18 ideas
21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |