Husserl and the Infinite
Husserl And The Infinite

Summary/Abstract: Edmund Husserl began his academic career as a mathematician, studying with some of the best mathematicians of his time (like Weierstrass and Kronecker). Subsequently, he turned to philosophy, field in which he also had the extraordinary opportunity to work with one of the most influential philosophers of the nineteenth century: Franz Brentano. In Husserl’s early work these two influences generate a unique mix and I think that it is very interesting to investigate the way in which Husserl deals with some of the most fundamental problems of mathematics and philosophy of mathematics, like the problems posed by concepts such as that of infinity. In this article1 I will analyse Husserl’s conception of the infinite as expressed in the paragraph Unendliche Mengen of his Philosophie der Arithmetik (PA).2 I will give a short exposition on his distinction between proper and symbolic presentations and then proceed to the logical distinctions that Husserl makes between finite and infinite symbolic collections. Subsequently (in section 2.3), I will discuss Husserl’s addition of surrogate presentations as a sub-type of symbolic presentations in his short treatise Zur Logik der Zeichen (Semiotik).3 In this later text (which was originally intended as an appendix to the never published second volume of the PA) Husserl gives a more detailed account of how we can conceive of the infinite, using surrogate presentations. Allow me to begin, however, with a brief survey of Husserl’s mathematical background and of other important influences that he underwent in this early period. Especially interesting in this respect is the influence, both mathematical and philosophical, of Bernard Bolzano. I will not focus on the vast impact that the teachings of Brentano and Stumpf had on Husserl, since these have already been abundantly discussed elsewhere.

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