56 ideas
| 5515 | Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit] |
| 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] |
| 5516 | Reduction can be by identity, or constitution, or elimination [Parfit, by PG] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 3539 | Personal identity is just causally related mental states [Parfit, by Maslin] |
| 5514 | Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit] |
| 1393 | One of my future selves will not necessarily be me [Parfit] |
| 5521 | If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit] |
| 5522 | Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit] |
| 1392 | If we split like amoeba, we would be two people, neither of them being us [Parfit] |
| 5519 | It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit] |
| 5520 | If two humans are merged surgically, the new identity is a purely verbal problem [Parfit] |
| 1391 | Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit] |
| 5518 | It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit] |
| 4988 | Folk psychology may not be reducible, but that doesn't make it false [Kirk,R on Churchland,PM] |
| 4987 | Eliminative materialism says folk psychology will be replaced, not reduced [Churchland,PM] |
| 7518 | If folk psychology gives a network of causal laws, that fits neatly with functionalism [Churchland,PM] |
| 7519 | Many mental phenomena are totally unexplained by folk psychology [Churchland,PM] |
| 7520 | Folk psychology never makes any progress, and is marginalised by modern science [Churchland,PM] |
| 9762 | We should focus less on subjects of experience, and more on the experiences themselves [Parfit] |