Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl-Reference-Cited by-同舟云学术

Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl

Published:2020-06-30 Issue:2 Volume:49 Page:
ISSN:2449-836X
Container-title:Bulletin of the Section of Logic
language:
Short-container-title:B Sect Log

Author:

Aranda Víctor

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.

Publisher

Uniwersytet Lodzki (University of Lodz)

Subject

Logic,Philosophy

Reference23 articles.

1. [1] S. Awodey, E. Reck, Completeness and Categoricity. Part I, History and Philosophy of Logic, vol. 23 (2002), pp. 1–30.

2. [2] R. Carnap, Untersuchungen zur allgemeinen Axiomatik, Wissenschaftliche Buchgesellschaft, Darmstadt (2000).

3. [3] S. Centrone, Logic and philosophy of mathematics in the early Husserl, Springer, Dordrecht (2010).

4. [4] J. J. Da Silva, Husserl's two notions of completeness, Synthese, vol. 125 (2000), pp. 417–438.

5. [5] J. J. Da Silva, Husserl and Hilbert on completeness, still, Synthese, vol. 193 (2016), pp. 1925–1947.

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