**By Carlo Ierna**

While writing my MA thesis, I still thought that Husserl was developing an original application of Brentano’s method to a new area. The mainstream interpretation generally considered Husserl’s early works as an innovative combination of his mathematical background (after studying mathematics in Berlin he did his dissertation on the calculus of variations in Vienna) and the philosophical teachings of Brentano and Stumpf, who supervised his 1887 habilitation work *On the Concept of Number* that formed the basis for his first book, the 1891 *Philosophy of Arithmetic*.

However, during my doctoral research at the Husserl-Archives Leuven, I had the chance to study notes from Stumpf’s and Brentano’s lectures that Husserl had attended right before his habilitation. These lecture notes suggested that there was far more available to Husserl than merely some general methodological principles. Furthermore, I discovered that nearly everyone from the School of Brentano had already written on the philosophy of mathematics before Husserl! The mainstream picture turned out to be a little too simplistic. The surprising number of works in the School of Brentano on the philosophy of mathematics reduces, or at least contextualizes, Husserl’s originality considerably. This then became the main topic for my first postdoc: to investigate whether there really was such a thing as a Brentanist philosophy of mathematics, working my way back from Husserl.

The first book length work on the philosophy of mathematics produced in the School of Brentano was Stumpf’s 1870 habilitation treatise *On the Foundations of Mathematics*, which had just been published in 2008. Through manuscripts, letters, and lectures, I was able to trace the vertical lineage of the Brentanist philosophy of mathematics from Husserl back to Stumpf and Brentano. Yet, this still merely pointed to a continuity from teacher to pupil: an original influence from Brentano’s lectures on Stumpf’s habilitation work, and then a joint influence of both on Husserl. However, I actually wanted to make a stronger claim: that there is a Brentanist philosophy of mathematics in the School of Brentano at large. For this I also needed independent parallels and horizontal connections between the members of the School. These were not at all hard to find. Indeed, there is one particular author from the School of Brentano that presents several amazing parallelisms to Husserl’s development. Exactly like Husserl, he was a student of Brentano, influenced by Meinong’s works on relations, wrote an academic work containing psychological analyses of the concept of number in the mid-1880s, and then published another one on the philosophy of mathematics in 1891: Christian von Ehrenfels. However, the parallels between Husserl and Ehrenfels are still not enough. What we need is an explicit acknowledgement of their connections within the School of Brentano. Such acknowledgement is found first of all in the abundance (for the time) of references made in Ehrenfels’ 1891 article to other writings in the Brentanist philosophy of mathematics, including Husserl’s 1887 habilitation thesis and Benno Kerry’s articles on the subject. Moreover, that such works belonged together in a common tradition is underscored by Alois Höfler’s (also a Brentanist) combined review of Husserl’s *Philosophie der Arithmetik*, Ehrenfels’ 1891 article, and Kerry’s series of articles. This shows that there was a wider awareness of the cross-connections with respect to their common interests and theories regarding the philosophy of mathematics. Hence, we can truly speak of a network of connections and therefore a Brentanist philosophy of mathematics (I argue more extensively for this in my forthcoming article “The Brentanist Philosophy of Mathematics in Edmund Husserl’s Early Works” in *Essays on Husserl’s Logic and Philosophy of Mathematics*, ed. Stefania Centrone, *Synthese Library*, 2016).

In the most general terms, the core tenets of the School would include the claims that number is a multiplicity of units, given by the mental operation of counting and “*Zusammenfassung*” (“grasping together”, i.e. collecting) operated on “somethings” (*Etwas überhaupt*), in which case one and zero are not, properly speaking, numbers. Higher numbers, beyond our presentational capacity, are to be understood as presented improperly, i.e. symbolically, through signs provided in a systematic way by a (positional) numeral system. Numbers are neither empirical facts, nor platonic entities, but essentially conceptual in nature, without being purely subjective creations, but have “existence” in the sense of being logically possible, i.e. non-contradictory. Against John Stuart Mill on the one side and Immanuel Kant on the other, mathematics is neither inductive nor synthetic, but a deductive, analytical a priori discipline (see my “Brentano and Mathematics” ).

Why, however, should anyone care about this? Isn’t this just a historical curiosity? What is so important about members of a school sharing the same ideas? Brentano and his students (with the exception of Husserl) have not generally been considered as being closely associated with mathematics. My research rectifies this situation. Moreover, the consensus is that most of Brentano’s pupils became heterodox sooner rather than later, going on to found their own schools and movements. This further obscured the common origin of some of their theories. While tremendously influential, if Brentano is remembered at all, it is mostly as mere precursor of his students. They would at most share his method, but not his results. In what sense can we even speak of a school then? Their surprising interest in and broad agreement on the philosophy of mathematics shows that at least with respect to some topics and issues they were clearly working from a common theoretical framework on a shared project. Moreover, they needed to come up with a serious alternative to both Platonism and empiricism, while preserving the status of mathematics as an objective, presuppositionless, and the most exact science.

Thanks to the detailed analyses of intentionality and intentional objects, the Brentanists were able to clearly distinguish consciousness and the object of consciousness, and hence psychology and logic. In her 1917 dissertation on *Recent Logical Realism*, Helen Huss Parkhurst even claimed that intentionality was no less than the "fundamental dogma of logical realism", picking out Stumpf, Marty, Meinong, and Husserl as heirs of Bolzano as much as of Brentano. Since mathematics is a prime example of a science that involves a mental direction upon objects that are neither physical, nor (subjectively) psychical, its clarification became a core concern for the School of Brentano. In Husserl’s words, this concern was ultimately with the question of the relation between the subjectivity of knowing and the objectivity of knowledge, a question that for the Brentanists arose first and foremost in the philosophy of mathematics.

In my next post I will outline how this is connected to my current research project on the ideal of “Philosophy as Science” in the School of Brentano.

elaborate insights

Posted by: Charles Ndung'u | 07/01/2016 at 01:35 AM