From Political Arithmetic to “Social Mathematic”

The main question is how to use the calculus of probability in a legitimate way. Calculation should be handled cautiously because it can be dangerous in the hands of “charlatans” (Condorcet 1994a: 337): in politics, it is so easy to impress people with the use of some numbers in order to influence their opinions and choices.

Some “ridiculous” applications of calculus to political questions have also been made, but “how many applications, just as ridiculous, have not been made in each part of physics?” (Condorcet 1785: clxxxix). In his 1771-72 correspondence with Piero Verri (Condorcet 1994a: 68-74), Condorcet had also criticized Verri’s attempt, with the aid of the mathematician Paolo Frisi, to formalize economic theory in the sixth edition of his Meditazioni sulla Economia Politica. He considered that this was a complex undertaking which could not be achieved with simple and careless solutions - the same erroneous method was still to be applied less than three decades later by two geometres, Nicolas-Franςois Canard in his Principes d’economie politique and above all Charles-Franςois de Bicquilley in his Theorie elementaire du commerce, both works presented at the Institut in 1799 and respectively published in 1801 and 1804 (Crepel 1998).

All these critiques notwithstanding, the use of calculus could no longer be dispensed with. Condorcet stressed that with its help it is possible to reason in a more precise way, to go further than “what reason alone can do”, and avoid the negative influence of vague impressions due to imperfect knowledge, prejudices, interests or passions. In this perspective, he had the ambitious project to develop “political arithmetic” into a systematic science - this field being defined as “the application of calculus to political sciences” in his 1784 eponymous entry for the Encyclopedie methodique. In his eyes, the first attempts by William Petty or John Graunt were almost insignificant.

Serious things only started with the works of Jan De Witt and, above all, Jakob Bernoulli (1654-1705) (Ars Conjectandi, posthumously published in 1714) and his nephew Nicolas I Bernoulli (1687-1759) (Dissertatio Inauguralis Mathematico-juridica, de Usu Artis Conjectandi in Jure, 1709). Probability theory was used there to solve economic and juridical questions of marine insurance, life annuities, calculation of interest or the problem of the “absent” (after how many years can an absent person be considered as dead with a sufficient probability?). However, the science was new, and all remained to be done. It is this same science that Condorcet, in an even more ambitious way than before, called “social mathematic” in his 1793 “Tableau general” (on the different editions of this important text and their shortcomings, see Crepel and Rieucau 2005):

I prefer the word mathematic, although now no longer used in the singular, to arithmetic, geometry or analysis because these terms refer to particular areas of mathematics... whereas we are concerned... with the applications in which all these methods can be used........................................................................... I prefer the

term social to moral or political because the sense of these words is less broad and less precise. (Condorcet 1994b: 93-4, original emphasis)

Condorcet died the following year and could not accomplish his programme. However, he had already some outstanding achievements to his credit.

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Source: Faccarello G., Kurz H.D.(eds.). Handbook on the History of Economic Analysis, Volume 1: Great Economists Since Petty and Boisguilbert. Cheltenham: Edward Elgar,2016. — 813 p.. 2016

From Political Arithmetic to “Social Mathematic”

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