26 ideas
3035 | Dialectic involves conversations with short questions and brief answers [Diog. Laertius] |
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] |
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] |
1816 | Sceptics say demonstration depends on self-demonstrating things, or indemonstrable things [Diog. Laertius] |
1819 | Scepticism has two dogmas: that nothing is definable, and every argument has an opposite argument [Diog. Laertius] |
3064 | When sceptics say that nothing is definable, or all arguments have an opposite, they are being dogmatic [Diog. Laertius] |
3033 | Induction moves from some truths to similar ones, by contraries or consequents [Diog. Laertius] |
1838 | Cyrenaic pleasure is a motion, but Epicurean pleasure is a condition [Diog. Laertius] |
1769 | Cynics believe that when a man wishes for nothing he is like the gods [Diog. Laertius] |
5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |