"It's that, before Tarski and Gödel, no one clearly distinguished syntax and semantics" I think this is right, but Hilbert came already close much earlier. Bu

"It's that, before Tarski and Gödel, no one clearly distinguished syntax and semantics" I think this is right, but Hilbert came already close much earlier. But "Before this, logic had been strictly syntactical and proof theoretic" is at least misleading. Traditional logic was more conceptional. Frege's "formalism" was a great innovation, but he remained within the conceptual tradition (Frege-Hilbert controversy). "What Hilbert offers us, in 1899, is a systematic and powerful technique that can be used across all formalized disciplines to do just this: to prove consistency and independence. In doing so, he lays the groundwork, in concert with various of his contemporaries, for the emergence of contemporary model-theoretic techniques." https://plato.stanford.edu/entries/frege-hilbert/ https://plato.stanford.edu/entries/frege-hilbert/