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
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Karasmanis, V. (2011). Continuity and Incommensurability in Ancient Greek Philosophy and Mathematics. In: Anagnostopoulos, G. (eds) Socratic, Platonic and Aristotelian Studies: Essays in Honor of Gerasimos Santas. Philosophical Studies Series, vol 117. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1730-5_22
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