Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl

Víctor Aranda

doi:10.18778/0138-0680.2020.07

Authors

Víctor Aranda Universidad Autónoma de Madrid, Departamento de Lingüística General, Lenguas Modernas, Lógica y Filosofía de la Ciencia

DOI:

https://doi.org/10.18778/0138-0680.2020.07

Keywords:

Husserl, completeness, categoricity, relative and absolute definiteness, imaginary numbers

Abstract

Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" 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 definiteness" as semantic completeness and argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers.

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