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Antoine-Augustin Cournot,
(28 Aug 1801 - 31 Mar 1877)
French economist and mathematician.
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Science Quotes by Antoine-Augustin Cournot, (8 quotes)
Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.
— Antoine-Augustin Cournot,
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 4. From the original French, “Quiconque connaît la notation algébrique, lit d'un clin-d'œil dans une équation le résultat auquel on parvient péniblement par des règles de fausse position, dans l'arithmétique de Banque.”
Generalisations which are fruitful because they reveal in a single general principle the rationale of a great many particular truths, the connections and common origins of which had not previously been seen, are found in all the sciences, and particularly in mathematics. Such generalisations are the most important of all, and their discovery is the work of genius.
— Antoine-Augustin Cournot,
From Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique (1851), 28, as translated by Merritt H Moore in An Essay on the Foundations of Our Knowledge (1956), 24. From the original French: “Il y a dans toutes les sciences, et en mathématiques particulièrement, des généralisations fécondes, parce qu’elles nous montrent dans une vérité générale la raison d’une multitude de vérités particulières dont les liens et la commune origine n’étaient point aperçus. De telles généralisations sont des découvertes du génie, et les plus importantes de toutes.”
One always finds among men who are reputed to be reasonable some evidence of this tendency to inquire into the reason of things; of this desire to know not simply how things are, but why they are one way rather than another; and, consequently, of this awareness of a relation which is not gained through the senses, this notion of an abstract bond by virtue of which one thing is subordinated to another which determines and explains it.
— Antoine-Augustin Cournot,
From Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique (1851), 21, as translated by Merritt H Moore in An Essay on the Foundations of Our Knowledge (1956), 18. From the original French: “Toujours est-il que, chez tous les hommes réputés raisonnables, on retrouve, à certains degrés, cette tendance à s’enquérir de la raison des choses; ce désir de connaître, non pas seulement comment les choses sont, mais pourquoi elles sont de telle façon plutôt que d’une autre; et, partant, cette intelligence d’un rapport qui ne tombe pas sous les sens; cette notion d’un lien abstrait en vertu duquel une chose est subordonnée à une autre qui la détermine et qui l’explique.”
Scientists have been only too willing to show their haughty disregard for philosophy. It is also true that in going against the practices of one’s own time and in ignoring the fashion prevailing in the schools and in books, one runs the risk of being very poorly received. But, after all, each philosopher works in his own way, and each brings to his philosophical speculations the imprint of his other studies and the turn of mind which they have given him. The theologian, the jurist, the mathematician, the physicist, and the philologist can each be recognised at a glance by the way in which he wears the mantle of philosophy.
— Antoine-Augustin Cournot,
From Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique (1851), Preface, ii, as translated by Merritt H Moore in An Essay on the Foundations of Our Knowledge (1956), 3. From the original French: “Les savants à montrer volontiers leur peu d’estime pour la philosophie. Il est vrai qu’en allant ainsi contre les habitudes de son temps, et en s’écartant de la manière qui prévaut dans les écoles et dans les livres, on court grand risque d’être fort peu goûté: mais enfin, chacun philosophe à sa mode, et
porte dans la spéculation philosophique l’empreinte de ses autres études, le pli d’esprit que lui ont donné d’autres travaux. Le théologien, le légiste, le géomètre, le médecin, le philologue se laissent encore reconnaître à leur manière de draper le manteau du philosophe.” [Notice from the original French, “médecin”, was given by Moore as “physicist”, but a true translation would be “doctor” or “physician.” —Webmaster]
The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.
— Antoine-Augustin Cournot,
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 3-4. From the original French, “L’emploi des signes mathématiques est chose naturelle toutes les fois qu'il s'agit de discuter des relations entre des grandeurs ; et lors même qu’ils ne seraient pas rigoureusement nécessaires, s’ils peuvent faciliter l’exposition, la rendre plus concise, mettre sur la voie de développements plus étendus, prévenir les écarts d’une vague argumentation, il serait peu philosophique de les rebuter, parce qu'ils ne sont pas également familiers à tous les lecteurs et qu'on s'en est quelquefois servi à faux.”
The philosophy of mathematics still consists essentially in discerning the rational order of dependence of as many abstract truths as the sagacity of inventive minds has successfully and laboriously discovered, often by very roundabout means.
— Antoine-Augustin Cournot,
From Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique (1851), Vol. 2, 235, as translated by Merritt H Moore in An Essay on the Foundations of Our Knowledge (1956), 475. From the original French: “La philosophie des mathématiques consiste encore essentiellement à discerner l'ordre et la dépendance rationnelle de tant de vérités abstraites que la sagacité des inventeurs a successivement et laborieusement découvertes, souvent par des voies si détournées.”
Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.
— Antoine-Augustin Cournot,
In Antoine-Augustin Cournot and Nathaniel T. Bacon (trans.), Mathematical Theory of the Principles of Wealth (1897), Preface, 3.
True physics was founded the day when Galileo, rejecting fruitless speculations, conceived the idea … of defining the general form to give to experiments, by assigning for their immediate purpose the measure of all that can be measurable in natural phenomena.
— Antoine-Augustin Cournot,
From the original French, “La vraie physique a été fondée le jour où Galilée, rejetant des spéculations depuis si longtemps stériles, a conçu l’idée … de préciser la forme générale à donner aux expériences, en leur assignant pour objet immédiat la mesure de tout ce qui peut être mesurable dans les phénomènes naturels,” in De l’origine et des limites de la correspondance entre l’algèbre et la géométrie (1847), 375. English version by Webmaster using Google translate. This may be the basis of Thomas-Henri Martin describing Galileo’s experimental method , often translated as Measure what is measurable, and make measurable what is not so, from the original French in Galilée: Les droits de la science et la méthode des sciences physiques (1868), 289. Note that in both cases, the words were narrative by the authors, not quoting actual words by Galileo. What the authors wrote was in their own words, and should not be attributed to Galileo with quotation marks.
See also:
- 28 Aug - short biography, births, deaths and events on date of Cournot's birth.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
