20 ideas
9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
9984 | We can have a series with identical members [Tait] |
15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
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] |
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] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |