28 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] |
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] |
8203 | All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine] |
19419 | Not all of perception is accompanied by consciousness [Leibniz] |
19421 | Souls act as if there were no bodies, and bodies act as if there were no souls [Leibniz] |
8202 | Meaning is essence divorced from things and wedded to words [Quine] |
8201 | The distinction between meaning and further information is as vague as the essence/accident distinction [Quine] |
19420 | Death and generation are just transformations of an animal, augmented or diminished [Leibniz] |
19416 | Not all of matter is animated, any more than a pond full of living fish is animated [Leibniz] |
19422 | Every particle of matter contains organic bodies [Leibniz] |
19418 | Mechanics shows that all motion originates in other motion, so there is a Prime Mover [Leibniz] |
19417 | All substances are in harmony, even though separate, so they must have one divine cause [Leibniz] |