The Place and Value of Logic in Louis Couturat’s Philosophical Thinking

Abstract

Louis Couturat is known for affirming and defending the works of logic available during his lifetime, especially those of Russell and the Italian school. His work of conceptual analysis is exceptional and unique in its ability to put in relation the mathematicians of his time, for which his reputation is well deserved. Taking a closer look at his work at large, the place and value of logic are not simple problems for Couturat. On one hand, the logic differs from the Greek methods of Aristotelian logic, and yet it has no place in mathematics a logic unlike the algebraic school Couturat frequently addresses. On the other hand, he discovers the logic of Russell as a novelty and invention, to which he gives, in agreement with Lalande and Itelson, the old name of Logistics. He complicates things further in his unpublished Manuel de Logistique (written in 1905), where he presents it as an ancient science to which symbols have been added (however, we know he does not like the use of symbols as Peano instituted). Couturat is therefore in a complex relationship with the logic of his time. The following is an attempt to unfold the consequences (Our main source for this text on Louis Couturat will be the correspondences with Bertrand Russell between 1897 and 1913, edited and annotated by us. It is all the more valuable because we have letters from both contributors (and is the most important scientific correspondence of Russell’s) (Russell, Correspondance sur la philosophie, la logique et la politique avec Louis Couturat (1897–1913), édition et commentaire par Anne-Françoise Schmid, Paris, Kimé, 2 volumes, 735p, 2001).