22 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] |
10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
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] |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
10004 | Our minds are at their best when reasoning about objects [Hofweber] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |