21 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] |
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] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
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] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |