While discussion strong normalization proofs, this comment contrasts the "normal forms model" with "purely syntactic methods".
This brings me back to a more basic question: can we still distinguish syntactic and semantic constructions strictly, in the face of syntax-based models? What about term models for algebras, Henkin models for first-order logics? What about structural operational semantics? Since term models can be isomorphic to syntax, it seems hard to make a firm distinction.
Until I studied the difference between proof theory and model theory in logic, I was even baffled by the idea that "static type systems are a syntactic method". After all, a type system reasons about types, which are an abstraction of program behavior (and with dependent types, an arbitrarily precise one).