ABSTRACT
This chapter discusses Husserl’s criticism of Frege in Philosophy of Arithmetic (1891) and then his later attitude towards logicism as expressed in Logical Investigations (1900-01). In Philosophy of Arithmetic, Husserl holds that logicists offer needless and artificial definitions of notions such as equivalence and number. Frege criticized Husserl’s approach in Philosophy of Arithmetic as psychological, thus shifting the focus of the debate away from logicism. However, Frege’s criticism could be seen to lead Husserl to his later transcendental phenomenological concept of correlation and, with it, to a more developed criticism of logicism. In this regard, the division of labor between mathematics and philosophy established in Prolegomena to the Logical Investigations (1900) is crucial. It implies that in Husserl’s view, formal methods fail to shed philosophical insight on the essence of mathematics. In his picture, the fundamental notions in need of philosophical clarification are, instead of number and quantity, the notions that are central to abstract structural mathematics. Contrary to Frege, who can only elucidate the primitive concepts, Husserl engages in detailed description of their constitution.
