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Continuity and Incommensurability in Ancient Greek Philosophy and Mathematics

  • Vassilis Karasmanis
Chapter
Part of the Philosophical Studies Series book series (PSSP, volume 117)

Abstract

Aristotle, in the sixth Book of his Physics, discusses extensively the problem of continuity. Continuity is the main and essential characteristic of magnitudes. The continuum is found only in magnitudes and all magnitudes are continuous. Both philosophers and mathematicians distinguish between arithmetic and geometry in the sense that arithmetic deals with numbers and geometry with magnitudes.1 Magnitudes are continuous; numbers are discrete. In the Categories (4b20–24) Aristotle says that “of quantities some are discrete (diôrismenon), others continuous (suneches)… . Discrete are numbers and language; continuous are lines, surfaces, bodies, and also, besides these, time and place.”2

Keywords

Definite Quantity Regular Pentagon Original Assertion Infinite Divisibility Continuous Magnitude 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.National Technical University of AthensAthensGreece

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