Mathematics, Economics and Philosophy
Cournot was a mathematician, an economist and a philosopher. In the preface to his 1838 Recherches he writes that he intends to apply “the forms and symbols of mathematical analysis” to the theory of wealth (1838 [1980]: 3).
He is led to use the theory of continuous functions and of infinitesimal calculus, of which he gave an elementary exposition three years later (1841). It is, however, less easy to understand whether his economic analyses benefited from his reflection on probabilities, history and philosophy of science.In Theorie des chances et des probabilites (1843) Cournot stresses that the word probability has two meanings, being either the measure of our ignorance or the measure of the possibility of things. However, when he applies his theory to aleatory markets and insurance, this point is not stressed. What characterizes his approach is his rejection of Bernoulli’s solution of the Saint Petersburg paradox. While admitting that, for an individual, the importance of a sum of money depends on his wealth, he does not think that it is possible to measure utility and to establish a functional relationship between the utility of a sum of money and this wealth. He analyses a random market without referring to the notion of moral expectation.
In L’enchainement des idees fondamentales dans les sciences et dans l,histoire (1861), he deals with economic optimism and maintains that the idea that the greatest general good necessarily results from conflicting private interests is not susceptible of a logical proof. If the motto Laissez faire, Laissez passer must triumph in the end, it is not because of a theoretical proof in its favour, but because only artificial and arbitrary rules are proposed against it.
The 1838 Recherches are devoted to the mathematical principles of the theory of wealth. In the 1863 Principes Cournot came back to his former approach but referred also to his Esssai sur le fondement des connaissances (1851) and to the analysis he made there of the Platonic opposition between science and opinion.
From this point of view, political economy is in an ambiguous position. Cournot (1863 [1981]: 326) states “that it does not admit and will never completely admit the regular, systematic and always progressive construction, which belong to the sciences... and never completely rely on unshakable and universally accepted bases”. First, while some propositions of the theory of wealth could be rigorously proved, their meanings depend on considerations drawn from “social economics” and this last field is not based on science but on opinion. As an example, he contrasts the scientific definition of wealth as the sum of the values of the goods, to the meaning the word well-being has in social economics. The value of income does not measure men’s well-being.Secondly, the abstractions to which economists must resort to simplify questions are not shared by all economists and could sometimes appear artificial and arbitrary. Depending on the facts they judge essential or of secondary importance, economists formulate hypotheses and reach different conclusions even if they all reason correctly. Cournot does not abandon his 1838 ambition, but he feels it necessary to stress its dangers: “The mathematical apparatus... leads us unfortunately to think that one confers to these hypotheses a value that they effectively have in the interpretation of natural phenomena, but that they cannot have to the same degree in the interpretation of social phenomena” (1863 [1981]: 329-30).