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Ideas for 'Parmenides', 'fragments/reports' and 'Theory of Knowledge (2nd ed 1977)'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Things get smaller without end [Anaxagoras]
     Full Idea: Of the small there is no smallest, but always a smaller.
     From: Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II
     A reaction: Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea).
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
     Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
     From: Plato (Parmenides [c.364 BCE], 144a)
     A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.