27 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] |
| 19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
| 19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
| 19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
| 19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
| 19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
| 19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
| 19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
| 19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |
| 5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |