18 ideas
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
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] |
10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
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] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
22868 | The value and truth of knowledge are measured by success in activity [Dewey] |
22865 | Habits constitute the self [Dewey] |
22871 | The good people are those who improve; the bad are those who deteriorate [Dewey] |
22876 | Democracy is the development of human nature when it shares in the running of communal activities [Dewey] |
22875 | Democracy is not just a form of government; it is a mode of shared living [Dewey] |
22874 | Individuality is only developed within groups [Dewey] |