Tackling three of Frege's problems

Edmund Husserl on sets and manifolds

Claire Ortiz Hill

pp. 79-104

in: Axiomathes 13 (1), 2002.

Abstract

Edmund Husserl was one of the very first to experience the directimpact of challenging problems in set theory and his phenomenology first began to takeshape while he was struggling to solve such problems. Here I study three difficultiesassociated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and "Russell's" paradox.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory andto develop his own theory of manifolds. I define certain issues involved and discuss howHusserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl'stheories about sets and manifolds out of the realm of abstract theorizing and promptfurther exploration of uncharted philosophical territory rich in philosophical implications.

Cited authors

Husserl Edmund

Frege Gottlob