88 ideas
| 11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| 18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| 7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
| 5772 | The idea of a variable is fundamental [Russell] |
| 18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
| 4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
| 18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
| 7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
| 10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
| 15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
| 2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
| 7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
| 18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
| 6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
| 10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
| 11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
| 1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
| 7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
| 21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
| 6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
| 6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
| 7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
| 7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
| 12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
| 4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
| 21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
| 12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
| 7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
| 11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
| 6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| 18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
| 7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
| 6063 | Russell can't attribute existence to properties [McGinn on Russell] |
| 18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell] |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| 4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
| 5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
| 5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
| 5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
| 16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
| 16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
| 4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
| 16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
| 7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
| 7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
| 21726 | In graspable propositions the constituents are real entities of acquaintance [Russell] |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |
| 5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |