Louis Couturat -Traité de Logique algorithmique

The manuscript of the Traité de Logique algorithmique resulted from lectures Couturat gave at the University of Caen in 1898/99 on recent developments in symbolic logic, on the relations of logic and mathematics, and on the scope of the methods of mathematics. It is the only one of several manuscripts Couturat mentioned in his correspondence that meanwhile has been rediscovered. It is an outstanding document of the popularization and propagation of symbolic logic around 1900. It allows to better understand the difficult relations of algebraic logic and the so-called logistic program which surpasses the simple alternative of logic as an application of algebra vs. logic as the foundation of mathematics. The complicated interactions in the historical developments of these two currents become manifest in Couturat's hesitations and changing attitudes within his own intellectual biography. The publication of this manuscript helps to achieve a much more complete picture of the latter.

Résumé
Louis Couturat (18681914) was an outstanding intellectual of the turn of the nineteenth to the twentieth century. He is known for his work in the philosophy of mathematics, for his critical and editorial work on Leibniz, for his attempt to popularise modern logic in France, for his commitment to an international auxiliary language, as well as for his extended correspondence with scholars and mathematicians from Great Britain, the United States, Italy, and Germany. From his correspondence we know of four unpublished manuscripts on logic and its history, which were largely complete and some of which must have been of considerable size. We publish here for the ?rst time in a critical edition the only one of these manuscripts that has been rediscovered: the Traité de Logique algorithmique, presumably written in the years 18991901. It is a highly interesting document of the academic reception and popularisation of symbolic logic in France. It provides evidence of the discussions and controversies which accompanied the creation of logic as a new branch of science. At the same time it completes the picture of Couturat's work, which has been opened up to systematic study by the publication of important parts of his correspondence during the last decade. We append the article on Symbolic Logic of 1902 which Couturat wrote in collaboration with Christine Ladd- Franklin for Baldwin's Dictionary of Philosophy and Psychology.

Contenu
Transcription of the Manuscript.- Définitions et notations : A. Logique des concepts.- Définitions et notations : B. Logique des propositions.- Principes.- Lois de la multiplication et de l'addition.- Lois de la négationa.- Développement des fonctions.- Théorie des équations.- Sur les opérations inverses : Soustraction et division.- Théorie des inégalités.- Calcul des propositions constantesa.- Calcul des jugements variables (ou des probabilités)1.- Comparaison avec la Logique classique1.- Conclusions.- Critical Apparatus.- Variants and Annotations.