Single Idea 10259

[catalogued under 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 Reference

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.