Combining Texts

Ideas for 'Defending the Axioms', 'The Republic' and 'Mental Files'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

8726	Geometry can lead the mind upwards to truth and philosophy [Plato]
	Full Idea: Geometry can attract the mind towards truth. It can produce philosophical thought, in the sense that it can reverse the midguided downwards tendencies we currently have.
	From: Plato (The Republic [c.374 BCE], 527b)
	A reaction: Hence the Academy gate bore the inscription "Let no one enter here who is ignorant of geometry". He's not necessarily wrong. Something in early education must straighten out some of the kinks in the messy human mind.

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)