In his 1905 work on the logical foundations of geometry, Royce proposed a logic based on the “obverse” or O-relation that could provide a means of understanding any system of order. Royce explains that this relation, which he calls the O-relation, “in logical terms,... is the relation in which (if we were talking of the possible chances [choices] open to one who had to decide upon a course of action) any set of exhaustive but, in their entirety, inconsistent choices would (...) stand to one another” (Royce, 1951, 385). This focus on the process of making choices turns on the idea that the action of making a choice produces an asymmetrical relation and so a key part of Royce’s project was to demonstrate the.. (shrink)