Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T21:06:25.600Z Has data issue: false hasContentIssue false
  • English
  • Français

MATHEMATICS IS THE LANTERN: VITO VOLTERRA, LÉON WALRAS, AND IRVING FISHER ON THE MATHEMATIZATION OF ECONOMICS

Published online by Cambridge University Press:  18 December 2018

Sonya Scott
Sonya Scott*
Affiliation:
York University.
Get access Rights & Permissions [Opens in a new window]

Abstract

The interdisciplinary project to unite the field of mathematics with the social and biological sciences marks the work of Vito Volterra, one of Italy’s most prominent mathematicians of the twentieth century. This paper explores the connections between Volterra’s 1901 inaugural address at the Accademia dei Lincei in Rome and the work of two of his contemporaries, Léon Walras and Irving Fisher. All three thinkers were ardent advocates of the mathematical turn in economic thinking. This paper argues, however, that it is the previously unexplored relationship between Volterra and Fisher that sheds the most light on the way in which mechanical physics contributed to the project of mathematization within economics more generally. Furthermore, it explores the way in which mathematical inquiry postulated a new and coherent abstraction of the economy, at the same time that it gave epistemological authority to the economist.

Type
Articles
Information
Journal of the History of Economic Thought , Volume 40 , Issue 4 , December 2018 , pp. 513 - 537
Copyright
Copyright © The History of Economics Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank Roberto Baranzini, Director of the Centre Walras-Pareto at the University of Lausanne, for access to archival materials. I also extend my gratitude to the Bibliothèque cantonale et universitaire Lausanne, and to the Archives of the Accademia dei Lincei Rome. I am indebted to both Daniele Besomi and Mark Peacock for their generous feedback and insight. Finally I would like to thank the anonymous peer reviewers for their careful reading and commentary.

References

REFERENCES

Baranzini, Roberto. 2005. Léon Walras e la moneta senza velo (1860–1886): contributo analitico ed epistemologico alla ricostruzione del modello monetario walrasiano. Milan: UTET Libreria.Google Scholar
Barber, William. 2005. “Irving Fisher of Yale.” The American Journal of Economics and Sociology 64 (1): 43–55.CrossRefGoogle Scholar
Barone, Enrico. 1894. “A Proposito delle Indagini del Fisher.” Giornale degli Economisti 8 (5): 413–439.Google Scholar
Berryman, Alan. 1992. “The Origins and Evolution of Predator–Prey Theory.” Ecology 73 (5): 1500–1535.CrossRefGoogle Scholar
Boumans, Marcel. 2001. “Fisher’s Instrumental Approach to Index Numbers.” History of Political Economy 33 (Annual Supplement): 313–344.CrossRefGoogle Scholar
Boumans, Marcel. 2005. How Economists Model the World into Numbers. New York: Routledge.Google Scholar
Brainard, William, and Scarf, Herbert. 2005. “How to Compute Equilibrium Prices in 1891.” The American Journal of Economics and Sociology 64 (1): 57–83.CrossRefGoogle Scholar
Breslau, Daniel. 2003. “Economics Invents the Economy: Mathematics, Statistics and Models in the Work of Irving Fisher and Wesley Mitchell.” Theory and Society 32 (3): 379–411.CrossRefGoogle Scholar
Colander, David, Holt, Richard, and Rosser, Barkley. 2004. “The Changing Face of Mainstream Economics.” Review of Political Economy 16: 485–499.CrossRefGoogle Scholar
Cournot, Antoine Augustin. [1838] 1960. Researches in to the Mathematical Principles of the Theory of Wealth. Translated by Bacon, Nathaniel T.. New York: A. M. Kelley.Google Scholar
De Zan, Mauro, and Pizzarelli, Chiara. 2013. “Il carteggio fra Giovanni Vailati e Vito Volterra.” Rivista di Storia dell’Università di Torino 2 (2): 61–132.Google Scholar
Faucci, Riccardo. 2014. A History of Italian Economic Thought. New York: Routledge.CrossRefGoogle Scholar
Fisher, Irving. 1898. “Cournot and Mathematical Economics.” The Quarterly Journal of Economics 12 (2): 119–138.CrossRefGoogle Scholar
Fisher, Irving. 1892. Mathematical Investigation in the Theory of Value and Prices. New Haven: Transactions of the Connecticut Academy of Arts and Sciences, IX.Google Scholar
Gasca, Ana Millán. 2002. “Mathematical Theories versus Biological Facts: A Debate on Mathematical Population Dynamics in the 30s.” In Israel, Giorgio and Gasca, Ana, eds., The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology. Boston: Birkhäuser, pp. 1–54.Google Scholar
Guerraggio, Angelo, and Paoloni, Giovanni. 2013. Vito Volterra. New York: Springer.CrossRefGoogle Scholar
Hodgson, Geoffrey M. 1993. “The Mecca of Alfred Marshall.” The Economic Journal 113 (407): 406–415.CrossRefGoogle Scholar
Hume, David. [1758] 1825. “Of Commerce.” Essays and Treatises on Several Subjects, etc . Edinburgh: Bell & Bradfute, and W. Blackwood.Google Scholar
Ingrao, Bruna, and Israel, Giorgio. 1990. The Invisible Hand: Economic Equilibrium in the History of Science. Cambridge, MA: MIT Press.Google Scholar
Israel, Giorgio. 1996. La mathématisation du réel. Essai sur la modélisation mathématique. Paris: Seuil.Google Scholar
Israel, Giorgio, and Gasca, Ana. 2002. The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology. Boston: Birkhauser Verlag.CrossRefGoogle Scholar
Israel, Giorgio, and Nurzia, Laura. 1989. “Fundamental Trends and Conflicts in Italian Mathematics between the Two World Wars.” Archives internationales d’histoire des sciences 39 (122): 111–143.Google Scholar
Jaffé, William. 1983. William Jaffé’s Essays on Walras. Edited by Walker, Donald. New York: Cambridge University Press.Google Scholar
Jevons, Stanley. [1871] 1970. The Theory of Political Economy. Baltimore: Penguin.Google Scholar
Johannisson, Karin. 1990. “Society in Numbers: The Debate over Quantification in 18th-Century Political Economy.” In Frangsmyr, Heilbron, ed., The Quantifying Spirit in the Eighteenth Century. Berkeley: University of California Press, pp. 343–362.Google Scholar
Kant, Immanuel. [1781] 1998. The Critique of Pure Reason. Translated by Guyer, Paul, edited by Wood, Allen. New York: Cambridge University Press.Google Scholar
Knuuttila, Tarja. 2011. “Modelling and Representing: An Artefactual Approach to Model-Based Representation.” Studies in History and Philosophy of Science 42: 262–271.CrossRefGoogle Scholar
Koopmans, Tjalling. 1957. Three Essays on the State of Economic Science. Toronto: McGraw-Hill.Google Scholar
Le Gall, Philippe. 2002. “Entre sciences de la nature et sciences humaines: l’économie, science des échanges interdisciplinaires.” Revue d’Histoire des Sciences Humaines 2: 3–11.CrossRefGoogle Scholar
Marshall, Alfred. [1890] 1969. Principles of Political Economy. New York: Augustus M. Kelley.Google Scholar
Mirowski, Phillip. 1984. “Physics and the Marginalist Revolution.” Cambridge Journal of Economics 8: 361–379.CrossRefGoogle Scholar
Mirowski, Phillip. 1989. More Heat than Light. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Mitchell, Wesley Clair. 1927. Business Cycles: The Problem and Its Setting. New York: National Bureau of Economic Research.Google Scholar
Morgan, Mary S. 2012. The World in the Model: How Economists Work and Think. New York: Cambridge University Press.CrossRefGoogle Scholar
Morgan, Mary, and Knuuttila, Tarja. 2012. “Models and Modelling in Economics.” Handbook of the Philosophy of Science: Philosophy of Economics . Amsterdam: North Holland.Google Scholar
Mouck, Tom. 1995. “Irving Fisher and the Mechanistic Character of Twentieth Century Accounting Thought.” The Accounting Historian’s Journal 22 (2): 43–83.CrossRefGoogle Scholar
Pareto, Vilfredo. 1906. “Applicazione della matematica all’economia politica.” Giornale degli Economisti 33 (2): 424–453.Google Scholar
Porter, Theodore M. 2001. Economics and the History of Measurement. In Klein, Judy L. and Morgan, Mary S., eds., The Age of Economic Measurement. Durham: Duke University Press, pp. 4–22.Google Scholar
Sandmo, Agnar. 2007. “Retrospectives: Léon Walras and the Nobel Peace Prize.” Journal of Economic Perspectives 21 (4): 217–228.CrossRefGoogle Scholar
Schabas, Margaret. 2014. A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics. Princeton: Princeton University Press.Google Scholar
Schumpeter, Joseph. [1954] 1994. History of Economic Analysis. New York: Oxford University Press.Google Scholar
Scott, Sonya M. 2013. Architectures of Economic Subjectivity: The Philosophical Foundations of the Subject in the History of Economic Thought . New York: Routledge.Google Scholar
Shackle, George L. S. 1972. Epistemics and Economics. London: Cambridge University Press.Google Scholar
Tobin, James. 1985. “Neoclassical Theory in America: J. B. Clark and Fisher.” The American Economic Review 75 (6): 28–38.Google Scholar
Tobin, James. 2005. “Iriving Fisher (1867–1947).” The American Journal of Economics and Sociology 64 (1): 19–42.CrossRefGoogle Scholar
Turk, Michael H. 2012. “The Mathematical Turn in Economics: Walras, the French Mathematicians and the Road Not Taken.” Journal of the History of Economic Thoguht 34 (2): 149–167.CrossRefGoogle Scholar
Volterra, Vito. 1901. “Sui tentative di applicazione delle matematiche alle scienze biologiche e sociale. Discorso letto il 4 novembre 1901 alla inaugurazione dell’anno scolastico nella R. Università di Roma.” Giornale degli Economisti 23 (2): 436–458.Google Scholar
Volterra, Vito. 1906. “L’Economia Matematica: Ed il nuovo manuale del prof. Pareto.” Giornale degli Economisti 32 (17): 296–301.Google Scholar
Walker, Donald. 2006. Walrasian Economics. New York: Cambridge University Press.CrossRefGoogle Scholar
Walras, Léon. [1874] 1952. Elements of Pure Economics. Translated by Jaffé, William. Illinois: Richard D. Irwin.Google Scholar
Walras, Léon. [1909] 1987. “Économique et Mécanique.” In Dockès, Pierreet al., eds., Auguste et Léon Walras Oeuvres Économiques Complètes: VII Léon Walras, Mélanges D’Économie Politique et Sociale. Paris: Economica, pp. 330–341.Google Scholar
Walsh, Vivian, and Gram, Harvey. 1980. Classical and Neoclassical Theories of General Equilibrium: Historical Origins and Mathematical Structure. New York: Oxford University Press.Google Scholar
Weintraub, Roy. 2002. How Economics Became a Mathematical Science. Durham: Duke University Press.CrossRefGoogle Scholar
Weisberg, Michael. 2007. “Who Is a Modeler?” British Journal of the Philosophy of Science 58: 207–233.CrossRefGoogle Scholar
Whittaker, Edmund T. 1941. “Vito Volterra. 1860–1940.” Obituary Notices of Fellows of the Royal Society: 691–729.CrossRefGoogle Scholar