Intuition in mathematics

on the function of eidetic variation in mathematical proofs

Dieter Lohmar

pp. 73-90

in: Mirja Hartimo (ed), Phenomenology and mathematics, Berlin, Springer, 2010

Abstract

Intuition is of central importance for the phenomenological access as a whole and it also turns out to be decisive in the analysis of cognition in mathematics. But sensibility can not be the source of intuition in abstract formal sciences. Therefore I first delineate some basic traits of cognition in terms of Husserl's categorial intuition. Then I investigate in a special case of cognition, i.e., the eidetic method of Husserl, the so-called Wesensschau. This intuition of essences is a special case of categorial intuition and it is characterized by apodictic evidence. Thus it may solve the question of intuitivity together with the problem of necessary validity. My way to argue for this thesis is to analyze some intuitive steps in simple proofs and point out some rules that enable an implicit variation. Following the traces of the eidetic method in mathematical intuition it turns out that not only in material mathematics like in geometry, but also in formal mathematics, there is a special kind of implicit eidetic variation that serves as the source of intuitivity in proofs.

Cited authors

Husserl Edmund