Combining Texts

Ideas for 'A Résumé of Metaphysics', 'De Anima' and 'Set Theory and the Continuum Hypothesis'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

1729	We perceive number by the denial of continuity [Aristotle]
	Full Idea: Number we perceive by the denial of continuity.
	From: Aristotle (De Anima [c.329 BCE], 425a19)
	A reaction: This is a key thought. A being (call it 'Parmenides') which sees all Being as One would make no distinctions of identity, and so could not count anything. Why would they want numbers?

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

14248	We could accept the integers as primitive, then use sets to construct the rest [Cohen]
	Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
	From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
	A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.