28 ideas
9470 | Modal logic is not an extensional language [Parsons,C] |
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
12797 | If plural variables have 'some values', then non-count variables have 'some value' [Laycock] |
9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
12794 | Plurals are semantical but not ontological [Laycock] |
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] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
17694 | Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock] |
17695 | Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock] |
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] |
18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
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] |
12792 | The category of stuff does not suit reference [Laycock] |
12799 | Descriptions of stuff are neither singular aggregates nor plural collections [Laycock] |
12818 | We shouldn't think some water retains its identity when it is mixed with air [Laycock] |
13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
12795 | Parts must be of the same very general type as the wholes [Laycock] |
17696 | 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock] |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
12791 | It is said that proper reference is our intellectual link with the world [Laycock] |