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3 ideas
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 |
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. |