20 ideas
8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
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] |
8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |