37 ideas
7791 | The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle] |
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] |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
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] |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
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] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
11002 | Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read] |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
21500 | We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI] |
21501 | If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI] |
6556 | If anything is to be probable, then something must be certain [Lewis,CI] |
21498 | Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI] |
5828 | Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI] |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |