This essay explores an ideal notion of form (mathematical structure) that embraces logical, phenomenological, and ontological form. Husserl envisioned a correlation among forms of expression, thought, meaning, and object—positing ideal forms on all these levels. The most puzzling formal entities Husserl discussed were those he called ‘manifolds’. These manifolds, I propose, are forms of complex states of affairs or partial possible worlds representable by forms of theories (compare structuralism). Accordingly, I sketch an intentionality-based semantics correlating these four Husserlian levels of (...) form—thereby integrating logic, phenomenology, and ontology. (shrink)

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.

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. (shrink)

The article introduces and discusses an unpublished manuscript by Edmund Husserl, conserved at the Husserl-Archives Leuven with signature K I 26, pp. 73a–73b. The article is followed by the text of the manuscript in German and in an English translation. The manuscript, titled “The Transition through the Impossible” ( Der Durchgang durch das Unmögliche ), was part of the material Husserl used for his 1901 Doppelvortrag in Göttingen. In the manuscript, the impossible is characterized as the “sphere of objectlessness” ( (...) Sphäre der Gegenstandslosigkeit ) and Husserl addresses the question whether and when it is warranted to perform a transition through the impossible to obtain valid results for the sphere of objectivity. (shrink)

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.