79 ideas
| 8605 | In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis] |
| 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] |
| 8607 | Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis] |
| 8606 | A supervenience thesis is a denial of independent variation [Lewis] |
| 8580 | Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis] |
| 8571 | Universals are wholly present in their instances, whereas properties are spread around [Lewis] |
| 10717 | Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver] |
| 16217 | Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley] |
| 8613 | Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis] |
| 8585 | Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis] |
| 8586 | Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis] |
| 8589 | For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis] |
| 15460 | All perfectly natural properties are intrinsic [Lewis, by Lewis] |
| 15726 | Natural properties fix resemblance and powers, and are picked out by universals [Lewis] |
| 7031 | Lewis says properties are sets of actual and possible objects [Lewis, by Heil] |
| 8572 | Any class of things is a property, no matter how whimsical or irrelevant [Lewis] |
| 18433 | There are far more properties than any brain could ever encodify [Lewis] |
| 8604 | We need properties as semantic values for linguistic expressions [Lewis] |
| 14499 | Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki] |
| 15120 | Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne] |
| 8573 | Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis] |
| 8569 | I suspend judgements about universals, but their work must be done [Lewis] |
| 21961 | Physics aims to discover which universals actually exist [Lewis, by Moore,AW] |
| 8576 | The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis] |
| 8570 | To have a property is to be a member of a class, usually a class of things [Lewis] |
| 8574 | Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis] |
| 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] |
| 8579 | Psychophysical identity implies the possibility of idealism or panpsychism [Lewis] |
| 8614 | A sophisticated principle of charity sometimes imputes error as well as truth [Lewis] |
| 8615 | We need natural properties in order to motivate the principle of charity [Lewis] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 8608 | Counterfactuals 'backtrack' if a different present implies a different past [Lewis] |
| 8584 | Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis] |
| 8581 | Physics discovers laws and causal explanations, and also the natural properties required [Lewis] |
| 15727 | Physics aims for a list of natural properties [Lewis] |
| 8611 | A law of nature is any regularity that earns inclusion in the ideal system [Lewis] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |