Combining Texts

Ideas for 'Defending the Axioms', 'Sources of the Self' and 'Phaedo'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

13155	If you add one to one, which one becomes two, or do they both become two? [Plato]
	Full Idea: I cannot convince myself that when you add one to one either the first or the second one becomes two, or they both become two by the addition of the one to the other, ...or that when you divide one, the cause of becoming two is now the division.
	From: Plato (Phaedo [c.382 BCE], 097d)
	A reaction: Lovely questions, all leading to the conclusion that two consists of partaking in duality, to which you can come by several different routes.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17615	Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
	Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals.
	From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40)