22 ideas
23249 | The early philosophers thought that reason has its own needs and desires [Frede,M] |
21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
10011 | Identity is a level one relation with a second-order definition [Hodes] |
21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
10027 | Mathematics is higher-order modal logic [Hodes] |
10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
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] |
10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |