Husserl’s Theory of Manifolds and Ontology: From the Viewpoint of Intentional Objects

This study purports a unifying view of the ontology of mathematics and fiction presented in Husserl’s 1894 manuscript “Intentional Objects” [Intentionale Gegenstände] in relation to his theory of manifolds. In particular, I clarify that Husserl’s argument supposes deductive systems of mathematical theories and fictional work as well as their “correlates,” which are mathematical manifolds in the former cases. This unifying view concretizes the concept of manifolds as an ontological concept that is not bound to mathematics. Although mathematical and fictional objects differ in whether they are purely formal or materially filled, the concept of manifolds can be extended to admit materially filled objects, thus encompassing the two into the unitary theory of manifolds. By contrast, reviewing the subsequent developments of Husserl’s theory of manifolds naturally leads to restricting its concept to be strictly formal. This notion is consistent with the view that describes manifolds as forms of worlds and states of affairs; however, I suggest that the concept of the manifold is more fundamental than the concept of the world and state of affairs