Husserl and Weyl on Definiteness

The chapter compares the development of the notion of definiteness in Husserl’s and Weyl’s writings during the first two decades of the twentieth century. It uses and further elaborates a distinction between intensional and extensional definiteness. Intensional definiteness (ID-ness) of a condition means that it is sharp and well-defined; this ensures that for any given object a, it is decidable whether the condition applies to it or not. Extensional Definiteness (ED-ness) is about circumscription or demarcation of a totality of objects. When these notions are employed to analyse Husserl’s and Weyl’s work, interesting shifts can be found in the developments of their thought. The comparison between Husserl and Weyl suggests a further distinction between explicit and implicit forms of ID-ness and ED-ness. All forms of definiteness can be found in Husserl’s manuscripts, whereas Weyl’s focus is restricted to the explicit forms of definiteness. In particular, in his lecture course from 1918, Husserl employs the notion of definiteness for judgment-theoretically explicated intensional definiteness, whereas Weyl uses the notion in 1918 for explicitly constructed sets. The latter notion, as Weyl later explains, circumscribes the domain of admissible quantification in mathematical definitions.