Combining Texts

Ideas for 'Parmenides', 'De Re and De Dicto' and 'Necessity, Essence and Individuation'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

14648	Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga]
	Full Idea: Can't I name all the real numbers in the interval (0,1) at once? Couldn't I name them all 'Charley', for example?
	From: Alvin Plantinga (De Re and De Dicto [1969], p.40)
	A reaction: Plantinga is nervous about such a sweeping move, but can't think of an objection. This addresses a big problem, I think - that you are supposed to accept the real numbers when we cannot possibly name them all.

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.