Combining Texts

Ideas for 'Parmenides', 'Contemporary Philosophy of Mind' and 'On the Elements of Being: I'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

16150	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.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

3143	Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey]
	Full Idea: Physics is committed to arithmetic, which seems committed to abstract objects such as numbers, and its causal explanations seem to appeal to properties, such as mass and charge.
	From: Georges Rey (Contemporary Philosophy of Mind [1997], 2.3)