Proper use of math in economics
from Lars Syll
27. ii. 06
My dear Bowley,I have not been able to lay my hands on any notes as to Mathematico-economics that would be of any use to you: and I have very indistinct memories of what I used to think on the subject. I never read mathematics now: in fact I have forgotten even how to integrate a good many things.
But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules — (1) Use mathematics as a short-hand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This last I did often.
I believe in Newton’s Principia Methods, because they carry so much of the ordinary mind with them. Mathematics used in a Fellowship thesis by a man who is not a mathematician by nature — and I have come across a good deal of that — seems to me an unmixed evil. And I think you should do all you can to prevent people from using Mathematics in cases in which the English language is as short as the Mathematical …
Your emptyhandedly,
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The attitude to mathematics of Marshal is highly biased against its use, even in economics. This is unreasonable unless one is deliberately trying to keep economics save and secure as a political subject, about which arguments both for and against a particular aspect carry equal weight.
Many people including myself, wish for economics to become more scientific and to have the capability of proving something (or some policy) is better than something else, Also most science is found to be mathematical in nature, which actually is a short-hand way of saying the same thing in words, I believe that it is what Marshal had to say on this subject that should be discarded, if not burnt!
By the introduction of a means of expression of the macroeconomic situation in terms of aggregate quantities and idealized entities (or role-players), one can develop the subject using Systems Analysis, along the lines that Wasley Leontief provided in his input/output method, to show how our social system actually works. This advance is very far from anything Marshal could have dreamed of.
Technology depends greatly upon methods that employ numerical computations to reverse engineer and to project probability in a purely rational model of predictive power. Having said that knowledge is not mathematics, quantification is methodology and the results are reliable knowledge. It seems to me that there is a presuppositional bias for technological quantification as the only pure science existing in contemporary society, and I suspect this is a direct result of its unfettered acceptance of utility as the foundation of ontology as well as epistemology. Or is it a matter of selective contempt for uncertainty unless it is embraced by the upper elite tiers of physics as a model puzzle yet unsolved at the core of Omani-prescient power and controls? Or is it pure conceit? Quantification has, in fact, brought us to the edge of total destruction as much as it has aided in the advance of scientifically confirmed technical controls over materialism and the balancing of natural forces.
It is curious that you call Marshall’s statement as being unreasonable, since it is highly reasoned and logically deduced from his concern for meaningful and verifiable reality. After all, even the highest level of quantifiable physics must be finally verified by empirical recognition and predictable / reliable results confirming proofs that are meaningful. The real question is why so-called hard-science appears to be so threatened by the so-called soft sciences, and why authentic reality must be coded as a quantity or it does not exist?
Numbers are tools. People are fools. Put them together and you do not get “science” or knowledge in any ultimate reality of comprehensive fulfillment.
Let me add a comment six years later after the discussion.
I cannot understand why Lars Syll posted this citation from Marshall. Although “[t]he attitude to mathematics of Marshal is highly biased against its use” (as David Chester put it), this brief mail does not deny that mathematics is useful in economics explorations. On the contrary, it admits that mathematics is (if not always) useful. He only advises that it is not wise to express the results and the reasoning process in mathematical formulations.
At the time of Marshall, majority of economists were not trained well in mathematics. The situation was even worse for the wider audience who are interested in economics. At that time, it is normal that Marshall felt it necessary to translate the results into English (or any prose that people can understand). Now there are many economists who understand mathematics or do not understand any prose unless it is written in mathematics. In such a situation, what kind of message this mail of Marshall’s can have. Lars Syll does not explain his interpretation. It is very probable that he had expected that people becomes more cautious of mathematics use in economics. But, it is based on a wrong reading.
if I repeat, Marshall’s advice above does not deny the use of mathematics in economics. Marshall even admitted that mathematics was necessary in the course of research. This is extremely contradictory to what Lars Syll often argues. As far as I understand from reading many of Syll’s posts (in this six years), he is thinking that use of mathematics is the source of “What went wrong with economics”. But it is in opposition to what Marshall have wrote in this mail.
N.B. I am not defending Marshall. I am very skeptic of his economics. Although he has various good points (mainly based on his good common sense on the economic life of humans), he is still one of founding fathers of neoclassical economics.
Marshall: a monument of scientific incompetence
Comment on ‘Proper use of math in economics’
Marshall was unable to render an appropriate portrayal of the market. For the correct three-dimensional depiction see https://commons.wikimedia.org/wiki/File:AXEC_001.png and for the underlying rationale see (2014a).
Marshall could not tell the difference between profit and income which is not exactly a recommendation for an economist. For the correct Profit Law see (2014b).
Marshall’s application of mathematics bordered on utter dilettantism:
“In patriotic duty bound, the Cambridge of Newton adhered to Newton’s fluxions, to Newton’s geometry, to the very text of Newton’s Principia … Thus English mathematics were isolated: Cambridge became a school that was self-supporting, self-content, almost marooned in its limitations.” (Forsyth, quoted in Mirowski, 2004, p. 355)
“Marshall … was a product of this system, which valued … down-to-earth geometry over continental analysis, and regimented conformity in puzzle solving and humble prostration before timeless truths over originality.” (Mirowski, 2004, p. 355)
Quite unsurprisingly Marshall applied mathematics incorrectly.
“As was standard with Marshall, the narrative told one story, the mathematics another.” (Mirowski, 1995, p. 299)
Compare Marshall’s approach to the creative use of mathematics by a genuine scientist:
“Experience can of course guide us in our choice of serviceable mathematical concepts; it cannot possibly be the source from which they are derived; experience of course remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics.” (Einstein, 1934, p. 167)
The botched application of mathematics by Marshall and the Orthodoxy is no reason to dismiss it.
“When very sound and proper mathematics is misused and misapplied to fairyland problems without any basis in the real world, that fact that the mathematics itself is impeccable makes the whole obnoxious game just that more offensive.” (Blatt, 1983, p. 173)
Rule number one of the good hand and brain craftsman: never blame the tool. Not much of Marshall will be part of a truly scientific economics. Certainly not his burn-phrase.
This is the way forward:
“… perhaps the most legitimate research program in economics should generate its own mathematical tools simultaneously with its development of the economic theory, …” (Mirowski, 1986, p. 221), see also (Velupillai, 2005, pp. 866-870), (Morishima, 1984, p. 67)
To quote Marshall affirmatively on mathematics is self-defeating.
Egmont Kakarot-Handtke
References
Blatt, J. (1983). How Economists Misuse Mathematics. In A. S. Eichner (Ed.), Why
Economics is Not Yet a Science, pages 166–186. Armonk, NY: M.E. Sharpe.
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science,
1(2): 163–169. URL http://www.jstor.org/stable/184387.
Kakarot-Handtke, E. (2014a). Economics for Economists. SSRN Working Paper
Series, 2517242: 1–29. URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=
2517242.
Kakarot-Handtke, E. (2014b). The Three Fatal Mistakes of Yesterday Economics:
Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2489792.
Mirowski, P. (1986). Mathematical Formalism and Economic Explanation. In
P. Mirowski (Ed.), The Reconstruction of Economic Theory, pages 179–240.
Boston, MA, Dordrecht, Lancaster: Kluwer-Nijhoff.
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University
Press.
Mirowski, P. (2004). The Effortless Economy of Science?, chapter Smooth Operator:
How Marshall’s Demand and Supply Curves Made Neoclassicism Safe for Public
Consumption but Unfit for Science. Durnham, London: Duke University Press.
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.
Velupillai, K. (2005). The Unreasonable Ineffectiveness of Mathematics in Economics.
Cambridge Journal of Economics, 29: 849–872.
Formidable and worth filing for multiple future reference…Thank you Lars Syll for this one!
Dec. 18, 2014
I must admit that I am impressed by the nine line paragraph of Bruce Woych, regarding both the good intentions and intellectual integrity of the great Alfred Marshall. It’s all he really needed to say. For the enlightenment of those who have nothing better to do than trash Keynes’s highly effective mentor, in a rather “know-nothing” style, I submit the following brief summary of Alfred Marshall’s capabilities and education.
He demonstrated early in his youth a natural aptitude for mathematics. He received his higher education at St. John’s College, Cambridge: Where he achieved the rank of Second Wrangler in the 1865 Cambridge Mathematical Tripos. Marshall went on to study Physics. But left it following a mental health crisis not related to his educational achievements. When he recovered, he then furthered his higher education by turning to philosophy. Especially the area where logical form and mathematics overlapped. That doesn’t sound like “utter dilettantism” “highly biased against” or “botched application” to me. It is spurious quantification, not the attempts at quantification per se, that has inflicted so much damage on economics. Thomas Picketty, like his mentor Karl Marx, and most of the neoclassical chaps are the most guilty Doctor Dementos of spurious quantifiability. As all thoughtful readers of TELOS & TECHNOS understand.
Marshall believed that by applying mathematical rigour to economics, the scientific credibility of the economics profession would be greatly reinforced. But he tried to arrest the natural tendency to excessive abstruseness. Which tempt the most well-intentioned mathematical practitioners. Which Marshall feared could easily overwhelm the practical content of the subject. And make it unapproachable to intelligent and well intentioned laymen, political leaders & authentic reformers. Marshall was a real scholarly workhorse. Who had nothing of the embittered polemicist or perpetual -motion critique- monger in his nature. We should all emulate his modus operandi. And keep in mind that he was born in 1842: Not 1942.
A politically incorrect & hearty MERRY CHISTMAS to all.
Norman L. Roth, Toronto, Canada.
Please GOOGLE: {1} Norman Roth, Origins of Markets {2} Economics of Technos, Roth
{3} telos & technos
Marshall and some skewed arguments
Second comment on ‘Proper use of math in economics’
Mathematics, it is trivial, can be misapplied and abused. But in this case, the misapplication has to be criticized and not mathematics per se. Equally trivial, a false theory cannot be repaired by formalization. For example, the supply-demand-equilibrium model is an inappropriate representation of what happens in a market and this conceptual defect does not disappear by writing f(S)=f(D). Equally trivial: mathematics is sometimes not applicable to the problem at hand. And finally, being a tool mathematics should not dominate the argument but be kept in the background.
So, mathematics can be applied for the wrong reasons but, and this is important for Heterodoxy, it can also be rejected for the wrong reasons. It is pretty obvious that Marshall did so.
“Indeed the fact that leading theorists such as Marshall openly downgraded the role of mathematics enabled the largely innumerate rank and file of professional economists to retain a sense of confidence in their own scientific contribution.” (Deane, 1983, pp. 6-7)
The second wrong reason is to keep the discussion deliberately on the level of loose verbal reasoning.
“Another danger is that you may ‘precise everything away’ and be left with only a comparative poverty of meaning. … Such a problem was avoided, said Keynes, by Marshall who used loose definitions but allowed the reader to infer his meaning from ‘the richness of context’.” (Coates, 2007, p. 87)
Here the obstinate self-deception of the so-called social sciences makes itself felt. Vagueness is a means to say something without knowing anything.
“By having a vague theory it is possible to get either result. … It is usually said when this is pointed out, ‘When you are dealing with psychological matters things can’t be defined so precisely’. Yes, but then you cannot claim to know anything about it.” (Feynman, 1992, p. 159)
The precision and rigor of mathematics is a good prophylaxis against self-deception.
“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)
With his burn-phrase Marshall still helps political economics and hinders theoretical economics. Political economics is, as everybody knows, scientifically worthless.
“I refer to the considerable haziness of economic theorizing, to the regrettable fact that concepts are frequently ambiguous, often used in different manners, that their interrelations are not made clear, and, foremost, that the assumptions seldom show a clear relationship either to the facts of everyday life or to those specifically collected and examined.” (Morgenstern, 1941, pp. 361-362)
It seems that Marshall has become the patron saint of all confused confusers of economics (2013). Heterodoxy has no good reason to idealize him.
Egmont Kakarot-Handtke
References
Coates, J. (2007). The Claims of Common Sense. Moore, Wittgenstein, Keynes and
the Social Sciences. Cambridge, New York, NY, etc.: Cambridge University Press.
Deane, P. (1983). The Scope and Method of Economic Science. Economic Journal,
93(369): 1–12. URL http://www.jstor.org/stable/2232161.
Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
Hutchison, T.W. (1960). The Significance and Basic Postulates of Economic Theory.
New York, NY: Kelley.
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 http://ssrn.com/abstract=2207598.
Morgenstern, O. (1941). Professor Hicks on Value and Capital. Journal of Political
Economy, 49(3): 361–393. URL http://www.jstor.org/stable/1824735.
“People who say it cannot be done should not interrupt those who are doing it.” G. B. Shaw. And if those who claim they are doing it, aren’t? We have been down this path often, Egmont, and if you knew more about the history of thought, you would be less sure about how “you are doing it.” Walras claimed he was doing it in the late nineteenth century, did he? The proponent of the new paradigm in economics after WWII claimed they were “doing it” only to land us in the cul-de-sac argument that we are now carrying on in this blog about real world economics. From these scientists we got more arrogance and fascist behavior in the educational establishment than enlightenment.
I think Marshall’s attack on the use of mathematics is somewhat apt.
Mathematics is a helper tool. It serves well if the subject for which mathematical models are created is sufficiently understood.
In those cases in which we do not know enough to build reasonable models the use of mathematics is often just mathematically disguised speculation and toy modelling.
Of course it would be great to have a tried and tested complex quantitative model for economic relationships, something similar to what the natural sciences have developed.
But the hard part is to get reasonable axioms from which conclusion can be drawn. In natural sciences to arrive at those axioms centuries of careful observation and documentation were needed. And of course the axioms in the natural sciences are always experimentally tested.
In economics the hard part is to get reasonable axioms. So any modelling in economics should be based on a very thorough reasoning what assumptions were made, why they were made, what was possibly omitted etc.
And papers and discussions concerning observations and non-mathematical non-deductive reasoning may well be more helpful than the n-th toy model with barely explained fantastic assumptions which won’t ever be empirically tested and basically serves no other purpose but to fill publication lists.
Here is the problem, I, as a practicing historian, have had trying to use the work of social scientists to clarify the study of history.
Historians are concern with specificities as to time and place. One problem they have with social scientists, is their penchant to engage in reifying, to regard something abstract as a real or concrete thing. Take the idea of a technopole, a cluster of variables that promotes innovation. Historians are interested in investigating specific technopoles, like Silicon Valley, and a lot has been written about SV in terms of it being a clustering of innovation factors. But I always got nervous when social scientists turned SV into an abstraction, an innovation archetype, one stripped of specificities, and called it a real or concrete thing.
In Michael Best’s study The New Competitive Advantage (2000), he selects historical production systems and designs analytically neutral production models for each of them. One historical model he selected was Silicon Valley, which, through the process of reification, he turned into a neutral analytical system characterized by “cluster dynamics,” to which he gave the name “open system dynamic.” (p. 142)
If we looked at a problem in physics, like determining the accuracy of iron balls fired from cannons, and called the problem one of an “opens system dynamic,” we could work out firing tables that could quite accurately predict where all the balls shot from a canon would land. If, we study factors composed in a “cluster dynamics’ of an ‘open system dynamic” reified from the specific historical case of SV we would not be able to construct a new open system dynamic Technopole from this information. In other words, the ‘cluster dynamics’ extrapolated lack predictability.
For an historian, the social scientist’s attempt to turn these neutral analytical categories into a real or concrete thing, is useless because it leaves out variables in the process of reification that might be determinant historically.
I found this to be the case when I set about trying to explain why Germany outstripped France as a technological civilization between 1860 and 1914. Neoclassical economics certainly provided no useful models with which to deal with the problem. What I found on my own as an explanation came from research into comparative education. Moreover, the conclusions I drew from this research, is that the causal agents in education had much less to do with economic than noneconomic structures (just as the development of Information Technology in SV can be explained more by the Cold War than by Economics).
If economists find historical studies to be useless in economics because the study of history is not science, historians have the same problem with social science; it’s neutral analytical categories are not useful to clarify historical process. I decided to participate on this blog in the hope that economics could become something I could use in historical analysis. I haven’t yet, but hope springs eternal.
Comparative method in Historical Economic Perspectives in Western Thought:
German Historical School:
http://en.wikipedia.org/wiki/Historical_school_of_economics
“The historical school held that history was the key source of knowledge about human actions and economic matters, since economics was culture-specific, and hence not generalizable over space and time. The school rejected the universal validity of economic theorems. They saw economics as resulting from careful empirical and historical analysis instead of from logic and mathematics. The school also preferred reality, historical, political, and social, as well as economic, to mathematical modelling.The historical school held that history was the key source of knowledge about human actions and economic matters, since economics was culture-specific, and hence not generalizable over space and time. The school rejected the universal validity of economic theorems. They saw economics as resulting from careful empirical and historical analysis instead of from logic and mathematics. The school also preferred reality, historical, political, and social, as well as economic, to mathematical modelling.”
============================================
Social Market Economy:
“http://en.wikipedia.org/wiki/Social_market_economy”
“The social market economy (German: Soziale Marktwirtschaft) is a form of market capitalism combined with a social policy favoring social insurance, and is sometimes classified as a coordinated market economy. The social market economy was originally promoted and implemented in West Germany by the Christian Democratic Union (CDU) under Chancellor Konrad Adenauer in 1949.[3] Its origins can be traced to the interwar Freiburg school of economic thought.
The social market economy was designed to be a third way between laissez-faire economic liberalism and socialist economics.[5] It was strongly inspired by ordoliberalism[6] and the tradition of Catholic social teaching or, more generally, Christian ethics.”
============================================
English Historical School
http://en.wikipedia.org/wiki/English_historical_school_of_economics
The economists of the English historical school were in general agreement on several ideas. They pursued an inductive approach to economics rather than the deductive approach taken by classical and neo-classical theorists. They recognized the need for careful statistical research. They rejected the hypothesis of “the profit maximizing individual” or the “calculus of pleasure and pain” as the only basis for economic analysis and policy. They believed that it was more reasonable to base analysis on the collective whole of altruistic individuals.[4] Historical economists of the nineteenth century also rejected the view that economic policy prescriptions, however derived, would apply universally, without regard to place or time
Historical economists viewed classical and neoclassical economics as too formal and as a rationalization of free-trade policies[1] in a colonial and imperial setting.
Here is the answer in the formal nutshell:
Into this formula, which applies to the economy as a whole, the specificities of time and place have to be inserted just as you have to insert these specificities into a physical formula.
Explanation is different from the description of a historical event. For example: from the laws of physics follows how the Titanic sank, but not why ship and iceberg met at the specific time at the specific place. These initial conditions have to be taken as given.
For the theory that underlies the formula above see “The Synthesis of Economic Law, Evolution, and History” http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2500696
It may also be helpful to learn what Popper said about ‘explaining in principle’:
“My thesis is that only in this way [explaining in principle] can we explain and understand a social event (only in this way because we never have sufficient laws and initial conditions at our disposal to explain it with their help).” (Popper, 1994, p. 168)
Theoretical economics does not explain specific historical events. No science does. Moreover, the formula above covers the ECONOMIC aspect of history and NOT the social aspect. It does not predict but can be tested with an accuracy of two decimal place with historical data.
With regard to the future, the formula above represents a stochastic simulation that replaces the set of deterministic equations of the orthodox approach. You can run it on a spreadsheet.
Egmont Kakarot-Handtke
References
Popper, K. R. (1994). The Myth of the Framework. In Defence of Science and Rationality. London, New York, NY: Routledge.
Those are interesting remarks. My thoughts are the following:
Every scientific or academic discipline has a certain field of inquiry. In my view the field economics should be about the general aspects of production and distribution.
Now, if we look at one concrete historical situation, like the development of a computer industry in Silicon Valley, we can have different perspectives or goals:
a) we can try to gather what happened historically in that particular situation and how that is perceived over time or
b) we can try to find abstract mechanisms that might have been at work in that particular situation but which could also be made to work in different situations.
I say b) is not possible without a) because if we do not have some knowledge of what happened we have no basis for an analysis of possible abstract mechanisms at work.
On the other hand I would argue that a) is possible without b). It is probably even better to first look at the available data unbiased by theoretical concepts.
Surely, if there are certain abstract concepts that are valid, they might be used to interpret historical data. The problem with economics as it is today is that it is ruled by neoclassical theory. And that theory is provably false. So don’t expect to get any useful concepts from there.
Heterodox economic theory on the other hand is actually not a theory but a ragbag of more or less disparate viewpoints and theories. Those theories all have their merits as possible inputs into economic research but IMHO the discipline as a whole has not come very far–precisely because of the incredibly destructive effect of neoclassical theory. Also economics is highly politicized because one major field of application is policy advice.
I don’t want to totally squash your hopes. But for now you’ll have to cherry-pick and ponder economic theories yourself. Don’t expect any sound academic consensus soon.
Looking through the veil of historical detail
Comment on Paul Schächterle
With regard to historical detail you should know better because economists have the privilege to be the heirs of one of the greatest methodologists. Even physicists listened to J. S. Mill:
“They [Einstein and Dirac] agreed that science was fundamentally about explaining more and more phenomena in terms of fewer and fewer theories, a view they had read in Mill’s A System of Logic.” (Farmelo, 2009, p. 137)
And what do economists know since 1874?
“Since, therefore, it is vain to hope that truth can be arrived at, either in Political Economy or in any other department of the social science, while we look at the facts in the concrete, clothed in all the complexity with which nature has surrounded them, and endeavour to elicit a general law by a process of induction from a comparison of details; there remains no other method than the à priori one, or that of ‘abstract speculation.’” (Mill, 1874, V.55)
The historicist looks — metaphorically — at the flight path of a colored leaf on a windy autumn day. And after observing 1.000 flights he is none the wiser. A physicist regards the historical details as disturbances, throws a canon ball from a tower and comes up with the Law of Free Fall.
Certainly, the Law of Free Fall is an abstraction and it does not predict the leaf’s trajectory. Obviously the historicist and the scientist have different methodologies. Loosely speaking, economics is about laws and not historical detail.
We agree that Orthodoxy is a failure. However, the problem with Heterodoxy is that it is methodologically still in the pre-Millean Neanderthal. A sure sign is that Marshall is cited with approval.
“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)
Since all theories are built upon axioms, Heterodoxy has to come up with its own axiomatic foundations. Dead-horse-kicking, loose verbal reasoning, and hiding in the thickness of confusion is not sufficient in the longer run.
Burn your defunct methodology!
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.
Mill, J. S. (1874). Essays on Some Unsettled Questions of Political Economy. On the Definition of Political Economy; and on the Method of Investigation Proper To It. Library of Economics and Liberty. URL http://www.econlib.org/library/
Mill/mlUQP5.html#EssayV.OntheDefinitionofPoliticalEconomy.
Egmont,
I do not for a moment believe what you write about history and explanation. I just think that theoretical economists are lousy historians and consequently do not know enough history to see its usefulness in economics. What I suggest is that there are historically based variables that are important to economics that you, as a scientists, would not recognize as a variable in your explanatory models in that they cannot be reified into neutral analytical categories (bedause they are tied to specificities of time and place). These historically specific variables historians find through painstaking research that economists need to consider not ignore. There are lots of examples to illustrates what I mean.
For example, I believe you think that the triumph of a scientific paradigm in economics results from the superiority of scientific method over nonscientific. You tell us that every time you comment. But historical investigation tells us that the principal “cause” of the triumph of the scientific paradigm in economics is geo=political, it’s a result of the political-military restructuring of American institutions during the Cold War. If you explain the triumph of theoretical importance as a result of a superior thought system, then you are in deep trouble because almost every day there is a post on this blog that explains that the principles and axioms of neoclassical economics are false. If this is true, then you cannot explain the triumph of neoclassical economics in department of economics, in its own terms. You need noneconomic explanations along the lines of geopolitical machinations because they show that the triumph of the thought system you champion is an expression of state and social systems specific to time and place not the inherent superiority of the thought system itself. This knowledge taints the scientific claim of theoretical economics.
As an adjunct to this perspective I would add that “Economics” (proper) received a black eye for not “fortune telling” the tea leafs and not recognizing the cues (let alone the cures) of what comes to be known as our most recent economic crash of circa 2007. Even as a market failure this questions how equivocations can reach a predictive value and adjust real time events with an adequate prognosis. But for many of us we feel that the professional Economists (specialists and authorities) should also be capable of establishing objective exposures of what amounts to subjective advantages abused in the systems that run our economy. In that regard, looting of the treasury and financial black box machinations should be legitimate and justifiable substrates to apply ‘scientific methods or observation and measurement’ in ways that protect not just the public but the very health of the Nation in real terms.
Instead, we see financial derivatives slice and dice the real economy on a path dependent expansion that pits a vicious economic zero sum game against what many average honest business sector believe is an honest and balanced playing field. And while the upper financial tier is playing dice with the real economy, (ranting of high risk winners and losers in this casino capitalism of crony false economy), institutional market insurance buys up the risk evasion and aversion under the assumption that it can not all crash at once and take their share. And while the scope and scale of economic disequilibrium falls into an inverted relationship between poverty, austerity and wealth formation, it all comes under a euphemistic absurdity of creative destruction in the headings of corporate rationalizations and executive bulletins explaining their success and succession planning as formulas of equilibrium and invisible hands.
In the meantime, this monetarism has gone on to create the global grid that promises recovery and development all over the world but literally utilizes markets as sterilized neocolonialism exploits and call it free market liberalization…, homogenizing wealth tactics and calling it harmonization while wrecking traditional economic systems and turning independent people into dependency clones under market determinism that does not respect or tolerate cultural variation in its colonial portfolios.
All this backed by economic power politics known as soft wars now dominating the prospects of supremacy in markets and in survival.
So where are the numbers? Why of course, they are measuring the one dimensional prospects for more of the same…growth at any cost.
No trouble of any sort
Comment on Robert R Locke
You say: “If you explain the triumph of theoretical importance as a result of a superior thought system, then you are in deep trouble because almost every day there is a post on this blog that explains that the principles and axioms of neoclassical economics are false.”
You have obviously some trouble to keep things properly apart.
(i) It is one thing to say theory A is true/false.
(ii) It is another thing to say that theory A is supported in various ways in country X to the detriment of theory B, C, ….
Even if we agree perfectly on the historical fact (ii) this does not imply anything about the truth or falsity of theory A. This is an entirely separate question. Scientists focus on (i) and historians on (ii). This is not to deny that both questions get mixed up in the mind of a concrete scientist in a concrete historical setting. However, as a matter of principle, the political success of a theory does not prove anything for or against its scientific value.
What I say is:
(i) Neoclassical theory is a failure.
(ii) The behavioral axioms of the neoclassical approach are not the proper starting point of theoretical economics. This explains (i).
(iii) The set of structural axioms provides the correct formal foundations of theoretical economics. Structural axioms are methodologically superior to behavioral axioms (2014).
(iv) From the structural axiom set follow testable propositions (see the formula above, for example).
(v) If anybody thinks that the structural axiom set is false, he is invited to refute one proposition that follows deductively from it.
(vi) Methodological discussions are no substitute for a test. In fact, they are a distraction. Only the test counts.
Whether some government agency has promoted neoclassical theory during the cold war is irrelevant for the true/false question. Neither government, nor church, nor history has anything to say about true/false, it never had, and never will. This is not to deny that these institutions try to exert illegitimate/incompetent influence on theoretical economics. This is an organizational problem but not a scientific problem.
The best that theoretical economics can give history at the moment is the formula above. Take it, ignore it, or try to refute it.
Egmont Kakarot-Handtke
References
Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2489792.
“Neither government, nor church, nor history has anything to say about true/false, it never had, and never will.”
Oh how we wish this were true, but I assure you that when the pentagon pushed the adoption of the new scientific paradigm in the teaching of economics, the government was determining in US higher education what was true or false. When Islamic mysticism eliminated Green rationalism from Persian thought, it determined what was true and false in the culture for centuries. It is naïve to think that ruthless suppression has nothing to do with determining true and false. True and false is itself a cultural event, and the sort of conversations we are having about this subject on this blog is an expression of the Western thought world’s emphasis on rationality. Ever run across the expression “reason freaks,” that is what people in Japan have called Westerns for their emphasis on reason to determine true and false.
Egmont, I meant Greek, not Green. And may I add that the essential ingredient needed to pursue true/false is not rational thought but freedom.
(v) If anybody thinks that the structural axiom set is false, he is invited to refute one proposition that follows deductively from it.
I read long ago, a comment by the German neoclassical economist Erich Schneider, that “a theoretical proposition, like a dogma, cannot be denied.” He went on to say “The most that can be said is that a theoretically correct proposition is not relevant because its assumptions do not apply to the present situation. That does not mean that the proposition is wrong . It only means that the proposition does not apply to present circumstances (ist nicht aktuell).” And that is what the historian is talking about, he is interested in the actual (whatever the time period) and so are most people when confronted by economic events. It is a pretty sorry science that cannot help mankind confront actual circumstances.
Prophets of Preemptive Vanitization
Comment on Robert R Locke
You quote the neoclassical economist Erich Schneider saying: “The most that can be said is that a theoretically correct proposition is not relevant because its assumptions do not apply to the present situation.”
This, of course, is absolutely correct for neoclassical theory. In science thing are quite different.
“To give a causal explanation of an event means to deduce a statement which describes it, using as premises of the deduction one or more universal laws, together with certain singular statements, the initial conditions.” (Popper, 1980, p. 59)
Schneider has to be put into the group of people who think because they cannot solve a problem nobody else can. This logical error is known as fallacy of composition. Let us call this large group of annoying bystanders the Prophets of Preemptive Vanitization. Typical statements of these prophets are that bodies that are heavier than air cannot fly or:
“There is no objective truth in economics. Nobody understands the whole picture. Everybody gets a piece of it.” (Roosevelt http://larspsyll.wordpress.com/?s=Understanding+capitalism)
The classical answer to Preemptive Vanitization is:
“People who say it cannot be done should not interrupt those who are doing it.” G. B. Shaw
Egmont Kakarot-Handtke
References
Popper, K. R. (1980). The Logic of Scientific Discovery. London, Melbourne, Sydney: Hutchison, 10th edition.
From Marshall to Georgescu-Roegen
Third comment on ‘Proper use of math in economics’
Above, Norman L. Roth gave a fine characterization of Marshall. I have nothing to add, except that nobody doubts Marshall’s personal qualities. However, they are not relevant for the question of why Marshall openly downgraded mathematics.
Marshall was well acquainted with the Cambridge version of mathematics which focused on geometry. Now, you cannot study geometry and Newton without coming across Euclid. In my mind, nobody who understands only a little of Euclid’s role in the history of science can ever say ‘Burn the mathematics.’
Newton’s Principia start with the famous Axioms, or the Laws of motion and the role of Euclidean geometry for Newtonian physics cannot be overestimated.
“During five years, Humphrey saw Newton laugh only once. He had loaned an acquaintance a copy of Euclid. The acquaintance asked what use its study would be to him. ‘Upon which Sir Isaac was very merry.’ (Westfall, 2008, p. 192)
There is a direct line of highest praise from Newton to Einstein:
“We honour ancient Greece as the cradle of western science. She for the first time created the intellectual miracle of a logical system, the assertions of which followed one from another with such rigor that not one of the demonstrated propositions admitted of the slightest doubt — Euclid’s geometry. This marvellous accomplishment of reason gave to the human spirit the confidence it needed for its future achievements. The man who was not enthralled in youth by this work was not born to be a scientific theorist.” (Einstein, 1934, p. 164)
And this last sentence contains my argument against Marshall’s mathematical competence.
Curiously, there is one among the Top 20 heterodox economists http://larspsyll.wordpress.com/?s=Top+20, who understood better than Marshall what mathematics was all about.
“We are therefore justified in saying that with Euclid’s Elements the causa materialis of geometry underwent a radical transformation; from a more or less amorphous aggregate of propositions it acquired an anatomic structure. Geometry itself emerged as a living organism with its own physiology and teleology, …. And this true mutation represents not only the most valuable contribution of the Greek civilization to human thought but also a momentous landmark in the evolution of mankind comparable only to the discovery of speech or writing.” (Georgescu-Roegen, 1966, p. 9)
There is no better way to run Heterodoxy into the ground than to forget what Georgescu-Roegen has said about mathematics and to praise what Marshall has said.
Paul Schächterle correctly observes: “In economics the hard part is to get reasonable axioms. So any modelling in economics should be based on a very thorough reasoning what assumptions were made, why they were made, what was possibly omitted etc.”
Exactly so!
The claim of Heterodoxy to replace Orthodoxy with something better implies the replacement of the accustomed behavioral axioms with something better. There is no way around this.
Burn the neoclassical axioms! And then take these:
http://www.axec.org/#!axioms/cy2g
Egmont Kakarot-Handtke
References
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science,
1(2): 163–169. URL http://www.jstor.org/stable/184387.
Georgescu-Roegen, N. (1966). Analytical Economics, chapter General Conclusions
for the Economist, pages 92–129. Cambridge, MA: Harvard University Press.
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge:
Cambridge University Press, 17th edition.
Well, frankly, for my taste these “AXEC” assumptions (and the categories or dimensions they are supposed to cover) are not properly explained, nor can I see any references to empirical observation.
Also, are those “terms of use” some kind of joke?
Quote from the AXEC-website:
“The AXEC axiom set and its logical implications is protected by trademark. When you plan to apply it to the solution of theoretical and practical problems or on any other occasion whatever in order to generate income, profit, scientific reputation, or public attention please send first a notification to permission@axec.de.”
No problem
Comment on Paul Schächterle
If you find the structural axioms useful you can use them: “Students are entitled to use the structural axiom set or a subset thereof for research and education without prior notification and are exempt from use fees.”
If your axioms are better — use yours.
Egmont Kakarot-Handtke
Agree with Paul Schächterle. In science, axioms have to be based on self-evident truths, facts of observation or well-reasoned hypotheses, i.e. justifications are required for them to be taken seriously.
I agree, Paul. Those “terms of use” is an absolutely ridiculous joke!
It is self-evident that for Lyonwiss it is indeed self-evident that the sun goes up.
“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, p. 328 fn. 57)
References
Cohen, I. B. (1977). History and the Philosopher of Science. In F. Suppe (Ed.), The Structure of Scientific Theories, pages 308–349. Urbana, IL, Chicago, IL: University of Illinois Press.
Egmont, In Euclidean geometry, “parallel lines never meet” is an axiom based on (in its domain) a “self-evident truth”, not “that the sun goes up”.
Self-evidence: an urgent update
Comment on Lyonwiss
Whether the parallel axiom is an axiom or not is by no means self-evident. As a matter of fact, this question haunted mathematicians for over two thousand years and led to the invention of non-Euclidean geometries.
Self-evidence is no scientific criterion at all. At least Popper and I are of this opinion.
“The view of classical rationalism that the ‘axioms’ of certain systems, e.g. those of Euclidean geometry, must be regarded as immediately or intuitively certain, or self-evident, will not be discussed here. I will only mention that I do not share this view.” (Popper, 1980, p. 72)
And this is what axiomatization is all about:
“The attempt is made to collect all the assumptions, which are needed, but no more, to form the apex of the system. They are usually called the ‘axioms’ (or ‘postulates’, or ‘primitive propositions’; no claim of truth is implied in the term ‘axiom’ as here used). The axioms are chosen in such a way that all the other statements belonging to the theoretical system can be derived from the axioms by purely logical or mathematical transformations.” (Popper, 1980, p. 71)
Egmont Kakarot-Handtke
References
Popper, K. R. (1980). The Logic of Scientific Discovery. London, Melbourne, Sydney: Hutchison, 10th edition.
What engine?
Fourth comment on ‘Proper use of math in economics’
The utilitarist’s view of mathematics:
“Use mathematics as a short-hand language, rather than as an engine of inquiry.” (Marshall, above)
The scientist’s view of mathematics/formalization/axiomatization:
“Formalisation was not to be merely a mechanical check on the integrity of scientific reasoning, but through the process of axiomatisation, mathematics was to be an engine of discovery.” (Weintraub, 1998, p. 1844), see also (Suppes, 1968, p. 653)
Having declined the tried and tested ‘engine of inquiry’ it does not come as a surprise that Marshall discovered nothing of scientific value but instead became the hero of those who are enthusiastic about the Cambridge methodology of common sense and loose verbal reasoning.
What Marshall took home from the Tripos is that mathematics is good for saving ink. This is as far beside the point as can be. The whole question is about methodology and the point of mathematics/formalization/axiomatization is:
“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, p. 1109)
I, too, agree with Paul Schächterle. Those who do not intend to build higher but are happy in the scientific slums do not need any mathematics/formalization/axiomatization. All others are indeed happy that they do not get out there but gather around the Marshall monument.
Egmont Kakarot-Handtke
References
Hilbert, D. (2005). Axiomatic Thought. In W. Ewald (Ed.), From Kant to Hilbert. A
Source Book in the Foundations of Mathematics, volume II, pages 1107–1115.
Oxford, New York, NY: Oxford University Press. (1918).
Suppes, P. (1968). The Desirability of Formalization in Science. Journal of
Philosophy, 65(20): 651–664.
Weintraub, E. R. (1998). Controversy: Axiomatisches Mißverständnis. Economic
Journal, 108(451): 1837–1847. URL http://www.jstor.org/stable/2565847.
In my paper entitled “Deification of Science and its Disastrous Consequences” available at http://ssrn.com/abstract=2260052, I have made the following argument. Math and Science have ENTIRELY different methodologies which are suitable to them. Because of the spectacular success of the axiomatic method in Mathematics, people naturally started using the same method for science. This proved to be an equally spectacular failure. The scientific method involves making observations about nature and then GUESSING at laws which generate the observed patterns — that is induction. Later, one can verify these guesses by the means of experiments. To see that scientific laws and mathematical laws are entirely different creatures, do the following simple thought experiment. Consider the Pythagorean Theorem. It would make no sense to draw triangles and measure their sides to verify it, or to attempt to find a counterexample to the law. In contrast, because scientific laws are established on basis of empirical evidence and guesses, EVERY law is subject to empirical verification and has the potential to be refuted empirically. As Popper put it, if there is no potential observation which could conflict with the law, then it is not a scientific law The observational and empirical aspect of science means that it cannot be axiomatic. GREAT progress in science resulted PRECISELY from dropping the axiomatic methodology and switching to an observational and inductive process which led to scientific laws which could never be proven, UNLIKE mathematical laws. The failure of economics is due to the use of axiomatic method, which is eminently unsuitable for natural science, as was proven in the course of history.
I agree to a certain extent, but I also think you are throwing out the baby with the bathwater.
Axiomatic-deductive reasoning is just applied logic. And naturally using logic in science is OK.
But of course science is much more than logic. Part of science is “proving” (testing, trying to falsify) the axioms the go into a deductive model. Since axioms by definition cannot be proven by deduction, there goes the deductive method for large parts of science. Enters observation, induction, non-deductive reasoning etc. just like you describe in your paper.
Social sciences also have the problem that you might not be able to find objective units of measurement for certain aspects of inquiry. Then it is not even sure that you can apply quantitative logic (i.e. mathematics) in a reasonable way.
The problem with neoclassical economists is that they just invent their “axioms” and that they additionally use flawed logic.
The problem with confusing science with the axiomatic method is that that leaves out a major part of scientific work.
B.t.w. IMHO also mathematics itself is not freely invented but rooted in concepts found in nature (e.g. natural numbers, geometry).
Over the cliff
Fifth comment on ‘Proper use of math in economics’ with special reference to Asad Zaman
You write: “Math and Science have ENTIRELY different methodologies which are suitable to them.”
True. And it is exactly one of the great wonders how in the end this fits together so nicely.
“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)
A famous paper of Wigner is titled ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’ (1979). And this led Velupillai to wonder about the ‘The Unreasonable Ineffectiveness of Mathematics in Economics.’ (2005)
One possible answer could be that the cause of this unreasonable ineffectiveness lies in the scientific incompetence of economists. This hypothesis has been advanced by a well-known representative of the real sciences. See:
‘The Farce That Is Economics: Richard Feynman On The Social Sciences’
http://www.zerohedge.com/news/2014-10-18/farce-economics-richard-feynman-social-sciences
Not only physicists have wondered about unreasonable effectiveness but mathematicians, too:
“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. … It is only in this sense of the word ‘form’ that one can call the axiomatic method a ‘formalism’.” (Bourbaki, 2005, p. 1276)
You write: “The scientific method involves making observations about nature and then GUESSING at laws which generate the observed patterns — that is induction.”
This is simply false and inductivists should know this by now. The real question is this:
“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)
You write: “Consider the Pythagorean Theorem. It would make no sense to draw triangles and measure their sides to verify it, or to attempt to find a counterexample to the law.”
This is simply false.
“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)
You write: “As Popper put it, if there is no potential observation which could conflict with the law, then it is not a scientific law.”
True. And this is why theoretical economics deals only with testable propositions. And this in turn is the reason why the structural axiomatic paradigm is superior to both the orthodox and heterodox approaches (2014).
You write: “The observational and empirical aspect of science means that it cannot be axiomatic.”
This, again, is simply false.
“But the axioms Science is the attempt to make the chaotic diversity of our sense-experience correspond to a logically uniform system of thought” … (Einstein, quoted in Clower, 1998, p. 409)
You write: “GREAT progress in science resulted PRECISELY from dropping the axiomatic methodology and switching to an observational and inductive process which led to scientific laws which could never be proven, UNLIKE mathematical laws.”
Exactly the opposite is true.
“It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them which give us the key to the understanding of the phenomena of Nature. Experience can of course guide us in our choice of serviceable mathematical concepts; it cannot possibly be the source from which they are derived; experience of course remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics. In a certain sense, therefore, I hold it to be true that pure thought is competent to comprehend the real, as the ancients dreamed.” (Einstein, 1934, p. 167)
You write: “The failure of economics is due to the use of axiomatic method, which is eminently unsuitable for natural science, as was proven in the course of history.”
The falsity of this conclusion is unsurpassable.
The fact of the matter is that economics is a failed science because Orthodoxy got the axiomatic foundations wrong and Heterodoxy has none at all.
The absurdity of the situation consists in the plain fact that Orthodoxy at least understands the crucial importance of axiomatization while heterodox economists do not even see the task before them.
At first sight it looks tragic, but then it is only a slapstick: All those who are marching to the tunes of Marshall’s Burn-Hymn are directly going over the scientific cliff.
Egmont Kakarot-Handtke
References
Bourbaki, N. (2005). The Architecture of Mathematics. In W. Ewald (Ed.), From
Kant to Hilbert. A Source Book in the Foundations of Mathematics, volume II,
pages 1265–1276. Oxford, New York, NY: Oxford University Press. (1948).
Brown, K. (2011). Reflections on Relativity. Raleigh, NC: Lulu.com.
Clower, R. W. (1998). New Microfoundations for the Theory of Economic Growth?
In G. Eliasson, C. Green, and C. R. McCann (Eds.), Microfoundations of Economic
Growth., pages 409–423. Ann Arbour, MI: University of Michigan Press.
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.
Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics:
Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2489792.
Velupillai, K. (2005). The Unreasonable Ineffectiveness of Mathematics in Economics.
Cambridge Journal of Economics, 29: 849–872.
Wigner, E. P. (1979). Symmetries and Reflections, chapter The Unreasonable Effectiveness
of Mathematics in the Natural Sciences, pages 222–237. Woodbridge,
CT: Ox Bow Press.
I have posted a response this comment on the WEA Pedagogy Blog Post: Is Scientific Methodology Axiomatic?
I looked at you’re (asad zaman) web page again, including the exchanges on ‘social epistemology’ (islamic economics articles—i agree with the other author (choudhury) actually–its funny: he cites herman daly, and you cite j b rosser (chaos theory, my area); wars of wor(l)ds). I see you have a PhD from stanford, have an early paper in Annals of Statistics (a very complex journal), taught in Belgium at Louvain ( some of my friends parents taught there too—van Parijis of ‘guaranteed annual income’ was and may still be there). I think economics is like Islam, or Christianity, democracy, communism, or anything else. It doesnt mean anything. It doesn’t matter except historically what Darwin, Einstein, Hayek, Marx, Smith, or various ancient texts (bible , etc.) say, despite any professed claim of interest in the ‘afterlife’. (I wonder why you have such a detailed CV given that I would guess this won’t matter in any afterlife). Abdus Salam from Pakistan of a dissident Islamic faith won a noble in physics, but his group was mostly expelled from there (as were many christian and jewish groups in europe , bahais in iran, many small religious groups currently in iraq being killed) and shi’ites and sunnis are going at it in the ‘mideast’. So i wonder whether you can deal with any applied problems—eg should the taliban kill schoolchildren in pakistan or not, shoot a girl for studying or not? . (I havent been to Pakistan, unless you consider Kashmir part of that). I have relatives studying at MIT (where i see you have a ba in math). Like 2 peas in a pod.
Who is afraid of axioms?
Joint comment on ‘Proper use of math in economics’ and ‘The failure of economics is due to the use of axiomatic method’
With the example of general equilibrium theory directly before their eyes heterodox economists seem to have settled on the opinion that a theory is a logical exercise which is based on arbitrary assumptions called axioms that have no empirical content whatsoever. It is therefore important to recall briefly what a theory is.
“A theory consists of a number of assumptions which logically function as axioms. Through specification and by introducing initial conditions, we may deduce predictions from them. If the predictions prove to be valid we may also say that the assumptions are realistic.” (Klant, 1994, p. 75)
Contrary to the impression received from orthodox economics, a theory is not a self-contained fictional construct but refers to reality. And exactly here comes the ambiguity in. As a matter of fact, equilibrium theory has explicitly cut the tie to reality.
“Allegiance to rigor dictates the axiomatic form of the analysis where the theory, in the strict sense, is logically entirely disconnected from its interpretations.” (Debreu, 1959, p. x)
This is true for mathematics proper. It is completely false when axiomatization is applied outside mathematics.
“Formal axiomatic systems must be interpreted in some domain … to become an empirical science.” (Boylan und O’Gorman, 1995, p. 198)
The assessment that orthodox economics is not much more than a formalized shell game with economic terms is therefore fully justified.
“… GE theory is explicitly defended as a purely formal presentation of the determination of economic equilibrium in a decentralized competitive economy, having no practical value except as a benchmark …” (Blaug, 1994, p. 126)
By consequence, equilibrium economics is NOT a theory in the proper sense.
“Suffice it to say that, in my opinion, what we presently possess by way of so-called pure economic theory is objectively indistinguishable from what the physicist Richard Feynman, in an unflattering sketch of nonsense ‘science,’ called ‘cargo cult science’.” (Clower, 1994, p. 809)
The fundamental defect of orthodox economics does not consist in axiomatization but in applying the WRONG axioms.
“Much of economic theory is based on three questionable assumptions: (1) the world is deterministic; (2) decision makers act as if they know the values of all relevant parameters; and (3) consumers and firms respectively, act as if they were maximizing utility and profit.” (Stigum, 1991, p. 29)
The first task of Heterodoxy is therefore to formulate a theory that is based on a DIFFERENT set of axioms. Axioms, though, do not follow simply from looking at what appears as reality.
“Indeed, there is no such thing as an uninterpreted observation, an observation which is not theory-impregnated.” (Popper, 1994, p. 58)
Therefore, the old induction/deduction chestnut has to be put aside.
“… there is not and cannot be any fundamental opposition between ‘theory’ and ‘fact finding,’ let alone between deduction and induction.” (Schumpeter, 1994, p. 45)
Heterodox economists are mistaken to think that because the orthodox axioms are false axiomatization is dispensable.
“It would be a mistake to lower the level of analysis and clarification. The only way possible is a thorough reexamination of the theory’s basic hypotheses, i.e., a true paradigmatic revolution.” (Ingrao and Israel, 1990, p. 362)
And this brings us directly to J. S. Mill’s Starting Problem.
“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)
Based on good methodological reasons, I propose to move from subjective to objective axiomatic foundations.
http://www.axec.org/#!axioms/cy2g
To my knowledge there is presently no superior set of axioms available.
Egmont Kakarot-Handtke
References
Blaug, M. (1994). Why I am Not a Constructivist. Confessions of an Unrepetant
Popperian. In R. E. Backhouse (Ed.), New Directions in Economic Methodology,
pages 109–136. London, New York, NY: Routledge.
Boylan, T. A., and O’Gorman, P. F. (1995). Beyond Rhetoric and Realism in Economics.
Towards a Reformulation of Economic Methodology. London: Routledge.
Clower, R. W. (1994). Economics as an Inductive Science. Southern Economic
Journal, 60(4): 805–814.
Debreu, G. (1959). Theory of Value. An Axiomatic Analysis of Economic Equilibrium.
New Haven, London: Yale University Press.
Ingrao, B., and Israel, G. (1990). The Invisible Hand. Economic Equilibrium in the
History of Science. Cambridge, MA, London: MIT Press.
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. (1866).
Popper, K. R. (1994). The Myth of the Framework. In Defence of Science and
Rationality., chapter Science: Problems, Aims, Responsibilities, pages 82–111.
London, New York, NY: Routledge.
Schumpeter, J. A. (1994). History of Economic Analysis. New York, NY: Oxford
University Press.
Stigum, B. P. (1991). Toward a Formal Science of Economics: The Axiomatic
Method in Economics and Econometrics. Cambridge, MA: MIT Press.
https://ideas.repec.org/p/wpa/wuwpmh/0504003.html Mathematics and Economics: Use, Misuse, or Abuse? by Francesco Boldizzoni (Università Bocconi) and
Arnaldo Canziani (Università di Brescia)
Abstract
“The development of a mechanistic analytical approach – since mid-19th century to WWI, and beyond – is a well-known story in European economic thought, the story of Cournot, Jevons, Walras, Edgeworth, Pareto, and many others. We could refer to this tradition as “mathematical deductivism”, i.e. the use of mathematics as a demonstrative tool, which implies plenty of axioms and theorems, generally connected to maximizing behaviours. But along the 20th century, both the diffusion of more sophisticated mathematics and ‘political’ circumstances – mainly the Keynesian claim to build workable theories – opened a new phase, the “mathematical descriptivism”: mathematics started to be used to give form to the economic matter, and to satisfy the simplest requirements of economic policy as well. Contrary to these vulgatae, a third use of mathematics could be anyway suggested, the approach based on “multiple indeterminations”. Within such a framework, economic dynamics is treated in more and more flexible ways by n degrees of freedom, so reflecting the stochastic complexity of the economic reality. To carry out this task, the paper goes through the work of three Italian pioneers of the 20th century (Demaria, Brambilla, De Finetti) analyzing the interactions between social exogenous variables and their endogenous effects.”
http://michael-hudson.com/1999/09/the-use-and-abuse-of-mathematical-economics-2/
The Use and Abuse of Mathematical Economics
September 24, 1999
By Michael Hudson
[excerpted]
“Over the past generation, courses in mathematical economics have displaced the traditional courses in economic history and the history of economic thought that might have familiarized students with alternatives to today’s monetarist orthodoxy. Equilibrium theorizing has expunged a broad understanding of how economies work, and even the long dynamics of economic history, especially where the dynamics of debt are concerned.
The failure of mathematical economics to analyze our epoch’s financial strains suggests that its aim has not really been to explain the world as much as to censor perceptions that imply that the financial status quo is unstable and hence must be regulated”
“This poses the question of whether the most important phenomena and dynamics are being mathematized. Do today’s general equilibrium, monetarist and national income and product models correlate the appropriate phenomena, or do they omit key dynamics?
To contemporary economists, mathematics has become the badge of scientific method. But is the use of mathematics scientific ipso facto? To what extent may it be methodologically abused?”
Those axioms are just well known identities, basically. I see you cite Velupillai—now at NSSR (there is one other person up there who ocassionaly makes sense, the others just seem to occasionaly stumble upon something meaningiful—eg foley) . I’d say they are 2 main economics theories now and he has one and there one other, plus you can add some slightly more heterodox approaches. (Basically, a ‘stochastic lagrangian’—you need kinetic and potential energy, and bring in some noise terms. This has been done since the 70’s but mostly ignored. )
There are TWO different purposes of axiomatic development.
Purpose 1: To provide for a systematic presentation and development of an existing body of knowledge. This is a bit like creating a grammar for a language in order to study formally what is known intuitively by native speakers.
Purpose 2: This is an efficient way to DEVELOP knowledge — as the quote by Mill suggests. We first look for the right set of axioms — certain proposition which can be universally accepted, and then use these to derive all other parts of our knowledge.
As far as purpose 1 is concerned, it can be used on a limited and simple body of knowledge. For example Maxwells axioms can be used to formalize electromagnetics, but NOT all of physics. As far as I know, there is NO axiomatization of our current bodies of scientific knowledge for Physics, Chemistry, Biology, and other hard sciences — I have taken most of them at university level, and none of the texts that I studied used an axiomatic approach to the study of the subject.
A claim that scientific knowledge can be axiomatized seems false for many reasons. At all points there are many theories and propositions of varying levels of certainty. Furthermore, as Kuhn observed, all theories are born refuted — the theory is in contradiction with SOME observations, and extending these theories to resolve these contradictions is part of normal science. Bodies of knowledge which contain conflicting statements, and also statements of varying level of certainty cannot be axiomatized, since axiomatics can only deal with CERTAIN truths and falsehoods, and not with probabilities and certainly not with the simultaneous presence of conflicting information.
The second proposition can also be interpreted in TWO different ways. ONE is that this is actually how scientists operate — they find certainties and build upon them using logical processes. Any study of history of science, as done by Kuhn and MANY others for example, will show that this is not true. This is not how scientists work. So it is empirically false.
The second interpretation is normative — this is how scientists SHOULD work, if they are to proceed efficiently. HOW would one prove such a proposition? Perhaps by showing it in practice, taking some field and proceeding in this way to derive the knowledge in a more efficient one than was actually done by the scientists who had worked in more random and ad hoc ways. This leads to the question of how do we assess whether one methodology is better than another?
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: What is it that Egmont can do with his axioms that others cannot do? Can Egmont explain the global financial crisis, and the subsequent recession (as for example Mian and Sufi have done?). Of course it is not enough to provide an explanation — Andrew Lo has provided a 21 Book Review of 21 different book length explanations none of which seems completely satisfactory and many of them conflict with each other. A correct explanation cannot simply add to the list of possible explanations but must also explain why it is correct and why others are wrong. It would seem to require a meta theoretic explanation outside the range of the axiomatic method. To put the point being made more concisely: EVEN IF a set of axioms can be used to explain some economic event, this does not establish the validity of the axioms — because there are a infinity of theories which provide a perfect fit to any finite set of data. THUS JUSTIFICATION of a set of axioms can only be tentative, and would require META-THEORETIC methods, going outside the axiom set to examine collections of different types of axiomatizations and other ways of producing and organizing knowledge, and then using META-criteria for evaluation and comparison.
To see why this is necessary and also difficulty, we have to take into account the arguments that I have made in a separate post: “Is Scientific Methodology Axiomatic?”
This post provides a self-contained discussion of two points: Mathematical truths are analytic — true by virtue of definitions and logic, without any reference to observations of real world — scientific laws are synthetic, subject to verification and possible refutation by empirical observations. In order to use axiomatic method in science, one has to provide a mapping of abstract theoretical entities and relations in the axiomatic system to real world matter and properties — this mapping can be right or wrong (in the sense that it may or may not satisfy the axioms) — mathematical truth of theorems within axiomatic system does not validate the mapping, which is always subject to change and refutation. To take a simple example, suppose that the gravitational constant changes smoothly and slowly with time. Then an axiomatic system based on a certain value will provide a good approximation to reality for a certain period, but will progressively become worse. The confirmation does not guarantee good forecasting abilities for an axiomatic system.
The second problem with axiomatic approach are the Undecidability and Incompleteness Theorems of Godel. These show that there will always be truths about the system which remain outside the bounds of provability for any collection of axioms. This means that no axiomatization can provide a complete description of all truths. 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. That does not mean that the axiom are wrong or useless, just that they have a limited domain of applicability. The situation has often arisen in physics where different sets of principles IN CONFLICT WITH EACH OTHER are used to account for experiments in different context. For example, Light as a wave and light as a particle are both justified in different contexts. Thus even conflicting systems of axioms may be in simultaneous use and also useful simultaneously.
Post-Kuhnian understanding of science and axiomatics is rather complex, with no obvious and simple theory of knowledge attached.
I actually consider this post reasonable, and the issue partly comes from how one defines axiomatization (see also Hilbert’s 6th problem).
My view is the two sets of equations, one coming from general relativity (which can be written on a page like Egmont’s system) and the other from relativistic quantum field theory (‘the standard model’) (also can be fit on a page) —and its unknown if these are really compatible (or consistant) with each other constitute the axioms of physics. They are not presented like the axioms of ZFC set theory however (I view them as defining a subset of that ‘mathematical universe’)—i think they are reducible to them just as Principia Mathematica reduced arithmatic to logic essentially. Chemistry can be derived largely from physics, and biology as well (though things like ‘purpose’ and ‘consciousness’ are out of that picture) , and so on.
(I disagree that light being both a wave and a particle represents a conlflicting system of axioms—this follows from representing light as a mathematical wave (the psi fuinction)—one axiom, and then interpreting its behavior in different contexts using born’s rule (another axiom). The fact that people use the terms waves and particles is their problem, not the axioms. Human problems, botjh social and psychological or philosophical, I dont consider axiomatized like the ‘hard sciences’ (though alot of them probably could be to some extent; I see that as a political problem because its possible if they were alot of publishing would be seen as unnecesary and irrelevant). (For clarification one also needs planck’s and de broglie’s axioms for the psi function).
Of course people invent specific vocabularies and grammars at various levels out of conveniance—thats why you have chemistry, or sociology. I pretty much see english or any other language as being axiomatized by rules of grammar etc—any ‘well formed fragment’ or wff (in logic) has something like a subject, object, verb , punctuation etc. (Language is somewhat of an open system since one can create new words, though often using the same letters). (Language is sort of the ‘metalanguage’ of sciences—ie you can talk about the physical axioms and their consequences. You have a mapping from sets, to empirical observations described by physics, and another to language which is about ‘concepts’.
(All the axiomatic systems, including logic and math, it appears to me are not universally accepted nor seen as neccesarily complete, but usually there is a sort of ‘common core’ people agree on. Whether a poem is good grammar may be an object of controversy; similarily for various mythological or historical descriptions or accounts—are they real or fiction?)
Witness
Witness the human species
playing math,
science,
and economics
for brain-sport
while mothers and fathers and children starve
on a planet of abundance
Please see my post on the WEA Pedagogy blog, which expresses the same sentiments in a lengthier but less poetic way:
Yes, Ack. Chesterton opened his Collected Poems with
“Ill fairs the land, to hastening ills a prey,
Where wealth accumulates and men decay
…
But irony, that glares like judgement day
Sees men accumulated and wealth decay”.
Previously, though, in “Whats Wrong With the World”, he had made a typically serious joke to the effect that when Rome is burning, that may be good reason to inquire why the fire engine isn’t working.
The question to me, as someone who actually has done a fair amount of ‘social justice’ work (including at food banks and such) and also a fair amouint of protesting on similar issues as well as envirojnmental ones, I wonder whether you have any suggestions for what should be done. People are starving all over the world and they are getting killed in huge conflicts in central africa, syria, and so on. I go to my various groups and protests and see many people have ipods, tablet computers etc., partly at times to ‘play games’ to make the various projects tolerable or to fill in down time, and sometimes as tools to help coordinate and manage such operations. I know people who do academic work on computers managing agricultural systems, and you have to do a lot of math and computer stuff to be able to do that. Others use ‘social media’ to organize various campaigns on these issues. Perhaps they should have just gone out and grown food somewhere? And maybe sent it to where its needed (like a refugee camp where the people who control the camp will loot it and sell it so they can buy weapons, often also from the USA). I have an in law getting her degree writing poetry (witness appears to be one to me). Maybe rather than play at economics writing poetry would be better to help the starving?
As we should all know by now (from following this blog) there is no credible answer to the underlying problem that is causing disagreement here; or, anywhere else in structured thought for that matter. And, it doesn’t matter how complicated the terminology gets; or, how many references are given to try and substantiate one’s claim. The reason its irresolvable is because “certainty” is missing from the equation. As a result, we don’t know where to start our construction of theory; or, what should be allowed into its purview. This problem stems from the fact that “beginning” itself is an incomprehensible difference — both ours as well as the world that exists outside of us. Hence both are reduced to mystery for us.
Yes, I’ve heard of the “big bang” — a term (I believe) that applies to the successful copulation of the incomprehensible resulting in the birth of endless animate as well as inanimate progeny. But, that is merely a cop out for show. Obviously, no one has the foggiest idea of how the beginningcame about. Similarly, we have no idea of what might have preceded it. Is anybody so intoxicated here with their own self wisdom that they might be willing to proffer a guess? I kinda doubt it. Even Hawking knew better. He called it all unknowable.
In addition to those problems, man is and will forever remain a work in process — another unknown that complicates our ability to determine validity in thought. As a result, as we change so too does our conclusions. Once flat, the earth is now round. Once the center of the universe, now it no longer is. The list goes on and on. One thing that is true however is that we are constrained by limitation as it finds form within physicality, and that has dictates its own peculiar form of certitude. In other words, when we attempt to characterize what we think we know (via limitation) or by way of a language of unity (progressively defined) it results in a language that precludes us from thinking about anything other than limitation. And so, we are faced with another dead end. This is the same problem that formal education suffers from; and, it’s high time that both we and it owned up to this problem. Formed within a box, those who are cultured there find it impossible to think outside of that box. This is particular problematic at a point in time when it has become absolutely necessary to do so. In case nobody has noticed, gradualism no longer cuts it when immediacy demands otherwise. (see: http://www.edenorg.com/edp-08.htm).
As you have indicated Ishi, mystery stalks the earth. Rather than address it, the impotent elect to turn away. After all, what is one to do against such mighty forces assembled against them — but, to capitulate. For haven’t the poor always been among us, and isn’t it their misfortune to be born that way and thus destined to suffer? Evolution seems to suggest so, via its theory regarding the survival of the fittest. Ah, the deception that deceivers promote when first they attempt to deceive themselves to cover-up their deception. If you are rich and find taking advantage of the poor good sport, obviously evolution has you covered, So, why not embrace it?
But, that shouldn’t be the case with the brain trust assembled here. Most have absorbed structured learning and gone on to qualify life relative to real experience. Also, many in their later years don’t have all that much to look forward to — time wise. Thus, it behooves them to give consideration to the importance of spirituality, just in case there is more. So, given this added incentive, if they were to put their collective heads together, something positive could be imagined to come from it. The only constraint that seems to be preventing them from contributing to the necessary, is that metal masturbation is simply too rewarding to just give up, regardless of how compelling circumstance might be. Comfortable enough in the fruits of their labor, fear has yet to compel these mental giants to move. I believe that you might just be right when you say “rather than play at economics writing poetry would be better to help the starving? Surely nothing could be worse than playing at economics.
I have said this before and I am going to continue to repeat it until it sinks in. It’s time to get going people. When you are a child you are expected to play at childish things. Now that you are adults it’s time to act responsibly. We need to come up with a game plan to turn the current momentum that promises to destroy mankind around. Ideas anyone. It can’t be that complicated.
I totally agree with this post. there are many works that have been awarded the Nobel prize yet they are of little or no value at all.take for instance Asset pricing that the three authors some times disagree on some issues yet it was awarded the Nobel. it seems like many so called economists are thrilled not by the practical or realistic approach that a published paper discusses but because of the mathematics involved in it. they are only thrilled by the mathematics and not the realistic contribution that a paper gives. it is really a sad truth that many economics theories don,t solve real life problems and i wonder why they are being given attention