33 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] |
| 13134 | We negate predicates but do not negate names [Westerhoff] |
| 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] |
| 13124 | Categories can be ordered by both containment and generality [Westerhoff] |
| 13117 | How far down before we are too specialised to have a category? [Westerhoff] |
| 13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
| 13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
| 13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
| 13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
| 13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
| 13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
| 13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
| 13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
| 13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
| 13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
| 13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
| 18424 | If two people can have phenomenally identical experiences, they can't involve the self [Brogaard] |