28 ideas
| 21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
| 8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
| 8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
| 8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
| 8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
| 8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
| 8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
| 8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
| 8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |