18 ideas
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
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] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
6011 | There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara] |