29 ideas
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] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them 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] |
15200 | How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin] |
14761 | Change is not just having two different qualities at different points in some series [McTaggart] |
2608 | For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer] |
22936 | A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin] |
4231 | Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe] |
8591 | There could be no time if nothing changed [McTaggart] |
22935 | The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin] |
7802 | A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle] |
4230 | A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe] |
15199 | The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin] |
16689 | The schools said spirits lack extension, and wonder how many could dance on a needle's point [More,H] |