Husserl on the Concept of <i>Anzahl</i>

This article addresses the concept of Anzahl (cardinal number) as understood by the early Husserl, who made it the foundation of his Philosophy of Arithmetic (1891). The discussion is developed through a comparative approach: after retracing the key features of the characterization of the cardinal number presented in that work, the paper examines the criticisms Husserl directs at three alternative theories – two of which are found within the Philosophy of Arithmetic itself, and one is presented in a lecture given in 1901. These comparisons provide an opportunity to appreciate the specificity of certain aspects of Husserl’s philosophy of mathematics, which is centered on the acts performed by the subject. Moreover, they offer valuable insights for re-examining two recurring themes in The Crisis of European Sciences and Transcendental Phenomenology (1954): the problematic relationship between mathematical ideality and the Lebenswelt, and the preference for a mathematical practice centered on a symbolic mode of thought.