83 ideas
11912 | Substantive metaphysics says what a property is, not what a predicate means [Molnar] |
11920 | A real definition gives all the properties that constitute an identity [Molnar] |
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] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
15541 | Maybe particles are unchanging, and intrinsic change in things is their rearrangement [Lowe, by Lewis] |
11919 | Ontological dependence rests on essential connection, not necessary connection [Molnar] |
11929 | The three categories in ontology are objects, properties and relations [Molnar] |
11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
11915 | If atomism is true, then all properties derive from ultimate properties [Molnar] |
11916 | 'Being physical' is a second-order property [Molnar] |
11956 | 'Categorical properties' are those which are not powers [Molnar] |
11928 | Are tropes transferable? If they are, that is a version of Platonism [Molnar] |
11933 | A power's type-identity is given by its definitive manifestation [Molnar] |
11932 | Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar] |
11934 | The physical world has a feature very like mental intentionality [Molnar] |
11947 | Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar] |
11952 | The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar] |
11953 | Some powers are ungrounded, and others rest on them, and are derivative [Molnar] |
11943 | Dispositions can be causes, so they must be part of the actual world [Molnar] |
11939 | If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar] |
11914 | Platonic explanations of universals actually diminish our understanding [Molnar] |
11913 | For nominalists, predicate extensions are inexplicable facts [Molnar] |
11962 | Nominalists only accept first-order logic [Molnar] |
11917 | Structural properties are derivate properties [Molnar] |
11955 | There are no 'structural properties', as properties with parts [Molnar] |
11918 | The essence of a thing need not include everything that is necessarily true of it [Molnar] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
11963 | What is the truthmaker for a non-existent possible? [Molnar] |
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] |
11951 | Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar] |
11936 | The two ways proposed to distinguish mind are intentionality or consciousness [Molnar] |
11935 | Physical powers like solubility and charge also have directedness [Molnar] |
11944 | Rule occasionalism says God's actions follow laws, not miracles [Molnar] |
11960 | Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar] |
11937 | We should analyse causation in terms of powers, not vice versa [Molnar] |
11954 | We should analyse causation in terms of powers [Molnar] |
11961 | Causal dependence explains counterfactual dependence, not vice versa [Molnar] |
11959 | Science works when we assume natural kinds have essences - because it is true [Molnar] |
9448 | Location in space and time are non-power properties [Molnar, by Mumford] |
11930 | One essential property of a muon doesn't entail the others [Molnar] |
11957 | It is contingent which kinds and powers exist in the world [Molnar] |
11921 | The laws of nature depend on the powers, not the other way round [Molnar] |
11931 | Energy fields are discontinuous at the very small [Molnar] |