Reference and analysis

Productive mathematical and scientific research often takes place when more concrete discourse whose main intent is to establish and clarify reference is yoked with more abstract discourse whose main intent is analysis. The opposition between referential discourse and analytic discourse is explained by a detailed account of Leibniz’s notion of analysis as a search for the conditions of intelligibility of things, as well as the solvability of problems, in relation to his debates with Locke in the Nouveaux Essais, and then examining its continuation in the work of Ernst Cassirer. I argue that Cassirer tends to read the superposition of discourses too strongly as unification, as if the referential discourse disappeared entirely into the analytic discourse; to contest this reading, I tell a historical narrative about the investigation of the circle. The circle, like the cosmos, always has further surprises to reveal; its determinate oneness is never exhausted by an analytic discourse.