Louis Couturat (1868-1914): Early symbolic logic and the dream of a characteristica universalis

Oliver Schlaudt

Philosophy Department
University of Heidelberg, Germany

It is known that Bertrand Russell turned to logic after having become acquainted with the work of the Italian mathematician Giuseppe Peano. He was personally introduced to the latter in 1900, at the First International Congress of Philosophy in Paris, by a French colleague, responsible for the Logic Section of the Congress: Louis Couturat.

Who was this French philosopher? History of logic almost completely ignores him, because he didn't contribute to the field. Nevertheless he played an important role in the development of the discipline. He was among the first who grasped the appeal of the new "algorithmic logic", renewing Leibniz' dream of a characteristica universalis, and started very early to integrate modern logic into the philosophy curriculum at the French university. He wrote several introductory works on logic for the French public. And he created a vast network of correspondents, extended from Argentina to Russia, including among others Russell, Peano, Peirce, MacColl, Frege and Schroeder. He devoted himself to mutually connect these scholars and to make circulating their ideas through the scholarly world at a maximum speed.

In this tutorial, we will try to grasp the work of Couturat in its entire scope, ranging from his work on Leibniz to the philosophy of mathematics, epistemology, and logic. Beyond his published work we will also consult his correspondence and his unpublished manuscripts (e.g. on the history of mathematical logic).


1. Louis Couturat
In the first session, I will provide an overview over the life and the work of Louis Couturat. In particular, I will elaborate his philosophical programme which eventually led him to study contemporary advances in symbolic logic and to make considerable efforts for introducing symbolic logic in France. I will also present and analyze his various activities as a reviewer, editor, conference organizer, international "mail box", partisan of international auxiliary languages, and so on.

2. Philosophy of logic
In the second section, I will outline Couturat's philosophy of logic, focussing on two major topics: firstly, the relation between logic and mathematics and in particular the question of logicism, discussed by Couturat in form of the alternative "algebra of logic or logic of algebra"; secondly, I will show how Couturat's criticisms of various systems of symbolic systems fits into a larger semiotic approach, covering also mathematics, the algebras of the natural sciences (e.g. chemical formulae) and even natural languages.

3. History of logic
The third and last session will focus Couturat's construction of a "History of mathematical logic" in his unpublished series of lectures at Collège de France in 1904/05. We will especially analyze the relation between the contemporary discussions in logic and the kind of questions Couturat tried to answer in his historical account.

Selection of Couturat's works:
  • De l'infini mathématique (1896)
  • La Logique de Leibniz (1901), English translation by Donald Rutherford: The Logic of Leibniz
  • with Christine Ladd-Franklin: "Symbolic Logic", in: J.M. Baldwin, Dictionary of Philosophy and Psychology (1902)
  • Les principes des mathématiques, avec un un appendice sur la philosophie mathématique de Kant (1903) L
  • L'algèbre de la logique (1905), English translation by Lydia Robinson: The Alegbra of Logic
  • Traité de logique algorithmique (posth., 2010)
    On Couturat:
  • Michel Fichant, Sophie Roux, eds., Louis Couturat (1868-1914) - Mathématiques, langage, philosophie. Paris: Classiques Garnier
  • L'Œuvre de Louis Couturat - de Leibniz à Russell, Actes du colloque international organisé à L'École normale supérieure en juin 1977

    Back to the 6th Universal Logic School !