85 ideas
| 6052 | Definitions identify two concepts, so they presuppose identity [McGinn] |
| 6064 | Regresses are only vicious in the context of an explanation [McGinn] |
| 6088 | Truth is a method of deducing facts from propositions [McGinn] |
| 6084 | 'Snow does not fall' corresponds to snow does fall [McGinn] |
| 6085 | The idea of truth is built into the idea of correspondence [McGinn] |
| 6083 | The coherence theory of truth implies idealism, because facts are just coherent beliefs [McGinn] |
| 6086 | Truth is the property of propositions that makes it possible to deduce facts [McGinn] |
| 6087 | Without the disquotation device for truth, you could never form beliefs from others' testimony [McGinn] |
| 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] |
| 6051 | In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn] |
| 6055 | Both non-contradiction and excluded middle need identity in their formulation [McGinn] |
| 6059 | Identity is unitary, indefinable, fundamental and a genuine relation [McGinn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 6042 | The quantifier is overrated as an analytical tool [McGinn] |
| 6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
| 6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
| 6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
| 6070 | Existence is a primary quality, non-existence a secondary quality [McGinn] |
| 6062 | Existence can't be analysed as instantiating a property, as instantiation requires existence [McGinn] |
| 6065 | We can't analyse the sentence 'something exists' in terms of instantiated properties [McGinn] |
| 6082 | If causal power is the test for reality, that will exclude necessities and possibilities [McGinn] |
| 6075 | Facts are object-plus-extension, or property-plus-set-of-properties, or object-plus-property [McGinn] |
| 6058 | Identity propositions are not always tautological, and have a key epistemic role [McGinn] |
| 6053 | Identity is as basic as any concept could ever be [McGinn] |
| 6043 | Type-identity is close similarity in qualities [McGinn] |
| 6044 | Qualitative identity is really numerical identity of properties [McGinn] |
| 6046 | Qualitative identity can be analysed into numerical identity of the type involved [McGinn] |
| 6045 | It is best to drop types of identity, and speak of 'identity' or 'resemblance' [McGinn] |
| 6066 | Existence is a property of all objects, but less universal than self-identity, which covers even conceivable objects [McGinn] |
| 6054 | Sherlock Holmes does not exist, but he is self-identical [McGinn] |
| 6047 | All identity is necessary, though identity statements can be contingently true [McGinn] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 6049 | Leibniz's Law says 'x = y iff for all P, Px iff Py' [McGinn] |
| 6048 | Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn] |
| 6050 | Leibniz's Law presupposes the notion of property identity [McGinn] |
| 6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
| 6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
| 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] |
| 6081 | Necessity and possibility are big threats to the empiricist view of knowledge [McGinn] |
| 6071 | Scepticism about reality is possible because existence isn't part of appearances [McGinn] |
| 6077 | Semantics should not be based on set-membership, but on instantiation of properties in objects [McGinn] |
| 6074 | Clearly predicates have extensions (applicable objects), but are the extensions part of their meaning? [McGinn] |
| 5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
| 6072 | If Satan is the most imperfect conceivable being, he must have non-existence [McGinn] |
| 6073 | I think the fault of the Ontological Argument is taking the original idea to be well-defined [McGinn] |