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Ideas for 'German Philosophy: a very short introduction', 'Phil Applications of Cognitive Science' and 'Defending the Axioms'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

4045	Children may have three innate principles which enable them to learn to count [Goldman]
	Full Idea: It has been proposed (on the basis of observations) that young children have three innate principles of counting - one-to-one correspondence of number to item, stable order for numbers, and cardinality (which labels the nth item counted).
	From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.60)
	A reaction: I like the idea of observed patterns as central (which is the one-to-one principle). But the other two principles are plausible, and show why pure empiricism won't work.

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)