Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl

Víctor Aranda

Bulletin of the Section of Logic (2020)

  • Volume: 49, Issue: 2
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Víctor Aranda. "Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl." Bulletin of the Section of Logic 49.2 (2020): null. <http://eudml.org/doc/295512>.

@article{VíctorAranda2020,
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.},
author = {Víctor Aranda},
journal = {Bulletin of the Section of Logic},
keywords = {Husserl; completeness; categoricity; relative and absolute definiteness; imaginary numbers},
language = {eng},
number = {2},
pages = {null},
title = {Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl},
url = {http://eudml.org/doc/295512},
volume = {49},
year = {2020},
}

TY - JOUR
AU - Víctor Aranda
TI - Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 2
SP - null
AB - 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.
LA - eng
KW - Husserl; completeness; categoricity; relative and absolute definiteness; imaginary numbers
UR - http://eudml.org/doc/295512
ER -

References

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