Abstract

The problems of clarifying the fundamental logical and mathe­matical concepts, and hence of accomplishing a truly radical grounding of logic and mathematics, were precisely what motivated the very beginnings of Husserl’s phenomenology. This paper is divided into two main parts. The first part focuses on the meaning and structure of Husserl’s explanation of the “logical and psychological” nature of fundamental arithmetical concepts. Particular emphasis is placed on the strategy of Philosophy of Arithmetics (1891) of analysing cardinal numbers in concepts (pivotal yet just as much harmful to philosophy) such as Vorstellungen, mental phenomena and repre­sentations. Together with Arend Heyting and Hermann Weyl, it was the phenomenologist-mathematician Oskar Becker who was the main actor in the second round in the complex dialogue between meta-mathematics and phenomenological philosophy. The second part of this paper aims to clarify Becker’s attempt to apply the theory of actualization of intentionality to the problem of the mode of being of the mathematical and the criterion of mathematical existence.