RESUMÉ – Situe historiquement au confluent de l’arithmétisation de l’analyse et de l’élaboration de la théorie des nombres transfinis, “De l’infini mathématique” s’attache à reconnaître à l’infini le statut de véritable objet mathématique ; mais le problème véritable, une fois mise en évidence l’insuffisance de la genèse arithmétique et algébrique des concepts et principes mathématiques, réside dans la possibilité de leur fondation philosophique sur des notions et principes rationnels et extramathématiques.

At the turn of the century, Russell, Husserl and Couturat singled out Leibniz the logician as an important precursor of the way they thought philosophy should be done. Like their most gifted contemporaries they conceived of philosophy as essentially argumentative and - as Russell put it in a 1911 talk in French - analytic. Unsurprisingly, the search for the best arguments and analyses meant that good philosophy was cosmopolitan. William James and Ernst Mach were read everywhere. James studied Mach (...) and the pupils of Brentano, whom Stout introduced to Cambridge. Moore recognised the deep kinship between his work on ethics and that of Brentano. Russell was influenced by Peano, used and criticised Meinong and was attacked by Poincaré. Pragmatism was subjected to a series of criticisms by realists in German and in English but gradually began to win adherents, for example in Italy, where Vailati and Calderoni introduced both pragmatism and Austrian philosophy of mind. (shrink)