 The conditionals that result from the initial \(O\)-collection include \(\neg A \supset B\) with respect to \(C\), \(\neg B \supset A\) with respect to \(C\), \(\neg C \supset A\) with respect to \(B\), and so on. Since \(O\)-relations are symmetrical, there are as many alternative “courses” of action as there are possibilities of negation and selection of antecedents and origins. Since the conditionals are possibilities, they could also be represented “\(\Diamond (\neg C \supset B)\), \(A\)” where \(A\) represents a shared propositional  parameter.[14]  “It is now possible,” Royce concludes, “to point out that the elements of \(\Sigma\) possess the properties of a system of logical classes, or of entities to which the ordinary algebra of logic applies” (1905, 427). The resulting conditionals operate in a system that is like a relevant possible world logic were the truth of the conditional is dependent on its truth assignment through the propositional parameter that orders antecedent and consequent. However, Royce cautions against reliance on logics that are primarily interested in conditional relations. Such interest is a result of our “intellectual habits” but “in several respects inferior to the more direct expression in terms of \(O\)-relations. … When, in fact, we attempt to describe the relations of the system \(\Sigma\) merely in terms of the antecedent-consequent relation, we not only limit ourselves to an arbitrary choice of origin, but miss the power to survey at a glance relations of more than a dyadic, or triadic character” (381–2).