13 ideas
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] |
13639 | Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro] |
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] |
21557 | Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
10558 | Abstract objects are actually constituted by the properties by which we conceive them [Zalta] |
10557 | Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta] |