Why should we speak about a complementarity of sense and reference?

Abstract

Reflection on the theme of the paper makes one to remember Sir Snow's 1959 lecture on The Two Cultures in which Snow had advanced the thesis that the sciences and the humanities had become split into two cultures and had argued that this division had become a major handicap to solving the world's problems. Mathematics education itself has always been negatively be influenced by this rift. For example, in educational context it is frequently claimed that “mathematics is a language since it provides both a conveyance for and a substantiation of our thoughts. It is that aspect of mathematics that explains the key role it plays in modern science” (EFFROS 1998, p.132). But mathematics is no mere language, as everyone will find out if he tries to order a new door to his apartment with words alone and without measurements. The paper will argue historically and in semiotic terms proposing a methodology based on the conception of a complementarity of meaning and reference of knowledge representations.