52 ideas
| 15327 | Kripke's semantic theory has actually inspired promising axiomatic theories [Kripke, by Horsten] |
| 15343 | Kripke offers a semantic theory of truth (involving models) [Kripke, by Horsten] |
| 14966 | The Tarskian move to a metalanguage may not be essential for truth theories [Kripke, by Gupta] |
| 14967 | Certain three-valued languages can contain their own truth predicates [Kripke, by Gupta] |
| 16328 | Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 15435 | If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis] |
| 15451 | I assume there could be natural properties that are not instantiated in our world [Lewis] |
| 15433 | Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis] |
| 15436 | Universals are meant to give an account of resemblance [Lewis] |
| 15438 | We can add a primitive natural/unnatural distinction to class nominalism [Lewis] |
| 15448 | The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis] |
| 15449 | If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis] |
| 15439 | The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis] |
| 15441 | The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis] |
| 15445 | Butane and Isobutane have the same atoms, but different structures [Lewis] |
| 15434 | Structural universals have a necessary connection to the universals forming its parts [Lewis] |
| 15437 | We can't get rid of structural universals if there are no simple universals [Lewis] |
| 15446 | Composition is not just making new things from old; there are too many counterexamples [Lewis] |
| 15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
| 15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 15450 | Maybe abstraction is just mereological subtraction [Lewis] |
| 15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |