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Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl
Bulletin of the Section of Logic, Tome 49 (2020) no. 2.

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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.
Keywords: Husserl, completeness, categoricity, relative and absolute definiteness, imaginary numbers 
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     author = {Aranda, V{\'\i}ctor},
     title = {Completeness, {Categoricity} and {Imaginary} {Numbers:} {The} {Debate} on {Husserl}},
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     url = {http://geodesic.mathdoc.fr/item/BSL_2020_49_2_a1/}
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Aranda, Víctor. Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl. Bulletin of the Section of Logic, Tome 49 (2020) no. 2. http://geodesic.mathdoc.fr/item/BSL_2020_49_2_a1/