Abstract

The author has endeavoured to define two main trends in the research on the foundations of mathematics, constructivism and structuralism. He gives many examples in axiomatic set theory, e.g. the continuum hypothesis, and in intuitionism, e.g. the notion of choice sequence, in order to show that the two approaches are complementary. The paper contains some original ideas, concerning the structure of the continuum and the constructive horizon, and is completed by an appendix. The paper is an attempt at the justification of a constructivist philosophy in the making