Combining Texts

Ideas for 'De Anima', 'Proof that every set can be well-ordered' and 'Paradox without Self-Reference'

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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 / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
     Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory.
     From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I