Single Idea 10753

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

Full Idea

Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence.

Gist of Idea

Logical consequence is intuitively semantic, and captured by model theory

Source

Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2)


A Reaction

If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation.