Up to now I have been writing mostly on my future plans and forthcoming works, I think it is time to tell you something more about my current research project: The Philosophy of Mathematics and Logic in the School of Brentano.
I have been concentrating mostly on mathematics, because this is the most innovative and fruitful part of my project. Franz Brentano and his School are not usually taken into consideration in the history and philosophy of mathematics. However, Brentano appears remarkably well-informed and quite interested in the mathematical research of his time. Moreover, it is surprising to see that most of his more prominent students worked on the philosophy of mathematics. Beyond such an apparent common interest in the matter, this also suggests the presence of a shared theoretical core, prompting the question: was there a Brentanist philosophy of mathematics?
It is instructive to consider a list of works on the philosophy of mathematics in the School of Brentano (roughly chronologically):
- Carl Stumpf’s 1870 habilitation essay Über die Grundsätze der Mathematik (On the Foundations of Mathematics)
- Benno Kerry’s habilitation thesis Grundzüge einer Theorie der mathematischen und nicht-mathematischen Grenzbegriffe (Fundamental Outline of a Theory of Mathematical and non-Mathematical limit Concepts) in 1885, published posthumously in 1890.
- Christian von Ehrenfels’ 1885 dissertation Größenrelationen und Zahlen: Eine psychologische Studie (Relations of Magnitude and Numbers. A psychological Study)
- Edmund Husserl’s habilitation work Über den Begriff der Zahl (On the Concept of Number) in 1887
- Konrad Zindler’s 1889 prize-winning essay “Beiträge zur Theorie der Mathematischen Erkenntniss” (“Contributions to the Theory of Mathematical Knowledge”)
- Ehrenfels’ article “Zur Philosophie der Mathematik” (“On the Philosophy of Mathematics”) in 1891
- Husserl’s Philosophie der Arithmetik (Philosophy of Arithmetic) of 1891
- Stumpf’s Über den Begriff der mathematischen Wahrscheinlichkeit in 1892
This is not an exhaustive list, for various reasons. For instance, sometimes mathematical topics were addressed in a broader context, e.g. in Kerry’s series of articles “Über Anschauung und ihre psychische Verarbeitung” in the 1880s or in Höfler and Meinong’s 1890 Logik. Above I just list the main works that focus specifically on mathematics, right from the title. Moreover, besides these published works, there are numerous unpublished manuscripts in which the members of the School of Brentano address mathematics and related topics (many of Husserl’s manuscripts, various of Stumpf’s and Brentano’s lectures, Brentano’s manuscripts on Megethologie, etc.). While these are of course not easily or freely accessible, most of the material I quoted above is in the public domain and available on-line.
I’ll certainly be posting more about this here, but you can also check out my (programmatic) article on “Brentano and Mathematics” (Revue Roumaine de Philosophie, 55 (1), 149-167) which represents a first step towards answering the question “was there a Brentanist philosophy of mathematics?”.
Peter Simons said:
Carlo this looks very interesting: I wish you every success in pursuing the project. – Peter Simons