38 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] |
18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
11886 | There are problems both with individual essences and without them [Mackie,P] |
11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
11892 | Things may only be counterparts under some particular relation [Mackie,P] |
11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |