Journée "Louis Couturat"

Paul ZICHE (Department Wijsbegeerte, Université Utrecht, Pays-Bas)

"Introduction: Logic, formalization, and divergent standards of rationality"

The introduction will sketch the relevant background for addressing the achievements of Couturat: the broad agreement shared by virtually all scientific disciplines in the second half of the 19th century that the search for new forms of general sciences, and for more general foundations of the existing sciences, was indispensable; the crucial role that developments in 19th century mathematics – in particular Grassmann’s theory of extensions and innovations in algebra – played within this project; and the extremely surprising forms of coexistence of what seems today to be incompatible forms of rationality. As a case study, (some of the) various accounts of formalization as developed in Couturat’s time will be discussed: ideal languages in the sense of mathematical logic and of ideal languages for everyday use; Husserl’s intricate discussion of the difference between formalization and generalization; the discussions – inspired by Kant – about the role of intuition resp. of pure thought in mathematics; the different contexts in which the ideal of ‘purity’ was discussed.

 

Clara Silvia ROERO (Département des mathématiques "G. Peano", Université Turin, Italie)

"Louis Couturat et les italiens: Les relations avec les historiens, les philosophes et les mathématiciens"

In my talk I would to trace the relationships Couturat had in Italy with some historians of science, philosophers and mathematicians, with whom he shared common interests (Leibniz, logic, philosophy, history of science, international language, social issues, . . . ). Among the main protagonists I’ll mention Giuseppe Peano, Giovanni Vacca, Giovanni Vailati, Giovanni Papini, Eugenio Rignano, Federigo Enriques and Vito Volterra, but also Filippo Turati, Nicola Mastropaolo, Mario Gliozzi, Ugo Cassina and Sebastiano Timpanaro. Through unpublished letters, manuscripts, reviews and articles I’ll try to show the strategies they used to oppose to B. Croce’s and G. Gentile’s attacks and to create an alternative to their power.

 

Erika LUCIANO (Département des mathématiques "G. Peano", Université Turin, Italie)

"La propagation de la logique mathématique de Peano en France: Couturat et la communauté de l'analyse"

Between 1890 and 1908 the energies of Peano and his School were absorbed by the writing and the international promotion of the Formulaire de Mathématiques, an encyclopaedic treatise on elementary mathematics, written in logic language, which soon became an object of discussion because of its particular structure and nature. To understand how this work was received in France, an essential figure is that of L. Couturat, the author of numerous essays on Peano’s logic, who wrote a detailed review of it for the Bulletin des Sciences mathématiques, with the aim of « making [the Formulaire] more readable » for those of his fellow-countrymen who were mathematicians and philosophers.

In the course of my talk, in the light of the unpublished correspondence of Couturat with Borel, I propose to (1) illustrate the relations between Couturat and the community of the French analysts of the time, bearing in mind both his training as a mathematician at the École Normale Supérieure, and his work as ‘co-editor’ of the Revue de Métaphysique et de Morale; (2) describe the dynamics of the spread of Peano’s symbolic logic, following the work of divulgation carried out by Couturat; (3) show how the fate of the reception of Peano’s logic was indissolubly linked – rightly or wrongly – to the particular cultural context of the foundational discussions on the theory of sets (theories of Cantor, axiom of choice, etc.).

 

Anne-Françoise SCHMID (Institut National des Sciences Appliquées (INSA) de Lyon)

"La notion de critique dans la philosophie des sciences de Louis Couturat".

Louis Couturat a été kantien, puis il a vivement rejeté le kantisme. Pourtant, à travers ce changement important et assez rapide – comme en témoigne sa correspondance avec Bertrand Russell -, son idée de critique et sa fonction dans les relations entre philosophie et mathématiques sont restées identiques. Nous allons décrire cet invariant, montrer son importance dans la philosophie des sciences de Couturat et ses suites dans la tradition française. Nous évaluerons les conséquences de cette idée dans la pratique épistémologique.

 

Amirouche MOKTEFI (Institut de Recherches Interdisciplinaires sur les Sciences et la Technologie (IRIST), Strasbourg)

"Couturat et la tradition de l'algèbre de la logique".

 

Oliver SCHLAUDT (Institut de philosophie à l'Université Heidelberg / LHSP - Archives H. Poincaré, Nancy)

"La contribution de Couturat à la théorie de la mesure"

Louis Couturat in his De l’infini mathématique of 1896 was probably the first philosopher who formulated a representational theory of measurement. According to Couturat, measurement basically consists in assigning numbers to quantities. This notion of measurement emerged in the context of the arithmetization of analysis and the axiomatization of quantity; it was spelled out for the first time by the mathematician Rodolfo Bettazzi in his Teoria delle Grandezze of 1890.

Later, due to N.R. Campbell and S.S. Stevens, this idea became common in measurement theory. Modern measurement theory successfully studies the mapping of empirical relational systems onto the (rational or real) numbers. Notwithstanding the great success of the representational theory of measurement in clarifying technical problems, in recent years an increasing number of philosophers criticised its inability to treat epistemological questions. This epistemological lack may be due to the fact that the representational theory of measurement disposed of the concept of quantity which in this framework is not required. Couturat, on the contrary, still kept hold of the concept of quantity and put it into philosophical use. He developed a sophisticated conceptual framework whose power he proved in his severe critique of Russell’s On the relations of number and quantity of 1898. In De l’infini mathématique, he applied his concept of quantity in a discussion of von Helmholtz’s Messen und Zählen of 1887. He accused von Helmholtz of circularity and opposed to von Helmholtz’s empiricism a still challenging rationalist point of view.

Today Couturat’s contributions to measurement theory are largely unknown, what is also true in general of the origins of the representational theory of measurement. In view of the philosophical shortcomings of the representational theory of measurement, a revision of Couturat’s ideas however is promising. In this talk, Couturat’s arguments will be analysed and put into the context of his thought on geometry, science, and logic.