79 ideas
| 22611 | Metaphysics can criticise interpretations of science theories, and give good feedback [Ingthorsson] |
| 12129 | 'Truth' may only apply within a theory [Kuhn] |
| 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] |
| 22609 | Philosophers accepted first-order logic, because they took science to be descriptive, not explanatory [Ingthorsson] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 22629 | Basic processes are said to be either physical, or organic, or psychological [Ingthorsson] |
| 22633 | Indirect realists are cautious about the manifest image, and prefer the scientific image [Ingthorsson] |
| 22606 | Neo-Humeans say there are no substantial connections between anything [Ingthorsson] |
| 22631 | Properties are said to be categorical qualities or non-qualitative dispositions [Ingthorsson] |
| 22632 | Physics understands the charge of an electron as a power, not as a quality [Ingthorsson] |
| 22627 | Compound objects are processes, insofar as change is essential to them [Ingthorsson] |
| 22613 | Most materialist views postulate smallest indivisible components which are permanent [Ingthorsson] |
| 22612 | Endurance and perdurance just show the consequences of A or B series time [Ingthorsson] |
| 22625 | Science suggests causal aspects of the constitution and persistance of objects [Ingthorsson] |
| 22620 | If causation involves production, that needs persisting objects [Ingthorsson] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 22636 | Every philosophical theory must be true in some possible world, so the ontology is hopeless [Ingthorsson] |
| 22638 | Worlds may differ in various respects, but no overall similarity of worlds is implied [Ingthorsson] |
| 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] |
| 6809 | Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird] |
| 12128 | In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn] |
| 22605 | Humeans describe the surface of causation, while powers accounts aim at deeper explanations [Ingthorsson] |
| 22607 | Time and space are not causal, but they determine natural phenomena [Ingthorsson] |
| 22608 | Casuation is the transmission of conserved quantities between causal processes [Ingthorsson] |
| 22621 | Causation as transfer only works for asymmetric interactions [Ingthorsson] |
| 22614 | Interventionist causal theory says it gets a reliable result whenever you manipulate it [Ingthorsson] |
| 22639 | Causal events are always reciprocal, and there is no distinction of action and reaction [Ingthorsson] |
| 22615 | One effect cannot act on a second effect in causation, because the second doesn't yet exist [Ingthorsson] |
| 22616 | Empiricists preferred events to objects as the relata, because they have observable motions [Ingthorsson] |
| 22617 | Science now says all actions are reciprocal, not unidirectional [Ingthorsson] |
| 22619 | Causes are not agents; the whole interaction is the cause, and the changed compound is the effect [Ingthorsson] |
| 22635 | People only accept the counterfactual when they know the underlying cause [Ingthorsson] |
| 22634 | Counterfactuals don't explain causation, but causation can explain counterfactuals [Ingthorsson] |
| 22637 | Counterfactual theories are false in possible worlds where causation is actual [Ingthorsson] |
| 22624 | A cause can fail to produce its normal effect, by prevention, pre-emption, finks or antidotes [Ingthorsson] |
| 22622 | Any process can go backwards or forwards in time without violating the basic laws of physics [Ingthorsson] |
| 22618 | In modern physics the first and second laws of motion (unlike the third) fail at extremes [Ingthorsson] |
| 22630 | If particles have decay rates, they can't really be elementary, in the sense of indivisible [Ingthorsson] |
| 22610 | It is difficult to handle presentism in first-order logic [Ingthorsson] |