Crítica, Revista Hispanoamericana de Filosofía, Volume 39, number 117, diciembre 2007
The Completeness of the Real Line
[La completud de la línea real]
Matthew E. Moore
Department of Philosophy
Brooklyn College

Abstract: 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.
Keywords: infinitesimals, geometry, intuition, space, continuity

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