19 ideas
16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
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] |