Bacon on higher-order logic
In the dark old days of early logic, there was only syntax. People introduced formal languages and laid down axioms and inference rules, but there was nothing to justify these except a claim to "self-evidence". Of course, the languages were assumed to be meaningful, but there was no systematic theory of meaning, so the axioms and rules could not be justified by the meaning of the logical constants.
All this changed with the development of model theory. Now one could give a precise semantics for logical languages. The intuitive idea of entailment as necessary truth-preservation could be formalized. One could check that some proposed system of axioms and rules was sound, and one could confirm – what had been impossible before – that it was complete, so that any further, non-redundant axiom or rule would break the system's soundness.