16 ideas
19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
17879 | Axiomatising set theory makes it all relative [Skolem] |
13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
12454 | Intuitionists only accept denumerable sets [Brouwer] |
12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |