77 ideas
15833 | Tell cleverness from answers, but wisdom from questions [Mahfouz] |
19160 | A comprehensive theory of truth probably includes a theory of predication [Davidson] |
19151 | Antirealism about truth prevents its use as an intersubjective standard [Davidson] |
19144 | 'Epistemic' truth depends what rational creatures can verify [Davidson] |
19148 | There is nothing interesting or instructive for truths to correspond to [Davidson] |
19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
19147 | Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson] |
19172 | To define a class of true sentences is to stipulate a possible language [Davidson] |
19136 | Many say that Tarski's definitions fail to connect truth to meaning [Davidson] |
19139 | Tarski does not tell us what his various truth predicates have in common [Davidson] |
19153 | Truth is basic and clear, so don't try to replace it with something simpler [Davidson] |
19170 | Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson] |
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] |
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] |
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] |
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] |
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] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
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] |
19169 | Predicates are a source of generality in sentences [Davidson] |
19149 | If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson] |
19163 | You only understand an order if you know what it is to obey it [Davidson] |
19152 | Utterances have the truth conditions intended by the speaker [Davidson] |
19162 | Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson] |
19131 | We recognise sentences at once as linguistic units; we then figure out their parts [Davidson] |
19156 | Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson] |
19176 | The concept of truth can explain predication [Davidson] |
19133 | If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson] |
19132 | Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson] |
19158 | 'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson] |
19154 | The principle of charity says an interpreter must assume the logical constants [Davidson] |
19161 | We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson] |