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)

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.

The article introduces and discusses an unpublished manuscript by Edmund Husserl, conserved at the Husserl-Archives Leuven with signature K I 26, pp. 73a–73b.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)