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.