The Completeness of the Real Line (La completud de la línea real)

Critica 39 (117):61 - 86 (2007)
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. /// En general se asume que las líneas físicas son líneas reales, esto es, que la estructura aritmética de los números reales corresponde de manera única a la estructura geométrica de líneas en el espacio, y que otros sistemas de números, como los hiperreales de Robinson, no logran corresponder a la estructura del espacio. En este artículo se examinan y rechazan las justificaciones intuitivas de la posición de consenso. En la medida en que pueda estar justificada, la convicción de que las líneas físicas son líneas reales es una hipótesis científica que algún día podríamos rechazar.
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