Abstract
This paper sheds new light on Samuelson’s early methodology as presented in his Foundations of Economic Analysis (1947) by reflecting on the similarity between his mathematical economics and Edwin B. Wilson’s mathematics. Wilson was Samuelson’s professor of advanced mathematical and statistical economics; he was also a protégé of Josiah Willard Gibbs. Wilson defined mathematics as a language that consisted of three interconnected aspects: postulational, axiomatic, and operational. In his Foundations, in a Wilsonian style, Samuelson wrote in the opening page, ‘Mathematics is a Language’ and claimed that he offered operationally meaningful theorems. In this paper, it is argued that these maxims embodied Wilson’s approach, which framed Samuelson’s mathematical and statistical thinking around 1940 and which led him to present his work as being mathematically, theoretically, and empirically well founded. Wilson’s and Percy Bridgman’s operational methodologies are also compared and Wilson is presented as a mediator between Bridgman and Samuelson.
Acknowledgments
I am thankful to Gonçalo Fonseca, Wade Hands, Jean-Sébastien Lanfant, and Michel Zouboulakis, as well as two anonymous referees for their comments on previous versions of this paper. The usual caveat applies.
Notes
1. Not extensively, see (Blaug, Citation1980; Boland, Citation1989; Caldwell, Citation1982; Cohen, Citation1995; Hands, Citation2001; Hausman, Citation1992; Mongin, Citation2000a; Ross, Citation2014; Wong, Citation1973, 1978).
6. E. Wilson to J. Whittemore, 23 April 1924 (PEBW, HUG4878.214 Box 7, folder U-V).
7. On Wilson and sciences, see (Carvajalino Citation2016), chapter one.
8. Wilson pleaded for an intermediate kind of mathematics, namely not only concerned with pure mathematical consistency and acting as intermediary between mathematics and subject matters. This intermediate mathematics was more accessible for students, he thought. For Wilson’s pleas, see (Wilson, Citation1903b, Citation1911b, Citation1913, Citation1915); for the kind of mathematics that he regarded as intermediate, see (Wilson, Citation1911a).
10. E. Wilson, unpublished and undated paper (Papers of Edwin Bidwell Wilson (PEBW), Harvard University Archives (HUA), HUG4878.214, Box 3, Folder: Miscellaneous Papers, Chapter I. General Introduction).
11. For Wilson, for example, the conservation of energy and continuity were only working hypotheses, namely temporary convenient conventions (Wilson, Citation1914).
14. E. Wilson to C. Snyder, 2 June 1934 (PEBW, HUA, HUG4878.203, Box 24).
19. E. Wilson, unpublished and undated paper (PEBW, HUA, HUG4878.214, Box 3, Folder Miscellaneous Papers, Chapter I. General Introduction, p. 1).
20. On Wilson and Spearman, see (Lovie & Lovie, Citation1995).
22. E. Wilson to A. Hoernlé, 4 March 1920 (PEBW, HUA, HUG4878.203, Box 2, Folder 1917–20 H).
24. E. Wilson to L. Henderson, June 4, 1930 (PEBW, HUA, HUG4878.203, Box 38, Folder E-K).
25. E. Wilson to J. B. Johnston (PEBW, HUA, HUG4878.203, Box 25, Folder I-J-K).
26. Wilson’s and Bridgman’s ideas about science were emblematic expressions of American pragmatism, a philosophy of practice. These pragmatists regarded science as a human practice and sought to establish a balance between American individualism and the promotion of genuinely American scientific communities. See (Hookway, Citation2013; Menand, Citation2002; Misak, Citation2016; Mullin, Citation2007).
27. See chapters 1–3 of Foundations.
28. Samuelson was probably reflecting on Wilson’s skepticism of classical statistics and econometrics. Wilson was particularly critical of Karl Pearson and Ronald Fisher’s mathematical statistics as well of Ragnar Frisch’s econometrics.
30. E. Wilson, Notes on Economics (PEBW, HUA, HUG4878.214, Box 1).
32. E. Wilson, Notes on Economics (PEBW, HUA, HUG4878.214, Box 1).
35. P. Samuelson to E. Wilson, 25 Jan. 1939 [1938] (Paul A. Samuelson Papers, David M. Rubenstein Rare Book & Manuscript Library at Duke University, Box 77).
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Funding
This work was supported by Fonds de Recherche du Québec-Société et Culture.
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