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Axiomatics — the economics fetish
Mainstream — neoclassical — economics has become increasingly irrelevant to the understanding of the real world. The main reason for this irrelevance is the failure of economists to match their deductive-axiomatic methods with their subject.
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. Nevertheless, it has become almost an article of faith in modern economics. I am not aware, but would be interested to know, whether, and if so how widely, this misunderstanding has been propagated in other (purportedly) empirical disciplines. The requirement of the axiomatic method in economics betrays a kind of snobbishness and (I use this word advisedly, see below) pedantry, resulting, it seems, from a misunderstanding of good scientific practice …
This doesn't mean that trying to achieve a reduction of a higher-level discipline to another, deeper discipline is not a worthy objective, but it certainly does mean that one cannot just dismiss, out of hand, a discipline simply because all of its propositions are not deducible from some set of fundamental propositions. Insisting on reduction as a prerequisite for scientific legitimacy is not a scientific attitude; it is merely a form of obscurantism
The fetish for axiomitization in economics can largely be traced to Gerard Debreu's great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium … The subsequent work was then brilliantly summarized and extended in another great work, General Competitive Analysis by Arrow and Frank Hahn. Unfortunately, those two books, paragons of the axiomatic method, set a bad example for the future development of economic theory, which embarked on a needless and counterproductive quest for increasing logical rigor instead of empirical relevance …
I think that it is important to understand that there is simply no scientific justification for the highly formalistic manner in which much modern economics is now carried out. Of course, other far more authoritative critics than I, like Mark Blaug and Richard Lipsey have complained about the insistence of modern macroeconomics on microfounded, axiomatized models regardless of whether those models generate better predictions than competing models. Their complaints have regrettably been ignored for the most part. I simply want to point out that a recent, and in many ways admirable, introduction to modern macroeconomics failed to provide a coherent justification for insisting on axiomatized models. It really wasn't the author's fault; a coherent justification doesn't exist.
David Glasner
It is — sad to say — a fact that within mainstream economics internal validity is everything and external validity nothing. Why anyone should be interested in that kind of theories and models — as long as mainstream economists do not come up with any export licenses for their theories and models to the real world in which we live — is beyond my imagination. Sure, the simplicity that axiomatics and analytical arguments bring to economics is attractive to many economists. But …
Simplicity, however, has its perils. It is one thing to choose as one's first object of theoretical study the type of arguments open to analysis in the simplest terms. But it is quite another to treat this type of argument as a paradigm and to demand that arguments in other fields should conform to its standards regardless, or build up from a study of the simplest forms of argument alone a set of categories intended for application to arguments of all sorts: one must at any rate begin by inquiring carefully how far the artificial simplicity of one's chosen modal results in these logical categories also being artificially simple. The sorts of risks one runs otherwise are obvious enough. Distinctions which all happen to cut along the same line for the simplest arguments may need to be handled quite separately in the general case; if we forget this, and our new found logical categories yield paradoxical results when applied to more complex arguments, we may be tempted to put these rules down to defects in the arguments instead of in our categories; and we may end up by thinking that, for some regrettable reason hidden deep in the nature of things, only our original, peculiarly simple arguments are capable of attaining to the ideal of validity.
Economists' slapstick methodology
Comment on 'Axiomatics — the economics fetish'
When the promoters of the so-called social sciences, which have produced not much of real scientific value in the last 2500 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 obvious 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 with 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." (Einstein, 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, Marxism, and Austrianism have to give way to an axiomatically unified economic theory — the sooner, the better.
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL http://www.jstor.org/stable/184387.
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Halévy, E. (1960). The Growth of Philosophic Radicalism. Boston, MA: Beacon Press.
Redman, D. A. (1997). The Rise of Political Economy as Science. Methodology and
the Classical Economists. Cambridge, MA, London: MIT Press.
Schmiechen, M. (2009). Newton's Principia and Related 'Principles' Revisited, volume 1. Norderstedt: Books on Demand, 2nd edition.
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge:
Cambridge University Press, 17th edition.
Garrett Connelly
Okay. Good thinking. Now. How do place the urban legend that young information theorists started with six verbal information theory postulates (eg. information is preserved regardless of adversity) and reached the abstract mathematics of string theory and struggled for the theory of everything?
I mean. Is it true? Did they do that? I will be saddened to learn it's an urban legend.
Geoff Davies
A lot of physicists were seduced by the idea they were uncovering "universal laws" or reading the mind of God. The examples of Newton and Einstein show very simply that this was not so. Einstein's theory of gravity superseded Newton's, so evidently Newton's wasn't a universal fixed law. Some day Einstein's theory may also be superseded.
What they were doing, rather, was perceiving patterns, and then deducing the consequences of such a pattern using mathematics. The perception of a pattern, an inverse square law or curving space-time, is not a logical, rational process, it's a process of cognition.
There are two stages in science. One is the perception and description of a pattern. The second is the deduction of implications. A description of a pattern may be put in a very concise mathematical form, and you may describe that form as axioms. They ought really to be described as hypotheses, possibly describing the world out there. The logical deduction from the axioms indeed can be a rigorous process, but the point of doing it is not to show how clever and rigorous you can be, but to deduce implications that can be compared with observations e.g the orbit of Mercury. It is that comparison that completes the process of science, and that is so lacking in economics.
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.
So this whole business of mathematical rigour is not only greatly overrated in economics, but its role is quite misunderstood: by many physicists as well as many economists. in some parts of science there may be observations of great precision, in which case careful mathematical deductions of comparable precision are required. In other parts of science observations may be much less precise, although often just as capable of deciding between hypotheses. In the latter case great mathematical precision is not required, and may mislead the scientist about the significance of the work.
So I think EKH's comment propagates some confusion.
larrymotuz
"The perception of a pattern, an inverse square law or curving space-time, is not a logical, rational process, it's a process of cognition."
So very, very true, Mr. Davies. The myths of Prometheus and Epimetheus come to mind here.
Promethus is ready-witted; Epimetheus is his scatter-brained brother who, unware of patterns (and thus always unware of what might lie ahead) is never wary, for to 'beware' is to 'be wary' about what patterns portend.
Epimetheus is, in many senses, unable to act except instinctively. Though he lives within patterns of nature and has been shaped by those patterns, his attention is not drawn to their significance, or to what their recurrence may betoken. He senses but cannot be sensible. He reacts to the moment within a pattern but always fails to see what may be coming next. [Analogously, he 'hears' notes but never the 'music'.]
Epimetheus is responsive to stimuli as they occur. But unlike his brother, Epimetheus cannot ever ask,"What's next? or, "What come after this."
Prometheus 'cognits' patterns and has learned that patterns re-occur. This recurrence of within patterns sheds light on what possibly lies ahead.
Epimetheus has a retentive memory of events but lacks the neuro-architecture to perceive patterns as such. He cannot use his memory to provide any practica insight into what may lie ahead. He cannot process the information that stiulate his actions. His unaware-ness of patterns makes him unable to be wary of them.
Prometheus has become sensitive to what patterns signifiy, though what a pattern augurs is its 'meaning' to Prometheus. His congition of patterns and changes within them provide him hints about what may lie in the future.But, though Prometheus extracts meaning from patterns, this 'meaning' is not axiomatic but speculative. [Just as 'seeing' the future through examining the entrails of a chicken is 'speculation'.]
The common features within a pattern provide a schema that offer presentiments, not axioms from which one can logically deduce an inherent order.
Abstraction heralds a new form of pattern and thinking from these. That is why Socrates refers to the rise of abstract thought –the axiomatic-deductive order that follows from unambiguous definition–as the coming of a 'second Prometheus".
Yet, we must not be fooled into believing that the order of abstraction is sufficient to describe the reality within which we live, which is why deduction must always be 'tested' against induction.
Excellent remark. Very well put. I concur.
Plato had Socrates say about abstraction/definition [Philebus], "A gift of heaven, which, as I conceive, the gods tossed among men by the hands of a new Prometheus…" I wrongly remembered 'second Prometheus' in my earlier comment.
Thanks larrymotuz, I was unaware of Epimetheus.
I spent four decades studying the Earth's interior. I didn't start from the Schrödinger equation, I started from emergent phenomena like compressibility and fluid flow. In a subject in which the observations are all indirect (taken at the Earth's surface) and often not terribly precise, one learns to be careful about the limits of one's observations. Sometimes precise mathematics or computation are called for, and sometimes not.
I think about macro economics in a similar way. Even if there were a decent general theory of interacting economic agents, which there is not, it would not necessarily be a good place to start to understand the global financial crisis.
A much better place to start is to notice there was a huge buildup of debt which became unpayable and collapsed. One can model that process rather simply and learn some useful things about what might have been the causes and consequences of the G FC. I used this example in a post in 2014:
https://rwer.wordpress.com/2014/03/10/a-science-of-economies/
In my paper on the Deification of Science, I have explained why axiomatics is entirely the wrong approach to social sciences, and why this approach was adopted even though it is clear from elementary arguments that human being have free will, and do not behave according to any conceivable mathematical law. Human behavior cannot be axiomatized, and it is a mistake to try to do so. See:
Deification of Science and Its Disastrous Consequences, (2015) International Journal of Pluralism in Economics Education, Vol 6, No.2, 181-197 — Avaiable from Inderscience website: http://www.inderscience.com/offer.php?id=72595
pre-publication draft available from SSRN:
From your draft: " The logic of the ancients was entirely correct: empirical methods can never lead to certainty. However, this means that instead of abandoning empirical methods like the ancients, we must abandon the quest for certainty. Scientific method is pragmatic. Learning to live with good guesses which may be in some neighborhood of the truth leads to excellent practical results."
Yes, we must abandon that quest for certainty inherent in strictly axiomatic-deductive systems, for they are only logical certainties. While logical certainty is a guide, it is not necessarily descriptive of what one is logically certain about: I.e., the 'reality' it purports to describe.
Very much like your viewpoint. Thank you.
Ishi Crew
i read a bit of both principia mathematica (russel and whitehead—takes 300 pages to prove 1+1=2) and the 'bourbaki' school andrei weil (number theory)—they have quite a few fields's medalists and noble prizes in physics last 10 years in my field too) . but those axiomatics went too far. i'd just say read emile durkheim. french sociologist from the 1800'si still believe in axiomatics—even people who dont believe in them are already operating with axioms. .
The universe and the goldfish bowl
Comments on 'Axiomatics — the economics fetish'
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."*
(ii) "Human behavior cannot be axiomatized." (preceding post)
While (ii) is correct (i) is provably false; see my refutation on the parallel thread.**
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.***
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 a paradigm shift, i.e. the replacement of orthodox axioms by heterodox axioms. To denounce the axiomatic-deductive method as 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. Anyone surprised that economics is a failed science? 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 modl of how the economy works, is anyone surprised that economic problems cannot be solved but only worsend or shifted?
Ingrao, B., and Israel, G. (1990). The Invisible Hand. Economic Equilibrium in the
History of Science. Cambridge, MA, London: MIT Press.
* https://larspsyll.wordpress.com/2016/01/21/axiomatic-economics-the-bourbaki-debreu-delusion/
** 'Full methodological illiteracy'
https://larspsyll.wordpress.com/2016/01/21/axiomatic-economics-the-bourbaki-debreu-delusion/
*** 'Lars Syll creatively destructs Wren-Lewis'
http://axecorg.blogspot.de/2016/01/lars-syll-creatively-destructs-wren.html
EKH, I said "sometimes", and your examples are not the sort of cases I was referring to. My example of a cooling magma ocean in the post I linked to is a case where only order-of-magnitude precision leads to important understanding. Understand before you mock.
This question suffers from a common and chronic failure to understand the distinction between mathematics and science.
Mathematics is an abstract logical construction resting on various axioms. It is quite distinct from the observable world. Its usefulness is in its ability to link assumptions (the equivalent of axioms in mathematics) to consequences, so the latter can be compared with the observable world.
Axioms have a place in mathematics and logic, but not in science. Euclid's geometry, built from a few axioms, resembles our observable world, but Einstein showed us that Riemann's geometry resembles the world more closely. Both are quite valid logical constructs. The question for science is whether either one resembles the world we can observe. Because Euclid's geometry so closely resembles our familiar world, many have presumed it provides a rigorous description of our familiar world, but it turns out to be only a useful approximation.
Science is the process of finding usefully accurate descriptions of things we can observe. It is not about timeless laws, nor about truth. As larrymotuz puts it, science is pragmatic.
I am sympathetic to Asad Zaman's implied sentiment that we are not deterministic robots. However modern systems science reveals chaotic and complex systems that can never be predicted in detail, and yet useful descriptions of their behaviour may still be possible. In a similar way, important aspects of market booms and crashes can be understood even though precise timing of the crash cannot be predicted, and even though we can never know the mental processes of all those involved in the market.
The methodology of confused agenda pushers
Comment on Geoff Davies of Jan 23 on 'Axiomatic economics — the Bourbaki-Debreu delusion'
You mix up two issues that are related but need to be kept apart in order to get out of the morass 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 using 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)
To be precise, 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.
Precision indeed relates to to 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 economist (= 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 in taking the nonentities 'maximization-and-equilibrium' (Krugman) as axioms which are not by any stretch of the imagination related to anything in the real world. It should be pretty obvious to Zaman and you* 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.
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 http://todayinsci.
com/E/Einstein_Albert/Einstein-GeometryAndExperience.htm.
Hutchison, T.W. (1960). The Significance and Basic Postulates of Economic Theory. New York, NY: 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, pages 33–47. London, New York, NY: Routledge.
Redman, D. A. (1993). Economics and the Philosophy of Science. New York, NY, Oxford: Oxford University Press.
* For more refutation go to my blog and enter Zaman in the search-field
http://axecorg.blogspot.de/
From Mr. Davies: "Science is the process of finding usefully accurate descriptions of things we can observe. It is not about timeless laws, nor about truth."
EKH: You quote Karl Popper: "Never aim at more precision than is required by the problem at hand."
Both statements are 'true', though I 'prefer' Mr. Davies notion of science as a search for 'useful' descriptions rather than 'true' ones.
The core micro-economic theoretic assumes that all goods in all amounts carry positive levels of subjective satisfaction for consumers. Since people have likes and dislikes, this is not a very realistic assumption. For it is possible to benefit from consuming a good irrespective of whether one 'wants' to consume that good. For instance we know that President George H. W. Bush, when a boy, got nutrients from eating broccoli even though he did not want to eat broccoli. The lad, George, faced a constraint called MOM and dutifully ate his broccoli, presumably because of the opportunity costs he faced if he didn't eat it.
Or, take something like water. For survival purposes, we require about 2.2 litres per day. For food preparation purposes(cooking), we require more. For basic hygiene (washing and bathing), we require still more. And, for waste disposal to prevent all manner of diseases (by flushing away wastes), even more still. Each of these needs for water presents a different set of minimum exigencies for the purchase and use of water: a hierarchy of different needed amounts of water to just provide for the different purposes.
At the most exigent level, namely 2.2 litres of water per day, the demand' for water is utterly insensitive to changes in the price of water. George Bernard Shaw once said that people in a desert without water would trade all they had, and eventually sell themselves and their children into slavery to obtain it, if need be.
What the price system 'determines', EKH, is simply that people with more ability to pay are able to provide themselves with [and thus realize] a greater set of hierarchal benefits than those with less of an ability to pay.
Biological 'demand' is not a function of relative prices, but of metabolism which we could call 'inelastic' with respect to price. Other forms of 'demand' are also not a function of relative prices, but, and rather, of a hierarchy of human needs.
Reality is, EKH, that hierarchies of needs exist because of biological, social and cultural, technological, institutional, legal, political and other constraints restricting consumer choices. Each set of constraints has its own exigency function.
Let's go back to your Popper quote: "Never aim at more precision than is required by the problem at hand." "True", but I'll add that never aiming at less precision than is required by the problem at hand is also "true".
The neoclassical and Austrian micro-theoretics, with their emphasis upon 'subjective preferences' [and always positive at THAT!], "impose" less precisions than is required by the problem at hand: namely why people use goods to obtain a diverse set of benefits depending upon how these goods are being used. The 'order' that arises out of 'ability to pay' within these systems should not be confused with maximizing 'welfare' or 'well-being'.
BTW, marginalist economics is not and has never been 'political economy', for it removed value in use, budget formation, and the distribution of income from economic analysis. By so doing it became less precise than demanded for 'useful' analysis.
EKH, I really don't see how you can know what those you label heterodox economists think and want to do. I do know economics is not mathematics, where axioms are appropriate, and not a science insofar as economists think it is. Your own fetish is making you arrogant.
Perhaps your reference to Hutchinson above may help us settle our differences. I can accept that scientists postulate interpretations, but real scientists try these tentatively, not axiomatically: the issue being not whether they are always true (or false) but whether they consistently make sense of all we can observe. Euclidian and Reimann's geometries are logical postulates – remembering 'logos' means word, and recognising mathematics as a language – but in order to decide experimentally whether or when to apply them, real science has to involve postulates about reality. Newton's causal forces are equivalent to today's conservation of energy, see Mirowski's "More Heat than Light".
Nor are "imaginary" and irrational (circular) numbers any less imaginary than rational or real numbers: the distinction merely labels a complete difference, as in a Euclidian right angle determinable by symmetry. The equation of Pythagoras's theorem is also that of a circle, which may be constructed using a linear measure but requires complex numbers to account in the same measure for positions on its circumference. Relabelling chremistics (money-making) as economics and reducing all prices to countable numbers does not change the reality that monetary prices are imaginary and the real prices of using positive feedback to increase growth of monetary circulation are observable as social and (differently) ecological degradation. I was modelling that sixty years ago, monitoring the effects of using reaction to increase amplifier gain in a radio set. First it narrowed the bandwidth, until one could hear only the tune and not the orchestra. A little more and it burst into squeals of oscillation, displaying as highly harmonic square waves tuned to the frequency of circulation time. Have you noticed how towns now all look the same, and weather cycles predictably violent?
Excellent! Every 'scientific' hypothesis is a 'speculation' rather than an 'axiom'. Speculations need to be proven (or falsified) as accurate descriptions of an observed pattern (or predicted one different from what alternative 'speculations' lead to). 'Logos' as 'word or language' gives birth to 'logic' as the order of 'logos' –of any language itself–and this order is predicated upon the axioms inherent within the logos, and from which the 'order' may be deduced.
The 'truth' content of axioms cannot be proven. What can be proven (or falsified) is their adequacy as unique descriptors of any particular reality.
Can't get out behind the curve?
Comment on larrymotuz of Jan 25 on 'Axiomatics — the economics fetish'
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 since 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 since more than 200 years economic axioms are NOT worthy or fit. And this is why economics is a failed science.
Klant, J. J. (1994). The Nature of Economic Thought. Aldershot, Brookfield, VT: Edward Elgar.
Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications to Social Philosophy, volume 3, Books III-V of Collected Works of John Stuart Mill. Indianapolis, IN: Liberty Fund. URL http://www.econlib.org/library/Mill/mlP.html.
You quote Mill: ""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)"
Well, Mill was wrong.
There are no propositions/speculations that can be reasonably received without proof within science. These must always be treated as working hypotheses. The most important work of science is to determine which hypotheses/speculations are useful descriptors as such and which are not as such. Nor is THAT recondite mental philosophy, though it requires a creative imagination about possible patterns that lie outside already 'discovered' patterns that have already proven their usefulness for some purposes.
Axioms are premises. They are not hypotheses/speculations. Consistent deductions from axioms cannot be falsified, for they are logically 'true' in and of themselves irrespective of their concordance with any reality outside of the axioms.
Hypotheses/speculations are always subject to falsification because they are not 'true' in and of themselves. In short, evidence about their 'descriptive validity to a point' must lie outside the speculations themselves.
You describe me as a hobby economist. I suspect that's because I'm not an academic economist, merely a professional (albeit retired) always practical one.
That is not to say that I have not conducted very serious economic investigations into many economic activities. It is rather to say that I seldom found any practical use for the body of mainstream theory in any practical studies I was making. In fact, my government (Canadian) used my studies as a guide to policies and programs largely because I spoke in a language where I actually measured 'benefits' and impacts and effects in terms of those benefits measured in various units of account: sometimes money units but more often not.
So, I have never been a 'hobby' economist. I have rather not been an 'academic' one. These, in my terms, are mostly 'hobby' economists who start with presumptions, fail to show they have any validity in the real world, and who then proceed to construct castles in the air.
I am currently reconstructing the foundations of economic analysis.
I am doing so by re-introducing value-in-use alongside value-in-exchange, thus abandoning the neoclassical and Austrian frameworks. By re-introducing values-in-various-uses, I can bring into economic analysis the process of budget formation itself and how economic inequalities impact upon consumption and thereby economic path formation. In so doing, I naturally must depart from all mainstream theory about 'demand', 'supply', and 'equilibria', none of which take into account values-in-use nor the kind of analysis that emerges when there are exigencies to consumption (as exist for both people and firms).
Indeed, when I re-introduce values-in-various-uses, I am struck by Jevon's point that "All is consumption" –a point Marshall disagreed with — so, though I find it sometimes useful to treat firms as 'producers' for some purposes, I find it far more useful to treat them as 'consumers' competing with other consumers for the use of resources much of the time. We are, as human beings and economic agents, 'producers-who-consume', with all 'economic agents' being (necessarily) 'consumers': I.e., users of goods to obtain benefits of diverse kinds from a range of possible uses.
I have read your 'macro' contributions. These fail to capture my interest for the singular reason that in a monetary economy, money is itself the only numeraire. I say, contrarily to Hicks, that there are no numeraire commodities other than money itself. The outputs of the economy or of labour have money value but you cannot simply plug in this money value as THE output of the economy or of labour as if there is such a creature as a representative Output for either the economy or labour. Your 'model', in short, is far too simple relative to the phenomena you are attempting to 'model'.
I am not about 'debunking' economics as Steve Keen is. He is mostly working from within to show the failures of neoclassicism as a theoretic. I am constructing a new paradigm for all forms of economic analysis. Though I think Keen's work is outstanding as critique — and, insofar as I understand him, I fully concur with his critique — that 'critique' by itself is not sufficient to the task at hand :: the magnum opus :: which goes beyond critique to construct a new framework for analysis.
Will I succeed? Well, no. The 'best' I can do is put some elements into their proper place within a new paradigm that can capture the influence of these elements in hypothetical terms subject to falsification through solid statistical analysis. I don't expect academic, mainstream economists to do that analysis. I expect those who are qualified to do so.
And those are the people you seem to be dismissive of.
EKH: "You say: "The 'truth' content of axioms cannot be proven." WOW, YES, this is exactly what axiom means …".
Dictionary definition: "A self-evident truth: a universally received principle". Agreed, the axioms of capitalism are not WORTHY, and in that sense disproven, but they are not proven because they have been taken as self-evident, and so not in need of proof. One might also comment on their content having been wrapped in weasel words so that the packaging deceives, or suggest reading Harris's "I'm OK, You're OK" about trusting,uncritical children subconsciously learning to see the world distorted by their father's prejudices.
"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)".
Not being English and familiar with David Hume, Einstein is attacking a straw man of "free invention". The reality is that he hasn't seen the alternative of choice between limited options, and Hume in fact choosing not to believe in causal energy (in theological terms Spirit) because he couldn't see it.
I would like to repeat my support for the statement of Geoff Davies:
"[I]n some parts of science there may be observations of great precision, in which case careful mathematical deductions of comparable precision are required. In other parts of science observations may be much less precise, although often just as capable of deciding between hypotheses."
This relates to the problem of measurability. How can you measure economic activity? Are there other units than money? What is money? (Gold, issued paper and coin currencies, credits of various types and currencies with various contractional conditions?)
How can you measure the value or purchasing power of a currency? Even if that were solved, how do we compute the different purchasing power for different sets of goods (different consumptions patterns)? How is purchasing power related to preferences and distribution of assets among multiple bearers? How do we track changes over time?
All those problems are not solvable in the same way as measurements in the natural sciences. Because of that alone, economics is fundamentally different.
I therefore have to strongly disagree with Egmont Kakarot-Handtke's following statement:
"This settles the matter because in a monetary economy we have a natural precision of two decimal places."
No we don't. We have some currencies, yes. But that is just a very loose and flabby unit of measurement for which we do not have an exact economic meaning.
I, however, agree with Egmont when he states:
"[N]umerical precision and 'precision and rigor in the statement of premises' are related but fundamentally different things."
I am very much in support of clear, understandable statements. Those can be, but do not have to be mathematical in nature. If they are mathematical, the issuer should be aware of the problems of measurement and should make all efforts to show how the described model can be seen in reality and can theoretically be falsified. Pure statements of balances mechanics ("Saldenmechnik") may be useful, but their relevance to the real world should be well illustrated.
"We have some currencies, yes. But that is just a very loose and flabby unit of measurement for which we do not have an exact economic meaning."
But, we do have an exact economic meaning: namely, value-in-exchange; I.e., what goods/services trade for in units of money.
But, such exactitude in terms of money units tells us nothing about the 'values' goods have for us in terms other than those currency units of account. What is loose and flabby is trying to construct 'economics' solely around values-in-exchange and so-called 'preferences' that do not allow for some people having to consume what is 'dis-satisfactory' to realize essential needs (or, some of the time, not even realize or meet them due to affordability problems).
Or have I misunderstood you?
You say the exact economic meaning of a sum of money in some currency is its value-in-exchange, i.e. the goods traded for one unit of that currency.
But the prices of goods always change. Therefore the value-of-exchange of the currency always changes. Also prices of different goods are different. Thus one could say the value-in-exchange of a currency depends on what kind of goods the user wants to buy. And all this changes over time. That is why I said that sums of money are a loose and flabby unit of measurement.
To illustrate this with a more real world problem: The statistical agencies try to measure the rate of change of the purchasing power of currencies – the call that the "inflation" rate. But how do you measure the rise in prices? Which goods do you consider? How do you account for quality changes? So they create a "representative" basket of certain goods in certain quality and certain quantities and watch the cost for that basket. But what if your consumption pattern does not match the basket chosen by the statistical agency? The change in cost for your real consumption may be very different from the change in cost for the "representative" basket.
A very related problem to this is: the consumptions patterns are very dependent on your level of income. If you are poor you spend your money on different things than if you are rich. So whose consumption pattern should be reflected in the "representative" basket?
I hope that shows how different measurement in economics is from measurement in the natural sciences.
Am ill, so please pardon my delay getting back to you.
I'd like you start by looking at
http://www.meta-calculator.com/online/syfwpm4tcuei
There, I have assumed that there are two goods, X and Y, and that there are two 'consumers'. These consumers need to obtain some constant of benefit Qbk (not shown) from their consumption of X and Y. It does not matter what Qbk is but it is a measurable benefit. Thus, it is not 'consumer satisfaction' but is rather 'objective utility': a specific benefit that can be obtained only by having and using the good/service in a particular way. Here, for simplicity, I am assuming that not only that X and Y are perfect substitutes for each other in terms of this very specific objective benefit, but that they are equally beneficial; I.e., bx per unit of X = by per unit of Y. [That is simply a simplying and thus non-essential assumption.]
Now, since you are talking about changes in the purchasing power of a currency, I have decided to start off with px = py for a total price of one dollar for any basket 'available' along Y = 10 – X. Since any 'available' basket on or along Y = 10 – X can be purchased for the same expenditure, $1.00, the one's each chooses can be said to 'reveal' their preferences in terms of how they get their benefits.
These two consumers have chosen very different baskets of [X,Y] for the same unit dollar of expenditure. One–let's call him, her or it A–chooses [2,8]; the other–let's call him, her or it B– chooses [8,2]. {If 'it' was a firm and X and Y were unit inputs, then different production processes might account for these 'revealed' preferences by A and B respectively.}
Now, what will happen if prices change?
Let's say the price of x doubles.*
Then, as you have said, there is no unique change in purchasing power. It is clear from the new 'availability' line, Y = 10 – 2x that $1.00 is no longer sufficient to purchase either basket of [X,Y] that has been 'reveal' preferred.
Which is where budget formation comes in. If these consumers from force of habit or, if firms, facing other costs associated with changing their production processes, 'choose' to continue purchasing their original baskets, then A's dollar budget expenditure must rise to .2(2) + .1(8) = $1.20, whereas B's budget dollar expenditure must rise to .2(8) + .1(2) = $1.80. So, whther it is a person or a firm consuming X and Y, they do not experience equivalent declines in purchasing power, and that is due to their distinct 'preferences'.
Now, let's examine the baskets the 'market' considers equivalent. The lines from the origin have the equation Y =px/py*X.
When the prices were identical, the Basket [5,5] was equivalent in terms of costs for X and for Y. But, when I doubled the price of X, the market equivalent basket shifted to [3.25, 6.75].
So, what has happened to purchasing power in market terms? The basket [5,5] once cost $1.00 and now costs $1.50, so, in terms of these two goods, purchasing power has declined by half [($1.50- $1.00)/$1.00. {If we used more goods than X and Y, we could still make this calculation, for it is simply the Budgetxi at t+1 minus the Budgetxi at t all over Budgetxi at t. {This is not how the revised CPI in the U.S. is calculated.Note that a fall or rise in purchasing power is inversely related to the sign of the quotient.} Note that this calculation is independent of 'preferences' as well as any ability consumers have to afford their 'preferences'.
As I have set up this example, those who cannot afford to increase their budgets are 'forced' by 'prices' to 'consume' only Y.
I hope this serves to clarify my earlier comment to you.
*Paul, you can change both 'prices' by different amounts simultaneously if you wish to. Since the price of any basket [X,Y] is simply pxX + pyY — and since this always equals the 'new' budget needed to continue to purchase the same basket as before — you can easily show that 'preferences' affect individual economic agents differently.
Numerical precision is very context-dependent, so it's pointless making general statements.
For example it was reported that there was $600 trillion worth of debt before the GFC. We don't need to know that number to 2 decimal places, which would be 15 significant figures. One significant figure is sufficient to tell us that debt was about 10 times annual global output, a very large amount of debt for the productive economy to carry.
Quote: "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 since more than 200 years […]"
IMHO it is the "economist" view of axioms that is mistaken. And that misunderstanding is based on the confusion of
— "logical proof" and
— "empirical proof".
Note: Since single point empirical evidence can never prove a theory in the strict sense, "empirical proof" means the continuous failed attempt to falsify an assumption by empirical evidence.
An axiom, now, is an assumption that can not be *logically* "proven", i.e. deduced. It is a base assumption from which other statements are logically derived but which is not itself derived.
But, of course any statement about the real world that has any scientific meaning *can* be empirically "proven", i.e. potentially falsified. That goes by definition. A statement that can't be falsified empirically is not a scientific statement but instead a statement of belief.
That goes for axioms as well. Any empirical disprove of correctly deduced statements falls back on the axioms. A physical experiment, for example, that is not compatible with a body of theoretical statements (a model), indirectly empirically disproves at least one of *the axioms* of the model.
Deep in the methodological woods
(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'
http://axecorg.blogspot.de/2016/01/full-methodological-illiteracy.html
(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 since 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?'
http://axecorg.blogspot.de/2016/01/are-economists-natural-born-scientific.html
and 'Economics as fool's paradise'
http://axecorg.blogspot.de/2016/01/economics-as-fools-paradise.html
Morishima, M. (1984). The Good and Bad Use of Mathematics. In P. Wiles, and G. Routh (Eds.), Economics in Disarry, pages 51–73. Oxford: Blackwell.
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 17th edition.
" … are pure methodological junk, yet Heterodoxy has not managed since more than 140 years to replace them."
Most heterodox economists have been critiquing rather than replacing. Heterodox behaviorists following Daniel Kahneman, for example, challenge the hedonic calculus quite successfully, undermining both micro and macro by so doing.
In my view, we are not rational calculators with always positive preferences for goods. We do not have indifference curves for the simple reason that indifference plots leave out the 'real' opportunity costs of failing to consume 'needed' inputs: namely, that we might be failing to provide for ourselves, avoiding worse outcomes, if we actually 'behaved' as these models suggest. Always positive preferences effectively mean that we are indifferent to the actual outcomes of our decisions, which is observationally not 'true' either for human beings or any other economic agents engaged in any economic activities.
To construct a new paradigm requires abandoning the older one. In fact, the 'marginalist revolution' abandoned the value-in-use perspectives of classical economists and their predecessors. This, in my view, was and is the central error made by utilitarians during the latter half of the 19th century. A second error — and it doesn't matter whether it was 'made' by Pareto or by Hicks — was the construction of always positive but subjective indifference analysis out of the marginalist approach.
Sometimes to go forward, we must retreat.
I am not saying anything that Ricardo would have disagreed with, EKH. I am saying that a person with two bags of 'corn' is twice as 'better off' in a non-monetary sense as is the person with one bag of corn.
And I am also saying that this reconstruction has begun.
Silwyson
That the velocity of light c is constant, is a fundamental axiom of the theory of relativity. This axiom was not self-evident. It has now been tested empirically dozens of times, each time with different methods and generally with greater precision. The latest result (2009) shows c is constant to 17 decimal places. If c were found definitely not to be a constant at the 18th decimal place, there may be a revolution in physics. These facts falsify the generalizations of many comments above.
EKH keeps trying to rule me out of order, but the issue is the role of axioms in economics and I say they have no role.
There is no place for absolutes in science: axioms, truth, proof belong in mathematics and logic. Science deals with hypotheses and comparisons with observations. The criterion for a good theory is whether it provides a useful guide to the behaviour of the observable world.
I am also careful to say "observable world", not "real world". We can do science without having to debate what "reality" might mean.
I agree completely with this and your earlier comments on this thread.
A hypotheses in science is always a speculation awaiting falsification. If sufficient empirical observation supports the speculation, it transforms into a 'theory'. (That's perhaps more simply put than it ought to be but, in my view, speculations — even when buttressed by 'math' — remain just that.
Mainstream economic 'theory' is merely a set of speculations buttressed by math but generally lacking observational/empirical support. I exclude Leontief type input-output analysis from the 'mainstream' theory it is wrapped up in in modern macro-analysis.
Having given it some thought, I don't think I agree completely with either Sylwyson or Geoff. The following arguments are of course "speculative".
Something that troubled me in 1956 was the cosmic phenomenon of "red shift", suggesting a loss of energy rather than the Doppler effect increase of approaching motion. That in itself now suggests to me that light (an observable waveform) is not the ultimate, but (discounting an ether) represents an energy increment on energetic motion with zero detectable variation. So I think there is still room for a revolution in physics, but by rejecting Hume's denial of the "wind" of causation (and indeed the impossibility of perpetual motion), not by Hume's quantification of what we observe.
Geoff's "We can do science without having to debate what "reality" might mean" is of course following Hume's line, based on his not being able to see what goes on inside heads, hence "black box" theories of Economic Men with nothing in them. That may work for physics and chemistry, but not for computers and humans reacting to symbols rather than forces. The significance of the word "reality" is different. For physical science the meaning of an equation or description of is a human reference to an object which, fed into a computation, will generate information representative of the behaviour of the object. Fed to such a computation in a human and/or computer, the prior meta-question arises as to whether the information is data about an object, or – directly or indirectly – subjective programing of the activity of the person or computer. The difference corresponding somewhat paradoxically to the difference between the imaginary and the real, and any science which neglects the consequences of our acting on data is, I suggest, trivial.
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