59 ideas
| 7920 | Descriptive metaphysics aims at actual structure, revisionary metaphysics at a better structure [Strawson,P] |
| 7922 | Descriptive metaphysics concerns unchanging core concepts and categories [Strawson,P] |
| 7921 | Close examination of actual word usage is the only sure way in philosophy [Strawson,P] |
| 10842 | The fact which is stated by a true sentence is not something in the world [Strawson,P] |
| 10843 | Facts aren't exactly true statements, but they are what those statements say [Strawson,P] |
| 10844 | The statement that it is raining perfectly fits the fact that it is raining [Strawson,P] |
| 10841 | The word 'true' always refers to a possible statement [Strawson,P] |
| 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] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [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] |
| 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] |
| 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] |
| 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] |
| 8358 | There are no rules for the exact logic of ordinary language, because that doesn't exist [Strawson,P] |
| 6413 | 'The present King of France is bald' presupposes existence, rather than stating it [Strawson,P, by Grayling] |
| 8354 | Russell asks when 'The King of France is wise' would be a true assertion [Strawson,P] |
| 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] |
| 16980 | We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P] |
| 16979 | It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 2975 | That honey is sweet I do not affirm, but I agree that it appears so [Timon] |
| 9282 | I can only apply consciousness predicates to myself if I can apply them to others [Strawson,P] |
| 9263 | A person is an entity to which we can ascribe predicates of consciousness and corporeality [Strawson,P] |
| 8356 | The meaning of an expression or sentence is general directions for its use, to refer or to assert [Strawson,P] |
| 10430 | Reference is mainly a social phenomenon [Strawson,P, by Sainsbury] |
| 10448 | If an expression can refer to anything, it may still instrinsically refer, but relative to a context [Bach on Strawson,P] |
| 8355 | Expressions don't refer; people use expressions to refer [Strawson,P] |
| 8357 | If an utterance fails to refer then it is a pseudo-use, though a speaker may think they assert something [Strawson,P] |
| 9281 | The idea of a predicate matches a range of things to which it can be applied [Strawson,P] |