Louis Couturat, the French philosopher and logician, studied at the École Normale Supérieure and earned an agrégé in philosophy and a licentiate in mathematics. He taught philosophy at the universities of Toulouse and Caen but soon gave up teaching in order to devote all of his time to his own researches.

Couturat first attracted attention with his important doctoral thesis, L'infini mathématique (Paris, 1896). At a time when the mathematicians were still questioning the validity of Georg Cantor's theories and when the majority of French philosophers, led by Charles Renouvier, were resolute advocates of finitism, Couturat presented a vigorous case in behalf of an actual infinite. In opposition to the formalist theories of number of Julius Dedekind, Leopold Kronecker, and Hermann Helmholtz, he bases number on magnitude—not on a strictly spatial intuition but on magnitude considered as the object of a...