61 ideas
| 13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
| 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] |
| 13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
| 13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
| 13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
| 13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
| 13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
| 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] |
| 13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
| 13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
| 13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
| 13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
| 13393 | Any entity has the unique property of being that specific entity [Jubien] |
| 13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
| 13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
| 13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
| 13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
| 13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
| 13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
| 13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
| 13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
| 13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
| 13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
| 13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
| 13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 13391 | Modality concerns relations among platonic properties [Jubien] |
| 13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
| 13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
| 13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
| 13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
| 13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |