105 ideas
| 9355 | One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt] |
| 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] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [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] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [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] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [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] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [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] |
| 22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
| 23283 | Necessity implies possibility, but in experience it matters which comes first [Williams,B] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
| 4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [Williams,B] |
| 3238 | 'Dead person' isn't a contradiction, so 'person' is somewhat vague [Williams,B] |
| 3239 | You can only really love a person as a token, not as a type [Williams,B] |
| 7946 | The memory criterion has a problem when one thing branches into two things [Williams,B, by Macdonald,C] |
| 2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
| 2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
| 24008 | Reference to a person's emotions is often essential to understanding their actions [Williams,B] |
| 24009 | Moral education must involve learning about various types of feeling towards things [Williams,B] |
| 4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
| 9284 | Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B] |
| 2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
| 22455 | Many ethical theories neglect the power of regretting the ought not acted upon [Williams,B] |
| 4114 | Philosophers try to produce ethical theories because they falsely assume that ethics can be simple [Williams,B] |
| 22453 | Moral conflicts have a different feeling and structure from belief conflicts [Williams,B, by Foot] |
| 22454 | We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot] |
| 22450 | If moral systems can't judge other moral systems, then moral relativism is true [Williams,B, by Foot] |
| 2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
| 20168 | Blame usually has no effect if the recipient thinks it unjustified [Williams,B] |
| 20167 | Blame partly rests on the fiction that blamed agents always know their obligations [Williams,B] |
| 4128 | Intuitionism has been demolished by critics, and no longer looks interesting [Williams,B] |
| 4366 | We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse] |
| 4132 | The category of person is a weak basis for ethics, because it is not fixed but comes in degrees [Williams,B] |
| 24007 | Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B] |
| 4134 | The weakness of prescriptivism is shown by "I simply don't like staying at good hotels" [Williams,B] |
| 4135 | Some ethical ideas, such as 'treachery' and 'promise', seem to express a union of facts and values [Williams,B] |
| 22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
| 22408 | Consequentialism assumes that situations can be compared [Williams,B] |
| 22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
| 4120 | It is an error of consequentialism to think we just aim at certain states of affairs; we also want to act [Williams,B] |
| 23282 | If all that matters in morality is motive and intention, that makes moral luck irrelevant [Williams,B] |
| 4252 | Promise keeping increases reliability, by making deliberation focus on something which would be overlooked [Williams,B] |
| 4116 | A weakness of contractual theories is the position of a person of superior ability and power [Williams,B] |
| 2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
| 4112 | A crucial feature of moral thought is second-order desire - the desire to have certain desires [Williams,B] |
| 24010 | An admirable human being should have certain kinds of emotional responses [Williams,B] |
| 23279 | It is important that a person can change their character, and not just be successive 'selves' [Williams,B] |
| 23280 | Kantians have an poor account of individuals, and insist on impartiality, because they ignore character [Williams,B] |
| 3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
| 4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
| 4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
| 4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
| 4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
| 4249 | "Ought implies can" is a famous formula in connection with moral obligation [Williams,B] |
| 2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
| 4121 | Why should I think of myself as both the legislator and the citizen who follows the laws? [Williams,B] |
| 22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
| 4122 | If the self becomes completely impartial, it no longer has enough identity to worry about its interests [Williams,B] |
| 2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
| 24012 | Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B] |
| 2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
| 22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
| 23278 | For utilitarians states of affairs are what have value, not matter who produced them [Williams,B] |
| 4124 | Utilitarian benevolence involves no particular attachments, and is immune to the inverse square law [Williams,B] |
| 4245 | Ethical conviction must be to some extent passive, and can't just depend on the will and decisions [Williams,B] |
| 4246 | Taking responsibility won't cure ethical uncertainty by; we are uncertain what to decide [Williams,B] |
| 3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
| 3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
| 3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
| 4247 | It is a mark of our having ethical values that we aim to reproduce them in our children [Williams,B] |
| 4131 | Most women see an early miscarriage and a late stillbirth as being very different in character [Williams,B] |
| 4133 | Speciesism isn't like racism, because the former implies a viewpoint which belongs to no one [Williams,B] |
| 1468 | If meaning is use, then religious sentences have meaning because they are used to assert an intention about how to live [Braithwaite, by PG] |
| 2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |