Generative linguistics has a longer prehistory than most linguists realize. The rewriting systems that Chomsky brought into linguistics as generative grammars were explicitly defined more than a century ago, as part of a project to formalize inference rules in logic, and were later applied to studying mathematical properties of certain kinds of infinite sets. Their developer was the mathematician and logician Emil Leon Post, whose work was inspired by Clarence Irving Lewis and Cassius Jackson Keyser. Post also proved the first two theorems about what linguists now call generative capacity. The idea of deploying Post’s systems within linguistics was first suggested in 1950 by the logician Paul Rosenbloom. I review the relevant pre-1950 work, and explore the reasons for its having remained so little known among linguists.