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The Young Paul Samuelson: Mathematics as a Language, the Operational Attitude, and Systems in Equilibrium

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Paul Samuelson

Part of the book series: Remaking Economics: Eminent Post-War Economists ((EPWE))

Abstract

In his Foundations of Economic Analysis, which was an extension of his dissertation defended in 1940 at Harvard University, the young Paul Samuelson argued that he was providing economics with new scientific foundations. In these texts, believing that “Mathematics is a Language,” Samuelson connected mathematics and economics while adopting an operational attitude and treating the individual and aggregate levels of the economy as systems in stable equilibrium. His work resonated with the work of preeminent Harvard figures of the 1930s, particularly the physicist Percy Bridgman’s operationalism and the physiologist Lawrence Henderson’s ideas about systems in equilibrium. However, the connection between Samuelson and these figures still remains opaque. In this chapter, it is noted that Samuelson wrote his dissertation and Foundations under the significant influence of his professor of mathematical economics at Harvard, Edwin Bidwell Wilson, who defined mathematics as a language. I argue that Wilson acted as a mediator between his Harvard colleagues and Samuelson.

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Notes

  1. 1.

    For the first volume of a detailed and comprehensive intellectual biography of Samuelson, see Backhouse (2017).

  2. 2.

    Huntington was reacting to foundational debates in mathematics and science as these debates were developing in the USA around 1910.

  3. 3.

    See Papers of Edwin Bidwell Wilson (hereafter PEBW), Harvard University Archives (HUA), HUG4878.214, Box 3, Folder Miscellaneous Papers, Chapter I. General Introduction (unpublished and undated).

  4. 4.

    On Wilson’s ideas about too much or too little mathematics, see Wilson (1928b). More generally, for a full account of Wilson’s definition of mathematics as a language, see Carvajalino (2018a).

  5. 5.

    Wilson to Hoernlé, 4 March 1920, PEBW, HUA, HUG4878.203, Box 2, Folder 1917–1920 H.

  6. 6.

    On Bridgman’s operational attitude, see Isaac (2012), Hands (2004), and Walter (1990) as well as Hands in this volume.

  7. 7.

    Wilson’s and Bridgman’s ideas about science significantly reflected the ideas of American pragmatism. During the 1920s, Wilson was asked to write the biographical memoir of Charles Sanders Peirce, one of the most important American pragmatists. Wilson never finished the memoir. However, he read some of Peirce’s work and eventually engaged with some aspects of it. Wilson was particularly impressed by Peirce’s ideas on statistical inference (Wilson 1923a, b, 1926a, b, 1927a, b).

  8. 8.

    Wilson to Bumstead, 18 December 1915, PEBW, HUA, HUG4878.203, Box 1, Folder 1914–1916 B; underlining in original.

  9. 9.

    Wilson to Cannon, 8 May 1923, PEBW, HUA, HUG4878.203, Box 4, Folder C, 2).

  10. 10.

    See Leonard (2016) and Rutherford (2011).

  11. 11.

    Wilson to Henderson, 25 January 1932, PEBW, HUA, Box 19, Folder H.

  12. 12.

    See Isaac (2012), Cot (2011) and Heyl (1968).

  13. 13.

    A non-comprehensive listing includes Samuelson (1937a, b, 1938a, b, c, d, e, 1939a, b, c, d, e, 1940), Schumpeter et al. (1939), and Nixon and Samuelson (1940).

  14. 14.

    Wilson’s influence on Samuelson’s dissertation was not only relevant from the perspective of the operational attitude. Wilson was also significantly influential at the theoretical level. In his courses, Wilson had defined equilibrium in consumer theory precisely with time-independent inequalities of discrete magnitudes, which he called the Gibbs conditions. He had also mentioned the Le Châtelier’s Principle and had explained that the continuous and the discrete could be interconnected by a one-to-one correspondence, as suggested in Samuelson’s use of the Correspondence Principle.

  15. 15.

    Samuelson to Wilson, 25 January 1939, Paul A. Samuelson Papers, David M. Rubenstein Rare Book & Manuscript Library, Duke University, Box 77.

References

  • Backhouse, R.E. (2014) “Paul A. Samuelson’s Move to MIT,” History of Political Economy, 46: 60–77.

    Article  Google Scholar 

  • Backhouse, R.E. (2017) Founder of Modern Economics: Paul A. Samuelson, Volume 1: Becoming Samuelson, 1915–1948. New York, Oxford University Press.

    Google Scholar 

  • Bridgman, P. (1927) The Logic of Modern Physics. New York, Macmillan.

    Google Scholar 

  • Cannon, W. (1943) “Biographical Memoir of Lawrence Joseph Henderson 1878–1942,” National Academy of Sciences of the United States, 23: 31–58.

    Google Scholar 

  • Carvajalino, J. (2018a) “Edwin Bidwell Wilson and Mathematics as a Language,” Isis, 109: 494–514.

    Article  Google Scholar 

  • Carvajalino, J. (2018b) “Edwin B. Wilson and the Rise of Mathematical Economics in America, 1920–1940,” History of Political Economy, 50: 229–259.

    Article  Google Scholar 

  • Carvajalino, J. (2018c) “Samuelson’s Operationally Meaningful Theorems: Reflections of E.B. Wilson’s Methodological Attitude,” Journal of Economic Methodology, 25: 143–159.

    Article  Google Scholar 

  • Carvajalino, J. (2019) “Edwin B. Wilson, More Than a Catalytic Influence for Paul Samuelson’s Foundations of Economic Analysis,” Journal of the History of Economic Thought, 41: 1–25.

    Article  Google Scholar 

  • Cot, A. (2011) “A 1930s North American Creative Community: The Harvard ‘Pareto Circle’,” History of Political Economy, 43: 131–159.

    Article  Google Scholar 

  • Dill, D. (1977) “L.J. Henderson, His Transition from Physical Chemist to Physiologist; His Qualities as a Man,” The Physiologist, 20: 1–15.

    Google Scholar 

  • Fenster, D.D. and K. Parshall (1994) “A Profile of the American Mathematical Research Community: 1891–1906,” in E. Knobloch and D. Rowe (eds.) The History of Modern Mathematics: Images, Ideas, and Communities. Boston, Academic Press: vol. 3, 179–227.

    Google Scholar 

  • Ferry, R.M. (1942) “Lawrence Joseph Henderson: 1878–1942,” Science, New Series, 95: 316–318.

    Article  Google Scholar 

  • Hands, D.W. (2004) “On Operationalisms and Economics,” Journal of Economic Issues, 38: 953–969.

    Article  Google Scholar 

  • Henderson, L. (1913) The Fitness of the Environment: An Inquiry into the Biological Significance of the Properties of Matter. New York, Macmillan.

    Google Scholar 

  • Henderson, L. (1917) The Order of Nature: An Essay. Cambridge, MA, Harvard University Press.

    Google Scholar 

  • Heyl, B.S. (1968) “The Harvard ‘Pareto Circle’,” Journal of the History of the Behavioral Sciences, 4: 316–334.

    Article  Google Scholar 

  • Hilbert, D. (1899) Grundlagen Der Geometrie. Leipzig, Teubner.

    Google Scholar 

  • Hunsaker, J. and S. Mac Lane (1973) “Edwin Bidwell Wilson, 1879–1964, A Biographical Memoir,” National Academy of Sciences (US), 43: 283–320.

    Google Scholar 

  • Huntington, E. (1904) “Sets of Independent Postulates for the Algebra of Logic,” Transactions of the American Mathematical Society, 5: 288–309.

    Article  Google Scholar 

  • Huntington, E. (1911) “The Fundamental Propositions of Algebra,” in J. Young (ed.) Monographs on Topics of Modern Mathematics. New York, Longmans, Green and Co.: 151–207.

    Google Scholar 

  • Isaac, J. (2012) Working Knowledge: Making the Human Sciences from Parsons to Kuhn. Cambridge, MA, Harvard University Press.

    Google Scholar 

  • Leonard, T. (2016) Illiberal Reformers: Race, Eugenics, and American Economics in the Progressive Era. Princeton and Oxford, Princeton University Press.

    Google Scholar 

  • Mayer, J. (1968) “Lawrence J. Henderson,” Journal of Nutrition, 94: 1–5.

    Article  Google Scholar 

  • Nixon, R.A. and P.A. Samuelson (1940) “Estimates of Unemployment in the United States,” Review of Economics and Statistics, 22: 101–111.

    Article  Google Scholar 

  • Parascandola, J. (1971) “Organismic and Holistic Concepts in the Thought of L.J. Henderson,” Journal of the History of Biology, 4: 63–113.

    Article  Google Scholar 

  • Parascandola, J. (1992) “L.J. Henderson and the Mutual Dependency of Variables: From Physical Chemistry to Pareto,” in C. Elliott and M. Rossiter (eds.) Science at Harvard University: Historical Perspectives. London and Toronto, Associated University Presses: 146–190.

    Google Scholar 

  • Parshall, K. and D. Rowe (1994) The Emergence of the American Mathematical Research Community, 1876–1900: J.J. Sylvester, Felix Klein, and E.H. Moore. Rhode Island, American Mathematical Society.

    Google Scholar 

  • Russell, B. (1901) Essai Sur Les Fondements de La Géométrie. Translated by A. Cadenat. Paris, Gauthier-Villars.

    Google Scholar 

  • Russell, B. (1903) The Principles of Mathematics, Volume 1. Cambridge, Cambridge University Press.

    Google Scholar 

  • Russett, C.E. (1966) The Concept of Equilibrium in American Social Thought. New Haven, CT, Yale University Press.

    Google Scholar 

  • Rutherford, M. (2011) The Institutionalist Movement in American Economics, 1918–1947: Science and Social Control. Cambridge, Cambridge University Press.

    Google Scholar 

  • Samuelson, P.A. (1937a) “A Note on Measurement of Utility,” Review of Economic Studies, 4: 155–161.

    Article  Google Scholar 

  • Samuelson, P.A. (1937b) “Some Aspects of the Pure Theory of Capital,” Quarterly Journal of Economics, 51: 469–496.

    Article  Google Scholar 

  • Samuelson, P.A. (1938a) “A Note on the Pure Theory of Consumer’s Behaviour,” Economica, New Series, 5: 61–71.

    Article  Google Scholar 

  • Samuelson, P.A. (1938b) “Welfare Economics and International Trade,” American Economic Review, 28: 261–266.

    Google Scholar 

  • Samuelson, P.A. (1938c) “The Empirical Implications of Utility Analysis,” Econometrica, 6: 344–356.

    Article  Google Scholar 

  • Samuelson, P.A. (1938d) “The Numerical Representation of Ordered Classifications and the Concept of Utility,” Review of Economic Studies, 6: 65–70.

    Article  Google Scholar 

  • Samuelson, P.A. (1938e) “Cost Theory and the Theory of International Trade: Reply by Mr. Samuelson,” American Economic Review, 28: 746–747.

    Google Scholar 

  • Samuelson, P.A. (1939a) “The End of Marginal Utility: A Note on Dr. Bernardelli’s Article,” Economica, 6: 86–87.

    Article  Google Scholar 

  • Samuelson, P.A. (1939b) “The Rate of Interest Under Ideal Conditions,” Quarterly Journal of Economics, 53: 286–297.

    Article  Google Scholar 

  • Samuelson, P.A. (1939c) “Interactions Between the Multiplier Analysis and the Principle of Acceleration,” Review of Economics and Statistics, 21: 75–78.

    Article  Google Scholar 

  • Samuelson, P.A. (1939d) “The Gains from International Trade,” Canadian Journal of Economics and Political Science, 5: 195–205.

    Article  Google Scholar 

  • Samuelson, P.A. (1939e) “A Synthesis of the Principle of Acceleration and the Multiplier,” Journal of Political Economy, 47: 786–797.

    Article  Google Scholar 

  • Samuelson, P.A. (1940) “The Theory of Pump-Priming Reexamined,” American Economic Review, 30: 492–506.

    Google Scholar 

  • Samuelson, P.A. (1941) Foundations of Analytical Economics: The Observational Significance of Economic Theory. PhD dissertation, Harvard University.

    Google Scholar 

  • Samuelson, P.A. (1947) Foundations of Economic Analysis. Cambridge, MA, Harvard University Press.

    Google Scholar 

  • Samuelson, P.A. (1947) [1983] Foundations of Economic Analysis. Enlarged edition. Cambridge, MA and London, England, Harvard University Press.

    Google Scholar 

  • Schumpeter, J.A., I. Fisher, J. Marschak and P.A. Samuelson (1939) “The Pure Theory of Production,” American Economic Review, 29: 118–120.

    Google Scholar 

  • Walter, M. (1990) Science and Cultural Crisis: An Intellectual Biography of Percy Williams Bridgman (1882–1961). Stanford, CA, Stanford University Press.

    Google Scholar 

  • Weintraub, E.R. (1991) Stabilizing Dynamics: Constructing Economic Knowledge. Cambridge, Cambridge University Press.

    Google Scholar 

  • Wilson, E.B. (1903a) “Review: Émile Borel, Leçons Sur Les Fonctions Méromorphes,” Bulletin of the American Mathematical Society, 9: 506–507.

    Google Scholar 

  • Wilson, E.B. (1903b) “The So-Called Foundations of Geometry,” Archiv Der Mathematik Und Physik, 6: 104–122.

    Google Scholar 

  • Wilson, E.B. (1904a) “The Foundations of Mathematics,” Bulletin of the American Mathematical Society, 11: 74–93.

    Google Scholar 

  • Wilson, E.B. (1904b) “The Theory of Waves,” Bulletin of the American Mathematical Society, 10: 305–317.

    Google Scholar 

  • Wilson, E.B. (1906) “The Foundations of Science,” Bulletin of the American Mathematical Society, 12: 187–193.

    Google Scholar 

  • Wilson, E.B. (1909) “Economics,” Bulletin of the American Mathematical Society, 15: 169–186.

    Google Scholar 

  • Wilson, E.B. (1911) “Mathematical Physics for Engineers,” Bulletin of the American Mathematical Society, 17: 350–361.

    Article  Google Scholar 

  • Wilson, E.B. (1912a) “The Fourth Dimension as a Text,” Science Conspectus, 2: 104–107.

    Google Scholar 

  • Wilson, E.B. (1912b) “Mathematical Economics,” Bulletin of the American Mathematical Society, 18: 462–474.

    Google Scholar 

  • Wilson, E.B. (1913) “Let Us Have Calculus Early,” Bulletin of the American Mathematical Society, 20: 30–36.

    Article  Google Scholar 

  • Wilson, E.B. (1915) “Some Books on Calculus,” Bulletin of the American Mathematical Society, 21: 471–476.

    Article  Google Scholar 

  • Wilson, E.B. (1918) “Insidious Scientific Control,” Science, New Series, 48: 491–493.

    Article  Google Scholar 

  • Wilson, E.B. (1923a) “First and Second Laws of Error,” Journal of the American Statistical Association, 18: 841–851.

    Article  Google Scholar 

  • Wilson, E.B. (1923b) “The Statistical Significance of Experimental Data,” Science, 58: 93–100.

    Article  Google Scholar 

  • Wilson, E.B. (1926a) “Empiricism and Rationalism,” Science, 64: 47–57.

    Article  Google Scholar 

  • Wilson, E.B. (1926b) “Statistical Inference,” Science, 63: 289–296.

    Article  Google Scholar 

  • Wilson, E.B. (1927a) “Probable Inference, the Law of Succession, and Statistical Inference,” Journal of the American Statistical Association, 22: 209–212.

    Article  Google Scholar 

  • Wilson, E.B. (1927b) “What Is Statistics?” Science, 65: 581–587.

    Article  Google Scholar 

  • Wilson, E.B. (1928a) “Review of The Abilities of Man, Their Nature and Measurement, by C. Spearman,” Science, 67: 244–248.

    Google Scholar 

  • Wilson, E.B. (1928b) “Too Little Mathematics—And Too Much,” Science, 67: 52–59.

    Article  Google Scholar 

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Authors and Affiliations

  1. University Paris VIII, Vincennes-Saint-Denis, Saint-Denis, France

    Juan Carvajalino

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  1. Juan Carvajalino
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Correspondence to Juan Carvajalino .

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  1. London, UK

    Robert A. Cord

  2. Center for Economics and the Environment, Lindenwood University, St. Charles, MO, USA

    Richard G. Anderson

  3. Department of Economics, University of Kansas, Lawrence, KS, USA

    William A. Barnett

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Carvajalino, J. (2019). The Young Paul Samuelson: Mathematics as a Language, the Operational Attitude, and Systems in Equilibrium. In: Cord, R., Anderson, R., Barnett, W. (eds) Paul Samuelson. Remaking Economics: Eminent Post-War Economists. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-56812-0_4

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