 Royce summarized the central ontological claims of his system this way: “whatever else the world contains, if it only contains a reasonable being who knows and intends his own acts, then this being is aware of a certain relation, the relation between performing and not performing any act which he considers in advance of action. And thus relations amongst acts are in such wise necessary facts, that whoever acts at all, or whoever, even in ideal, contemplates possible courses of action, must regard at least some of these relations as present in the realm of his conceived modes of action” (1913a, 120–1. When Royce introduced the formal system \(\Sigma\) in his 1905 paper, “The Relation of the Principles of Logic to the Foundations of Geometry,” he proposed six “laws” to which \(O\)-collections must conform. Restated, these six laws are as follows: