Otto Neurath's early work on the classification of systems of hypotheses in optics provided some of the key insights of Neurath's later philosophy of science. The chapter investigates how Neurath developed his theory of theory-classification in response to inconsistencies he stumbled upon while studying the historical theories. Neurath's empiricism and thoroughgoing fallibilism informed his mapping of the group of theories, locating "elementary notions" of theories and taking into account the "blurred margins" of theories. To replace false dichotomies the project provided a finer-grained analysis of theories and could be utilized to locate unconceived alternatives of a domain. The first sections discuss the close links between Neurath's optical essays, his notion of an "auxiliary motive," and his attack on pseudorationalism in the "Lost Wanderers of Descartes" paper. The last sections provide a comparison of the two essays, with an extended table of the elementary notions Neurath listed, and discuss Neurath's two-tier methodology for historical reconstruction.