77 ideas
| 7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
| 7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
| 7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
| 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] |
| 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] |
| 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] |
| 7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
| 7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
| 7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
| 7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
| 7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
| 7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
| 7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
| 7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
| 7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
| 7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
| 7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
| 7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
| 7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
| 7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
| 7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
| 7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
| 7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
| 7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
| 7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
| 7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
| 7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
| 7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
| 7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
| 7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
| 7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
| 7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
| 7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
| 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] |
| 7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
| 1422 | God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm] |