9875 | Frege was completing Bolzano's work, of expelling intuition from number theory and analysis [Frege] |
6426 | Intuitionism says propositions are only true or false if there is a method of showing it [Russell] |
8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
12454 | Intuitionists only accept denumerable sets [Brouwer] |
1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
9548 | A mathematical object exists if there is no contradiction in its definition [Waterfield] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |