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] |
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] |
8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
20759 | Feelings are prior to intelligence; we should be content to live with our simplest feelings [Rousseau] |
19854 | We all owe labour in return for our keep, and every idle citizen is a thief [Rousseau] |