Combining Texts

Ideas for 'Parmenides', 'In Defense of Absolute Essentialism' and 'Realistic Rationalism'

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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 / 1. Mathematical Platonism / b. Against mathematical platonism

2521	'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]
	Full Idea: Three objections to realism in philosophy of mathematics: mathematical objects have no space/time location, and so no causal role; that such objects are determinate, but reference to numbers aren't; and that there is no abstract/concrete distinction.
	From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxix)