88 ideas
| 12926 | Wisdom is the science of happiness [Leibniz] |
| 12903 | Wise people have fewer acts of will, because such acts are linked together [Leibniz] |
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| 12914 | Metaphysics is geometrical, resting on non-contradiction and sufficient reason [Leibniz] |
| 12915 | Definitions can only be real if the item is possible [Leibniz] |
| 12910 | The predicate is in the subject of a true proposition [Leibniz] |
| 19333 | A truth is just a proposition in which the predicate is contained within the subject [Leibniz] |
| 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] |
| 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] |
| 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] |
| 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] |
| 12920 | There is no multiplicity without true units [Leibniz] |
| 12319 | What is not truly one being is not truly a being either [Leibniz] |
| 12922 | A thing 'expresses' another if they have a constant and fixed relationship [Leibniz] |
| 13079 | A substance contains the laws of its operations, and its actions come from its own depth [Leibniz] |
| 12745 | Philosophy needs the precision of the unity given by substances [Leibniz] |
| 12921 | Accidental unity has degrees, from a mob to a society to a machine or organism [Leibniz] |
| 12746 | We find unity in reason, and unity in perception, but these are not true unity [Leibniz] |
| 12916 | A body is a unified aggregate, unless it has an indivisible substance [Leibniz] |
| 12919 | Unity needs an indestructible substance, to contain everything which will happen to it [Leibniz] |
| 12923 | Every bodily substance must have a soul, or something analogous to a soul [Leibniz] |
| 12704 | Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance [Leibniz] |
| 13077 | Basic predicates give the complete concept, which then predicts all of the actions [Leibniz] |
| 12908 | Essences exist in the divine understanding [Leibniz] |
| 12706 | Bodies need a soul (or something like it) to avoid being mere phenomena [Leibniz] |
| 12906 | Truths about species are eternal or necessary, but individual truths concern what exists [Leibniz] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 12904 | If varieties of myself can be conceived of as distinct from me, then they are not me [Leibniz] |
| 11981 | If someone's life went differently, then that would be another individual [Leibniz] |
| 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] |
| 12905 | I cannot think my non-existence, nor exist without being myself [Leibniz] |
| 19334 | I can't just know myself to be a substance; I must distinguish myself from others, which is hard [Leibniz] |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| 5033 | Nothing should be taken as certain without foundations [Leibniz] |
| 12913 | Nature is explained by mathematics and mechanism, but the laws rest on metaphysics [Leibniz] |
| 13089 | To fully conceive the subject is to explain the resulting predicates and events [Leibniz] |
| 5034 | Mind is a thinking substance which can know God and eternal truths [Leibniz] |
| 5032 | It seems probable that animals have souls, but not consciousness [Leibniz] |
| 5031 | Everything which happens is not necessary, but is certain after God chooses this universe [Leibniz] |
| 12911 | Concepts are what unite a proposition [Leibniz] |
| 12925 | Beauty increases with familiarity [Leibniz] |
| 12927 | Happiness is advancement towards perfection [Leibniz] |
| 15955 | I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena [Leibniz] |
| 12907 | Each possible world contains its own laws, reflected in the possible individuals of that world [Leibniz] |
| 12924 | Motion alone is relative, but force is real, and establishes its subject [Leibniz] |
| 12909 | Everything, even miracles, belongs to order [Leibniz] |
| 5030 | Miracles are extraordinary operations by God, but are nevertheless part of his design [Leibniz] |
| 12912 | Immortality without memory is useless [Leibniz] |
| 12917 | The soul is indestructible and always self-aware [Leibniz] |
| 12918 | Animals have souls, but lack consciousness [Leibniz] |