18 ideas
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |