Background

Couturat was born on January 17, 1868, in Ris-Orangis, France.

Education

Couturat studied at the École Normale Supérieure and earned an agrégé in philosophy and a licentiate in mathematics.

Career

Couturat 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.

He 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 magnitude - not on a strictly spatial intuition but on magnitude considered as the object of a "rational intuition." This is why, of the various generalizations of number - the arithmetical, the algebraic, the geometrical - he 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 mind - the 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.

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 men - all these converging concerns led him to devote himself more exclusively to a task which became a veritable apostolate for him - the 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.

Achievements

• Couturat sought a universal language and symbolic-logic system to study the history of philosophy and the philosophy of mathematics. To promote his international language of Ido based on the “rational intuition” of Esperanto, he helped to organize the International Congress of Philosophy (1900), to prepare Vocabulaire technique et critique de la philosophie (1926), and to establish Progresso (1908), a monthly publication written in Ido.

Works

More photos

• book

  • De l'Infini mathématique

    (French Edition)

    1896
  • La Logique De Leibniz D'après Des Documents Inédits

    (French Edition)

    1901
  • Opuscules Et Fragments Inedits de Leibniz

    (French Edition)

    1903
  • De Platonicis mythis 1896

Views

Initially trained as a mathematician, Couturat advocated the real existence of infinite numbers when Cantor's theories were widely rejected. He then became an advocate of the logistic programme in mathematics and a supporter of Russell’s views on the subject. A year in the Leibniz archives in Hanover revealed to him Leibniz’s logical writings, which he went on to publicize, becoming the inventor of the wellknown thesis that Leibniz’s metaphysics was a consequence of his logic. He later became interested in the universal-language movement, favouring Ido as a supposedly more logical alternative to Esperanto. On Leibniz, Couturat may perhaps have been misled by his own thoroughgoing metaphysicial rationalism: it is hard to understand how a content-free logic could supply the premises for a content-full metaphysics.

Interests

• Philosophers & Thinkers

  Gottfried Wilhelm Leibniz

Connections

Nothing is known of Couturat's own family.

References

• The Search for Mathematical Roots, 1870-1940
  2000
• Dictionary of Scientific Biography Volume 3
  1971