70 ideas
| 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] |
| 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] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [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] |
| 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] |
| 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] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [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] |
| 13141 | Negation: if σ ¬¬X then σ 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] |
| 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] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [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] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [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] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [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] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 4938 | Prior to language, concepts are universals created by self-mapping of brain activity [Edelman/Tononi] |
| 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] |
| 4934 | Cultures have a common core of colour naming, based on three axes of colour pairs [Edelman/Tononi] |
| 4924 | A conscious human being rapidly reunifies its mind after any damage to the brain [Edelman/Tononi] |
| 4932 | A conscious state endures for about 100 milliseconds, known as the 'specious present' [Edelman/Tononi] |
| 4931 | Consciousness is a process (of neural interactions), not a location, thing, property, connectivity, or activity [Edelman/Tononi] |
| 4923 | The three essentials of conscious experience are privateness, unity and informativeness [Edelman/Tononi] |
| 4941 | Consciousness can create new axioms, but computers can't do that [Edelman/Tononi] |
| 4930 | Consciousness arises from high speed interactions between clusters of neurons [Edelman/Tononi] |
| 4929 | Dreams and imagery show the brain can generate awareness and meaning without input [Edelman/Tononi] |
| 4940 | Physicists see information as a measure of order, but for biologists it is symbolic exchange between animals [Edelman/Tononi] |
| 4935 | The sensation of red is a point in neural space created by dimensions of neuronal activity [Edelman/Tononi] |
| 4936 | The self is founded on bodily awareness centred in the brain stem [Edelman/Tononi] |
| 4939 | A sense of self begins either internally, or externally through language and society [Edelman/Tononi] |
| 4925 | Brains can initiate free actions before the person is aware of their own decision [Edelman/Tononi] |
| 4933 | Consciousness is a process, not a thing, as it maintains unity as its composition changes [Edelman/Tononi] |
| 4928 | Brain complexity balances segregation and integration, like a good team of specialists [Edelman/Tononi] |
| 4927 | Information-processing views of the brain assume the existence of 'information', and dubious brain codes [Edelman/Tononi] |
| 4922 | Consciousness involves interaction with persons and the world, as well as brain functions [Edelman/Tononi] |
| 5793 | Concepts and generalisations result from brain 'global mapping' by 'reentry' [Edelman/Tononi, by Searle] |
| 4926 | Concepts arise when the brain maps its own activities [Edelman/Tononi] |
| 4937 | Systems that generate a sense of value are basic to the primitive brain [Edelman/Tononi] |
| 6613 | The natural kinds are objects, processes and properties/relations [Ellis] |
| 6616 | Least action is not a causal law, but a 'global law', describing a global essence [Ellis] |
| 6615 | A species requires a genus, and its essence includes the essence of the genus [Ellis] |
| 6614 | A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis] |
| 6612 | Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis] |