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'
***
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
***
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
***
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
***
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