21 ideas
9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
4037 | Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver] |
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] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
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] |
9809 | Mathematics inscribes being as such [Badiou] |
9811 | It is of the essence of being to appear [Badiou] |
4027 | Properties are respects in which particular objects may be alike or differ [Mellor/Oliver] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
4029 | Nominalists ask why we should postulate properties at all [Mellor/Oliver] |
4039 | Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver] |
9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |