21 ideas
16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
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] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |