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Abstract
In the 1870 s and 1880 s, the scientist, logician, and pragmatist philosopher Charles S. Peirce possessed an advanced knowledge of mathematical economics, having mastered and criticised Cournot as early as 1871. In 1884 he engaged in a multi-round debate with the editors of The Nation over the economics of trade liberalisation in the case of a proposed trade treaty with Spain concerning import tariffs on Cuban and Puerto Rican sugar. While the mathematical underpinings of Peirce’s intervention in the debate are not explicit, they are evident in light of Peirce’s unpublished writing on Cournot. The debate is reconstructed and related carefully both to Peirce’s understanding of mathematical economics and to his philosophy of science. Peirce’s intervention is one of the earliest intricate applications of mathematical economics to public policy.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 We thank two anonymous referees for helpful comments on an earlier draft.
2 Following standard conventions among Peirce scholars, references to Peirce’s Collected Papers (1931–1958) are generally indicated as “CP volume number.paragraph number” (e.g., “CP 6.289” = Collected Papers volume 6, paragraph 289). Some references are to larger divisions (e.g., chapters) and these are indicated explicitly (e.g., “CP 1, ch. 4.”) Similarly, some references to the Collected Papers are to material from editorial apparatus that is not divided into numbered paragraphs, and these are indicated by volume and page number (e.g., “CP 8, p. 283”). References to the Writings of Peirce (1982–2010) are given as “WP volume number.page number (e.g., “WP 5.26” = Writings volume 5, page 26).
3 Ketner and Putnam (Citation1992) provide a capsule summary of some of the key facts of Peirce’s life; and Brent (Citation1998) offers a full-scale biography.
4 Wible and Hoover (Citation2015) offers a detailed account of Peirce’s engagement with Cournot.
5 A comparison of the roughly contemporaneous works represented in Darnell’s (Citation1991) six edited volumes of early mathematical economics provides good evidence of the cutting-edge quality of Peirce’s “Economy of Research.” We are currently writing a book on Peirce’s engagement with economics. One chapter of that book will consider Peirce’s paper on the economy of research in detail, while a companion paper to this one addresses his analysis of Ricardian inference (Hoover and Wible Citation2017).
6 Peirce was familiar with the term “mathematical induction,” but rejected it as involving a confusion, since it is a form of deductive, and not inductive, reasoning. He most often calls it Fermatian inference, in honor of the French mathematician Pierre de Fermat, whom he credits with inventing it. He typically refers to the analogue for uncountably infinite numbers as the primipostnumeral syllogism. Peirce was familiar with Gregor Cantor’s proof of the existence of transfinite cardinal numbers, and the adjective “primipostnumeral” is his own coinage for the first such uncountably infinite number. He gives strong hints that he regards Ricardian inference as a synonym. See Hoover and Wible (Citation2017) for a detailed discussion.
7 Parts of the remainder of this section are drawn verbatim from Hoover and Wible (Citation2017, section 4).
8 Weighing into contemporary debates among political economists over Historismus versus a priori methods (and anticipating debates between Institutionalists and neoclassical economists), Peirce goes on: the Analytical Method “is reprobated by the whole Hegelian army, who think it ought to be replaced by the ‘Historic Method,’ which studies complex problems in all their complexity, but which cannot boast any distinguished successes” (CP 1.64; cf. Keynes Citation1917, 314–327; Robbins Citation1935, 79–83, Citation1998, Lectures 25 and 26; Schumpeter Citation1954, ch. 4, part 2).
9 Morgan (Citation2012, ch. 2, esp. sections 1–4) offer an interpretation of Ricardo as a modeler avant la lettre.
10 Peirce does use the term “model” in the sense of a physical representation and, importantly connects models to diagrams, which he regards as central to mathematical reasoning: “The word diagram is used here in the peculiar sense of a concrete, but possibly changing mental image of such a thing as it represents. A drawing or model may be employed to aid the imagination; but the essential thing to be performed is the act of imagining” [Peirce Citation1976, 219, fn. 1; emphasis added].
11 On the history of models in economics, see Morgan (Citation2012).
12 Peirce uses “retroduction,” “hypothesis,” and sometimes “presumption” as synonyms for “abduction.” Later Peirce (WP 8, ch. 49, esp. 290–291) provides a more extensive biographical account that explains Kepler’s reasoning process in greater detail.
13 Kent (Citation1987, p. 3) compares Peirce’s ability to reason with diagrams to Einstein’s thought experiments: “Einstein began using his thought experiments (Gedankenexperimente) at sixteen, and Peirce began training himself to think in diagrams when a young man, finding it a great advance over algebraic thinking….Both men traced their own creative initiatives to systematized diagrammatic thought.”
14 Peirce’s apparently idiosyncratic spelling follows the German, rather than the Latin, spelling of Kepler’s name, as it appears in his own in German letters. Kepler was apparently indifferent to the spelling variation in his contemporary published works (WP 8, p. 452).
15 Wible and Hoover (Citation2015) provide a detailed exposition of the content of these letters and manuscripts; it would be beyond our purpose to repeat them here.
16 Cournot is generally credited with being the first to draw supply and demand curves, although not to name them (Cournot Citation1838, 47 and 91; see also Blaug Citation1997, 189, 283, 301–306; and Wible and Hoover Citation2015). Humphrey (Citation1992, Citation2010) provides a rich history of the development of supply and demand analysis.
17 See Willis (Citation1903) and United States Tariff Commission (Citation1919) for further discussion of the treaty in its wider context.
18 Politically, “liberal” in nineteenth century America referred to adherents to the line of thought that can be identified with advocates of both personal liberty, going back, for example, to John Locke in seventeenth century England and with laissez faire political economy, going back to Adam Smith. “Liberal” in today’s American politics more typically refers to the social democratic and “progressive” views that focus on minority rights and distributive equity. As the meaning of “liberal” changed, so did the political orientations of both the Democratic Party and The Nation, so that they are can be consistently labeled as liberal, despite the change in the nature of liberalism.
19 The Writings of Charles S. Peirce (WP 5.144–148) reprint Peirce’s exchange with the editors of The Nation, beginning with his first reply, but they do not reprint the original article that prompted the first reply.
20 Converted to 2019 dollars using the consumer price index (CPI), this is the equivalent of $2.45 billion. Sugar was a relatively more important part of consumption bundles in 1884. An equivalent share of per capita GDP would amount $27.8 billion.
21 A referee queried the lack of any attention to general-equilibrium effects of a tariff reduction. In fact, the issues were not framed in either the exchange between Peirce and the editor of The Nation in a way that even implicitly raised questions of general-equilibrium effects. In the wider discussion at the time, the focus was almost exclusively on questions of government revenue, the price of sugar to consumers, and, to a smaller degree than most tariff issues, to protection of American producers. Cournot (Citation1838, chs. XI and XII) does address the issue of “social income,” which he defines essentially in the way that modern national accounting defines gross national income, as the sum of all wages, profits, and rents (p. 128). But he also notes that taking “the entire economic system into consideration . . . would surpass the powers of mathematical analysis and of our practical methods of calculation . . .” (p. 127).
22 Following Ricardo, Peirce recognizes two distinct, but logically similar margins. Here, he refers to what modern economists refer to as the extensive margin – that is, to the increasingly smaller output that arises from bringing intrinsically and increasingly worse land into production. Elsewhere, he also refers to the intensive margin – that is, to the increasingly smaller additions to output that result from the increasing use of inputs (labor, fertilizer, etc.). (See CP 4.115; Ricardo Citation1821[1951], pp. 70–72).
23 The editor also answers Peirce’s re-export argument by pointing out that tariff relief applies only to sugar actually grown in Puerto Rico or Cuba. He acknowledges that Cubans could export the full amount of their own domestic consumption, replacing it by imported sugar for their own use; but, since their domestic market is small, that would add little to their duty-free export capacity. He also acknowledges, but minimizes, the possibility of cheating on re-export.
24 Cournot’s (Citation1838), Chapter X. Of the Communication of Markets, is not referred to directly in Peirce’s extant writings on Cournot, but would be relevant to his Second Model.
25 Elsewhere, Peirce gives an analysis of the effect of a change of import duties on the price of consumer goods: “we must understand by the duty, not merely what goes to the government, but what has to be paid in consequence to brokers, bankers, and increased expenses of all kinds caused by the change in the law” (CP 4.115); cf. Cournot (Citation1838), 117.
26 Peirce goes on to name the newspaper in mind as the New York Post. But the reference is almost certainly to The Nation, which the Post had purchased in 1881 and which served as the Post’s weekly literary supplement. He packages his disagreement in fulsome praise of the newspaper in general. It is unclear whether Peirce is sincere, satirical, or venal: he earned essential income from writing for the Nation, as well as other periodicals.