WHY SHOULD WE SPEAK ABOUT A COMPLEMENTARITY OF SENSE AND REFERENCE?

Abstract

Until around 1800, Western philosophy believed that there were two types of conception in the world: the mental and the physical. Hence the extensive discussions about the analytical and synthetic knowledge that dominated the philosophy of Kant, the greatest Enlightenment philosopher. However, from the Peircean studies, the discussion about the conceptions has expanded, giving rise to the complementarity, which currently addresses the conceptions of extension and intensionof logic and philosophy. In the educational context it is often claimed that mathematics is a language, since it provides both a means of communication and a substantiation of our thoughts. As a result, mathematical fluidity is now considered the most important. From this perspective, the pedagogical principles underlying mathematics teaching become similar to those used in language teaching. But mathematics is not mere language. Language is a wonderful instrument of the human spirit, yet it serves logic, poetics, and rhetoric far better than mathematics. Thus, this article aims to show that the approach of elementary mathematics education must consist in teaching to read a term beyond its correspondence between letters and sounds, and also to permit the understanding how a skill set can be worked completely in abstract in relation to content. The semiotic methodology is utilized as input to analyze what is really the mathematics.

Keywords

• semiotics. complementarity. language. mathematics.