61 ideas
| 9724 | Until the 1960s the only semantics was truth-tables [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] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [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] |
| 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] |
| 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] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 18658 | The 'Kantian' self steps back from commitment to its social situation [Kymlicka] |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| 18650 | Teleological theories give the good priority over concern for people [Kymlicka] |
| 18664 | Maybe the particularist moral thought of women is better than the impartial public thinking of men [Kymlicka] |
| 18624 | Utilitarianism is not a decision-procedure; choice of the best procedure is an open question [Kymlicka] |
| 18626 | One view says start with equality, and infer equal weight to interests, and hence maximum utility [Kymlicka] |
| 18627 | A second view says start with maximising the good, implying aggregation, and hence equality [Kymlicka] |
| 18625 | To maximise utility should we double the population, even if life somewhat deteriorates? [Kymlicka] |
| 18638 | The difference principles says we must subsidise the costs of other people's choices [Kymlicka] |
| 18635 | Social contract theories are usually rejected because there never was such a contract [Kymlicka] |
| 18630 | Utilitarianism is no longer a distinctive political position [Kymlicka] |
| 18623 | The quest of the general good is partly undermined by people's past entitlements [Kymlicka] |
| 18628 | We shouldn't endorse preferences which reject equality, and show prejudice and selfishness [Kymlicka] |
| 18629 | Using utilitarian principles to make decisions encourages cold detachment from people [Kymlicka] |
| 18637 | Utilitarianism is irrational if it tells you to trade in your rights and resources just for benefits [Kymlicka] |
| 18663 | Modern liberalism has added personal privacy to our personal social lives [Kymlicka] |
| 18632 | Liberalism tends to give priority to basic liberties [Kymlicka] |
| 18656 | Marxists say liberalism is unjust, because it allows exploitation in the sale of labour [Kymlicka] |
| 18659 | The 'Kantian' view of the self misses the way it is embedded or situated in society [Kymlicka] |
| 18660 | Communitarians say we should pay more attention to our history [Kymlicka] |
| 18657 | Communitarian states only encourage fairly orthodox ideas of the good life [Kymlicka] |
| 18649 | If everyone owned himself, that would prevent slavery [Kymlicka] |
| 18640 | Libertarians like the free market, but they also think that the free market is just [Kymlicka] |
| 18651 | The most valuable liberties to us need not be the ones with the most freedom [Kymlicka] |
| 18661 | Ancient freedom was free participation in politics, not private independence of life [Kymlicka] |
| 18633 | Equal opportunities seems fair, because your fate is from your choices, not your circumstances [Kymlicka] |
| 18634 | Equal opportunity arbitrarily worries about social circumstances, but ignores talents [Kymlicka] |
| 18654 | Marxists say justice is unneeded in the truly good community [Kymlicka] |
| 18652 | The Lockean view of freedom depends on whether you had a right to what is restricted [Kymlicka] |
| 18655 | Justice corrects social faults, but also expresses respect to individuals as ends [Kymlicka] |