 Leibniz dreamed of a characteristica universalis—an exact idea-calculus in which it would be possible to arbitrate scientific disputes by calculation and which would serve as a “lodestar” to those “who navigate the sea of experiments” (Leibniz 1679/1989). In the last century, the Unity of Science movement hoped that a new logic would serve as a universal language in which to commensurate all of the sciences and—so united—apply their full power to the problems of the day. But, as the clash between the Copernican and Ptolemaic systems illustrates, stating two theories precisely and mathematically does not suffice to adjudicate disputes between them. To that end, a significant effort was devoted to developing a calculus in which to compute the precise bearing of evidence, and thereby arbitrate between theories. This calculus was conceived not as a boon to philosophy alone, but as a kind of common law to govern and coordinate the federated republics of science. Many of the formalisms covered in this article can be traced back to a program whose ambition may stagger our contemporary imaginations.