50 ideas
17713 | After 1903, Husserl avoids metaphysical commitments [Mares] |
18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
18789 | Intuitionist logic looks best as natural deduction [Mares] |
18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
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] |
18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
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] |
18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
18782 | The connectives are studied either through model theory or through proof theory [Mares] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
18783 | Many-valued logics lack a natural deduction system [Mares] |
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] |
18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
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] |
18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
17716 | Mathematics is relations between properties we abstract from experience [Mares] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
16065 | Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman] |
16067 | Constitution is not identity, because it is an asymmetric dependence relation [Wasserman] |
16069 | There are three main objections to seeing constitution as different from identity [Wasserman] |
16068 | The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman] |
16074 | Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman] |
17703 | Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares] |
17714 | Aristotelians dislike the idea of a priori judgements from pure reason [Mares] |
17705 | Empiricists say rationalists mistake imaginative powers for modal insights [Mares] |
17700 | The most popular view is that coherent beliefs explain one another [Mares] |
17704 | Operationalism defines concepts by our ways of measuring them [Mares] |
17710 | Aristotelian justification uses concepts abstracted from experience [Mares] |
17706 | The essence of a concept is either its definition or its conceptual relations? [Mares] |
18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
17701 | Possible worlds semantics has a nice compositional account of modal statements [Mares] |
17702 | Unstructured propositions are sets of possible worlds; structured ones have components [Mares] |
17708 | Maybe space has points, but processes always need regions with a size [Mares] |