The Completeness of the Real Line

It is widely taken for granted that physical lines are real lines, i.e., that the arithmetical structure of the real numbers uniquely matches the geometrical structure of lines in space; and that other number systems, like Robinson’s hyperreals, accordingly fail to fit the structure of space. Intui...

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Bibliographic Details
Main Author: Matthew E. Moore
Format: Article
Language:English
Published: Universidad Nacional Autónoma de México (UNAM) 2018-12-01
Series:Crítica
Subjects:
Online Access:https://critica.filosoficas.unam.mx/index.php/critica/article/view/583
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Summary:It is widely taken for granted that physical lines are real lines, i.e., that the arithmetical structure of the real numbers uniquely matches the geometrical structure of lines in space; and that other number systems, like Robinson’s hyperreals, accordingly fail to fit the structure of space. Intuitive justifications for the consensus view are considered and rejected. Insofar as it is justified at all, the conviction that physical lines are real lines is a scientific hypothesis which we may one day reject.
ISSN:0011-1503
1870-4905