Aplicacionismo o abstraccionismo: dos caras de la matemática.

Abstract

Exist two general visions about the mathematical one: (1) like science that self-development through deductive processes and (2) like science that serve as vehicle other sciences to explain and until predicting the real. Both visions have been categorized like: "abstraccionismo" (in the case of first) and "aplicacionismo" (in the case of second). The article presented here is has three objectives: (1) to explain both visions through two great theories exposed by two famous outstanding intellectuals in the subject at world-wide level. Being the theory that gives to foundation to the abstraccionismo exposed by the mathematician and French epistemologist Jean T. Desanti and, presented/displayed in its book Les Idéalités Mathématiques in 1968. And by its side the aplicacionismo, in the theory of the English mathematician John David Barrow who exposes it in his book of 1997 Why the world is mathematical? (2) Explain that both views are not exclusive and (3) Submit an integrationist vision of both trends for the teaching of this science.