Abstract

A comprehensive study of mathematical thought, taking the actual works for its basis, will examine mathematical activity first. Such activity has always set itself mutually dependent aims of two sorts:The solving of problems, i.e. determining some unknown element under precise conditions;And the achieving of a synthesis which, in the presence of new problems, simplifies and, if necessary, coordinates anew the known facts of whatever sort .This is what allows us to draw up a specific scheme regarding the historical evolution of deductive science, the dialectical aspect of that evolution has been stressed as far as possible. It brings in Logic in a natural way, and shows clearly how 〈mathematisation〉 operates in a wide field