26 ideas
1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
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] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [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] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all 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] |
3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |