50 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] |
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] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [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] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [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] |
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] |
11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
11886 | There are problems both with individual essences and without them [Mackie,P] |
11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
11892 | Things may only be counterparts under some particular relation [Mackie,P] |
11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |