Tackling three of Frege's problems: Edmund Husserl on sets and manifolds [Book Review]

Axiomathes 13 (1):79-104 (2002)
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Abstract

Edmund Husserl was one of the very first to experience the direct impact of challenging problems in set theory and his phenomenology first began to take shape while he was struggling to solve such problems. Here I study three difficulties associated 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 and to develop his own theory of manifolds. I define certain issues involved and discuss how Husserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl's theories about sets and manifolds out of the realm of abstract theorizing and prompt further exploration of uncharted philosophical territory rich in philosophical implications.

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References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
Ideas: General Introduction to Pure Phenomenology.Edmund Husserl - 1931 - New York: Routledge. Edited by William Ralph Boyce Gibson.
Basic laws of arithmetic.Gottlob Frege - 1893 - In The basic laws of arithmetic. Berkeley,: University of California Press.

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