Perspectives hétérodoxes de Russell sur la question des fondements

Abstract

Russell’s logicism consists of a thesis stating that all pure mathematics can be expressed in terms of logical constants and variables. It is usually assumed to be a reduction of pure mathematics to logic. Yet this thesis is a guarantee for the non-reduction of mathematics to number and quantity, of arithmetic to finite numbers only, of geometry to the Euclidean one, and of logic to syllogistic reasoning. Thus logicism cannot be interpreted as a dogmatically asserted doctrine of a logical foundation of mathematics. Besides, Russell’s philosophical work develops a critique concerning the themes related to foundations. All of Russell’s points of view on the links between logic and mathematics can only be understood if logic is considered as a full-fledged science and not as a formal language. This way to deal with logicism enhances “heterodoxical” perspectives to which Russell is led. Indeed, he is not always the “classic” that scholars too promptly identify. The present in­terpretation notably relies on the recently published correspondence between Bertrand Russell and Louis Couturat (1897-1913).