Axiomatic economics — total horseshit

28 December, 2014 at 17:33 | Posted in Theory of Science & Methodology | 7 Comments

Yours truly and people like Tony Lawson have for many years been urging economists to pay attention to the ontological foundations of their assumptions and models. Sad to say, economists have not paid much attention — and so modern economics has become increasingly irrelevant to the understanding of the real world.

an-inconvenient-truth1Within mainstream economics internal validity is still everything and external validity nothing. Why anyone should be interested in that kind of theories and models is beyond imagination. 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, they really should not be surprised if people say that this is not science, but autism!

Studying mathematics and logics is interesting and fun. It sharpens the mind. In pure mathematics and logics we do not have to worry about external validity. But economics is not pure mathematics or logics. It’s about society. The real world. Forgetting that, economics is really in dire straits.

Mathematical axiomatic systems lead to analytic truths, which do not require empirical verification, since they are true by virtue of definitions and logic. It is a startling discovery of the twentieth century that sufficiently complex axiomatic systems are undecidable and incomplete. That is, the system of theorem and proof can never lead to ALL the true sentences about the system, and ALWAYS contain statements which are undecidable – their truth values cannot be determined by proof techniques.keynes-(1) More relevant to our current purpose is that applying an axiomatic hypothetico-deductive system to the real world can only be done by means of a mapping, which creates a model for the axiomatic system. These mappings then lead to assertions about the real world which require empirical verification. These assertions (which are proposed scientific laws) can NEVER be proven in the sense that mathematical theorems can be proven …

Many more arguments can be given to explain the difference between analytic and synthetic truths, which corresponds to the difference between mathematical and scientific truths. As I have explained in greater detail in my paper, the scientific method arose as a rejection of the axiomatic method used by the Greeks for scientific methodology. It was this rejection of axiomatics and logical certainty in favour of empirical and observational approach which led to dramatic progress in science. However, this did involve giving up the certainties of mathematical argumentation and learning to live with the uncertainties of induction. Economists need to do the same – abandon current methodology borrowed from science and develop a new methodology suited for the study of human beings and societies.

Asad Zaman

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7 Comments

  1. As you know axiomization is an old problematic that in some ways is about ontology via logical grounding. Granted it has not succeeded but there are legitimate reasons for trying. Horseshit after all can be a helluva fertilizer (he, he)!!!

  2. Surely what we need to give up is pseudo-mathematical argumentation? Isn’t the real thing the best antidote to the merely pseudo?

  3. Keyes: “That is, the system of theorem and proof can never lead to ALL the true sentences about the system, and ALWAYS contain statements which are undecidable – their truth values cannot be determined by proof techniques.keynes-(1) More relevant to our current purpose is that applying an axiomatic hypothetico-deductive system to the real world can only be done by means of a mapping, which creates a model for the axiomatic system. These mappings then lead to assertions about the real world which require empirical verification. These assertions (which are proposed scientific laws) can NEVER be proven in the sense that mathematical theorems can be proven …”

    This describes a view of the philosophy of the natural sciences to which I subscribe. It becomes less relevant to the social sciences as the natural context involves a great deal more complexity than the physical sciences.

    The social sciences, including economics, are much more complex since they involve agents with exponentially more developed degrees of freedom and the ability to influence themselves through reflexivity, greatly increasing system complexity. The problem is that it does not and apparently cannot apply to the social sciences, where the foundational context is different owing to the difference in behavior of the elements of the system and also the subsystems.

    So it is not just a matter of eschewing the axiomatic method for an empirical/realistic one. The social sciences are not empirical in the same way as natural sciences owing to the difference in subject matter. The social sciences must develop methodology suitable to the subject matter in which the elements are biological rather than physical and as organisms have unique capabilities. Moreover, these organisms are not only able to create cultures and institutions that influence them but are required to in order to compete in the environment.

    Evolutionary theorist David Sloan Wilson has written fairly extensively about using an evolutionary paradigm in economics. See, for example, “Evolution as a general theoretical framework for economics and public policy”, Journal of Economic Behavior & Organization 90S (2013). Kenneth Boulding realized this about economics long ago and became a co-founder of General Systems Theory.

    Conventional economics is barking up the wrong tree and even heterodox economists need to pay more attention to what is going on in related disciplines — which Thomas Piketty also emphasized in Capital in the 21st Century.

  4. Here’s an apt quote from Peter Radford at The Radford Free Press today:

    “An economy conceived as a reaction to uncertainty cannot be understood, or even modeled, axiomatically. For its very nature is to evolve and mutate through time. It is not necessarily internally consistent or even logical. It is idiosyncratic, path dependent, and liable to lurch occasionally in different directions. Its choice of solutions to uncertainty may not be optimal: all that it needs is viability. It may get locked into paths of activity that prove, longer term, be to highly suboptimal. All it needs to do is to provide for survival. It needs to subsist and persist.

    “Uncertainty prevents it, ever except by luck, from arriving at the sort of pristine optimal equilibrium that orthodox economists set as the desired consequence of the economic systems they study. Indeed, the notion of such a system actually existing is so bizarre that it seems pointless – to me – to bother with it at all. I suppose that within the entire set of all possible configurations of the economy, one such pristine example must exist, but the likelihood of it being the one we are living in is infinitesimally small.

    “So, I repeat, why bother studying it? Especially when we appear to know so little about the one we are living in.”

  5. Total scientific Dadaism
    Comment on ‘Axiomatic economics – total horseshit’
    .
    In the intro Lars Syll writes: “Studying mathematics and logics is interesting and fun. It sharpens the mind. In pure mathematics and logics we do not have to worry about external validity. But economics is not pure mathematics or logics. It’s about society. The real world.”

    Economists have their philosophical roots in Bentham’s utilitarianism. And it seems that they never dare to get out of this shallow intellectual puddle and to swim in deeper waters. Have they never heard what real scientists have said about mathematics and axiomatization? Have Galilei or Newton or Einstein said that mathematics is fun? That a little intellectual gymnastics is good against mental enfeeblement?

    Above all: did one of these three better known scientists ignore the problem of external validity?

    Exactly the contrary! For all of them, mathematics was the key to reality — to the very reality that is producing what the myopic utilitarian experiences when he looks in all his nativity out of the window.

    “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)

    Lawson’s ontology suffers from several misunderstandings (2013).

    “The central message of Lawson’s critique of modern economics is that an economy is an “open system” but economists insist on dealing with it as if it were “closed.” (see intro to http://rwer.wordpress.com/2014/11/11/mainstream-macroeconomics-distorts-our-understanding-of-economic-reality/)

    This is true for equilibrium economics. And it is true that Orthodoxy is a failure. But now comes the logical blunder:

    “Modern economics has become increasingly irrelevant to the understanding of the real world. In his seminal book Economics and Reality (1997) Tony Lawson traced this irrelevance to the failure of economists to match their deductive-axiomatic methods with their subject.”

    While Orthodoxy indeed applies the deductive-axiomatic method there is no necessary connection between the method and closed systems. Physicists apply mathematics and the deductive-axiomatic method for the description of an universe that certainly displays no equilibrium and no closure in the sense of orthodox economics. What has to be rejected is the notion of equilibrium/closure and NOT the deductive-axiomatic method.

    Because they are fixated on equilibrium economics Tony Lawson and Lars Syll misunderstand the role of the deductive-axiomatic method for scientific research.

    Methodological discussions among economists are total scientific Dadaism.
    .
    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.
    Kakarot-Handtke, E. (2013). Crisis and Methodology: Some Heterodox Misunderstandings.
    SSRN Working Paper Series, 2083519: 1–25. URL http:
    //papers.ssrn.com/sol3/papers.cfm?abstract_id=2083519.

  6. From obscurity to enlightenment
    Comment on ‘Axiomatic economics – total horseshit’
    .
    I came across David Glasner’s post of 16 July, 2014 ‘Modern macroeconomics — obscurantist axiomatization’ on this blog https://larspsyll.wordpress.com/2014/07/16/modern-macroeconomics-obscurantist-axiomatics/

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

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

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

    “We are therefore justified in saying that with Euclid’s Elements the causa materialis of geometry underwent a radical transformation; from a more or less amorphous aggregate of propositions it acquired an anatomic structure. Geometry itself emerged as a living organism with its own physiology and teleology, …. And this true mutation represents not only the most valuable contribution of the Greek civilization to human thought but also a momentous landmark in the evolution of mankind comparable only to the discovery of speech or writing.” (1966, p. 9)

    Axiomatization then became a major issue for physicists with Newton.

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

    And so it became an issue in the so-called social sciences with Hume.

    “Like most of his fellow moral philosophers, Hume thought it was worth a try to make all sciences as rigorous as Newtonian physics …” (Redman, 1997, p. 111)

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

    “To Senior belongs the signal honor of having been the first to make the attempt to state, consciously and explicitly, the postulates that are necessary and sufficient in order to build up … that little analytic apparatus commonly known as economic theory, or to put it differently, to provide for it an axiomatic basis.” (Schumpeter, 1994, p. 575)

    So Glasner got it not quite correct:

    “The fetish for axiomatization in economics can largely be traced to Gerard Debreu’s great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium.”

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

    Glasner got it, again, not quite correct with:

    “The idea that a good scientific theory must be derived from a formal axiomatic system has little if any foundation in the methodology or history of science.”

    Exactly the opposite is true:

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

    The rest of Glaser’s argumentation is not much better (for the refutation of the awkward Gödel argument see here http://axecorg.blogspot.de/2014/12/still-in-woods.html).

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

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

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

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

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

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

    .
    References
    Blaug, M. (1998). Economic Theory in Retrospect. Cambridge: Cambridge University
    Press, 5th edition.
    Farmelo, G. (2009). The Strangest Man. The Hidden Life of Paul Dirac, Quantum
    Genius. London: Faber and Faber.
    Georgescu-Roegen, N. (1966). Analytical Economics, chapter General Conclusions
    for the Economist, pages 92–129. Cambridge, MA: Harvard University Press.
    Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like
    an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series,
    2207598: 1–16. URL http://ssrn.com/abstract=2207598.
    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. URL
    http://books.google.de/books?id=3bIkAQAAQBAJ&printsec=frontcover&hl=
    de&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false.
    Schumpeter, J. A. (1994). History of Economic Analysis. New York, NY: Oxford
    University Press.

  7. Lars, can you comment on this?

    http://www3.unifr.ch/econophysics/sites/default/files/Critique_Tony_Lawson_Neoclassical_Economics.pdf

    I know that you are a big fan of Tony Lawson, but the econophysicists do not seem to like him much. Tony is silent, so maybe you could step up to the plate.


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