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Single Idea 10691

[filed under theme 5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence ]

Full Idea

Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples.

Gist of Idea

Logical consequence needs either proofs, or absence of counterexamples

Source

JC Beall / G Restall (Logical Consequence [2005], 3)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.6

The 6 ideas with the same theme [different modes of logical consequence]:

19058 Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
9718 Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton]
10259 The two standard explanations of consequence are semantic (in models) and deductive [Shapiro]
10691 Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
13253 There are several different consequence relations [Beall/Restall]
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]