46 ideas
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [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] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [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] |
| 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] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [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] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [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] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [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] |
| 9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
| 8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| 8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
| 8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
| 10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
| 8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
| 8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
| 17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
| 17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
| 8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
| 8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
| 8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
| 4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |