more from this thinker | more from this text
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.
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] |