20 ideas
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |