10 ideas
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
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] |
13858 | The truth-functional account of conditionals is right, if the antecedent is really acceptable [Jackson, by Edgington] |