Full Idea
It is customary in logic to take a theory to be a set of sentences closed under logical consequence, whereas it is common in discussions of theories of truth to take a theory to be an axiomatized theory.
Gist of Idea
Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms
Source
Kit Fine (Semantic Necessity [2010], n8)
Book Reference
'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.74