 Let us now try to draw some lessons, and in particular ask whether the emergence of first-order logic was inevitable. I begin with an observation. Each stage of this complex history is conditioned by two sorts of shifting background consideration. One is broadly mathematical: the theorems that had been established. The other is broadly philosophical: the assumptions that were made (explicitly or tacitly) about logic and about the foundations of mathematics. These two things interacted. Each thinker in the sequence starts with some more or less intuitive ideas about logic. Those ideas prompt mathematical questions: distinctions are drawn: theorems are proved: consequences are noted, and the philosophical understanding is sharpened. At each stage, the question, “What is logic?” (or: “What is the correct logic?”) needs to be assessed against both the mathematical and the philosophical background: it makes little sense to ask the question in the abstract.