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THE MATHEMATICAL TURN IN ECONOMICS: WALRAS, THE FRENCH MATHEMATICIANS, AND THE ROAD NOT TAKEN

Published online by Cambridge University Press:  07 June 2012

MICHAEL H. TURK
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Abstract

One of the pivotal moments in the move toward mathematizing economics occurred at the turn of the twentieth century, with Leon Walras as perhaps its most ardent champion. Yet, there is no small irony here, in that the leading French mathematicians to whom Walras turned to buttress and defend the case for a mathematical economics, especially Henri Poincare and Emile Picard, laid out reservations to the scope of this mathematizing program. They even pointed to matters, including the hold of the past on future events and hysteresis, a subject already in the discourse of mathematical physicists, which might have fashioned economics differently from the neoclassical mold being formed. This alternate pathway, though, was not pursued at the time.

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Articles
Information
Journal of the History of Economic Thought , Volume 34 , Issue 2 , June 2012 , pp. 149 - 167
Copyright
Copyright © The History of Economics Society 2012

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References

REFERENCES

Arthur, W. Brian. 1989. “Competing Technologies, Increasing Returns and Lock-in by Historical Events. The Economic Journal 99: 116–131.CrossRefGoogle Scholar
Borel, Emile. [1907] 1972. “Un Paradoxe economique.” In Oeuvres de Emile Borel. Volume IV. Paris: CNRS, pp. 2197–2208.Google Scholar
Cross, Rod. 1995. “Metaphors and Time Reversibility and Irreversibility in Economic Systems.” Journal of Economic Methodology 2 (1): 123–134.CrossRefGoogle Scholar
Cross, Rod, and Allan, Andrew. 1988. “On the History of Hysteresis.” In Cross, Rod, ed., Unemployment, Hysteresis, and the Natural Rate Hypotheses. Oxford, UK: Blackwell, pp. 26–38.Google Scholar
Dantzig, Tobias. 1930. Number, The Language of Science. New York: The Macmillan Company.CrossRefGoogle Scholar
Darboux, Gaston. 1912. Eloges academiques et discours. Paris: Librairie Scientifique, A. Hermann et Fils.CrossRefGoogle Scholar
David, Paul. 1997. “Path Dependence and the Quest for Historical Economics.” Discussion Papers in Economic and Social History No. 20. University of Oxford, UK.Google Scholar
Delorme, R., and Hodgson, G.. 2005. “Complexity and the Economy: An Interview with W. Brian Arthur.” In Finch, J. and Orillard, M., eds., Complexity and the Economy. Cheltenham, UK: Edward Elgar, pp. 17–32.Google Scholar
Edgeworth, F.Y. [1881] 1932. Mathematical Psychics. London: C. Kegan Paul & Co. Reprint by London School of Economics.Google Scholar
Elster, Jonathan. 1976. “A Note on Hysteresis in the Social Sciences.” Synthese 33: 371–391.CrossRefGoogle Scholar
Ewing, James Alfred. 1891. Magnetic Induction in Iron and Other Metals. New York: The D. Van Nostrand Company.Google Scholar
Friedman, Michael. 1996. “Poincare’s Conventionalism and the Logical Positivists.” In Greffe, Jean-Louis, Heinzmann, Gerhard, and Lorenz, Kuno, eds., Henri Poincare: Science et Philosophie, Congres International, Nancy, France 1994. Berlin: Akademie, pp. 333–344.Google Scholar
Georgescu-Roegen, Nicholas. (1966. “Some Object Lessons From Physics.” In Analytical Economics: Issues and Problems. Cambridge, Mass.: Harvard University Press, pp. 47–82.Google Scholar
Grattan-Guinness, Ivor. 1992. “Structure-similarity as a Cornerstone of the Philosophy of Mathematics.” In Echeverria, Javier, et al. ., eds., The Space of Mathematics. Berlin: Walter de Gruyter, 91–111.CrossRefGoogle Scholar
Grattan-Guinness, Ivor. 1997. The Rainbow of Mathematics: A History of the Mathematical Sciences. New York: W.W. Norton and Company.Google Scholar
Hadamard, Jacques. 1906. “Compte rendu de Elementary Principles in Statistical Mechanics, de Gibbs” American Mathematical Society Bulletin 12: 194–210.CrossRefGoogle Scholar
Heinzmann, Gerhard, and Nabonnand, Phillipe. 2008. “Poincare: Intuitionism, Intuition, and Convention.” In van Atten, Mark, et al. ., eds., One Hundred Years of Intuitionism (1907–2007): The Cerisy Conference. Basel: Birkhauser Verlag, pp. 163–177.CrossRefGoogle Scholar
Ingrao, Bruna, and Israel, Giorgio. 1990. The Invisible Hand. Translated by McGilvray, Ian. Cambridge, Mass.: The MIT Press.Google Scholar
Jaffe, William. 1983. “Poincare and the Cardinal Measurability of Utility. In Walker, Donald, ed., Essays on Walras. Cambridge: Cambridge University Press, pp. 213–220.Google Scholar
Kneebone, G.T. [1963] 2001. Mathematical Logic and the Foundations of Mathematics. Mineola, NY: Dover Publications.Google Scholar
Marshall, Alfred. 1919. Industry and Trade. London: Macmillan and Co. Ltd.Google Scholar
Mirowski, Philip. 1988. “The Sciences Were Never at War?” In Against Mechanism. Totowa, NJ: Rowman and Littlefield, pp. 31–44.Google Scholar
Mirowski, Philip. 1989. More Heat than Light. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Mirowski, Philip. 1991. “The When, the How and the Why of Mathematical Expression in the History of Economic Analysis.” Journal of Economic Perspectives 5 (1): 145–157.Google Scholar
Picard, Charles Emile. 1905. La science moderne et son état actuel. Paris: Flammarion.Google Scholar
Poincare, Henri. 1905. Science and Hypothesis. Authorized translation by George Bruce Halsted; special preface by Poincare; and introd. by Josiah Royce. New York: The Science Press.Google Scholar
Porter, Theodore M. 2001. “Economics and the History of Measurment.” In Klein, Judy L. and Morgan, Mary S., eds., The Age of Economic Measurement. Durham: Duke University Press, pp. 4–22.Google Scholar
Roos, Charles Frederick. 1934. Dynamic Economics. Bloomington, IN.: Principia.Google Scholar
Samuelson, Paul. 1965. “Economic Theory and Mathematics—An Appraisal.” In Collected Scientific Papers: Volume 2. Cambridge, MA: MIT Press, pp. 1751–1761.Google Scholar
Samuelson, Paul. 1998. “How Foundations Came to Be.” Journal of Economic Literature 36 (3): 1375–1386.Google Scholar
Thom, Rene. 1991. Predire n’est pas expliquer: Entretiens avec Emile Noel. Paris: Flammarion.Google Scholar
Turk, Michael. 2006. “The Fault Line of Axiomatization: Walras’ Linkage of Physics with Economics.” European Journal of the History of Economic Thought 13 (2): 195–212.CrossRefGoogle Scholar
Turk, Michael. 2010. “The Arrow of Time in Economics: From Robinson’s Critique to the New Historical Economics.” European Journal of the History of Economic Thought 17 (3): 471–492.Google Scholar
Volterra, Vito. 1901. “Sui tentative di applicazione della Mathematiche alle scienze biologiche e sociale.” Giornale degli economist serie 2a (23): 436–458.Google Scholar
Walras, Leon. 1860. “Paradoxes economiques.” Journal des Economistes: 373–391.Google Scholar
Walras, Leon. 1965. Correspondence of Leon Walras and Related Papers. Volume III. Edited by Jaffe, William. Amsterdam: North-Holland Publishing Company.Google Scholar
Weintraub, E. Roy. 2001. “Measurement and Changing Images of Mathematical Knowledge.” In Klein, Judy L. and Morgan, Mary S., eds., The Age of Economic Measurement. Durham: Duke University Press, pp. 303–312.Google Scholar
Weintraub, E. Roy. 2002. How Economics Became a Mathematical Science. Durham: Duke University Press.Google Scholar