx, economics claims to be a science, but is NOT. Theoretical economics (= science) had been hijacked from the very beginning by political economists (= agenda pushers). Political economics has produced NOTHING of scientific value in the last 200+ years. #1

The fact is that economics is a failed science and that Heterodoxy has been complicit in the failure. #2 Whether this outcome was unintended/intended by individual economists does not matter. What counts is the collective effect, which is the perfect Glomarization of economics. There is not one policy proposal drawn from employment theory to monetary theory that embodies valid scientific knowledge about how the economy works, it is just opinion: “In order to tell the politicians and practitioners something about causes and best means, the economist needs the true theory or else he has not much more to offer than educated common sense or his personal opinion.” (Stigum)

Economists do not have the true theory. For every opinion, there is an equally plausible counter-opinion, and that is Glomarization ― hailed as pluralism and anything goes. #3

The political beauty of Glomarization is that it is paralyzing and therefore secures the status quo. Hayek, for one, instrumentalized this effect by arguing that just because of the lack of knowledge of economists and politicians about how the economy works, there is NO such thing as economic policy. For this epistemological reason, everything has to be left to the market as an information processor and knowledge producer.

To say economics needs a Paradigm Shift is to say that traditional Heterodoxy, too, has to be buried at the Flat-Earth-Cemetery. #4 This applies also to Asad Zaman, who has been refuted on all methodological counts. #5

By denying that, in principle, axiomatization produces logical consistency, and that state-of-the-art econometrics produces material consistency, heterodox methodologists in effect prevent scientific progress and indirectly support the political status quo.

#1The myth of economics knowledge

#2 Both orthodox and heterodox economists are cargo cult scientists

#3 The philosophy of know-nothingers

#4 Throw them out! Orthodox and heterodox economists are unfit for science

#5 Refutation of Asad Zaman’s heterodox methodology: all arguments you ever need

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REPLY to davetaylor1, Prof Dr James Beckman, Germany, on Aug 2

davetaylor1 argues: “According to my dictionary the word ‘axiom’ can refer either to a self-evident truth or a universally accepted principle. Economists seem to be assuming the first of these and forgetting about the importance of the second, as exemplified in the ways of denoting sounds and numbers.”

And Prof Dr James Beckman, Germany, asks: “Self-evident to whom?”

This shows only that both heterodox blatherers have NO idea what axiomatization is all about. “Self-evidence” is NOT a criterion of axioms; this has always been popular BS.

Note that Newton, under the title of Axiomata Sive Leges Motu, states (in modern language): “In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.”

This is NOT self-evident but an abstraction/idealization of observable motion on earth where an object does NOT move at a constant velocity.

All this is long known among people with more than two brain cells: “We may, therefore, agree with Ernst Mach, who very wisely pointed out that the law of inertia could hardly be ‘obvious’ or ‘self-evident’ since throughout most of recorded history men believed in a quite different law and would have denied the Cartesian-Newtonian inertial principle.” (Cohen, 1977)

The point of axiomatization is to clearly state the premises. As long as this is not done, any analysis and discussion will produce only proto-scientific garbage. Heterodox economists have never stated their axioms, and this is why Heterodoxy has never produced anything of scientific value. #1, #2, #3

#1 Don Lars and the axiomatic windmill

#2 For details of the big picture, see cross-references Axiomatization

#3 If it isn’t macro-axiomatized, it isn’t economics

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REPLY to davetaylor1, John Vertegaal, Craig on Aug 10

The elementary production-consumption economy is, for a start, defined by three macroeconomic axioms (Y_w=WL, O=RL, C=PX), two conditions (X=O, C=Y_w), and two definitions (Q_m≡C−Y_w, S_m≡Y_w−C). #1

#1 For details of the big picture, see cross-references Axiomatization

Key Issues: Axiomatization is still stuck at Keynes's juncture

My way is to begin with the beginning. (Lord Byron)

Beginnings are always difficult in all sciences. (Marx, 1990, p. 89)

There is no more fertile source of error than apparently trivial premisses. (Schumpeter, 1994, p. 269)

In fact, the history of every science, including that of economics, teaches us that the elementary is the hotbed of the errors that count most. (Georgescu-Roegen, 1970, p. 9)

If we open any book, even of mathematics or natural philosophy, it is impossible not to be struck with the mistiness of what we find represented as preliminary and fundamental notions, and the very insufficient manner in which the propositions which are palmed upon us as first principles seem to be made out, contrasted with the lucidity of the explanations and the conclusiveness of the proofs as soon as the writer enters upon the details of his subject. Whence comes this anomaly? Why is the admitted certainty of the results of those sciences in no way prejudiced by the want of solidity in their premises? (Mill, 1874, V.4)

When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing. (Aristotle, Analytica, Wikipedia)

For it can fairly be insisted that no advance in the elegance and comprehensiveness of the theoretical superstructure can make up for the vague and uncritical formulation of the basic concepts and postulates, and sooner or later ... attention will have to return to the foundations. (Hutchison, 1960, p. 5)

Whenever arithmetization [= axiomatization] can be worked out, its merits are above all words of praise. (Georgescu-Roegen, 1971, p. 15)

​Ein System von Gedanken muß allemal einen architektonischen Zusammenhang haben, d.h. einen solchen, in welchem immer ein Theil den andern trägt, nicht aber dieser auch jenen, der Grundstein endlich alle, ohne von ihnen getragen zu werden, der Gipfel getragen wird, ohne zu tragen. (Schopenhauer, 2016, p. 5)

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What particular reality is described by a given theory can be ascertained only from that theory's axiomatic foundation. Thus, Standard theory describes the economic process of a society in which the individual behaves strictly hedonistically, where the entrepreneurs seek to maximize his cash-profit, and where any commodity can be exchanged on the market at uniform prices and none exchanged otherwise. (Georgescu-Roegen, 1966, p. 361)

Macroeconomic theory took a major turn when it was argued that models of aggregate phenomena had to be based on ‘sound micro foundations’. In other words, the basic building blocks have to be agents, each of whose behaviour is based on the classical axioms of rationality which we impose on those agents in standard theory. (Kirman, 2010, p. 507)

..., before accepting the conclusions of any economist’s model as applicable to the real world, the careful student should always examine and be prepared to criticize the applicability of the fundamental postulates of the model; for, in the absence of any mistake in logic, the axioms of the model determine its conclusions. (Davidson, 2002, p. 41)

... one can axiomatize, without being committed to a formalist reading of the axiomatic system. Axiomatization is as old as Euclid, whereas formalism is a much later development. ... Poincaré, the most outstanding mathematician at the turn of the twentieth century, while acknowledging the value of axiomatic systems, rejected Hilbert’s formalism. Similarly, Frege, the leading logician of the period, while rejecting Hilbert’s formalism, extensively used the AA [Axiomatic Approach]. (Boylan and O'Gorman, 2007, pp. 430, 432)

The axioms that are used to define “rationality” are based on the introspection of economists and not on the observed behaviour of individuals. Economists from Pareto through Hicks to Koopmans have long made this point. Thus, we have wound up in the weird position of developing models that unjustifiably claim to be scientific because they are based on the idea that the economy behaves like a rational individual, when behavioural economics provides a wealth of evidence showing that the rationality in question has little or nothing to do with how people behave. (Kirman, 2009, p. 81)

But a principle that is not universally true is false. Thus the rationality principle is false. I think there is no way out of this. (Popper, 1994, pp. 172-173)

... General Equilibrium Theory has never justified its pricing axiom and certainly has not given any account of how wages are set when the economy is out of equilibrium. (Hahn, 1980, p. 135)

For instance, economists bend their research toward axiomatic theories that are almost embarrassing in their pre-scientific naiveté. Consider utility theory, for instance, which is now taking a drubbing at the hands of experimental psychology and neurophysiology. A scientific orientation would free us of such vestigial dogmas. (Dorman, 2008, p. 170)

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Any concept can be faultily used. (Schumpeter, 1994, p. 111)

My opinion continues to be that axiomatics, like every other tool of science, is no better than its user, and not all users are skilled. (Clower, 1995, p. 308)

... axiomatization facilitates the detection of logical errors within the model, and perhaps more importantly it facilitates the detection of conceptual errors in the formulation of the theory and in its interpretation. (Debreu, quoted in Ingrao and Israel, 1990, p. 362)

I am of the opinion that, certainly, for the purposes of research, it is always necessary to combine the intuition with the axioms. (Felix Klein, quoted in Weintraub, 2002, p. 25)

If then it is the case that the axiomatic basis of theoretical physics cannot be an inference from experience, but must be free invention, have we any right to hope that we shall find the correct way? (Einstein, 1934, p. 167)

As far as economics is concerned, only if we look for non-behavioral axioms.

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Economics still stands at what may be called Keynes's juncture:

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)

This insight is Keynes's most valuable methodological contribution. In practice, non-Euclidean translates to non-behavioral. Structural/systemic axiomatization is, in a sense, the realization of Keynes's methodological program as stated above. What his followers put into practice was his political program, which indeed has a weak theoretical foundation because Keynesians never came forth with the non-Euclidean axioms. Since the days when Keynes saw more clearly than his fellow economists that the 'classical' axioms had been refuted once and for all by the Great Depression, economics is in dire need of new formal foundations. There is no way back before Keynes, and to stay any longer at Keynes' juncture is equally impossible. New Classicals have not got the first point, New Keynesians not the second (cf. Quiggin, 2010). Lacking correct formal foundations, both approaches are agonizing detours.

Axiomatization is the prime task of theoretical economics. Without correct axioms, no correct theory. Without a correct theory, no understanding of how the monetary economy works. Without an empirically corroborated understanding, no useful economic policy advice. Without effective economic advice, no good reputation: "Late in life, moreover, he [Napoleon] claimed that he had always believed that if an empire were made of granite the ideas of economists, if listened to, would suffice to reduce it to dust" (Viner, 1963, p. 1). This was long before the Great Depression's fatal dustification. However, the opinion of any political executive is, in the last instance, not decisive. Nor is public opinion.

Much more important than any political reputation of economics is: Without correct axioms, no acceptance as science. There is no way around it, neither for Orthodoxy nor for Heterodoxy.

The basic concepts and laws which are not logically further reducible constitute the indispensable and not rationally deducible part of the theory. It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience. (Einstein, 1934, p. 165)

Einstein's First Imperative of Scientific Inquiry applies to structural axiomatization. Compliance with the First Imperative, though, does not guarantee that the correct set of axioms emerges automatically. The Second Imperative demands formal and material consistency. Both imperatives taken together rule conventional approaches out.


References
Boylan, T. A., and O’Gorman, P. F. (2007). Axiomatization and Formalism in Economics. Journal of Economic Surveys, 21(2): 426–446.
Clower, R. W. (1995). Axiomatics in Economics. Southern Economic Journal, 62(2): 307–319. URL
Dorman, P. (2008). What Would a Scientific Economics Look Like? real-world economics review, 47: 166–172. URL
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL
Davidson, P. (2002). Financial Markets, Money and the Real World. Cheltenham, Northampton: Edward Elgar.
Georgescu-Roegen, N. (1966). Analytical Economics, chapter Economic Theory and Agrarian Economics, 359–397. Cambridge: Harvard University Press.
Georgescu-Roegen, N. (1970). The Economics of Production. American Economic Review, Papers and Proceedings, 60(2): 1–9. URL
Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. Cambridge: Cambridge University Press.
Hahn, F. H. (1980). General Equilibrium Theory. Public Interest. Special Issue: The Crisis in Economic Theory, 123–138.
Hutchison, T.W. (1960). The Significance and Basic Postulates of Economic Theory. New York: Kelley.
Ingrao, B., and Israel, G. (1990). The Invisible Hand. Economic Equilibrium in the History of Science. Cambridge, London: MIT Press.
Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London: Macmillan.
Kirman, A. (2009). Economic Theory and the Crisis. real-world economics review, (51): 80–83. URL
Kirman, A. (2010). The Economic Crisis is a Crisis for Economic Theory. CESifo Economic Studies, 56(4): 498–535. DOI
Marx, K. (1990). Capital, Vol. I. London: Penguin Classics. (1876).
Popper, K. R. (1994). The Myth of the Framework. In Defence of Science and Rationality. London, New York: Routledge.
Quiggin, J. (2010). Zombie Economics. How Dead Ideas Still Walk Among Us. Princeton, Oxford: Princeton University Press.
Schopenhauer, A. (2016). Die Welt als Wille und Vorstellung, German Edition, Zenodot Verlagsgesellschaft. Kindle-Version.
Schumpeter, J. A. (1994). History of Economic Analysis. New York: Oxford University Press.
Viner, J. (1963). The Economist in History. American Economic Review, 53(2): 1–22. URL
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, London: Duke University Press.


Related 'Euclid and Keynes's Missing Axioms URL' and 'Why Post Keynesianism is Not Yet a Science URL or URL' and 'Walras's Law of Markets as Special Case of the General Period Core Theorem URL'


© 2013 EKH, except original quotes

Reminder: A human being is multidimensional; AXEC is about the scientific dimension. True or false relates to the material/formal consistency of an approach.  Other dimensions, in particular the moral dimension, are left out of the picture. So, somebody might be a good person, but their hypothesis is false, and vice versa, somebody might be a monster, but their hypothesis is true. Mixing the two aspects ruins every scientific debate. Keynesianism is refuted because of material/formal inconsistency, i.e., ultimately because of Keynes's scientific incompetence, not because of other reasons. Historical and biographical gossiping is characteristic, in particular, of the Austrian School of Economics. Social media is, by its very nature, 99,9 per cent gossip and 0,1 per cent science. For more details, see the AXECquery axiom.

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Graphic AXEC172

Axiomatics — the heterodox bugbear

Comment on Lars Syll on ‘Axiomatics — the economics fetish’

Blog-Reference

Why can heterodox economists not get their heads around the methodological fact that axiomatization and empiricism are not mutually exclusive but the two sides of the coin called theory?

“In Einstein's words, geometry constituted one of the oldest physical theories. In the preface to his Principia Newton treats geometry as a branch of mechanics, i.e. as a branch of physics: Therefore geometry is founded in mechanical practice and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring.” (Zahar, 1980, p. 3)

That axioms are strictly empirical was obvious to the economics founding fathers: “... in Mill's view, the axioms of Euclidian geometry are inductive.” (Whitaker, 1975, p. 1038)

The original commonsensical realism of axioms got out of sight in the process of ever-increasing refinement, precision, idealization, and the ever-increasing requirement of logical consistency.

Historically, axioms as the basis of subsequent deduction are themselves arrived at by intuitive induction. They are neither plucked out of thin air nor arbitrary. A direct proof of the fact that axioms are empirical is that Gauss set out to test them “One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean.” (Brown, 2011, p. 565)

Axioms are ‘realistic’ but in a highly refined form derived from the deeper reality: “... the repugnance which it [the axiomatic method] still meets here and there can only be explained by the natural difficulty of the mind to admit, in dealing with a concrete problem, that a form of intuition, which is not suggested directly by the given elements (and which often can be arrived at only by a higher and frequently difficult stage of abstraction), can turn out to be equally fruitful.” (Bourbaki, 2005, p. 1275)

Axiomatization is not an easy thing as more than 2500 years of history since Euclid testify and it is quite natural to get it wrong. This, clearly, is not a fault of the method but of the user: “My opinion continues to be that axiomatics, like every other tool of science, is no better than its user, and not all users are skilled.” (Clower, 1995, p. 308)

It is correct of Heterodoxy to insist that something went wrong with Debreu’s axiomatization of general equilibrium (Ackerman et al., 2004). The obvious error/mistake is that there exists no such thing as an equilibrium in the economy. It is simply an inexcusable methodological blunder to axiomatize a nonentity. As Clower said, not all users are skilled.

It is correct of Heterodoxy to reject the neo-Walrasian axioms. But to reject axiomatization as a method is stupid and ultimately self-defeating. Axiomatics is not a fetish but an indispensable tool to secure logical consistency. The classical economists understood this well.

“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)

Because neither Senior nor Debreu nor Heterodoxy has been successful, this task is still unfinished.#1 And this is why economics is, until this day, not much more than storytelling, ad hocery, and persistent confusion at the proto-scientific level.

Egmont Kakarot-Handtke


References
Ackerman, F., and Nadal, A. (Eds.) (2004). Still Dead After All These Years: Interpreting the Failure of General Equilibrium Theory. London, New York: Routledge.
Bourbaki, N. (2005). The Architecture of Mathematics. In W. Ewald (Ed.), From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Vol. II, 1265–1276. Oxford, New York: Oxford University Press. (1948).
Brown, K. (2011). Reflections on Relativity. Raleigh: Lulu.com.
Clower, R. W. (1995). Axiomatics in Economics. Southern Economic Journal, 62(2): 307–319. URL
Schumpeter, J. A. (1994). History of Economic Analysis. New York: Oxford University Press.
Whitaker, J. K. (1975). John Stuart Mill’s Methodology. Chicago Journals, 83(5): 1033–1050. URL
Zahar, E. (1980). Einstein, Meyerson and the Role of Mathematics in Physical Discovery. The British Journal for the Philosophy of Science, 31(1): 1–43. URL


#1 Towards the true economic theory
 
Related 'Lars Syll creatively destructs Wren-Lewis' and 'Axiomatized nonentities and the failure of methodologists'. For details of the big picture see cross-references Axiomatisation and cross-references Paradigm shift.

Immediately following Economists’ proto-scientific methodology.

Key Issues: Hilbert-Bourbaki-Mill and von Neumann's monster-structure

... for nothing is farther from the axiomatic method than a static conception of the science. We do not want to lead the reader to think that we claim to have traced out a definitive state of the science. (Bourbaki, 2005, p. 1274)

When we assemble the facts of a definite, more-or-less comprehensive field of knowledge, we soon notice that these facts are capable of being ordered. This ordering always comes about with the help of a certain framework of concepts [Fachwerk von Begriffen ] .... The framework of concepts is nothing other than the theory of the field of knowledge. ... If we consider a particular theory more closely, we always see that a few distinguished propositions of the field of knowledge underlie the construction of the framework of concepts, and these propositions then suffice by themselves for the construction, in accordance with logical principles, of the entire framework. ... The procedure of the axiomatic method, as it is expressed here, amounts to a deepening of the foundations of the individual domains of knowledge — a deepening that is necessary for every edifice that one wishes to expand and to build higher while preserving its stability. (Hilbert, 2005, pp. 1107-1109), original emphases

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)

Could all the phaenomena of nature be deduced from only thre [sic] or four general suppositions there might be great reason to allow those suppositions to be true. (Newton, quoted in Westfall, 2008, p. 642)

I find it quite amazing that it is possible to predict what will happen by mathematics, which is simply following rules which really have nothing to do with what is going on in the original thing. (Feynman, 1992, p. 171)

From the axiomatic point of view, mathematics appears thus as a storehouse of abstract forms — the mathematical structures; and it so happens — without our knowing why — that certain aspects of empirical reality fit themselves into these forms, as if through a kind of preadaptation. (Bourbaki, 2005, p. 1276)

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However, there also occur structures entirely without application, the so-called monster-structures (Bourbaki, 2005, p. 1275, fn. 9).

From the structural axiomatic point of view, the subjective-behavioral axioms yielded such a formalism without application. Its sole merit was "that of showing the exact bearing of each axiom, by observing what happened if one omitted or changed it."

Bourbaki cannot be made accountable for the conventional monster-structure. The same holds for Hilbert and, of course, Mill.

..., it was the von Neumann perspective that shaped general equilibrium theory ..., and thus reconstituted economic theory. (Weintraub, 2002, p. 78)

As a student of Hilbert and a proponent of axiomatization, von Neumann immediately realized that Walras's mathematics was insufficient:

The so-called "mathematical" economists in the narrower sense — Walras, Pareto, Fisher, Cassel, and hosts of other later ones — especially, have completely failed even to see the task that was before them. Professor Hicks has to be added to this list, which is regrettable because he wrote several years after decisive work had been done — in principle — by J. von Neumann and A. Wald. (Morgenstern, 1941, p. 369)

Von Neumann did not realize, though, that Walras' supply-demand-zero-profit-equilibrium was mistaken in the first place and never represented any feasible economy. It was only Walras's formalism that was eventually repaired. For von Neumann, general equilibrium was first and foremost a mathematical puzzle. To crack the nut, he advocated the fixpoint approach. With explicit disregard of economic content, the axiomatization of Walrasian economics was completed by Debreu and others. This, however, could not change the fact that equilibrium is a NONENTITY. What, in effect, had been solved was an angels-on-the-pinpoint problem. This subsequently became the core competence of standard economics. It is a curious fact that the physicists and mathematicians who came in great numbers with advanced tools to economics to help the indigenous folk (Mirowski, 1995) in effect moved the whole thing deeper into the Walrasian cul-de-sac.

It is difficult to contemplate the evolution of the economic science over the last hundred years without reaching the conclusion that its mathematization was a rather hurried job. (Georgescu-Roegen, 1979, p. 271)

Axiomatization in economics suffers from many misunderstandings (see also Crisis and Methodology: Some Heterodox Misunderstandings URL). This, clearly, is not an argument against the method but against economists.

The method of reasoning by chains of syllogisms is nothing but a transformation mechanism, applicable just as well to one set of premisses as to another; it could not serve therefore to characterize these premisses. (Bourbaki, 2005, pp. 1267-1268)

The deductive method does not prove that the premises are true. The truth of theorems and the truth of premises are entirely different questions. The deductive method guarantees that the conclusions are true if the premises are true.

***

Outside pure mathematics, the usefulness of axiomatization crucially depends on the real-world domain. Not everything is axiomatizable. There is, for example, no such thing as a behavioral axiom. By borrowing from physics and mathematics, the neoclassicals got the essentials wrong from the very beginning.

The bifurcation of motion into two fundamentally different types, one for natural motions of non-living objects and another for acts of human volition ... is obviously related to the issue of free will, and demonstrates the strong tendency of scientists in all ages to exempt human behavior from the natural laws of physics, and to regard motions resulting from human actions as original, in the sense that they need not be attributed to other motions. (Brown, 2011, p. 211)

Jevons' rhetorical question points exactly to the source of neoclassical confusion:

Must not the same inexorable reign of law which is apparent in the motions of brute matter be extended to the subtle feelings of the human heart? (Jevons, quoted in Mirowski, 1995, p. 219 )

Jevons had, with the laws of motion, the archetype of science on his mind:

But it was a second and more important quality that struck readers of the Principia. At the head of Book I stand the famous Axioms, or the Laws of motion … For readers of that day, it was this deductive, mathematical aspect that was the great achievement. (Truesdell, quoted in Schmiechen, 2009, p. 213)

What Jevons did not understand was that the trinity of law, axiom, and behavior does not work because behavior is original, as the scientists of all ages knew well (for details, see Objective Principles of Economics URL). With far-fetched analogies and his shallow scientific understanding, Jevons placed neoclassical economics on poor foundations (for details, see The Logic of Value and the Value of Logic URL), and there it stood, with some formal improvements, until recently.

For an outside observer without prior knowledge of habitual human reactions, behavior appears at first random. This is the point to start with, not introspection. The laws of motion of the human heart are pure kitsch and remain so in the abstract form of the first derivative of a utility function. From the marginal principle follows nothing that could help to understand how the market economy works. To think of human behavior in terms of deterministic laws is an unforgivable analytical blunder. It is the structure that is deterministic (see the Period Core), not the behavior.

***

... if we wish to place economic science upon a solid basis, we must make it completely independent of psychological assumptions and philosophical hypotheses (Slutzky, quoted in Mirowski, 1995, p. 362, see also Hudík, 2011).

This is the defining property of the objective/structural/systemic axiom set.


References
Brown, K. (2011). Reflections on Relativity. Raleigh: Lulu.com.
Bourbaki, N. (2005). The Architecture of Mathematics. In W. Ewald (Ed.), From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Vol. II, 1265–1276. Oxford, New York: Oxford University Press.
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Georgescu-Roegen, N. (1979a). Energy and Economic Myths, chapter Measure, Quality, and Optimum Scale, 271–296. New York, Toronto: Pergamon.
Hilbert, D. (2005). Axiomatic Thought. In W. Ewald (Ed.), From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Vol. II, 1107–1115. Oxford, New York: Oxford University Press.
Hudík, M. (2011). Why Economics is Not a Science of Behaviour. Journal of Economic Methodology, 18(2): 147–162.
Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications to Social Philosophy, Vol. 3, Books III-V of Collected Works of John Stuart Mill. Indianapolis: Liberty Fund.
Morgenstern, O. (1941). Professor Hicks on Value and Capital. Journal of Political Economy, 49(3): 361–393. URL
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.
Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited, Vol. 1. Norderstedt: Books on Demand, 2nd edition.
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, London: Duke University Press.
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 17th edition.

Related Euclid, Newton . For details about the Period Core, which represents a structural law, see The Synthesis of Economic Law, Evolution, and History URL.


© 2013 EKH, except original quotes

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Twitter/X Jan 13, 2026  Hilbert and Wiener

Twitter/X Jul 23, 2026  Solving Munchausen's Trilemma: Suspended from nothing

Economists’ proto-scientific methodology

Comment on Lars Syll on ‘Axiomatics — the economics fetish’

Blog-Reference and Blog-Reference

When the promoters of the so-called social sciences, which have produced not much of real scientific value in the last 2300 years, wreck their brains about the methodology of the genuine sciences, which started with the simple Law of the Lever and arrived in the meantime at the field equations of mass-space-time, the situation instantaneously becomes comical.

Heterodox economists, in particular, cannot see how axiomatics could help in the development of economic theory. They simply do not want to start research with some abstract axioms but with concrete facts. What they miss is the difference between the development and the representation of a theory.

Of course, Newton did not first write down a set of axioms and then started to think about gravitation. But after he had figured out the Law of Gravitation (by thinking about falling bodies under the apple tree, as folklore has it) he demonstrated in his Principia how this Law could be logically derived from the elementary axioms of motion just like the Pythagorean theorem had been derived from Euclid’s axioms.

“... it was ... [this] quality that struck readers of the Principia. At the head of Book I stand the famous Axioms, or the Laws of motion: … For readers of that day, it was this deductive, mathematical aspect that was the great achievement.” (Truesdell, quoted in Schmiechen, 2009, p. 213)

In his statements about methodology “... Newton had insisted on the certainty of an approach founded on rigorous method.” (Westfall, 2008, p. 346)

In view of Newton’s overwhelming success, this message was well received in the so-called social sciences: “Like most of his fellow moral philosophers, Hume thought it was worth a try to make all sciences as rigorous as Newtonian physics ...” (Redman, 1997, p. 111)

Eventually, the message hit economics: “His [Adam Smith’s] method is always the method of Newton, which we have already seen applied to psychology and morals: to attain, by generalization, certain simple truths, from which it will be possible to reconstruct, synthetically, the world of experience.” (Halévy, 1960, p. 100)

Basically, this idea is sound. In fact, it is identical to Einstein’s methodology: “The basic concepts and laws which are not logically further reducible constitute the indispensable and not rationally deducible part of the theory. It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” (1934, p. 165)

What Einstein describes here is nothing else than what in mathematics is called axiomatization. To recall, Einstein cooperated with Hilbert who was the towering figure of axiomatics at that time and instrumental in the formulation of the field equations. Modern physics is unthinkable without the prior move from Euclidean to non-Euclidean axioms.

No physicist would ever think of axiomatics as a fetish. Every time he uses a piece of mathematics the physicist indirectly benefits from axiomatics without thinking or talking much about it. Axiomatics is only a more formal expression for the physicists' idea of the formulation of a unified theory.

“Some day, when physics is complete and we know all the laws, we may be able to start with some axioms, and no doubt somebody will figure out a particular way of doing it so that everything else can be deduced.” (Feynman, 1992, p. 50)

Thus, axiomatics has always been, in a direct or indirect way, the physicists' great helper. In marked contrast, economists since Adam Smith messed things up. In our days, Orthodoxy got the axiomatic foundations of general equilibrium theory wrong and Heterodoxy has none at all. This methodological slapstick performance produced a heap of incoherent, contradictory, inconsistent models with no counterpart whatsoever in the real world.

Clearly, Walrasianism, Keynesianism, Marxianism, and Austrianism have to give way to an axiomatically unified economic theory — the sooner, the better.

Egmont Kakarot-Handtke


References
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Halévy, E. (1960). The Growth of Philosophic Radicalism. Boston,: Beacon Press.
Redman, D. A. (1997). The Rise of Political Economy as Science. Methodology and the Classical Economists. Cambridge, London: MIT Press.
Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited, volume 1. Norderstedt: Books on Demand BoD, 2nd edition. URL
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 17th edition.

Related 'Axiomatics — the heterodox bugbear'

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REPLY  The universe and the goldfish bowl, on Jan 22

On Geoff Davis
Einstein worked 10 years on the field equations, which describe — roughly speaking — the universe, and you argue “On the other hand, sometimes a rough back of the envelope calculation is all the mathematics you need to check whether your hypothesis compares well with observations or not.”

Of course, if you want to describe the goldfish bowl the back of the envelope is all you need. Your argument is a bit silly. Why don’t you tell the guys who are working hard on string theory that you can do it on an envelope and without the Schrödinger equation?

The most important thing is to be clear about the subject matter. Economics is about how the (world-) economy works, it is not about the mom-and-pop store which every half-baked consultant can easily overlook and model with a spreadsheet.

What we are talking about here is Debreu’s axiomatization of General Equilibrium which is a Walrasian total model and not a Marshallian partial (goldfish bowl) model.

By the way, with every back-of-the-envelope calculation, you benefit indirectly from the axiomatization of algebra and geometry. But this is usually beyond the bowl horizon of engineers and hobby economists.

On Asad Zaman
You argue rather confused:
(i) “The scientific method arose as a rejection of the axiomatic method used by the Greeks for scientific methodology.”#1
(ii) “Human behavior cannot be axiomatized.” (preceding post)

While (ii) is correct (i) is provably false; see my refutation on the parallel thread.#2

From (ii) follows that the DSGE approach has to be abandoned because it is based on a behavioral axiom. As Krugman put it on his blog “most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point.” Constrained optimization is a behavioral axiom (=starting point) of DSGE and as such methodologically inadmissible.#3

From the fact that Orthodoxy badly messed up axiomatization does not follow that (i) the axiomatic-deductive method has been abandoned in the genuine sciences, and (ii) that the method is a priori inapplicable in economics.

What instead follows is that the neo-Walrasian axioms have to be replaced “There is another alternative: to formulate a completely new research program and conceptual approach. As we have seen, this is often spoken of, but there is still no indication of what it might mean.” (Ingrao et al., 1990, p. 362)

There is only one way for Heterodoxy to beat Orthodoxy and this is a Paradigm Shift, i.e. the replacement of orthodox axioms with heterodox axioms. To denounce the axiomatic-deductive method as a fetish is a sure indicator of scientific incompetence. The fact of the matter is that the axiomatic-deductive method is Heterodoxy’s most powerful tool — if applied properly for the formulation of a ‘ completely new research program and conceptual approach’.

The current state of economics is this: Orthodoxy got the axiomatic foundations wrong and Heterodoxy has none at all. Is anyone surprised that economics is a failed science? Is anyone aware that economic policy proposals have no sound scientific foundation? And with orthodox and heterodox economists who have at best a commonsensical goldfish-bowl-model of how the economy works, is anyone surprised that economic problems cannot be solved but only worsened or shifted?


References
Ingrao, B., and Israel, G. (1990). The Invisible Hand. Economic Equilibrium in the History of Science. Cambridge, London: MIT Press.

#1 Lars P Syll Blog
#2 Full methodological illiteracy
#3 Lars Syll creatively destructs Wren-Lewis

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REPLY  The methodology of confused agenda pushers, comment on Geoff Davies of Jan 23

You mix up two issues that are related but need to be kept apart in order to get out of the swamp between true/false where blathering is rife.

With regard to precision, it is well-known that there are different degrees of precision in different walks of life, e.g. theoretical physics and engineering, therefore “... the following maxim holds for all sciences: Never aim at more precision than is required by the problem at hand. (Popper, quoted in Redman, 1993, p. 105)

This settles the matter because in a monetary economy, we have a natural precision of two decimal places. This translates into the rule to express every economic statement about the nominal sphere in rational numbers.  This, in turn, is sufficient to debunk Debreu’s approach which presupposes the real number space: “Unfortunately, we are stuck with the need to justify the use of irrational numbers such as square-root2, pi or e as economically meaningful prices and/or quantities.” (Nadal, 2004, p. 36)

In rather general terms we can agree that the use of irrational numbers is what Keynes called mock precision. On the other hand, one should not be content with a precision of less than two decimal places for nominal relationships.

Precision indeed relates to the question of axiomatization because Debreu’s axioms are defined in the rational number space, but the precision of concepts like income or profit is something different from numerical precision. The crucial point is that from vague premises any conclusion and the opposite can be derived and this is a senseless exercise: “Meanwhile, the best safeguard against overestimation of the range of applicability of economic propositions is a careful spelling out of the premises on which they rest. Precision and rigor in the statement of premises and proofs can be expected to have a sobering effect on our beliefs about the reach of the propositions we have developed.” (Hutchison, 1960, p. xxiii)

To repeat: numerical precision and ‘precision and rigor in the statement of premises’ are related but fundamentally different things.

The difference between political economists (= agenda pushers) and theoretical economists (= scientists) is that the former plead for ‘better vaguely right than precisely wrong’ and the latter plead for ‘better precisely right than vaguely wrong’. After all, political economists want to make their case here and now and are not so much interested in epistemic truth. Economics since Adam Smith is political economics and political economics is scientifically worthless.

It becomes a bit boring to reiterate that there is a difference between mathematics and physics or any other science. It is well-known among methodologists that “Formal axiomatic systems must be interpreted in some domain ... to become an empirical science.” (Boylan et al., 1995, p. 198)

And, lo and behold, this is what genuine scientists always have done with overwhelming success “It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the relations of real objects of this kind, which we will call practically-rigid bodies. To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the co-ordination of real objects of experience with the empty conceptual framework of axiomatic geometry. To accomplish this, we need only add the proposition: — Solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the relations of practically-rigid bodies.” (Einstein, 1921)

The scientific incompetence of economists consists of taking the nonentities ‘maximization-and-equilibrium’ (Krugman) as axioms that are not by any stretch of the imagination related to anything in the real world. It should be pretty obvious to Zaman and you#1 that the axiomatic-deductive method works only if the premises are “certain, true, and primary” (Aristotle), otherwise garbage-in-garbage-out. In more concrete terms: from the ‘maximization-and-equilibrium’ garbage follows the DSGE garbage, and this is not the fault of the axiomatic-deductive method.


References
Boylan, T. A., and O’Gorman, P. F. (1995). Beyond Rhetoric and Realism in Economics. Towards a Reformulation of Economic Methodology. London: Routledge.
Einstein, A. (1921). Geometry and Experience. Website. URL
Hutchison, T.W. (1960). The Significance and Basic Postulates of Economic Theory. New York: Kelley.
Nadal, A. (2004). Behind the Building Blocks. Commodities and Individuals in General Equilibrium Theory. In F. Ackerman, and A. Nadal (Eds.), The Flawed Foundations of General Equilibrium, 33–47. London, New York: Routledge.
Redman, D. A. (1993). Economics and the Philosophy of Science. New York, Oxford: Oxford University Press.

#1 For more refutation go to my blog and enter Zaman in the search field

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REPLY Can’t get out behind the curve?, comment on larrymotuz of Jan 25

You say: “The ‘truth’ content of axioms cannot be proven.” WOW, YES, this is exactly what axiom means and this should be known to every economist for more than 200 years: “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)

And here you have it in a nutshell: both Orthodoxy and Heterodoxy have failed at the opus magnum. That is the core of the whole methodological mess.

The fact that axioms need something like empirical proof has not escaped genuine scientists (which excludes economists) “This indicates that any attempt logically to derive the basic concepts and laws of mechanics from the ultimate data of experience is doomed to failure. If then it is the case that the axiomatic basis of theoretical physics cannot be an inference from experience, but must be free invention, have we any hope that we shall find the correct way?” (Einstein, 1934, pp. 166-167)

To your knowledge, genuine scientists (which excludes economists) have found the correct way and it has been clearly defined as scientific methodology: “Research is in fact a continuous discussion of the consistency of theories: formal consistency insofar as the discussion relates to the logical cohesion of what is asserted in joint theories; material consistency insofar as the agreement of observations with theories is concerned.” (Klant, 1994, p. 31)

It seems that Zaman, Davies, Motuz, and all the other hobby economists/retired engineers simply cannot get their heads around the most elementary methodological concept or even to look it up in Wikipedia: “An axiom or postulate as defined in classic philosophy, is a statement that is so evident or well-established, that it is accepted without controversy or question. Thus, the axiom can be used as the premise or starting point for further reasoning or arguments ... The word comes from the Greek axíōma ‘that which is thought worthy or fit’ or ‘that which commends itself as evident.’

The fact of the matter is that for more than 200 years economic axioms are not worthy or fit. And this is why economics is a failed science.


References
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL
Klant, J. J. (1994). The Nature of Economic Thought. Aldershot, Brookfield: Edward Elgar.
Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications to Social Philosophy, Vol. 3, Books III-V of Collected Works of John Stuart Mill. Indianapolis: Liberty Fund. URL

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REPLY  Deep in the methodological woods, comments

(i) On Geoff Davies of Jan 26

This thread is about axiomatics. You say ‘Numerical precision is very context-dependent, so it’s pointless making general statements.’ This is (i) trivially true and (ii) far beside the point, which is conceptual precision/consistency of foundational propositions of theories and not the numerical precision of empirical estimations.

(ii) On Paul Schächterle of Jan 26

As a rule, the proof of axioms is in the deductively derived conclusions. If what the theory says should be the case is actually the case, then the axioms are indirectly corroborated. If not, they are refuted qua modus tollens. “Whether an axiom is or is not valid can be ascertained either through direct experimentation or by verification through the result of observations, or, if such a thing is impossible, the correctness of the axiom can be judged through the indirect method of verifying the laws which proceed from the axiom by observation or experimentation. (If the axiom is deemed to be incorrect it must be modified or instead a correct axiom must be found.) (Morishima, 1984, p. 53)

All this is well-known since Newton: “Could all the phaenomena of nature be deduced from only thre [sic] or four general suppositions there might be great reason to allow those suppositions to be true.” (quoted in Westfall, 2008, p. 642)

For more proof of Zaman’s and your insufficient understanding of axiomatics see: ‘Full methodological illiteracy’

(iii) Methodological junk since Jevons/Walras/Menger

The axioms (= premises = starting point = foundational propositions) of standard economics, that is, “most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point” (Krugman), are pure methodological junk, yet Heterodoxy has not managed for more than 140 years to replace them. The methodological incompetence of both orthodox and heterodox economists is abysmal. For details see Are economists natural-born scientific failures? and Economics as fool’s paradise.


References
Morishima, M. (1984). The Good and Bad Use of Mathematics. In P. Wiles, and G. Routh (Eds.), Economics in Disarray, 51–73. Oxford: Blackwell.
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 17th edition.

Concluding Economists and methodology: the horror of all horrors