12 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] |
| 8203 | All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine] |
| 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] |
| 8202 | Meaning is essence divorced from things and wedded to words [Quine] |
| 11968 | The intension of a sentence is the set of all possible worlds in which it is true [Carnap, by Kaplan] |
| 8201 | The distinction between meaning and further information is as vague as the essence/accident distinction [Quine] |