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] |
| 20429 | Most of us are too close to our own motives to understand them [Fry] |
| 20424 | Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry] |
| 20427 | Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry] |
| 20433 | 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry] |
| 20430 | In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry] |
| 20431 | Art needs a mixture of order and variety in its sensations [Fry] |
| 20423 | If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry] |
| 20428 | Popular opinion favours realism, yet most people never look closely at anything! [Fry] |
| 20432 | When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry] |
| 20425 | In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry] |
| 20426 | For pure moralists art must promote right action, and not just be harmless [Fry] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |