Plurals and Second-Order Logic

Abstract

While plural logic can be interpreted in monadic second-order logic, the full system of second-order logic cannot be interpreted in plural logic. This means it is formally possible to eliminate plural logic in favor of monadic second-order logic. However, a number of philosophical considerations militate against such an elimination. The conclusion of this chapter echoes that of the preceding ones: although the two systems can occasionally be used for similar purposes, the notions they represent are different and must be kept apart.