20 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] |
13331 | Part and whole contribute asymmetrically to one another, so must differ [Fine,K] |
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] |
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] |
13332 | Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K] |
13333 | The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K] |
13326 | A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K] |
13327 | A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K] |
13329 | An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K] |
13330 | An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K] |
13328 | Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |