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Milhaud, Gaston (1858–1918)


Gaston Milhaud, a French philosopher, came to philosophy by way of mathematics, which he taught for nearly ten years in the lycées before becoming a professor of philosophy at the University of Montpellier. In 1909 he went to the University of Paris, where the chair of history of philosophy in its relationship to the sciences was created especially for him.

His courses on Antoine Augustin Cournot and Charles Renouvier were published (Études sur Cournot, Paris, 1927; La philosophie de Charles Renouvier, Paris, 1927). Under the influence of Paul Tannery, his works on the history of science were at first devoted to Greek science: Leçons sur les origines de la science grecque (Paris, 1893) and Les philosophes géomètres de la Grèce (Paris, 1900). Later they were extended to include modern science. Examples are Études sur la pensée scientifique chez les Grecs et chez les modernes (Paris, 1906); Nouvelles Études sur l'histoire de la pensée scientifique (Paris, 1911); and Descartes savant (published posthumously, Paris, 1923).

Milhaud was both a historian and an epistemologist. With Henri Poincaré, Pierre Duhem, and Édouard Le Roy he belongs to that group of French scholars who around 1900, following the path opened for them by Émile Boutroux, denounced scientific dogmatism, using as a basis the precise analysis of past and contemporary examples in history of science. They emphasized the role of spiritual initiative, and thus the element of contingency, in the construction of scientific theories. Milhaud himself generally avoided the dangerous words convention and commodité used by Le Roy and Poincaré. He spoke, rather, of free creations, of the activity of the mind, and of the spontaneity of reason (Le rationnel, Paris, 1898). In his thesis, Essai sur les conditions et les limites de la certitude logique (Paris, 1894), he maintained that certitude, which is founded on the principle of noncontradiction, is limited to the domain of pure mathematics. He believed that it was thus possible to establish a radical break between the realm of mathematical knowledge and the realm of knowledge of the real world.

However, almost immediately thereafter (2nd ed., 1897), he regretted having shown himself to be too much the logician: "I see today that even in the extreme example of absolute rigor dreamed of by the mathematician, the living and dynamic identity of thinking always takes precedence over the static immobility of the principle of identity." The fundamental concepts and principles of all sciences result from rational decisions that simultaneously transcend both experience and logic, in the sense that they are not determined by either external or internal necessities. Positivism is, therefore, outmoded. A "fourth stage" consists of the liberation of thought from the obstacles imposed on it by the dogmatism of Auguste Comte (Le positivisme et le progrès de l'esprit, Paris, 1902). Nonetheless, scientific contributions are not arbitrary, and they have a universal value, in that they have matured on a basis of fact and have gradually imposed themselves upon the mind as a network of relations in which logical exigencies are composed and harmonized with the demands of a practical and aesthetic order.

See also Boutroux, Émile; Comte, Auguste; Cournot, Antoine Augustin; Duhem, Pierre Maurice Marie; French Philosophy; Le Roy, Édouard; Mathematics, Foundations of; Philosophy of Science, History of; Poincaré, Jules Henri; Positivism; Renouvier, Charles Bernard.


For selections from Milhaud, see R. Poirier, Philosophes et savants français, Vol. II, La philosophie de la science (Paris, 1926), pp. 5580. A. Nadal, "Gaston Milhaud," in Revue d'histoire des sciences 12 (1959): 114, has a bibliography.

Robert Blanché (1967)

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Milhaud, Gaston


(b. Nîmes, France, 10 August 1858; d. Paris, France, 1 October 1918)

mathematics, philosophy of science.

Milhaud, a village near Nîmes, once belonged to the bishop of Nîmes and thus was able to shelter a Marrano community. Gaston Milhaud’s ancestors came from this locality. He was the third of the famous trio with the same Christian name who brought fame to Nîmes during the nineteenth century; the other two were the historian Gaston Boissier and the mathematician Gaston Darboux, whose student he was at the École Normale Supérieure.

In 1878 Milhaud qualified for both the éeole Normale Supérieure and the école Polytechnique; he chose the former. Agrégé in mathematics in 1881, he then taught mathematics at Le Havre for ten years. His meeting with Pierre Janet and the fruitful collaboration that followed during this period induced a shift in his interests. He translated du Bois-Reymond’s Théorie générate des fonctions; wrote a number of articles for such journals as Revue scientifique, Revue des études grecques, and Revue philosophique de la France et de l’éctranger; and was henceforth concerned with the philosophy of mathematics.

Appointed professor of mathematics at Montpellier in 1891, Milhaud gave a series of lectures on the origins of Greek science (published in 1893). In 1894, at Paris, he defended a Ph.D. dissertation on the conditions and limits of logical certainty. This remarkable work was decisive for his career. He was appointed to the chair of philosophy at the Faculty of Letters of Montpellier in 1895 and rapidly became, through his lectures and publications, a respected authority in a field that was then quite new. He also arranged meetings between investigators in various disciplines. In 1909 a chair was created for Milhaud at the Sorbonne in the history of philosophy in relation to science. Despite the decline in his health, which had always been delicate, he continued to be active and held this chair with distinction until his death.

It has been observed that the end of the nineteenth century witnessed two complementary movements in response to the crisis in the foundations of science: that of philosophers becoming scientists and that of scientists becoming philosophers. Milhaud is one of the best representatives of the latter trend. He modestly presented himself as a teacher who wished to do useful work in the history of science, which he conceived of as “inseparable from a critical examination of fundamental notions and inseparable from philosophical views that, underneath the precise data that are constantly accumulating, attempt to appear and to evaluate the progressive and continuous work being accomplished” (quoted in Pierre Janet, “Notice,” p. 57).

Acutely aware of the effort required to amass and criticize data, Milhaud declared that he was not learned in this respect. Nevertheless, his many works on Greek science show that he accepted the burdens of scholarship; and his study of the arguments of Zeno of Elea is important and still worth consulting. He was also responsible for renewing knowledge of Descartes as a scientist, and his writings on this subject remain a reliable source. It was Milhaud’s second son, Gérard, who with Charles Adam produced an improved edition of Descartes’s correspondence.

Milhaud oriented the study of the history of science more toward philosophy. Certain of his views, although representative of his time, are now outmoded, notably those of continuous progress and the analysis of the conditions, role, and scope of demonstration in mathematics and physics. But his writings on logical contradiction, the limits of the affirmations that it appears to permit, and the critique of scientifically inspired deterministic metaphysical systems are still of interest and justify the considerable influence he has exerted. Milhaud also illustrated his contention that “science progresses in proportion to the disinterestedness with which it is pursued.” Émile Boutroux said in proposing Milhaud’s election to the Académie des Sciences Morales et Politiques in 1918: “By the soundness and originality of his findings in both the theoretical and the historical domains regarding a question of paramount importance, that of the relation between certainty and truth, this conscientious, modest, and penetrating investigator has performed a lasting service to science and to philosophy” (Pierre Janet, “Notice,” p. 58).


I. Original Works. Milhaud’s books include Lecons sur les origines de la science grecque (Paris, 1893); Essai sur les conditions et les limites de la certitude logique (Paris, 1894; 4th ed., 1924); Le rationnel (Paris, 1898); Les philosophes géomètres de la Gréce: Platon et ses prédécesseurs (Paris, 1900; 2nd ed., 1934); Le positivisme et le progrés de l’esprit (Études critiques sur Auguste Comte) (Paris, 1902); Études sur la pensée scientifique chez les Grecs et chez les modernes (Paris, 1906); Nouvelles Études sur l’histoire de la pensée scientifique (Paris, 1911); Descartes savant (Paris, 1921); études sur Cournot (Paris, 1927); and La philosophie de Charles Renouvier (Paris, 1927).

Among Milhaud’s many articles, the following appeared in Revu de métaphysique et de morale: “Le concept du nombre chez les Pythagoriciens” (1893), 140–156; “Réponse à Brochard (1893), 400–404, concerning Zeno of Elea; “L’idée d’ordre chez Auguste Comte” (1901), 385–406; “Le hasard chez Aristote et chez Cournot” (1902), 667–681; and “La science et l’hypothèse par H. Poincare” (1903), 773–781, See also “Science et religion chez Cournot,” in Bulletin de la Société francaise de philosophie (Apr. 1911), 83–104.

II. Secondary Literature. See André Bridoux, “Souvenirs concernant Gaston Milhaud,” in Bulletin de la Société francaise de philosophie, 55 , no, 2 (1960), 109–112; Edmond Goblot, “Gaston Milhaud (1858–1918),” in Isis, 3 (1921), 391–395; Pierre Janet, “Notice sur Gaston Milhaud,” in Annuaire des anciens éléves de ;’éeole normale supérieure (1919), pp. 56–60; André Nadal. “Gaston Milhaud (1858–1918),” in Revue d’ histoire des sciences… (Paris), 12 , no. 2 (1959), 97–110; Dominique Parodi, La philosophie contemporaine en France (Paris, 1919), pp, 21l–216; and René Poirier, Philosophes et savants francais du XXe siécle, II, La philosophie de la science (Paris, 1926), 55–80; and “Meyerson, Milhaud et le probléme de l’épistémologie,” in Bulletin de la Société francaise de philosophie, 55, no. 2(1960), 65–94.

Pierre Costabel

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