# Cournot, Antoine-Augustin

# Cournot, Antoine-Augustin

(*b*. Gray, France, 28 August 1801; *d*. Paris, France, 31 March 1877)

*applied mathematics, philosophy of science*.

Of Franche-Comté peasant stock, Cournot’s family had belonged for two generations to the *petite bourgeoisie* of Gray. In his *Souvenirs* he says very little about his parents but a great deal about his paternal uncle, a notary to whom he apparently owed his early education. Cournot was deeply impressed by the conflict that divided the society in which he lived into the adherents of the *ancien régime* and the supporters of new ideas, especially in the realm of religion. One of his uncles was a conformist priest, the other a faithful disciple of the Jesuits, having been educated by them.

Between 1809 and 1816 Cournot received his secondary education at the *collège* of Gray and showed a precocious interest in politics by attending the meetings of a small royalist club. He spent the next four years idling away his time, working “en amateur” in a lawyer’s office. Influenced by reading Laplace’s *Système du monde* and the Leibniz-Clarke correspondence, he became interested in mathematics and decided to enroll at the École Normale Supérieure in Paris. In preparation, he attended a course in special mathematics at the Collège Royal in Besançon (1820–1821) and was admitted to the École Normale after competitive examinations in August 1821. However, on 6 September 1822 the abbé Frayssinous, newly appointed grand master of the University of France, closed the École Normale. Cournot found himself without a school and with only a modest allowance for twenty months. He remained in Paris, using this free time—which he called the happiest of his life—to prepare at the Sorbonne for the *licence* in mathematics (1822–1823). His teachers at the Sorbonne were Lacroix, a disciple of Condorcet, and Hachette, a former colleague of Monge. A fellow student and friend was Dirichlet.

In October 1823, Cournot was hired by Marshal Gouvion-Saint-Cyr as tutor for his small son. Soon Cournot became his secretary and collaborator in the editing and publishing of his *Mémoires* Thus, for seven years, until the death of the marshal, Cournot had the opportunity to meet the many important persons around the marshal and to reflect on matters of history and politics. Nevertheless, Cournot was still interested in mathematics. He published eight papers in the baron de Férussac’s *Bulletin des sciences*, and in 1829 he defended his thesis for the doctorate in science, “Le mouvement d’un corps rigide soutenu par un plan fixe.” The papers attracted the attention of Poisson, who at that time headed the teaching of mathematics in France. When, in the summer of 1833, Cournot left the service of the Gouvion-Saint-Cyr family, Poisson immediately secured him a temporary position with the Academy of Paris. In October 1834 the Faculty of Sciences in Lyons created a chair of analysis, and Poisson saw to it that Cournot was appointed to this post. In between, Cournot translated and adapted John Herschel’s *Treatise on Astronomy* and Kater and Lardner’s *A Treatise on Mechanics*, both published, with success, in 1834.

From then on, Cournot was a high official of the French university system. He taught in Lyons for a year. In October 1835 he accepted the post of rector at Grenoble, with a professorship in mathematics at the Faculty of Sciences. Subsequently he was appointed acting inspector general of public education. In September 1838, Cournot married and left Grenoble to become inspector general. In 1839 he was appointed chairman of the Jury d’Agrégation in mathematics, an office he held until 1853. He left the post of inspector general to become rector at Dijon in 1854, after the Fortoul reform, and served there until his retirement in 1862.

In the course of his long career as administrator, Cournot, who was extremely scrupulous in fulfilling his duties, was able to exert a strong influence on the teaching of mathematics in the secondary schools and published a work on the institution of public instruction in France (1864). At the same time he pursued a career as scientist and philosopher. While rector at Grenoble, he published *Recherches sur les prinipes mathématiques de la théorie des richesses* (1838). Between 1841 and 1875 he published all his mathematical and philosophical works.

Unassuming and shy, Cournot was considered an exemplary civil servant by his contemporaries. His religious opinions seem to have been very conservative. In politics he was an enthusiastic royalist in 1815, only to be disappointed by the restoration of the monarchy. In the presidential elections following the 1848 Revolution, he voted for Louis Eugène Cavaignac, a moderate republican. In 1851, sharply disapproving the organization of public instruction as directed by Louis Napoleon, he decided to become a candidate in the legislative elections in Haute-Saône; this election, however, was prevented by the coup d’état of 2 December.

Cournot’s background and his education made him a member of the provincial *petite bourgeoisie* of the *ancien régime*. But as a civil servant of the July monarchy and the Second Empire, he became integrated into the new bourgeoisie of the nineteenth century. Of certainly mediocre talents as far as pure mathematics was concerned, he left behind work on the philosophy of science, remarkably forceful and original for its period, that foreshadowed the application of mathematics to the sciences of mankind. Nobody could express better and more humorously Cournot’s importance than he himself when he reported Poisson’s appreciation of his first works: “He [Poisson] discovered in them a philosophical depth—and, I must honestly say, he was not altogether wrong. Furthermore, from them he predicted that I would go far in the field of pure mathematical speculation but (as I have always thought and have never hesitated to say) in this he was wrong” (*Souvenirs*, p. 154)

Cournot’s mathematical work amounts to very little: some papers on mechanics without much originality, the draft of his course on analysis, and an essay on the relationship between algebra and geometry. Thus, it is mainly the precise idea of a possible application of mathematics to as yet unexplored fields that constitutes his claim to fame. With the publication in 1838 of his *Recherches sur les principes mathématiques de la théorie des rishesses* he was a third of a century ahead of Walras and Jevons and must be considered the true founder of mathematical economics. By reducing the problem of price formation in a given market to a question of analysis, he was the first to formulate the data of the diagram of monopolistic competition, thus defining a type of solution that has remained famous as “Cournot’s point.” Since then, his arguments have of course been criticized and amended within a new perspective. Undoubtedly, he remains the first of the important pioneers in this field.

Cournot’s work on the “theory of chance occurrences” contains no mathematical innovation. Nevertheless, it is important in the history of the calculus of probability, since it examines in an original way the interpretation and foundations of this calculus and its applications. According to Cournot, occurrences in our world are always determined by a cause. But in the universe there are independent causal chains. If at a given point in time and space, two of these chains have a common link, this coincidence constitutes the fortuitous character of the event thus engendered. Consequently, there would be an objective chance occurrence that would nevertheless have a cause. This seeming paradox would be no reflection of our ignorance.

This objective chance occurrence is assigned a certain value in a case where it is possible to enumerate—for a given event—all the possible combinations of circumstances and all those in which the event occurs. This value is to be interpreted as a degree of “physical possibility.” However, one must distinguish between a physical possibility that differs from 0 (or 1)only by an infinitely small amount and a strict logical impossibility (or necessity).

On the other hand, Cournot also insisted on the necessary distinction between this physical possibility, or “objective probability,” and the “subjective probability” that depends on our ignorance and rests on the consideration of events that are deemed equiprobable^{1} since there is not sufficient cause to decide otherwise. Blaise Pascal, Fermat, Huygens, and Leibniz would have seen only this aspect of probability. Jakob I Bernoulli, despite his ambiguous vocabulary, would have been the first to deal with objective probabilities that Cournot was easily able to estimate on the basis of frequencies within a sufficiently large number of series of events.

To these two ideas of probability Cournot added a third that he defined as “philosophical probability.” This is the degree of rational, not measurable, belief that we accord a given scientific hypothesis. It “depends mainly upon the idea that we have of the simplicity of the laws of nature, of order, and of the rational succession of phenomena” (*Exposition de la théorie des chances*, p. 440; see also *Essai*, I, 98–99). Of course, Cournot neither solved nor even satisfactorily stated the problem of the logical foundation of the calculus of probability. But he had the distinction of having been the first to dissociate—in a radical way—various ideas that still were obscure, thus opening the way for deeper and more systematic research by more exact mathematicians. He also was able to show clearly the importance of the applications of the calculus of probability to the scientific description and explanation of human acts. He himself—following Condorcet and Poisson—attempted to interpret legal statistics (*Journal de Liouville*, **4** [1838], 257–334; see also *Exposition de la théorie des chances*, chs. 15, 16). But he also warned against “premature and abusive applications” that might discredit this ambitious project.

More than for his mathematical originality, Cournot is known for his views on scientific knowledge. He defined science as logically organized knowledge, comprising both a classification of the objects with which it deals and an ordered concatenation of the propositions it sets forth. It claims neither the eternal nor the absolute: “There can be nothing more inconsistent than the degree of generality of the data with which the sciences deal—data susceptible to the degree of order and the classification that constitute scientific perfection” (*Essai*, II, 189). Therefore, the fundamental characteristic of the scientific object must be defined differently. “What strikes us first of all, what we understand best, is the *form*,” Cournot wrote at the beginning of the *Traite de l’enchaînement des idées*, adding, “Scientifically we shall always know^{2} only the form and the order.” Thus, it was from this perspective that he interpreted scientific explanation and stressed the privilege of mathematics—the science of form par excellence. Even though establishing himself as forerunner of a completely modern structural concept of the scientific object, Cournot did not go so far as to propose a reduction of the process of knowledge to the application of logical rules. On the contrary, he insisted upon the domination of strictly formal and demonstrative logic by “another logic, much more fruitful, a logic which separates appearance from reality, a logic which connects specific observations and infers general laws from them, a logic which ranks truth and fact” (*Traité*, P. 6).

This discerning and inventive power orients and governs the individual steps of the strictly logical proof; it postulates an order in nature and its realization in the simplest ways^{3} This suggests the opposition Leibniz saw in the laws of logical necessity and the architectonic principles that make their application intelligible (see, e.g., Leibniz’ “Specimen dynamicum,” in his *Mathematische Schriften*, Gerhardt, ed., VI, 234–246) Cournot also declared himself, on several occasions, a great admirer of Leibniz. But to him the reason that governs the discovery of natural laws was not due to divine wisdom—he was always careful to separate religious beliefs (to which, incidentally, he adhered) from philosophical rationality. Reason, within scientific knowledge, denoted the ineluctable but always hazardous contribution of philosophical speculation. “Everywhere,” he assures us, “we must state this twofold fact, that the intervention of the philosophical idea is necessary as a guideline and to give science its dogmatic and regular form; it also must insure that the progress of the positive sciences is not hindered by the indecision of philosophical question” (*Essai*, II, 252). Thus philosophy, as research on the most “probable” hypotheses regarding the assumption of a maximum of order and a minimum of complexity, becomes an integral part of scientific practice. But if philosophical reason guides the organization of hypotheses, it is the role of logic, obviously, to exhibit consequences and of experience to provide the only evidence that can be decisive in their favor.^{4}

From this analysis one must conclude that science cannot be defined as a pure and simple determination of causes. For Cournot the word “cause” meant the generative antecedent of a phenomenon. He wanted science to add to the designation of causes the indication of reasons, i.e., the general traits of the type of order within which the causes act. And since the indication of reasons stems from philosophical speculation, it can only be probable—within a probability that itself is philosophical—that knowledge will advance to the extent that hypotheses are refined and corrected on the basis of experience.

In this sense, Cournot’s epistemology is a probabilism. And it is probabilism in another sense, too—since it insists upon the indissoluble connection between the “historic data” and the “theoretical data” in the sciences. Fortuitous facts, in the sense defined above, appear in our experience—by its very nature—and not through our ignorance of causes. These facts appear as knots of contingency within the tissue of theoretical explication and, according to Cournot, cannot be entirely removed from it.

The connection between science and history is defined more precisely by the classification of the sciences proposed in chapter 22 of the *Essai*. According to Cournot, the system of the sciences must show an order that his predecessors had vainly tried to reduce to one dimension. In order to describe this system, we need a double-entry table (Figure 1) that vertically approximates Comte’s system of division: mathématical sciences, physical and cosmological sciences, biological and natural sciences, noological and symbolic sciences, political and historical sciences. Horizontally there are three series: theoretical, cosmological, and technical. The technical series gives a special place and autonomous status to certain applied disciplines the importance and development of which “depend upon various peculiarities of the state of civilized nations and are not in proportion to the importance and philosophical standing of the speculative sciences to which they should be linked” (*Essai*, II, 266)

The distinction between the theoretical and the cosmological series corresponds to the separation of a historic and contingent element. This element will always be present in the sciences, even in the theoretical sciences (with the exception, perhaps, of mathematics), and will become more and more dominant as one passes from the physical sciences to the natural sciences (see *Traité*, p. 251). But if the very nature of the process of scientific knowledge demands that the philosophical element cannot be “anatomically” seperated, it allows for the establishment of sciences in which the historic element controls the contents and the method of knowing.

Another kind of separation appears in the system of the sciences that Cournot set forth and developed in his works following the *Essai*. This separation is the radical distinction between a realm of physical nature and a realm of life.

For Cournot, the scientific explanation of the phenomena of life requires a specific principle that, in the organism, must control the laws of physics and chemistry. As for man’s role among the living beings, it seems that Cournot linked it with the development of community life, for “the superiority of man’s instincts and the faculties directly derived from it… would not suffice to constitute a distinct realm within Nature, a realm in contrast with the other realms” (*Traité*, p. 365). On the other hand, he adds, “When I see a city of a million inhabitants… I understand very well that I am completely separated from the state of Nature…” (*ibid*., p. 366).

This separation from the state of nature is accomplished by man in the course of a development that causes him to cultivate successively the great organizational forms of civilized life: religion, art, history, philosophy, and science. Cournot was careful not to interpret such a development as a straight and continuous march, yet he did not fail to stress that only scientific knowledge could be the sign of great achievement and alone was truly capable of cumulative and indefinitely pursued progress.

## NOTES

1. Cournot’s definition of an objective probability as the quotient of the number of favorable cases divided by the number of possible cases also entails a hypothesis of equiprobability of these various cases (*Essai*, ch. 2). Cournot does not seem to have noticed this difficulty, which later concerned Keynes and F. P. Ramsey.

2. According to Cournot, order is a fundamental category of scientific thought that can be deduced neither from time nor from space, which it logically precedes. Moreover, it cannot be reduced to the notion of linear succession. Without proceeding to a formal analysis, Cournot very often showed that by “order” he meant any relationship that can be expressed by a multiple-entry table.

3. But Cournot rebelled against the reduction of the principle of order to a maxim postulating the stability of the laws of nature (*Essai*, I, 90).

4. Cournot was always very careful to distinguish between philosophy and science. The following text shows a very rare lucidity, considering when it was written:

In a century when the sciences have gained so much popularity through their applications, it would be a vain effort to try to pass off philosophy as science or as a science. The public, comparing progress and results, will not be fooled for long. And since philosophy is not—as some would have us believe—a science, one could be led to believe that philosophy is nothing at all, a conclusion fatal to true scientific progress and to the dignity of the human spirit [

Considerations, II, 222].

## BIBLIOGRAPHY

I Original Works. Cournot’s principes works are *Recherches sur les principes mathématiques de la théorie des**richesses* (Paris, 1838, 1938); *Traité éleémentaire de la théorie des fonctions et du calcul infinitésimal*, 2 vols. (Paris, 1841); *Exposition de la théorie des chances et des probabilitiés* (Paris, 1843); *De l’origine et des limites de la correspondance entre l’algèbre et la géométrie* (Paris, 1847); *Essai sur les fondements de la connaissance et sur les caractérs de la critique philosophique*, 2 vols. (Paris, 1861, 1911); *Traité de l’enchainement des idées fondamentales dans les sciences et dans l’histoire*, 2 vols. (Paris, 1861, 1912); *Considérations sur la marche des idées et des événements dans les temps modernes*, 2 vols. (Paris, 1872, 1934); *Matérialisme, vitalisme, rationalisme* (Paris, 1875); and *Souvenirs*, edited, with intro. and notes, by E. P. Bottinelli (Paris, 1913).

II. Secondary Literature. On Cournot or his work, see E. P. Bottinelli. A. *Cournot, métaphysicien de la connaissance* (Paris, 1913), which contains an exhaustive bibliography of Cournot’s work; E. Callot, *La philosophie biologique de Cournot* (Paris,1959); A. Darbon, *Le concept du hasard dans la philosophie de Cournot* (Paris, 1911); F. Mentré, *Cournot et la renaissance du probabilisme au XIX ^{e} siècle* (Paris, 1908); and G. Milhaud,

*Études sur Cournot*(Paris, 1927).

*Revue de métaphysique et de morale*(May 1905) is a special number devoted to Cournot; of special note are Henri Poincaré, “Cournot et les principes du calcul infinitésimal;” G. Milhaud, “Note sur la raison chez Cournot;” and H. L. Moore, “A.-A. Cournot,” a biographical study.

G. Granger

# Cournot, Antoine Augustin

# Cournot, Antoine Augustin

Antoine Augustin Cournot (1801–1877), French mathematician, economist, and philosopher, was born at Gray (Haute-Saône), the son of a notary. He came from a family of farmers who had lived in Franche-Comté since at least the middle of the sixteenth century. Until age 15, Cournot attended the *collége* at Gray; then, for the next four years, he read a great deal on his own, especially works by scientists and philosophers, such as Laplace and Leibniz. After preparing at Besançon, Cournot was admitted in 1821 to the scientific section of the École Normale Supérieure, in Paris. The school was closed by the reactionary regime the following year, but Cournot stayed in Paris and in 1823 received the licentiate in sciences. He attended sessions at the Académie des Sciences and associated with the principal scholars of the day; it was through one of them that he met Proudhon. In October 1823, Cournot entered the household of Marshal Gouvion Saint-Cyr in the double capacity of literary adviser to the marshal, who wanted to complete some unfinished manuscripts, and tutor to the marshal’s son.

Cournot spent ten years with the marshal, all the while continuing his scientific studies. In 1829 he received a doctorate in science, writing a main thesis in mechanics and a supplementary one in astronomy. He also studied law. A series of articles that he published on scientific questions attracted the attention of the great mathematician Poisson, who was then professor at the École Polytechnique and later at the University of Paris. Poisson was then in charge of the instruction in mathematics throughout France and arranged Cournot’s appointment to the chair of mathematical analysis in the faculty of sciences at Lyon. Cournot taught for only one year, however; subsequently, most of his life was spent in university administration, in which he was very successful. He became, successively, rector of the Academie de Grenoble in 1835, inspector general of the University of Dijon, and rector of the Academie de Dijon from 1854 to 1862. Cournot then accepted no further public positions and returned to Paris, where he died just as he was about to apply for membership in the Institut de France. Toward the end of his life he was nearly blind.

Cournot’s administrative work left him ample time for a great deal of scientific writing. Unfortunately, his books suffer from a lack of the stimulation that contact with an audience gives to teachers. Ten of his works appeared between 1838 and 1877. These books have three major themes: (1) algebra, infinitesimal analysis, and calculus of probabilities; (2) the theory of wealth; and (3) the philosophy of science, the philosophy of history, and even general philosophy. These themes were interdependent in Cournot’s work, and although the economic side will be stressed here, the profound unity of his thought must be remembered. Cournot started with mathematics, was then attracted to economics, and ended with a general interpretation of the world that was infused with his profound understanding of probabilities. It is the concept of probability that integrates the three parts of his work.

Cournot’s rather melancholic and solitary temperament considerably delayed the influence he was ultimately to have. Modest and self-effacing, he did nothing to make his books attractive. They tend to be austere, crowded with facts and proofs. Even the titles he chose reflect his modesty: *Researches, Essay*, and *Considerations.* It is not surprising, then, that he is less well known in the field of probability than Laplace and Poisson, less appreciated among economists than Bastiat, Say, or Proudhon (to mention only French economists), and less quoted in philosophy than Comte or Spencer. And yet Cournot, having the rare knowledge required to use the language of all of these authors, combined many of their qualities and made a quasi-prophetic synthesis of their ideas.

**Mathematics and probability theory.** Cournot’s mathematical works, econometrics aside, appeared between 1840 and 1850. In his *Exposition de la theorie des chances et des probabilités* (1843), he put forward a definition of statistics as that science which deals with collecting and coordinating numerous facts of every kind, in such a way as to obtain numerical relationships that are markedly independent of the anomalies of chance, and that manifest the existence of uniformly operating causes whose effects have been confounded, however, with other, accidental effects.

Cournot, living in the first half of the nineteenth century, stood at the crossroads of two ways of mathematical endeavor: the one originated with Pascal and Fermat and led to the work of Jacques Bernoulli, Gauss, Laplace, and Poisson on the doctrine of chances; the other, renouncing the mathematical study of chance and uncertainty, focused on the mathematics of rigorous determinations by algorithms that admit no margin of uncertainty— as if science were perfectly deterministic. This concept that the perfect is the determined was to play a major role in the development of the early science of economics, as one can see from the still current term “perfect competition.” Cournot fore-saw that science could not be intrinsically and definitively tied to such determinism. He believed that a science of margins and chances is not only viable but perhaps better suited to the needs of economics than a science of absolute, exact equilibria. Nonetheless, Cournot is often regarded as having introduced into economic theory the use of deterministic mathematics.

**Economics.** Cournot wrote three works in economics, in 1838, 1863, and 1877; thus, his career began and ended with writings on economics. When *Recherches sur les principes mathématiques de la théorie des richesses* (1838*a*) first appeared, it was such a fiasco that Cournot remained silent on the subject of economics for 25 years. He then wrote *Principes de la théorie des richesses* (1863), putting into “literary” language what he had previously said in the language of mathematics. Despite the concessions Cournot made in the form of presentation, the *Principes* was no better received than the *Recherches;* indeed, if Cournot had produced only his nonmathematical work, he would never have been recognized as anything but a minor figure.

Strictly speaking, to be sure, Cournot was not the first to have used mathematical language to express economic problems. There was Nicolas Canard, in France, whom Cournot did quote, but Canard did not have Cournot’s scope and erudition. Great erudition is needed to combine economics and mathematics, and if mathematical economics has had its setbacks, the reason is that it has not always been guided by such clear minds as Cournot’s.

Cournot’s great merit is that, without saying so explicitly, he was the first to construct a true theory of prices and markets. Chapter 4 of *Recherches*, entitled “Of the Law of Demand,” is the first model of its kind. Cournot was interested exclusively in the demand that is followed by an actual sale and that is, therefore, observable and measurable. He is recognized for having revealed the concept of function and for having made available to economists the immensely useful language of functional concepts. Sales are, in general, a decreasing function of price. This function is continuous, at least when the number of consumers is not limited. Moreover, the sales function is not purely abstract; it may be constructed on the basis of mean annually observed data. And since it is not merely an a priori function but an empirical, experimental one, Cournot may be considered to have made the initial step in developing econometrics.

In this econometric mode of analysis, a related idea is that of imperfection, hence of uncertainty and, in turn, of chance in measurement. Here again, Cournot’s knowledge of probabilities saved him from incorrectly associating mathematics with the idea of rigorous precision. He asserted that even if the object of numerical calculation “were unattainable, it would be nevertheless not improper to introduce the unknown law of demand into the analytical combinations, by means of an indeterminate symbol; for it is well known that one of the most important functions of analysis consists precisely in assigning determinate relations between quantities to which numerical values and even algebraic forms are absolutely unassignable” ([1838a] 1960, p. 48). We must give up trying to grasp what cannot be grasped rigorously. It is for this reason, perhaps, that we must reason mathematically “… by showing what determinate relations exist between unknown quantities, analysis reduces these unknown quantities to the smallest possible number, and guides the observer to the best observations for discovering their values. It reduces and coordinates statistical documents; and it diminishes the labour of statisticians …” (*ibid.*, pp. 48–49).

Cournot’s first construction is worked out in this spirit: it consists in drawing up, within suitable limits, tables of correspondence between the values of the demand, *D* = *f(p)*, and the price, *p.* In a second stage, the function *pf(p)*, the total value of the amount sold, is considered. This becomes the crux of the theory of markets. Long before Alfred Marshall, Cournot presented a theory of elasticity: depending on whether Δ*D*/Δp *D*/*p* or Δ*D*/Δ*p* > D/*p*, the price increase will make the product *pf(p)* larger or smaller. Hence commercial statistics should begin by dividing merchandise into two categories, depending on whether their current prices are lower or higher than the value making *pf(p)* a maximum. In this formulation, Cournot was truly a great innovator.

Instead of attacking the general price equilibrium directly, as Léon Walras and Vilfredo Pareto were later to do, Cournot proceeded by gradual steps. He started with monopoly, then considered competition limited to a few participants, and in the end took up the case of indefinite or unlimited competition, using the intercommunication of markets to complete his theory. This procedure has been criticized, for economists in the classical tradition follow the inverse procedure, starting with unlimited competition or, as they call it, perfect competition and ending up with monopoly. However, Cournot’s point of view has again been adopted in the modern theory of games and of the rational search for decisions. Although his theory of duopoly was criticized in 1883 by the mathematician Joseph Bertrand, the theory of bilateral monopoly was later to be erected on a similar base. The model with two parties was changed to a three-sided model (triopoly), and as the number of parties increased, the system was called oligopoly, pliopoly, and finally polypoly; the larger the number, the more closely the model approached that of classical competition. Today, makers of models no longer believe that there is an irreducible difference between models with many elements and those with few, but instead they relate the theory of markets to the general theory of economic interaction; hence their work is in the tradition of Cournot’s model, at first so poorly understood. There is still much to be learned from this 1838 model. Although Cournot has been rehabilitated, his contribution to economics has not been exhausted.

**Philosophy.** In Cournot’s philosophical works there emerge a philosophy of order and one of history. Cournot firmly maintained that, appearances to the contrary, chance does not imply disorder. By virtue of the theory of probabilities it is possible to see regularities: it is, as it were, the point of intersection of multiple independent causal series. And it permits the joining of the sciences with philosophy. The meaning of history, for all its incoherence, and the meaning of the future, for all its unpredictability, are profoundly related. To discover the course of ideas and events is the function of knowledge and the vocation of the human mind.

Cournot was a pioneer. He did nothing to court his contemporaries, and they, in turn, not only failed to appreciate him but ignored him. By a fitting reversal, his triumph came 80 years after his death. The most advanced of the econometric school recognize him as their ancestor. The theory of probabilities, whose full import Cournot realized, is a vital component of the structure of recent science. The problems that did not interest the men of his time are those that guide the building of tomorrow’s world; Cournot had anticipated the concern with predictions and decisions that now preoccupies economists.

Henri Guitton

[*For the historical context of Cournot’s work, see biographies of the*Bernoulli family; Gauss; Laplace; Poisson. *For discussion of the subsequent development of his ideas, see*Demand and supply; Oligopoly; Probability.]

## WORKS BY COURNOT

1829 *Mémoire sur le mouvement d’un corps rigide soutenu par un plan fixe.* Paris: Hachette.

(1838*a*) 1960 *Researches Into the Mathematical Principles of the Theory of Wealth.* New York: Kelley. → First published in French.

1838*b* Mémoire sur les applications du calcul des chances à la statistique judiciaire. *Journal de mathématiques pures et appliquées* 3:257–334. → This is an early example of work on what is now called “latent structure.”

(1841) 1857 *Traité élémentaire de la théorie des fonctions et du calcul infinitésimal.* 2d ed. Paris: Hachette.

1843 *Exposition de la théorie des chances et des probabilités.* Paris: Hachette.

1847 *De I’origine et des limites de la correspondance entre Valgebre et la géométric.* Paris: Hachette.

(1851) 1956 *An Essay on the Foundations of Our Knowledge.* New York: Liberal Arts Press. → First published in French.

(1861) 1911 *Traité de I’enchaînement des idées fondamentales dans les sciences et dans I’histoire.* New ed. Paris: Hachette.

1863 *Principes de la théorie des richesses.* Paris: Hachette.

(1872) 1934 *Considérations sur la marche des idées et des èvènements dans les temps modernes.* 2 vols. Paris: Boivin.

(1875) 1923 *Matérialisme, vitalisme, rationalisme: Études des données de la science en philosophie.* Paris: Hachette.

1877 *Revue sommaire des doctrines économiques.* Paris: Hachette.

1913 *Souvenirs (1760–1860*). With an introduction by E. P. Bottinelli. Paris: Hachette. → Published posthumously.

## SUPPLEMENTARY BIBLIOGRAPHY

[A. A. Cournot.] 1905 *Revue de métaphysique et de morale* 13:291–343. → The entire issue is devoted to Cournot.

Bertrand, J. 1883 [Book Reviews of] *Théories mathematiques de la richesse sociale*, par Léon Walras; *Recherches sur les principes mathematiques de la théorie de la richesse*, par Augustin Cournot. *Journal des savants* [1883]: 499–508.

Bompaire, FranÇois 1931 *Du principe de liberté économique dans I’oeuvre de Cournot et dans celle de I’école de Lausanne (Walras, Pareto*). Paris: Sirey.

Bottinelli, E. P. 1913 A. *Cournot: Métaphysicien de la connaissance.* Paris: Hachette.

Edgeworth, F. Y. (1894)1963 Antoine Augustin Cournot. Volume 1, pages 445–447 in Robert H. I. Palgrave, *Palgrave’s Dictionary of Political Economy.* New York: Kelley.

Liefmann-Kiel, Elisabeth 1937 Die wissenschaftliche Methode und das Gesamtwerk Cournots. *Archiv für mathematische Wirtschafts- und Sozialforschung* 3: 238–251.

Loiseau, Georges 1913 *Les doctrines économiques de Cournot.* Paris: Rousseau.

MentrÉ, FranÇois 1908 *Cournot et la renaissance du probabilisme au XIX ^{e} siécle.* Paris: Riviere.

MentrÉ, FranÇois 1927 *Pour qu’on Use Cournot.* Paris: Beauchesne.

Milhaud, Gaston S. (1902–1911) 1927 *Études sur Cournot.* Paris: Vrin.

Roy, RenÉ 1933 Cournot et I’école mathématique. *Econometrica* 1:13–22.

Second, J. 1911 *Cournot et la psychologie vitaliste.* Paris: Alcan.

# Antoine Augustin Cournot

# Antoine Augustin Cournot

The French mathematician, philosopher, and economist Antoine Augustin Cournot (1801-1877) was one of the founders of mathematical economics.

Antoine Augustin Cournot was born at Gray, Haute-Saône, on Aug. 28, 1801. In 1821 he entered a teachers' training college and in 1829 earned a doctoral degree in mathematics, with mechanics as his main thesis supplemented by astronomy. While studying at the college, he also served (1823-1833) as private secretary to Marshal de Gouvion Saint-Cyr. From 1834 he held successive positions as professor of analysis and mechanics on the science faculty of Lyons, rector of Grenoble Academy, chief examiner for undergraduate students, and, finally, rector of Dijon Academy (1854-1862). He died, nearly blind, in 1877.

Although Cournot was above all a mathematician and a member of the teaching profession, his numerous works show him also to have been a philosopher and economist. In the field of mathematics, in addition to his thesis on the movements of rigid bodies and celestial bodies, he devoted his efforts to two great problems: the theory of functions and the calculus of infinity (1841), and the theory of chance and probability (1843). These theories, above and beyond their mathematical significance, seemed to Cournot to hold an important place in man's general understanding of the world, but more specifically an understanding of the place of economics in man's life.

Cournot was a profound thinker: his advanced ideas on order and chance, enlightening both for science and mankind in general, are still prophetic. His economic concepts were broad in scope; his theories on monopolies and duopolies are still famous. In the field of economics he wrote few books or treatises. One book, however, has had an immense bearing on modern economic thought: *Recherches sur les principes mathématiques de la théorie des richesses* (*Researches on the Mathematical Principles of the Theory of Wealth*) was published in 1838 and reedited in 1938 with an introduction by Georges Lutfalla.

Unfortunately, this book met with no success during Cournot's lifetime because the application of the formulas and symbols of mathematics to economic analysis was considered audacious. In an attempt to improve the comprehensiveness of this work, Cournot rewrote it twice: In 1863 under the title *Principes de la théorie des richesses,* and in 1877 in *Revue sommaire des doctrines économiques.* These last two works are oversimplified and less informative versions of the original, since they were stripped of the mathematical language. Researches can, however, be thought of as the point of departure for modern economic analysis.

Having introduced the ideas of function and probability into economic analysis, Cournot derived the first formula for the rule of supply and demand as a function of price [*D* = *f*(*p*) ]. He made clear the fact that the practical uses of mathematics in economics do not necessarily involve strict numerical precision; economists must utilize the tools of mathematics only to establish probable limits and to express seemingly inaccessible facts in more absolute terms. Cournot's work is recognized today in the discipline called econometrics.

## Further Reading

S. W. Floss, *An Outline of the Philosophy of Antoine-Augustine Cournot* (1941), is a detailed, comprehensive study of Cournot's philosophic writings. Jacob Oser, *The Evolution of Economic Thought* (1963), includes a discussion of Cournot's theories. □

# Antoine Augustin Cournot

# Antoine Augustin Cournot

**1801-1877**

French mathematician who was among the first to apply mathematical principles and techniques to the study of economics. Cournot's early work in mechanics (a branch of physics) won him plaudits from Siméon Poisson, a prominent French mathematician of the time. With Poisson's recommendation, Cournot became a professor at Lyon and, later, in Grenoble, where he changed his interest to mathematical economics. Cournot's definition of the basic term "market" is still in use today, as are many of the tools he developed.

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