91 ideas
11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
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] |
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] |
11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
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] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
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] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
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] |
16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
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] |
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] |
9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |
5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |