13 ideas
9283 | Our ancient beliefs can never be overthrown by subtle arguments [Euripides] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
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] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |