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Single Idea 10695

[filed under theme 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |= ]

Full Idea

Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists).

Gist of Idea

Logical consequence is either necessary truth preservation, or preservation based on interpretation

Source

JC Beall / G Restall (Logical Consequence [2005], 2)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7

A Reaction

Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one.

The 16 ideas with the same theme [fitting with the truth of some formulae]:

19237 Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce]
13344 X follows from sentences K iff every model of K also models X [Tarski]
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
13347 Validity is a conclusion following for premises, even if there is no proof [Bostock]
13348 It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]
13349 Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
13626 Semantic consequence is ineffective in second-order logic [Shapiro]
13637 If a logic is incomplete, its semantic consequence relation is not effective [Shapiro]
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]
21611 Formal semantics defines validity as truth preserved in every model [Williamson]
10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
13240 A sentence follows from others if they always model it [Beall/Restall]
14506 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki]
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