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\noindent{\bf Antoine Augustin COURNOT}\\
b. 28 August 1801 - d. 30 March 1877
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\noindent{\bf Summary.} Unacknowledged in his own times as founder of mathematical
economics, Cournot was both mathematician and philosopher. He publicised the
ideas of Bienaym\'e on the ``variability of chances", and subjected the
probability calculus to a perspicacious philosophical critique.
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Cournot was born at Gray, in the Franche-Comt\'e (France);
his father was a merchant descended from a long line
of farmers. Antoine successfully completed his secondary studies at the Jesuit
College of Gray between 1809 and 1816 with ease, thanks (as he said)
to his wide reading. Among the books which he read were the {\it
Entretiens sur la pluralit\'e des mondes} of Fontenelle, and his
{\it \'Eloges des Acad\'emiciens}, Laplace's (q.v.) {\it Exposition du
syst\`eme du monde}, the {\it Logique} (partly inspired by Pascal, (q.v.) of
Port-Royal,
the centre of the Jansenist movement in France;
and the Leibniz-Clarke correspondence). In his {\it Souvenirs} Cournot
(1913, p. 35)
noted that these were the books ``which had a
decisive influence on all [his] subsequent ideas and studies".
After four rather idle years during which he studied law out of interest,
he was admitted to the Royal College of Besan\c{c}on,
in the special mathematics class, and later entered the \'Ecole
Normale in 1821 for a year, until the government closed it down on
6 September 1822. He then worked towards a licenciate degree in
Science at the Sorbonne, attending the lectures of Lacroix and
Hachette, and becoming friendly with Dirichlet. Thanks to Hachette,
he had the opportunity of meeting Amp\`ere and Laplace. He attended the
Academy of Sciences, where he heard Poisson (q.v.), Biot, Arago,
Gay-Lussac, Poinsot, Legendre (q.v.), Fourier and Cauchy deliver their
papers. He was awarded his licentiate degrees in Science in 1823,
and Law in 1827.
Unemployed after the closure of the \'Ecole Normale, he
became the tutor to Marshal Gouvion-Saint-Cyr's son, and
contributed to the writing of the Marshal's memoirs, published in
1831. A contributor to F\'erussac's {\it Bulletin des sciences
math\'ematiques}, he published numerous short notes in it from
1821 to 1831, as well as several articles from 1826 to 1831. In
February 1829, he defended his doctoral thesis {\it M\'emoire sur le
mouvement d'un corps rigide soutenu par un plan fixe}, as well as a
complementary thesis {\it De la figure des corps c\'elestes}.
In 1834, Cournot translated and edited Sir John Herschel's
{\it Treatise on
Astronomy} to which he made an {\it Addition} (Addendum), namely ``Sur la
distribution des
orbites com\'etaires" which was his first important contribution to the
calculus of probabilities and statistics. He also translated Kater
and Lardner's {\it Elements of Mechanics}, appending a chapter on the
measurement of forces in the work of machines. On Poisson's (q.v.)
recommendation, he was appointed Professor of Analysis and Mechanics
in the Faculty of Sciences at Lyons. He served there for only one
year, then being appointed Rector of the Grenoble Academy, with a
Chair in the Faculty of Sciences, which he occupied until 1838.
It was in 1838 that he published his {\it Recherches sur les
principes math\'ematiques de la th\'eorie des richesses}({\it \OE uvres
Compl\`etes}, Volume VIII). In this work, he applied the theory of
undetermined functions to economics. He thus made a fundamental
contribution to mathematical economics, and introduced a concept of
equilibrium, later rediscovered by the mathematician J.F. Nash, who was
unaware
of Cournot's earlier work, in the context of game theory. Nash was awarded
a Nobel Prize in
Economics. Although this work of Cournot marks a
fundamental advance in the history of political economy and
mathematical game theory, it had no success during Cournot's
lifetime, in contrast to his work on Herschel's
{\it Treatise on Astonomy} ({\it
Souvenirs}, p. 156). Cournot's work in economics was continued in
his {\it Principes de la th\'eorie des richesses} ({\it \OE uvres
Compl\`etes}, Volume IX), published in 1863, and his {\it Revue
sommaire des doctrines \'economiques} ({\it \OE uvres Compl\`etes},
Volume X), of 1877.
Also in 1838, Cournot published his second study in
probability and statistics, entitled ``M\'emoire sur les
applications du calcul des chances \`a la statistique judiciare"
in Liouville's {\it
Journal de Math\'ematiques pures et appliqu\'ees}.
Appointed Inspector of Education, 1836 to 1838, he
was named Inspector General in 1838, a post which he held until
1854, when he became Rector of the Dijon Academy until his
retirement in 1862. Meanwhile, he presided over the jury for the
Agr\'egation (higher doctorate) in mathematics from 1839 to 1843,
succeeding Poisson in this position. He retired to Paris, where he
died some 15 years later.
Leaving aside the works in economics
previously mentioned, as well as his pedagogical efforts, developed
in his {\it Des Institutions d'instruction publique en France},
({\it \OE uvres Compl\`etes}, Volume VII), of 1864, Cournot's opus
appears to have evolved, in broad terms, in two distinct
periods. Effectively, his {\it De l'origine et des
limites de la correspondance entre l'algebre et la g\'eom\'etrie}
(\OE uvres Compl\`etes, Volume VI-2), of 1847, which contains the first
proof of the
Criticality Theorem of his friend Bienaym\'e (q.v.) in the theory of
branching processes,
concludes the series
of his strictly mathematical publications, and leads on
to his great philosophical works published between 1851 and 1875.
It is likely that it was not only the eye disease from which he
suffered after 1843 which caused this reorientation, but also
Cournot's conviction that he was more creative in philosophy than
in mathematics. He writes in his {\it Souvenirs}, p. 154,
regarding Poisson's evaluation of his early papers: ``he found some
philosophical depth in them, in which opinion I truly think that he
was not wrong; furthermore, he predicted that I would make great
advances in the field of pure mathematical speculation, which was
(as I always thought and never hesitated to say) one of his errors".
But the chronological sequence of his two periods masks the profound unity of
Cournot's thinking; Cournot the mathematician never lost sight of the
philosophical implications of his research, while Cournot the
philosopher found in mathematics the special expression of the
power of pure reason. The guiding principle of his epistemology
is that science and philosophy must necessarily intermingle, but
without becoming confused, a principle which Euler had already
enunciated.
The probabilistic and statistical work of Cournot consists mainly
of the two studies of 1834 and 1838, previously mentioned, and the
{\it Exposition de la th\'eorie des chances et des probabilit\'es}
of 1843 ({\it \OE uvres Compl\`etes}, Volume I), copiously annotated by
Bernard Bru.
The {\it Addition} of 1834 gave him the chance to denounce the
common prejudice, according to which it was necessary in any
statistical analysis `` always to collect a large number of elements,
although this need is often not established by either theory or
experiment". It also allowed him to illustrate the fact that, just
as both descriptive and theoretical astronomy serve as a model for
other sciences, so also ``the statistics of stars ... must one day
serve as a model for all other disciplines".
The publication of the ``M\'emoire sur les applications du calcul
des chances \`a la statistique judiciaire" followed shortly after
Poisson's {\it Recherches sur la probabilit\'e des jugements} of
1837. In it he took up in a critical manner the analyses
involved, which, like Poisson, he compared with the {\it
Comptes g\'en\'eraux de l'administration de la justice criminelle},
published from 1825 on, without relying on the Bayesian methods of
Condorcet (q.v.) and Laplace. His main objective was to
introduce a conceptual clarification in this area, and show that
since legislators and geometers (that is: mathematicians)
must share the responsibility of
taking an overview of
legal organization from a general standpoint, rather than
through particular cases, both need statistics to validate
their analyses.
The contents of the two previous studies were integrated into
Cournot's major probabilistic and statistical work, the {\it
Exposition de la th\'eorie des chances} of 1843. This attempted to
present more than the rules and methods of the calculus of probabilities
and of statistics. As B. Bru ({\it Exposition}, Introduction,
p.IX), points out, it offers the first global exposition of the
theory of ``the variability of chances" of which the elements are to be
found dispersed among the works of his ``excellent friend"
Bienaym\'e.\footnote{For the relationship between Cournot and
Bienaym\'e see Heyde and Seneta (1977) and Bru, Bru, and Bienaym\'e
(1997). } But Cournot most especially
proposed to submit the principles and methods of the calculus of
probabilities and statistics to a critical analysis, aiming to
establish precisely their significance and effective scope.
Such an analysis
demands making a distinction between
mathematical and philosophical probabilities,
and arriving at an understanding of the
double meaning of mathematical probability, which is ``sometimes
connected to a certain measurement of our knowledge and sometimes
to a measurement of the possibility of events independent of the
knowledge we may have" (p. 4). In statistics too, Cournot insisted on
taking into account
the extent to which statistical analysis was subject to a
``preliminary judgement" which depended on philosophical
probabilities (p. 132), which is the crux of the continuing
frequentist/Bayesian dichotomy
in our time. As against the perception, still current in our day,
of statistics as simply accumulation of data and its description,
Cournot held that it
constituted a genuine science, whose aim was to obtain ``numerical
results relatively independent of the anomalies of chance, and
which indicate the existence of regular causes whose action is
combined with that of random causes"(p. 123). Cournot argued
that the question was ``far less to accumulate numbers whose
quantity lead to stable means, than to disentangle the
chance-affected influences which are mixed together" (p. 138), the discipline
of statistics
thus
offering a special instrument for bringing to light the
mechanisms of reality.
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\begin{thebibliography}{3}
\bibitem{1} Bru, B., Bru, M.-F. and Bienaym\'e, O. (1997). La statistique
critiqu\'ee par le
calcul des probabilit\'es: Deux manuscrits in\'edits d'Iren\'ee Jules
Bienaym\'e. {\it Revue
d'histoire des math\'ematiques,} {\bf 3}, 137-239.
\bibitem{2} Cournot, A.A. (1973-1989). {\it \OE uvres Compl\`etes}. 10 Volumes.
Vrin, Paris.
\bibitem{3} Cournot, A.A. (1913). {\it Souvenirs}. E.-P. Bottinelli (Ed.).
Hachette, Paris.
\bibitem{4} Faure, F. (1905). Les id\'ees de Cournot sur la statistique.
{\it Revue de M\'etaphysique et de Morale}, May, No.3, 395-411.
\bibitem{5} Heyde, C.C. and Seneta, E. (1977). {\it I.J. Bienaym\'e: Statistical
Theory
Anticipated.} Springer, New York.
\bibitem{6} Lexis, W. (1891). Cournot, Anton Augustin. In:
{\it Handw\"orterbuch der Staatswissenschaften} ( J. Conrad, L.
Elster, W. Lexis, Edg. Loening dir.), {\bf 2}, 889b-890a. Gustav Fischer, Jena.
\bibitem{7} Martin, Th. (1995). Probabiliti\'es et philosophie des math\'ematiques
chez Cournot. {\it Revue d'histoire des math\'ematiques},
{\bf 1}, 111-138.
\bibitem{8} Martin, Th. (1996). {\it Probabilit\'es et critique philosophique selon
Cournot}. Vrin, Paris.
\bibitem{9} Martin, Th. (1998). {\it Bibliographie cournotienne.} Annales
litt\'eraires de
l'Universit\'e de Franche-Comt\'e, Besan\c con.\\
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\hfill{Th. Martin}
\end{thebibliography}
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