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Ideas for 'fragments/reports', 'What is Cantor's Continuum Problem?' and 'The Origin of Forms and Qualities'

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3 ideas

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

10868	The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
	Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory.
	From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15

13517	If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
	Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either.
	From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

10271	Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
	Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas.
	From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl)
	A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass.