Somehow Things Do Not Relate: On the Interpretation of Polyadic Second-Order Logic

Abstract

Boolos has suggested a plural interpretation of second-order logic for two purposes: (i) to escape Quine’s allegation that second-order logic is set theory in disguise, and (ii) to avoid the paradoxes arising if the second-order variables are given a set-theoretic interpretation in second-order set theory. Since the plural interpretation accounts only for monadic second-order logic, Rayo and Yablo suggest an new interpretation for polyadic second-order logic in a Boolosian spirit. The present paper argues that Rayo and Yablo’s interpretation does not achieve the goal.