Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl - Aranda, Víctor (Bulletin of the Section of Logic, 2020)
Husserl's two notions of "defi niteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "de finite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute de finiteness" as semantic completeness and argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers.