Non-denoting terms and "imaginary" numbers

Abstract

This paper presents modern interpretations of Husserl’s solution to the so-called “problem of imaginary numbers”. The starting point of these interpretations are three different points of view on non-denoting terms: the many-sorted, the “nonexistent values” perspective and the “partial” approach. I will maintain that the last one is the most appropriate one for a reassessment of his Double Lecture, delivered in 1901. My proposal, that incorporates the existence predicate of free logics, gives an account of Husserl’s “existence axioms”, vindicating its essential role in the transition through the Imaginary.