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Ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'The Principles of Science'

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2 ideas

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

17836	The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
	Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself.
	From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217)

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

8628	I hold that algebra and number are developments of logic [Jevons]
	Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination.
	From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15
	A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here.