19 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
9406 | A class is natural when everybody can spot further members of it [Quinton] |
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] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |