Intuição na matemática. Sobre a função da variação eidética nas provas matemáticas

Abstract

In this paper, the author presents Husserl's method of eidetic variation. He starts with an analysis of how the method works in the case of empirical types corresponding to objects of everyday life, and he stress the results of its application, namely the gathering of a priori, apodictic knowledge about essences. The author examines the way this method can be applied to what Husserl called the material mathematics, for instance, Euclidean geometry. Finally, he addresses the main question regarding the possibility of using eidetic variation, and eidetic intuition, in formal mathematics. Analysing one example of a formal proof, he concludes that eideitic variation procedures are still at work in this realm. Precisely in the "implicit variation" that allows the mathematician to reason about any number whatsoever when developing is formal proofs, for instance, about any concrete natural number, when proving a theorem about N.