more from Robert S. Wolf

### Single Idea 13534

#### [catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

One of the most appealing features of first-order logic is that the two 'turnstiles' (the syntactic single |-, and the semantic double |=), which are the two reasonable notions of logical consequence, actually coincide.

Gist of Idea

In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide

Source

Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3)

Book Reference

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.172

A Reaction

In the excitement about the possibility of second-order logic, plural quantification etc., it seems easy to forget the virtues of the basic system that is the target of the rebellion. The issue is how much can be 'expressed' in first-order logic.