The customary distinction between syntax and semantics—and therefore also the ordinary formulation of logical completeness—is missing from many of history’s theorists’ accounts of logic. But some of them, including not only Gentzen but also De Morgan, Peirce, and Frege, seem nevertheless to have asked (and occasionally even boasted to have answered) whether anything is missing from their logical systems. Our reconstruction of Gentzen’s alternative accounts of logical completeness should inspire optimism on two fronts. Most obviously it suggests that many theorists might offer coherent conceptions of logic despite the absence of the question’s characteristic markers. Smiley provided further evidence for this view with his reconstruction of a completeness proof hidden in plain sight in Aristotle’s ancient investigations. Even more importantly, the very centrality of the idea of completeness suggests that its various conceptualizations will be the germ of entire alternative conceptions of logic. Our reconstruction of Gentzen’s thought seems to realize this suggestion. Further articulation of the Aristotelean scheme promises to be another entry. We point to Bolzano’s pointed remarks in 1837, and the provocative inversion of the customary relationship between form and content they depict, as a potentially rewarding next place to turn.