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Couturat, Louis (1868–1914)


Louis Couturat, the French philosopher and logician, studied at the École Normale Supérieure and earned an agrégé in philosophy and a licentiate in mathematics. He taught philosophy at the universities of Toulouse and Caen but soon gave up teaching in order to devote all of his time to his own researches.

Couturat first attracted attention with his important doctoral thesis, L'infini mathématique (Paris, 1896). At a time when the mathematicians were still questioning the validity of Georg Cantor's theories and when the majority of French philosophers, led by Charles Renouvier, were resolute advocates of finitism, Couturat presented a vigorous case in behalf of an actual infinite. In opposition to the formalist theories of number of Julius Dedekind, Leopold Kronecker, and Hermann Helmholtz, he bases number on magnitudenot on a strictly spatial intuition but on magnitude considered as the object of a "rational intuition." This is why, of the various generalizations of numberthe arithmetical, the algebraic, the geometricalhe regards the geometrical as the most rational. His reasoning consisted of offering the actual infinite as a new generalization of number, analogous to those that resulted in signed numbers, fractions, irrationals, and imaginaries. All of these numbers at first seemed to be arithmetical nonsense, but they took on meaning once they were recognized as suitable for representing new magnitudes and for allowing various operations on them that were hitherto impossible. The justification for infinite numbers is that they are indispensable for maintaining the continuity of magnitudes.

From this point on, Couturat's studies proceeded in three areas closely associated in his mindthe history of philosophy, logic and the philosophy of mathematics, and the development of a universal language.

After writing an essay (his Latin complementary thesis) on the myths of Plato, he devoted himself to Gottfried Wilhelm Leibniz, the great infinitist, whose reinterpretation he undertook independently of Bertrand Russell but at the same time and in the same sense. As indicated by the title of his book La logique de Leibniz (Paris, 1901), Couturat had at first intended simply to study the precursor of modern logistic. He soon perceived, however, that Leibniz's "logic was not only the heart and soul of his system, but the center of his intellectual activity, the source of all his discoveries, the obscure or at least concealed hearth from which sprang so many fulgurations. " The manuscripts he discovered at Hanover, a copious collection of which he published in Opuscules et fragments inédits de Leibniz (Paris, 1903), further strengthened Couturat in this conviction. Considering only Leibniz's known, celebrated works, if we wish to find the real root of his system, we must look not to the Monadology or the Theodicy but to the Discourse on Metaphysics, together with the Correspondence with Arnauld, which is, as it were, a commentary on the Discourse. Taking the old formula praedicatum inest subjecto in all its rigor, Leibniz held that every true proposition can be resolved into identities provided one pursues its analysis to the end. Contingent or factual truths differ from the necessary truths of reason only in respect to the infinite length of the analysis, an analysis which God alone is able to complete. Couturat showed, with supporting texts, that all the theses of the Leibnizian metaphysics are obtained from this position and derive their unity from it. The system thus appears as a panlogism.

It is likewise to his interest in Leibniz that we may ascribe, indirectly, Couturat's important study "La philosophie des mathématiques de Kant," published in the Revue de métaphysique (1904) on the centennial of Immanuel Kant's death. In L'infini mathématique Couturat had already criticized the Kantian antinomies that claim to establish the impossibility of an actual infinite. He now concluded that "the progress of logic and mathematics in the nineteenth century has invalidated the Kantian theory and decided the issue in favor of Leibniz" and his ideal of a completely "intellectualized" mathematics. The majestic edifice of the three Critiques lacks the indispensable basement of a logic on a level with science. "The brass colossus has feet of clay."

Deploring the fact that C. I. Gerhardt, in editing Leibniz, had separated the mathematical writings from the philosophical, Couturat could not but associate himself with the task assumed by the newly founded Revue de métaphysiqu? of working for a rapprochement, unfortunately broken off in the nineteenth century, between philosophers and scientists. After the establishment of the Revue in 1893, scarcely a year passed when he did not publish one or more articles in this spirit (some thirty at the time of his death, plus three that appeared posthumously). Rather than present original views, he dedicated himself with great disinterestedness to making known the views of others, mainly foreigners. He explained to French philosophers the mathematical logic of Guiseppe Peano, the universal algebra of Alfred North Whitehead, and the foundations of geometry and the principles of mathematics according to Russell. He vigorously defended both the new logic (to whose diffusion he contributed with his L'algèbre de la logique, Paris, 1905) and the Russellian logistic. This involved him in a celebrated controversy with his former teacher Jules Henri Poincaré. Although at the time Poincaré was often able to score against his opponent, subsequent developments in logic and mathematics have been more favorable to Couturat on many points.

Couturat's admiration for Leibniz, who dreamed of a universal language; his adherence to logistic that he saw as the source of an algorithm disengaged from the contingencies and irregularities of the natural languages; his participation in the organization of the first International Congress of Philosophy (Paris, 1900); his active collaboration with André Lalande in the preparation of the Vocabulaire technique et critique de la philosophie (Paris, 1926); and his rationalism, which one may characterize as militant in the sense that his purpose was less to rediscover reason in things than to work to make it rule among menall these converging concerns led him to devote himself more exclusively to a task which became a veritable apostolate for himthe creation and adoption of an international auxiliary language by the rationalization of Esperanto and Ido. He prepared himself for this mission first by studying and then by publishing, in collaboration with Léopold Léau, the Histoire de la langue universelle (Paris, 1903). After 1900, Couturat was the moving spirit of the Délégation pour l'Adoption d'une Langue Auxiliaire Internationale, initiated by Léau, and later of the Akademie di la Lingue Internaciona Ido. In 1908 he founded and directed until his death the monthly review Progreso, written in the reformed language and designed to propagate it. The opposition of many Esperantists and the death of Couturat, which happened to come at the very moment when a war that exacerbated national particularisms was breaking out, caused the abandonment of the project. His friends and admirers have often regretted that Couturat should have expended so much effort in vain and sacrificed his wide talent to a noble dream.

See also Cantor, Georg; Helmholtz, Hermann Ludwig von; History and Historiography of Philosophy; Kant, Immanuel; Leibniz, Gottfried Wilhelm; Plato; Poincaré, Jules Henri; Renouvier, Charles Bernard; Russell, Bertrand Arthur William; Whitehead, Alfred North.


works by couturat

L'algèbre de la logique. Paris: Gauthier-Vill, 1905. The 1914 edition (Paris) was republished at Hildesheim, Germany, in 1965, Georg Olms edition.

Les principes des mathématiques. Paris: Alcan, 1905. Republished under the same title with the addition of the article "La philosophie des mathématiques de Kant" in Hildesheim, Germany, in 1965.

La logique de Leibniz. Georg Olms edition. Hildesheim, Germany, 1961.

works on couturat

Cassirer, Ernst. "Kant und die moderne Mathematik. Mit Bezug auf Russells und Couturats Werke über die Prinzipien der Mathematik." Kantstudien (1907).

Lalande, André. "L'Oeuvre de Louis Couturat." Revue de métaphysique 22 (1914): 644688. Includes a detailed bibliography.

Robert Blanché (1967)

Translated by Albert E. Blumberg

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Couturat, Louis

Couturat, Louis

(b. Paris, France, 17 January 1868; d. between Ris-Orangis and Melun, France, 3 August 1914)

logic, mathematical philosophy, linguistics.

From early childhood Couturat displayed an exceptional mixture of intellectual and artistic talent, and at the lycée his precocity brought him many prizes. He was to become a master of ancient literature, as well as an outstanding critic in the logic of theoretical and applied sciences. Logic was his basic concern, and even his writings on aesthetics show his preoccupation with logical foundations.

When not yet twenty-two Couturat was honored with the lauréat du concours général in philosophy and in science. During his fourth year at the École Normale Supérieure he studied mathematics under Jules Tannery and then continued under Picard and Jordan, also taking courses with Poincare. He received his licentiate in mathematics on 25 July 1892. Thus prepared to handle problems in the philosophy of science, he published a paper on the paradox of Achilles and the tortoise in the Revue philosophique.

His Latin thesis for the doctorate was a scientific study of the Platonic myths in the Dialogues. For the French thesis he devoted himself to a study of the mathematical infinite. Couturat finished both theses by 12 May 1894, while serving at Toulouse as lecturer on Lucretius and Plato. He defended them at the Sorbonne in June 1896 and again was awarded top honors. In De l’infini mathématique he brought to metaphysicians and logicians the theories of the then new mathematics. His treatment of basic concepts served to invalidate the Kantian antinomies, for in the treatment of number and of continuity Couturat adopted a Cantorian stance with respect to an infinite that is defined with logico-mathematical precision. He maintained that a true metaphysics can be founded exclusively on reason. In De mythis Platonicis, he showed that the set of mythical passages does not represent the real thought of Plato as represented in the dialectical passages.

A leave of absence enabled Couturat to continue his scientific studies in Paris, where he audited the lectures of Edmond Bouty and Victor Robin. He was called to the University of Caen on 27 October 1897, to lecture on mathematical philosophy.

In October 1899 he returned to Paris on a second leave of absence for research on Leibniz’ logic, which, in the various editions, had appeared in fragmentary form only. Couturat believed that Leibniz’ metaphysics was a unique product of his logical principles. While in Hannover in 1900–1901 he had access at last to the unpublished works of Leibniz in the Royal Library. His researches resulted in the publication of La logique de Leibniz and another volume of more than 200 new Leibnizian fragments, Opuscules et fragments inédits de Leibniz, on which he based his theory of Leibniz’ logic.

The Leibniz studies brought Couturat into contact with Bertrand Russell and led to his influential edition (1905) of Russell’s Principia mathematica, with analytical commentary on contemporary works on the subject. Bergson then chose Couturat as his assistant in the history of logic at the College de France (1905–1906).

Influenced by Leibniz’ thoughts on the construction of a logical universal language, Couturat became a prime mover in the development of an auxiliary international language. On 1 October 1907 delegates from 310 societies throughout the world met and elected a committee to modify Esperanto. Couturat and Léau were the secretaries. With the collaboration of the Akademie di la Lingue Internaciona Ido, created in 1908, Couturat constructed the complete vocabulary of Ido, a language derived from Esperanto with reforms growing out of scientific linguistic principles. Couturat stood firmly for the application of his own logical principles, despite opposition from many quarters to changes in the already established forms of Esperanto.

Couturat never completed this work. At the age of forty-six and at the height of his intellectual power, he was killed while en route from Ris-Orangis to Melun on the very day Germany declared war on France. A twist of fate brought the speeding automobile carrying the French orders for mobilization into collision with the carriage in which Couturat, a noted pacifist, was riding.


I. Original Works. Couturat’s books include De l’infini mathématique (Paris, 1896); De mythis Platonicis (Paris, 1896; Hildesheim, 1961); La logique de Leibniz (Paris, 1901); Opuscules et fragments inédits de Leibniz (Paris, 1903); Histoire de la langue universelle (Paris, 1903), written with Léopold Léau; L’algèbre de la logique (Paris, 1905, 1914; Hildesheim, 1965); Les principes des mathématiques (Paris, 1905; Hildesheim, 1965), Étude sur la dérivation en Esperanto (Coulommiers, 1907); Les nouvelles langues internationales (Paris, 1908), sequel to the Histoire; and Étude sur la dérivation dans la langue internationale (Paris, 1910).

His interest in languages is shown in Dictionnaire internationale-français (Paris, 1908), in collaboration with L. de Beaufront; International-English Dictionary, English-International Dictionary (London, 1908), in collaboration with L. de Beaufront and P. D. Hugon; Internationaldeutsches Wörterbuch, Deutsch-internationales Wörterbuch (Stuttgart, 1908), in collaboration with L. de Beaufront and R. Thomann; Internaciona matematikal lexiko, en ido, germana, angla, franca ed italiana (Jena, 1910); and Dictionnaire français-international (Paris, 1915), in collaboration with L. de Beaufront.

A complete bibliography of his numerous papers is given in André Lalande, “L’oeuvre de Louis Couturat,” in Revue de métaphysique et de morale, 22 , supp. (Sept. 1914), 644–688.

II. Secondary Literature. Additional information is in Louis Benaerts, “Louis Couturat,” in Annuaire de l’Association amicale de secours des anciens élèves de l’Ècole normale supérieure (Paris, 1915); Robert Blanché, “Couturat,” in Encyclopedia of Philosophy (New York, 1967), II, 248–249; and Ernst Cassirer, “Kant and die moderne Mathematik. Mit Bezug auf Russells and Couturats Werke über die Prinzipien der Mathematik,” in Kantstudien (1907).

Carolyn Eisele

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"Couturat, Louis." Complete Dictionary of Scientific Biography. . 25 Jun. 2017 <>.

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