22 ideas
21560 | Any linguistic expression may lack meaning when taken out of context [Russell] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21561 | 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell] |
18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
21562 | There is no complexity without relations, so no propositions, and no truth [Russell] |
11181 | Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)] |
11184 | Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)] |
11180 | Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)] |
11186 | 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)] |
11185 | 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)] |
11182 | If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)] |
11183 | The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)] |
11187 | In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)] |
11189 | Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)] |