L'idée de mathématiques appliquées chez Comte

摘要

Trained as an engineer, Comte knew that science is mainly valued for its practical applications but, as a philosopher of science, he knew of theoretical applications too. The idea of applied science also lies at the core of his philosophy of science. Positivism is at loss before the a priori and Comte tried to find a way out in the distinction between what is abstract and what is concrete. As for mathematics, he defined it as the science of indirect measures and this already gives a central place to applications, since it is the way physicist uses mathematics which is paradigmatic. However, Comte saw the limit of such a definition, and answered some objections. We then show how the very idea of application is central to the positivist philosophy of science. Theoretical applications correspond to the dependencies between sciences as they are established by the classification: for instance, physics needs mathematics, and celestial geometry, as well as celestial mechanics, implies the application of these two branches of mathematics to a particular class of phenomena. Comte also paid a special attention to ill-founded applications, which he called “usurpations”, or mathematical “materialism”. The last section deals with practical applications and the way they quickly encounter so unmanageable difficulties that we have to drastically restrict the domain where mathematics de facto apply.