51 ideas
| 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] |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |
| 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] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 12408 | Sartre to Waitress: Coffee with no cream, please... [Sommers,W] |
| 12397 | Said Plato: 'The things that we feel... [Sommers,W] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 12407 | Barman to Descartes: Would you like another drink?... [Sommers,W] |
| 12399 | There was a young student called Fred... [Sommers,W] |
| 20963 | A philosopher and his wife are out for a drive... [Sommers,W] |
| 12404 | Dear Sir, Your astonishment's odd.... [Sommers,W] |
| 12403 | There once was a man who said: 'God... [Sommers,W] |
| 12402 | ..But if he's a student of Berkeley... [Sommers,W] |
| 12409 | The philosopher Berkeley once said.. [Sommers,W] |
| 14694 | "My dog's got synaesthesia." How does he smell? ..... [Sommers,W] |
| 12401 | A toper who spies in the distance... [Sommers,W] |
| 12410 | There once was a man who said 'Damn!... [Sommers,W] |
| 9392 | How do behaviourists greet each other? [Sommers,W] |
| 12405 | 'If you're aristocratic,' said Nietzsche... [Sommers,W] |
| 9391 | Why do anarchists drink herbal tea? [Sommers,W] |
| 12400 | Cries the maid: 'You must marry me Hume!'... [Sommers,W] |
| 16527 | Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W] |
| 17592 | The barman called 'Time!', and Augustine said..... [Sommers,W] |
| 15208 | The past, present and future walked into a bar.... [Sommers,W] |