Single Idea 13698

[catalogued under 5. Theory of Logic / K. Features of Logics / 4. Completeness]

Full Idea

You can establish facts of the form Γ|-φ while avoiding the agonies of axiomatic proofs by reasoning directly about models to conclusions about semantic consequence, and then citing completeness.

Gist of Idea

In a complete logic you can avoid axiomatic proofs, by using models to show consequences

Source

Theodore Sider (Logic for Philosophy [2010], 4.5)

Book Reference

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.105


A Reaction

You cite completeness by saying that anything which you have shown to be a semantic consequence must therefore be provable (in some way).