97 ideas
10468 | A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver] |
10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
10750 | Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver] |
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] |
10747 | Accepting properties by ontological commitment tells you very little about them [Oliver] |
10748 | Reference is not the only way for a predicate to have ontological commitment [Oliver] |
16661 | There are two sorts of category - referring to things, and to circumstances of things [Boethius] |
10721 | If properties are sui generis, are they abstract or concrete? [Oliver] |
10719 | There are four conditions defining the relations between particulars and properties [Oliver] |
10716 | There are just as many properties as the laws require [Oliver] |
10720 | We have four options, depending whether particulars and properties are sui generis or constructions [Oliver] |
10714 | The expressions with properties as their meanings are predicates and abstract singular terms [Oliver] |
10715 | There are five main semantic theories for properties [Oliver] |
10739 | The property of redness is the maximal set of the tropes of exactly similar redness [Oliver] |
10738 | Tropes are not properties, since they can't be instantiated twice [Oliver] |
10740 | The orthodox view does not allow for uninstantiated tropes [Oliver] |
10741 | Maybe concrete particulars are mereological wholes of abstract particulars [Oliver] |
10742 | Tropes can overlap, and shouldn't be splittable into parts [Oliver] |
10472 | 'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver] |
10724 | Located universals are wholly present in many places, and two can be in the same place [Oliver] |
10730 | If universals ground similarities, what about uniquely instantiated universals? [Oliver] |
7963 | Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver] |
7962 | Uninstantiated properties are useful in philosophy [Oliver] |
10727 | Uninstantiated universals seem to exist if they themselves have properties [Oliver] |
15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |
10722 | Instantiation is set-membership [Oliver] |
10744 | Nominalism can reject abstractions, or universals, or sets [Oliver] |
14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
10726 | Things can't be fusions of universals, because two things could then be one thing [Oliver] |
10725 | Abstract sets of universals can't be bundled to make concrete things [Oliver] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
10745 | Science is modally committed, to disposition, causation and law [Oliver] |
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] |
23308 | Reasoning relates to understanding as time does to eternity [Boethius, by Sorabji] |
5771 | Knowledge of present events doesn't make them necessary, so future events are no different [Boethius] |
5767 | Rational natures require free will, in order to have power of judgement [Boethius] |
5769 | Does foreknowledge cause necessity, or necessity cause foreknowledge? [Boethius] |
5768 | God's universal foreknowledge seems opposed to free will [Boethius] |
10746 | Conceptual priority is barely intelligible [Oliver] |
5762 | The wicked want goodness, so they would not be wicked if they obtained it [Boethius] |
5770 | Rewards and punishments are not deserved if they don't arise from free movement of the mind [Boethius] |
5764 | When people fall into wickedness they lose their human nature [Boethius] |
5756 | Happiness is a good which once obtained leaves nothing more to be desired [Boethius] |
5763 | The bad seek the good through desire, but the good through virtue, which is more natural [Boethius] |
5759 | Varied aims cannot be good because they differ, but only become good when they unify [Boethius] |
5754 | You can't control someone's free mind, only their body and possessions [Boethius] |
16692 | Divine eternity is the all-at-once and complete possession of unending life [Boethius] |
5752 | Where does evil come from if there is a god; where does good come from if there isn't? [Boethius] |
5757 | God is the supreme good, so no source of goodness could take precedence over God [Boethius] |
5758 | God is the good [Boethius] |
5760 | The power through which creation remains in existence and motion I call 'God' [Boethius] |
5753 | The regular events of this life could never be due to chance [Boethius] |
5765 | The reward of the good is to become gods [Boethius] |
5761 | God can do anything, but he cannot do evil, so evil must be nothing [Boethius] |
5766 | If you could see the plan of Providence, you would not think there was evil anywhere [Boethius] |