This presentation aims to clarify the historical and theoretical background of the studies included in this issue of Philosophiques, which focus on the work of Husserl during the period of Halle . After a brief description of Husserl’s early years of apprenticeship in philosophy between 1876 and his studies with Brentano in Vienna, I identify several steps that marked the development of his philosophy from his arrival in Halle to the publication of the Logical Investigations : his studies under the (...) direction of C. Stumpf, the publication of the first volume of Philosophy of Arithmetic, the researches belonging to the project of the second volume of this work, the abandonment of this project and the development of the phenomenology of the Logical Investigations. The last part of this paper is an examination of the philosophical issues underlying the disputatio on D. W. Smith’s recent book on Husserl’s philosophy. (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.

Dans l’essai Objets intentionnels de 1894, Husserl développe en réaction à Twardowski une théorie originale de l’assomption comme solution au problème des représentations sans objet. Après avoir examiné le détail de cette théorie et en avoir soulevé les difficultés, je montre dans cet article que la solution proposée par cette théorie doit être abordée de manière indépendante de celle qui sera développée plus tard dans les Recherches logiques et j’expose dans quelle mesure elle est ancrée dans la psychologie descriptive brentanienne (...) tout en mettant à profit certains outils de la logique de Bolzano. Enfin, j’indique que Husserl continuera à développer cette théorie après les Recherches logiques, confirmant ainsi qu’elle occupe une place de choix dans la théorie phénoménologique du jugement.In his essay Intentional Objects of 1894, Husserl develops in response to Twardowski an original theory of assumptions as a solution to the problem of objectless presentations. First, I analyze in this paper the main points of his theory and point out some of the difficulties it raises. I then suggest that the solution presented in this theory must be addressed independently of the one developed by Husserl later in the Logical Investigations and try to show in which extent his theory of assumptions is rooted in the brentanian descriptive psychology, although it makes good use of some logical tools from Bolzano’s Wissenschaftslehre. Since Husserl continues to work on this theory even after the Logical Investigations, it confirms the important place one should give to the theory of assumptions it the phenomenological theory of judgment. (shrink)

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 concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s (...) Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (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.