17 ideas
16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
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] |
16981 | With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke] |
4942 | The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke] |
16984 | I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke] |
9385 | The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke] |
4943 | Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke] |
16983 | Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |