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Single Idea 19237

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

Full Idea

The question of whether a deductive argument is true or not is simply the question whether or not the facts stated in the premises could be true in any sort of universe no matter what be true without the fact stated in the conclusion being true likewise.

Gist of Idea

Deduction is true when the premises facts necessarily make the conclusion fact true

Source

Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)

Book Ref

Peirce,Charles Sanders: 'Reasoning and the Logic of Things', ed/tr. Ketner,K.L. [Harvard 1992], p.142

A Reaction

A remarkably modern account, fitting the normal modern view of semantic consequence, and expressing the necessity in the validity in terms of something close to possible worlds.

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]