70 ideas
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
| 7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
| 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] |
| 9457 | The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette] |
| 7681 | Logic describes inferences between sentences expressing possible properties of objects [Jacquette] |
| 9463 | Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 7682 | Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette] |
| 7697 | On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette] |
| 9466 | Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette] |
| 9465 | Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette] |
| 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] |
| 9458 | Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette] |
| 9461 | Intensionalists say meaning is determined by the possession of properties [Jacquette] |
| 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] |
| 7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
| 7707 | To grasp being, we must say why something exists, and why there is one world [Jacquette] |
| 7687 | Existence is completeness and consistency [Jacquette] |
| 7692 | Being is maximal consistency [Jacquette] |
| 7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
| 7678 | Ontology must include the minimum requirements for our semantics [Jacquette] |
| 7683 | Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette] |
| 7684 | Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette] |
| 7703 | If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette] |
| 8511 | Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K] |
| 7685 | An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette] |
| 7699 | Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 7691 | The actual world is a consistent combination of states, made of consistent property combinations [Jacquette] |
| 7688 | The actual world is a maximally consistent combination of actual states of affairs [Jacquette] |
| 7695 | Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette] |
| 7694 | We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette] |
| 7706 | If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette] |
| 7704 | Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette] |
| 9460 | Extensionalist semantics forbids reference to nonexistent objects [Jacquette] |
| 9459 | Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette] |
| 7702 | The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette] |