16 ideas
18261 | A simplification which is complete constitutes a definition [Kant] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
8686 | Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend] |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
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] |
22277 | Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter] |
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] |
18260 | If we knew what we know, we would be astonished [Kant] |