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] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [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] |
7647 | The imagination alone perceives all objects; it is the soul, playing all its roles [La Mettrie] |
7645 | When falling asleep, the soul becomes paralysed and weak, just like the body [La Mettrie] |
23225 | The soul's faculties depend on the brain, and are simply the brain's organisation [La Mettrie] |
7652 | Man is a machine, and there exists only one substance, diversely modified [La Mettrie] |
7650 | All thought is feeling, and rationality is the sensitive soul contemplating reasoning [La Mettrie] |
7651 | With wonderful new machines being made, a speaking machine no longer seems impossible [La Mettrie] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
7648 | The sun and rain weren't made for us; they sometimes burn us, or spoil our seeds [La Mettrie] |
7646 | There is no abrupt transition from man to animal; only language has opened a gap [La Mettrie] |
7649 | There is no clear idea of the soul, which should only refer to our thinking part [La Mettrie] |