Husserl, Intentionality and Mathematics: Geometry and Category Theory

Abstract

The following text is divided in four parts. The first presents the inner relation between the phenomenological concept of intentionality and space in a general mathematical sense. Following this train of though the second part briefly characterizes the use of the geometrical concept of manifold (Mannigfaltigkeit) in Husserl’s work. In the third part we present some examples of the use of the concept in Husserl’s analyses of space, time and intersubjectivity, pointing out some difficulties in his endeavor. In the fourth and final part we offer some points of coincidence between phenomenology and category theory suggesting that the latter can work as a formal frame for ontology in the former. Our thesis is that intentionality operates in different levels as a morphism, functor and natural transformation.