31 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] |
| 7096 | We may still admire a person's character even if the traits are involuntary [Statman] |
| 20420 | The emotion expressed is non-conscious, but feels oppressive until expression relieves it [Collingwood] |
| 20421 | Art exists ideally, purely as experiences in the mind of the perceiver [Collingwood, by Kemp] |
| 20406 | Art clarifies the artist's mind and feelings, thus leading to self-knowledge [Collingwood, by Davies,S] |
| 7098 | There is a new sort of moral scepticism, about the possibility of moral theories [Statman] |
| 7099 | With a broad concept of flourishing, it might be possible without the virtues [Statman] |
| 7100 | Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman] |
| 7102 | Promises create moral duties that have nothing to do with character [Statman] |
| 7095 | Moral education is better by concrete example than abstract principle [Statman] |
| 7094 | Friends express friendship even when no utility is involved [Statman] |
| 7093 | Behaviour may be disgusting or inhumane, but violate no duty [Statman] |
| 7104 | The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman] |
| 7103 | Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman] |