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Single Idea 10259

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

Full Idea

The two best historical explanations of consequence are the semantic (model-theoretic), and the deductive versions.

Gist of Idea

The two standard explanations of consequence are semantic (in models) and deductive

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 7.2)

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.222

A Reaction

Shapiro points out the fictionalists are in trouble here, because the first involves commitment to sets, and the second to the existence of deductions.

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]