27 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] |
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] |
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] |
18439 | Because things can share attributes, we cannot individuate attributes clearly [Quine] |
18442 | You only know an attribute if you know what things have it [Quine] |
18441 | No entity without identity (which requires a principle of individuation) [Quine] |
18440 | Identity of physical objects is just being coextensive [Quine] |
21315 | A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler] |
21317 | Despite consciousness fluctuating, we are aware that it belongs to one person [Butler] |
21313 | If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler] |
21314 | Consciousness presupposes personal identity, so it cannot constitute it [Butler] |
21318 | If the self changes, we have no responsibilities, and no interest in past or future [Butler] |