22 ideas
21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
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] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
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] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
21785 | We are only free, with rights, if we claim our freedom, and there are no natural rights [Hegel, by Houlgate] |
22041 | Representatives by region ignores whether they care about the national interest [Hegel, by Pinkard] |
21781 | The absolute right is the right to have rights [Hegel] |