79 ideas
| 8187 | Frege was strongly in favour of taking truth to attach to propositions [Frege, by Dummett] |
| 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] |
| 18772 | We can treat designation by a few words as a proper name [Frege] |
| 14075 | Proper name in modal contexts refer obliquely, to their usual sense [Frege, by Gibbard] |
| 10424 | A Fregean proper name has a sense determining an object, instead of a concept [Frege, by Sainsbury] |
| 18773 | People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander' [Frege] |
| 4978 | The meaning of a proper name is the designated object [Frege] |
| 10510 | Frege ascribes reference to incomplete expressions, as well as to singular terms [Frege, by Hale] |
| 18937 | If sentences have a 'sense', empty name sentences can be understood that way [Frege, by Sawyer] |
| 18940 | It is a weakness of natural languages to contain non-denoting names [Frege] |
| 18939 | In a logically perfect language every well-formed proper name designates an object [Frege] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 9462 | Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Frege, by Jacquette] |
| 18936 | Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Frege, by Sawyer] |
| 10533 | We can't get a semantics from nouns and predicates referring to the same thing [Frege, by Dummett] |
| 4893 | Frege was asking how identities could be informative [Frege, by Perry] |
| 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] |
| 18752 | 'The concept "horse"' denotes a concept, yet seems also to denote an object [Frege, by McGee] |
| 22318 | Frege failed to show when two sets of truth-conditions are equivalent [Frege, by Potter] |
| 4980 | The meaning (reference) of a sentence is its truth value - the circumstance of it being true or false [Frege] |
| 9180 | Holism says all language use is also a change in the rules of language [Frege, by Dummett] |
| 4981 | The reference of a word should be understood as part of the reference of the sentence [Frege] |
| 15597 | Frege's Puzzle: from different semantics we infer different reference for two names with the same reference [Frege, by Fine,K] |
| 17002 | Frege's 'sense' is ambiguous, between the meaning of a designator, and how it fixes reference [Kripke on Frege] |
| 18778 | Every descriptive name has a sense, but may not have a reference [Frege] |
| 7805 | Frege started as anti-realist, but the sense/reference distinction led him to realism [Frege, by Benardete,JA] |
| 4976 | The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense [Frege] |
| 4977 | In maths, there are phrases with a clear sense, but no actual reference [Frege] |
| 4979 | We are driven from sense to reference by our desire for truth [Frege] |
| 15155 | Expressions always give ways of thinking of referents, rather than the referents themselves [Frege, by Soames] |
| 11126 | 'Sense' gives meaning to non-referring names, and to two expressions for one referent [Frege, by Margolis/Laurence] |
| 8164 | Frege was the first to construct a plausible theory of meaning [Frege, by Dummett] |
| 9817 | Earlier Frege focuses on content itself; later he became interested in understanding content [Frege, by Dummett] |
| 8171 | Frege divided the meaning of a sentence into sense, force and tone [Frege, by Dummett] |
| 4954 | Frege uses 'sense' to mean both a designator's meaning, and the way its reference is determined [Kripke on Frege] |
| 7304 | Frege explained meaning as sense, semantic value, reference, force and tone [Frege, by Miller,A] |
| 541 | Virtue comes more from habit than character [Critias] |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |