Full Idea
There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations.
Gist of Idea
Logical truths and inference are characterized either syntactically or semantically
Source
Michael Dummett (The Philosophy of Mathematics [1998], 3.1)
Book Reference
'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.136
A Reaction
Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth?