Giocoli, Nicola (2005): Mathematics as the role model for neoclassical economics (Blanqui Lecture). Published in: Arena R., Dow S. & Klaes M. (eds.), Open Economics: Economics in Relation to Other Disciplines, Routledge, London (2009): pp. 129-149.
Download (103kB) | Preview
Born out of the conscious effort to imitate mechanical physics, neoclassical economics ended up in the mid 20th century embracing a purely mathematical notion of rigor as embodied by the axiomatic method. This lecture tries to explain how this could happen, or, why and when the economists’ role model became the mathematician rather than the physicist. According to the standard interpretation, the triumph of axiomatics in modern neoclassical economics can be explained in terms of the discipline’s increasing awareness of its lack of good experimental and observational data, and thus of its intrinsic inability to fully abide by the paradigm of mechanics. Yet this story fails to properly account for the transformation that the word “rigor” itself underwent first and foremost in mathematics as well as for the existence of a specific motivation behind the economists’ decision to pursue the axiomatic route. While the full argument is developed in Giocoli 2003, these pages offer a taste of a (partially) alternative story which begins with the so-called formalist revolution in mathematics, then crosses the economists’ almost innate urge to bring their discipline to the highest possible level of generality and conceptual integrity, and ends with the advent and consolidation of that very core set of methods, tools and ideas that constitute the contemporary image of economics.
|Item Type:||MPRA Paper|
|Original Title:||Mathematics as the role model for neoclassical economics (Blanqui Lecture)|
|Keywords:||Axiomatic method, formalism, rationality, neoclassical economics|
|Subjects:||B - History of Economic Thought, Methodology, and Heterodox Approaches > B4 - Economic Methodology > B40 - General
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B20 - General
|Depositing User:||Nicola Giocoli|
|Date Deposited:||30 Sep 2011 16:20|
|Last Modified:||26 Apr 2016 04:45|
ALTMAN M. 2004, “The Nobel Prize in behavioral and experimental economics: a contextual and critical appraisal of the contributions of Daniel Kahneman and Vernon Smith”, Review of Political Economy, 16:1, 3-41.
BERGSTROM T.C. 2003, “Vernon Smith’s insomnia and the dawn of economics as experimental science”, Scandinavian Journal of Economics, 105:2, 181-205.
BOCCARDO G. 1877, “Matematica applicata all’Economia Politica”, in Dizionario Universale di Economia Politica e di Commercio, Milano: Treves, vol.II, 216-20.
BOURBAKI N. 1996 [1948; 1950], “The architecture of mathematics”, in: EWALD 1996, 1265-76.
BRAINARD W.C. & SCARF H.E. 2000, “How to compute equilibrium prices in 1891”, Cowles Foundation Discussion Papers, n.1272.
CHRIST C.F. 1952, “History of the Cowles Commission 1932-1952”, in Economic Theory and Measurement: A Twenty Years Research Report, 1932-1952, Chicago: Cowles Commission.
CORRY L. 1996, Modern Algebra and the Rise of Mathematical Structures, Basel: Birkhäuser.
__ 1997, “David Hilbert and the Axiomatization of Physics (1894-1905)”, Archive for History of Exact Sciences, 51, 83-198.
__ 2000, “The empiricist roots of Hilbert’s axiomatic approach”, in Hendricks V.F., Pedersen S.A. and Jørgensen K.F. (eds.), Proof Theory. History and Philosophical Significance, Dordrecht: Kluwer, 35-54.
DARDI M. 1983, “Piero Sraffa (1898-1983)”, Quaderni di Storia dell’Economia Politica, 3, 3-14.
DEBREU G. 1959, Theory of Value, New York: John Wiley & Sons.
__ 1984, “Economic theory in the mathematical mode”, American Economic Review, 74:3, 267-78.
__ 1987 , “Mathematical economics”, in Eatwell J., Milgate M. and Newman P. (eds.), The New Palgrave: A Dictionary of Economics, London: MacMillan, 399-404.
__ 1991, “The mathematization of economic theory”, American Economic Review, 81, 1-7.
DIEUDONNÉ J. 1970, “The work of Nicolas Bourbaki”, American Mathematical Monthly, 77, 134-45.
EVES H. 1990, Foundations and Fundamental Concepts of Mathematics. Third Edition, Mineola, NY: Dover
EWALD W. 1996, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Oxford: Clarendon Press, 2 vols.
FRISCH R. 1995 , “On a problem in pure economics”, in Bjerkholt O. (ed.), Foundations of Modern Econometrics. The selected essays of Ragnar Frisch, Cheltenham: Elgar, vol.I, 3-40.
__ 1995a , “New orientation of economic theory. Economics as an experimental science”, in Bjerkholt O. (ed.), Foundations of Modern Econometrics. The selected essays of Ragnar Frisch, Cheltenham: Elgar, vol.II, 481-95.
GIGERENZER G. 1996, “On narrow norms and vague heuristics: a reply to Kahneman and Tversky (1996)”, Psychological Review, 103:3, 592-6.
__ 2005, “Is the mind irrational or ecologically rational?”, in Parisi F. and Smith V.L. (eds.), The Law and Economics of Irrational Behavior, Stanford: Stanford University Press, 37-67.
GIOCOLI N. 2003, Modeling Rational Agents. From Interwar Economics to Early Modern Game Theory, Cheltenham: Elgar.
Giocoli N. 2003a, “Fixing the point. The contribution of early game theory to the tool box of modern economics”, Journal of Economic Methodology, 10:1, 1-39.
Giocoli N. 2003b, “History of economics becomes a science for cyborgs”, History of Economic Ideas, 11:2, 109-27.
GÖDEL K. 1986 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, in Collected Works, Oxford: Oxford University Press, vol.I, 126-95.
HILBERT D. 1996 , “Mathematical problems”, in EWALD 1996, 1096-105.
__ 1996a , “Axiomatic thought”, in EWALD 1996, 1107-15.
HILDRETH C. 1986, The Cowles Commission in Chicago, 1939-1955, Berlin: Springer.
HUTCHISON T.W. 2000, On the Methodology of Economics and the Formalist Revolution, Cheltenham: Elgar.
INGRAO B. & ISRAEL G. 1990 1987, The Invisible Hand, Cambridge: MIT Press.
ISRAEL G. 1977, “Un aspetto ideologico della matematica contemporanea: il ‘bourbakismo’ ”, in Donini E., Rossi A. & Tonietti T. (a cura di), Matematica e fisica: struttura e ideologia, Bari: De Donato, 35-70.
KAHNEMAN D. AND TVERSKY A. 1979, “Prospect theory: an analysis of decision under risk”, Econometrica, 47:2, 263-92.
KLINE M. 1980, Mathematics. The Loss of Certainty, Oxford: OUP.
KOOPMANS T.C. 1954, “On the use of mathematics in economics”, Review of Economics and Statistics, 36:4, 377-9.
LEE K.S. 2004, Rationality, Mind, and Machines in the Laboratory: A Thematic History of Vernon Smith’s Experimental Economics, Ph.D. dissertation, Notre Dame University.
LEONARD R.J. 1997, “Value, sign and social structure: the ‘game’ metaphor and modern social science”, European Journal of the History of Economic Thought, 4, 299-326.
__ 1998, “Ethics and the Excluded Middle. Karl Menger and Social Science in Interwar Vienna”, Isis, 89, 1-26.
MCCLOSKEY D. 2005. “The trouble with mathematics and statistics in economics”, mimeo.
MENGER K. 1979 [1933; 1937], “The new logic”, in Selected Papers in Logic and Foundations, Didactics, Economics, Dordrecht: Reidel.
MIROWSKI P. 2002, Machine Dreams. Economics Becomes a Cyborg Science, Cambridge, Mass.: CUP.
MOSCATI I. 2002, “History of consumer theory from Menger to Debreu”, Working Papers IEP, Università Bocconi – Milan, n.9.
__ 2003, Storia della teoria neoclassica del consumatore (1871-1959): una prospettiva neokantiana, Ph.D. dissertation, University of Florence.
__ 2003a, “How the rational consumer survived heterodox criticism: a neo-Kantian explanation”, paper presented at the 7th ESHET Conference, Paris, 30 Jan. – 1 Feb. 2003.
NOVICK D. 1954, “Mathematics: logic, quantity, and method”, Review of Economics and Statistics, 36:4, 357-8.
ORTMANN A. 2003, “Charles R. Plott’s collected papers on the experimental foundations of economic and political science”, Journal of Economic Psychology, 24, 555-75.
PUNZO L. 1989, “Von Neumann and Karl Menger’s Mathematical Colloquium”, in Dore M., Chakravarty S. and Goodwin R., John von Neumann and Modern Economics, Oxford: Clarendon Press, 29-65.
__ 1991, “The school of Mathematical Formalism and the Viennese Circle of mathematical economics” Journal of the History of Economic Thought, 13, 1-18.
__ 1999, “Clower on axiomatics” in Howitt P., de Antoni E. and Leijonhufvud A. (eds.), Money, Markets and Methods. Essays in Honor of Robert W. Clower, Elgar.
QUIGGIN J. 1982, “A theory of anticipated utility”, Journal of Economic Behavior and Organization, 3:4, 323-43.
RABIN M. 1998, “Psychology and economics”, Journal of Economic Literature, 36 (March), 11-46.
¬¬¬__ 2002, “A perspective on psychology and economics”, European Economic Review, 46, 657-85.
__ 2003, “The Nobel Memorial Prize for Daniel Kahneman”, Scandinavian Journal of Economics, 105:2, 157-80.
SCHWALBE U. 1999, “Irving Fisher’s Mathematical Investigations in the Theory of Value and Prices”, in: Loef H.-E. & Monissen H.G. (eds.), The Economics of Irving Fisher. Reviewing the Scientific Work of a Great Economist, Cheltenham: Elgar, 281-303.
STARMER C. 2000, “Developments in non-expected utility theory: the hunt for a descriptive theory of choice under risk”, Journal of Economic Literature, 38 (June), 322-82.
TVERSKY A. AND KAHNEMAN D. 1974, “Judgment under uncertainty: heuristics and biases”, Science, 185, 1124-31.
__ 1992, “Advances in prospect theory: cumulative representation of uncertainty”, Journal of Risk and Uncertainty, 5:4, 297-323.
VOLTERRA V. 1906, “L’economia matematica ed il nuovo manuale del Prof. Pareto”, Giornale degli Economisti, 32, 296-301.
VON NEUMANN J. 1983 1931, “The formalist foundations of mathematics”, in Benacerraf P. and Putnam H. (eds.), Philosophy of Mathematics. Selected Readings, Cambridge: CUP, 61-5.
__ 1961 , “The mathematician”, in Taub A.H. (ed.), John von Neumann. Collected works, Oxford: Pergamon Press, vol. I, 1-9.
__ AND MORGENSTERN O. 1953, Theory of Games and Economic Behavior, Princeton: Princeton University Press, 3rd edition.
WEINTRAUB E.R. 1985, General Equilibrium Analysis. Studies in Appraisal, Cambridge: Cambridge University Press.
__ 1998, “Controversy: axiomatisches mißverständnis”, Economic Journal, 108, 1837-47.
__ 2002, How Economics Became a Mathematical Science, Durham: Duke University Press.
WERDEN G.J. 2003-04, “Economic evidence on the existence of collusion: reconciling antitrust law with oligopoly theory”, Antitrust Law Journal, 71, 719-800.
WHITE M.V. 2004, “In the lobby of the energy hotel: Jevons’s formulation of the postclassical ‘economic problem’ ”, History of Political Economy, 36:2, 227-271.
WOLD H. 1943-44, “A synthesis of pure demand analysis”, Skandinavisk Aktuarietidskrift, 26, 85-118, 220-263; 27, 69-120.