Recent scholarship in the history of analytical philosophy has revealed that the conceptions of logic held by Frege, (early) Russell, and (early) Wittgenstein differ in crucial aspects from those that are dominant in analytical philosophy today. The former are called ‘universalist’, the latter ‘schematic’. This yields a novel research question: How did the historical transition from universalist to schematic conceptions within analytical philosophy occur? My project develops an answer to this question through an investigation of the early work of Carnap and Quine. By placing that work against the background afforded by the historical research on universalist conceptions of logic, I propose to examine in detail how both Carnap and Quine take decisive steps towards schematic conceptions of logic, steps that can be traced to their diverging ways of inheriting and transforming the prior conceptions of Frege, Russell, and Wittgenstein. Although Carnap and Quine both endorse – in general terms – the transition to a schematic conception of logic, there arise profound disagreements between them concerning the philosophical ramifications of that transition. What is at stake in those disagreements, is the self-understanding that analytical philosophers ought to have in the wake of this far-reaching transition to schematic conceptions of logic, a transition that continues to shape analytical philosophy to this day.