13 ideas
9764 | Inspiration and social improvement need wisdom, but not professional philosophy [Quine] |
9763 | For a good theory of the world, we must focus on our flabby foundational vocabulary [Quine] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |