Sraffa and Wittgenstein: Physicalism and constructivism

Abstract

After a brief review of facts and hypotheses concerning Piero Sraffa's intellectual exchanges with the philosopher Ludwig Wittgenstein and their content, a brief presentation of some of the basic ideas of Productions of Commodities by Means of Commodities is given, on the basis of which I argue, first, that Sraffa's ‘objectivism’ in economics is closely related to the ‘physicalism’ towards which Wittgenstein moved soon after his return to Cambridge and, secondly, that the mathematics of that book are in line with Wittgenstein's constructivist stance, as it is already found in his Tractatus Logico-Philosophicus.

Acknowledgments

A still unpublished ancestor to this paper was written jointly with Don Ross, for which we had occasion to thank Gilles Dostaler and Ken Hugues. I am solely responsible for the present paper. At the Naples conference ‘Piero Sraffa (1898–1983)’, Kevin Mulligan pointed out to me the connection with Wittgenstein's physicalism; for this, he is warmly thanked. I would like also to thank for their comments and help, Brian McGuinness, Heinz Kurz, Carlo Panico, Lionello Punzo, Neri Salvadori and Jonathan Smith, the Archivist at Trinity College, Cambridge. Heinz Kurz and Neri Salvadori were kind enough to grant me permission to quote from their unpublished work.

Notes

¹For biographical information about Sraffa, see Kaldor (1985) and Potier (1991); for Wittgenstein, see Monk (1990).

²The Sraffa Papers are deposited at the Wren Library, Trinity College, Cambridge. For information about their content, see Kurz (1998). Among these papers, one only finds ‘Notes on Wittgenstein's Blue Book, correspondence with G. H. von Wright and news cuttings of reviews of books by and on Wittgenstein’ (catalogue No. I21). There is also a ‘Fragment on Language’ (D3/12/70), the content of which bears affinity with ideas from Wittgenstein. As for Wittgenstein, almost all references to Sraffa in his Nachlaß are cited here. The only published letter, from Sraffa to Wittgenstein, dated 14 March 1936 (Wittgenstein, 1995, pp. 290–292), interesting as it may be, has also no philosophical content. Further letters from Wittgenstein to Sraffa were recently acquired by Trinity College. I have not been able to see the letters but was informed about their content by Jonathan Smith, archivist at Trinity, and Carlo Panico. The letters throw much light on the personal relations between Wittgenstein and Sraffa but they have almost no philosophical content. An undated letter contains reference to a discussion on what being in a rage looks like, where Sraffa clearly opposed Wittgenstein from a physicalist standpoint, in terms of contraction of facial muscles. This is further evidence in support of the claims in Section 2 below.

⁴For reasons unknown to me, the last three words were deleted for the printed version. According to Wolfgang Kienzler (1997, p. 53), the key word in this passage is ‘use’, which shows a ‘pragmatic tendency’ in the later Wittgenstein. For my part, I would point out that remarks such as this one open the door to the conception of mathematics as an ‘anthropological phenomenon’ that fascinated the later Wittgenstein (see, for example, Wittgenstein, 1978, VII, par. 33). However, the key point of this passage is that ‘the judge does not USE the statute book as a manual of anthropology’: the use of mathematical theorems is thus conceived by Wittgenstein as akin to jurisdiction.

³There are a few more remarks, for example Wittgenstein (1996, p. 26), which will not be examined here, for reasons stated below.

⁵On related points, see also Rhees (1996, p. 50), Jacquette (1998, p. 205).

⁶See, however, McGuinness (1986) or Kienzler (1997, pp. 51–55). As for McGuinness, see also the views reported in Sen (2004, p. 40), in accordance with the remarks in footnote 4 above.

⁷I shall discuss it in Marion (forthcoming b).

⁸I have discussed the influence of Ramsey on Wittgenstein in numerous places; see Marion (1995a; 1998, ch. 4; forthcoming a,).

⁹I can only allude to Roncaglia's multi-faceted discussion (Roncaglia, 1978, ch. 7). One interesting aspect is his claim that Sraffa may have imparted a strong dislike of ‘general’ theories that can decide any statement framed in the language of the theory. For criticisms of Roncaglia's discussion of the influence of Sraffa on Wittgenstein, see Arena (1982).

¹⁰In a conversation with Gilles Dostaler, Sraffa admitted that he could not have written his book had Marx not written Das Kapital and that he felt closer to Marx than to the ‘camoufleurs of capitalist reality’ (Dostaler, 1982, p. 103). Sraffa also said in that conversation that in his book he was describing the same phenomenon as Marx did, namely the class struggle between workers and capitalists; the latter describing it in terms of the appropriation by capitalists of the surplus value, while Sraffa thought that he described it algebraically, when the net product is divided between wages and profit, with the formula r = R(1–w), where r is the profit rate, w is the share of wages in the net product, and R is the Standard ratio or maximum rate of profit (Sraffa, 1960, p. 22). The distribution of the physical surplus is precisely what is at stake in the class struggle, according to Sraffa (Dostaler, 1982, p, 103).

¹¹Indeed, it is perhaps apposite to see in the perception of the evolution of economic theory away from problem-solving and towards a fully ‘theoretical’ science as a ‘bourgeois’ manoeuvre, the influence of Gramsci. Indeed, one could easily describe this manoeuvre in Gramscian terms as ‘hegemonic’. This is controversial: Nicholas Kaldor (1984, p. 149) has conjectured that Sraffa shifted his interest from money and banking to the classical theory of value as the result of Gramsci's influence, while Alessandro Roncaglia claims that there seems to be no such influence and that Sraffa's research and results should be judged independently from his political background (Roncaglia, 1983, p. 339; 2000, p. 11).

¹²I rely heavily in the following presentation on Kurz (2003), to which the reader is directed for details.

¹³One can trace the origin of this point of view in R. M. Goodwin's interpretation of tatônnement as an algorithm (Goodwin, 1951). But it could also serve to characterize the classical tradition, while it is somewhat lost in the neoclassical tradition, where the approach is of a more formalist nature. There is an obvious link between viewing economic theory as problem-solving and insisting on constructive content that has been expressed recently by Kumaraswamy Velupillai: ‘standard mathematical economics is replete with existential theorems without the slightest concern over their constructive or algorithmic status. […] It is also why economic theory has not been a pleasant playing field for those of us who would like to interpret the cardinal aim of the subject to be problem-solving’ (Velupillai, 2000, p. 181).

¹⁴To complicate matters, Neurath also spoke of the unified language as a purified version of everyday language, which he identified with the language of physics (Neurath, 1983, pp. 62, 91).

¹⁵I would like to thank Heinz Kurz for pointing this out to me.

¹⁶Lenin's critique of Mach was clearly off the mark. The motives for Gramsci's call for an ‘anti-Croce’ (Gramsci, 1971, p. 371) are complex and the attack on his idealism only part of it. For Gramsci's discussion of ‘subjectivism’ and ‘objectivism’, see Gramsci (1971, pp. 440–448). He did not simply reject ‘subjectivism’ but called for a synthesis (Gramsci, 1971, p. 402). In this, he is not followed by Sraffa.

¹⁷Hayek's first book, The Sensory Order, was an exercise in anti-‘objectivism’ (Hayek, 1952); see Nadeau (2001) for a discussion.

¹⁸See, for example, Boltzmann (1974, pp. 93f.). This is the ‘phenomenological thermodynamics’ mentioned by von Neumann (1945, p. 1).

¹⁹I thank Neri Salvadori for pointing out this note for me.

²⁰This opinion is, of course, not universally shared. For sceptical comments, see Schefold (2004, p. 317). Heinz Kurz and Neri Salvadori have also expressed their scepticism to me in private correspondence.

²¹For basic information on the various schools of constructivism in mathematics, the reader should consult Troelstra & van Dalen (1988) or Bridges & Richman (1987).

²²For a non-set-theoretical introduction to linear algebra that makes patent its constructive content, see Edwards (1995).

²³For an overview of the role of the Perron–Frobenius theorem, see Punzo & Velupillai (1984).

²⁴For example, in Schefold (1980) and Salvadori (1984).

²⁵Lionello Punzo (1989, 1991) has investigated the motives for von Neumann's use of topological methods in his dealings with Karl Menger's Mathematical Colloquium in Vienna and in the ‘formalist’ philosophy of Hilbert, by whom he was much influenced in the late 1920s.

²⁶Joan Robinson (1965, p. 34) famously wrote about Production of Commodities as a ‘prelude’ to a critique of the marginalist theory that ‘the function of pure logic is to liberate us from nonsense, not to tell us what we ought to believe’. This reading seems to me to be inaccurate for the very reason that Sraffa never conceived his model as disconnected from its interpretation.

²⁷Even though he did make some assumptions on returns; see Salvadori (1985).

²⁸There is a detailed analysis of that proof and the light it sheds on Wittgenstein's views on mathematics in Mancosu & Marion (2003).

²⁹I have offered my interpretation of Wittgenstein on mathematics in Marion (1998).

³⁰This fundamental feature of Wittgenstein's philosophy of mathematics is in line with Kronecker's ‘philosophy’; see Marion (1995b).

³¹One should note here that Maurice Dobb (1973, p. 8) quoted with approval par. 6.211 of the Tractatus in Theories of Value and Distribution since Adam Smith. This shows awareness and appreciation in Sraffa's entourage of Wittgenstein's standpoint on mathematics.

³²For a formal version of the algorithm, see Kurz & Salvadori (2001, pp. 272–273).

³³Little is known about A. G. D. Watson (1908–1982). He was a scholar and Fellow of King's and an Apostle. He is said to have introduced Wittgenstein to Turing. A mathematician, Watson published only one philosophy paper on ‘Mathematics and its Foundations’ (Watson, 1938), in which he expressed views akin to Wittgenstein's. According to Georg Henrik von Wright (private communication) Wittgenstein recommended reading that paper. During the war, Watson worked for the Admiralty, first on radio communication, then sonar. He finished his career working on oceanography. Watson was also known for his communist sympathies prior to the war; it was claimed after his death that he might have been a spy, linked to the famous Cambridge ring. It was only after the war that Watson travelled to Cambridge to help Sraffa.

³⁴See Brouwer (1975, Vol. 1) and Bridges & Richman (1987) for the differences between intuitionism and other constructivist schools.

³⁵On the rather complex philosophical relations between Brouwer and Wittgenstein, see Marion (2003).

³⁶Obviously, the issues are more complex. For a more detailed presentation, see Gandy (1982).

³⁷Some economists, e.g. Velupillai (2000), are now taking computability and polynomial-time computability seriously.

³⁸In Sraffa's background, I could only find such preoccupation in Enrico Barone's (1935) ‘The Ministry of Production in the Collectivist State’.