36 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] |
| 21495 | Theoretical and practical politics are both concerned with the best lives for individuals [Russell] |
| 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] |
| 21517 | Individuals need creativity, reverence for others, and self-respect [Russell] |
| 23857 | People in power always try to increase their power [Weil] |
| 21523 | We would not want UK affairs to be settled by a world parliament [Russell] |
| 21522 | Democracy is inadequate without a great deal of devolution [Russell] |
| 23856 | Spontaneous movements are powerless against organised repression [Weil] |
| 21521 | Anarchy does not maximise liberty [Russell] |
| 21528 | Groups should be autonomous, with a neutral authority as arbitrator [Russell] |
| 21527 | On every new question the majority is always wrong at first [Russell] |
| 21526 | Unfortunately ordinary voters can't detect insincerity [Russell] |
| 23859 | True democracy is the subordination of society to the individual [Weil] |
| 21525 | When the state is the only employer, there is no refuge from the prejudices of other people [Russell] |
| 21518 | Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell] |
| 21519 | We need security and liberty, and then encouragement of creativity [Russell] |
| 21524 | The right to own land gives a legal right to a permanent income [Russell] |
| 23858 | War is perpetuated by its continual preparations [Weil] |
| 23860 | Even if a drowning man is doomed, he should keep swimming to the last [Weil] |
| 21520 | That our heaven is a dull place reflects the misery of excessive work in life [Russell] |