31 ideas
12442 | 'Mickey Mouse is a fictional mouse' is true without a truthmaker [Azzouni] |
12439 | Truth is dispensable, by replacing truth claims with the sentence itself [Azzouni] |
12437 | Truth lets us assent to sentences we can't explicitly exhibit [Azzouni] |
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] |
12446 | Names function the same way, even if there is no object [Azzouni] |
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] |
12447 | That all existents have causal powers is unknowable; the claim is simply an epistemic one [Azzouni] |
12445 | If fictional objects really don't exist, then they aren't abstract objects [Azzouni] |
12449 | Modern metaphysics often derives ontology from the logical forms of sentences [Azzouni] |
12440 | If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni] |
12438 | In the vernacular there is no unequivocal ontological commitment [Azzouni] |
12441 | We only get ontology from semantics if we have already smuggled it in [Azzouni] |
12448 | Things that don't exist don't have any properties [Azzouni] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
12450 | The periodic table not only defines the elements, but also excludes other possible elements [Azzouni] |