Constraints on Counterpart Relations and the Redundancy of an Alternative Semantics for Counterpart Theory

Abstract

Within the philosophy of modality there is a divide between those who adhere to transworld identity and those who reject it in favour of counterpart theory. In this thesis I reconsider the constraints that we should put on counterpart relations and argue on semantic grounds that we should require them to be equivalence relations. Counterpart theory as a metaphysical doctrine and the corresponding logical system CT are introduced, and I discuss some reasons to think that there should be a plurality of counterpart relations. Moreover, I discuss why the language of CT lacks expressive power for sentences containing modal locutions that go beyond possibility and necessity. Thereafter, I argue that we should not allow entities to have multiple counterparts in a single world, because then necessity of identity and universal instantiation would not hold in CT. Subsequently, I show that certain intuitively valid inferences can only be valid if the relevant counterpart relation is symmetric and transitive. I generalize this argument and argue that every counterpart relation should be symmetric and transitive. Thus we should require counterpart relations to be equivalence relations. As a result, the counterpart-theoretic account of modality doesn’t require a specific semantics of its own, because quantified modal logic is suitable whenever the relevant counterpart relation is an equivalence relation. I give an outline of a logical framework which is essentially an extension of quantified modal logic, that would enable us to deal with multiple counterpart relations simultaneously if that need would ever arise. Lastly, I conclude that this means that counterpart-theoretic accounts of modality and accounts involving transworld identity have the same semantic structure, which reveals their differences to be of a purely metaphysical or ontological nature. Consequently, this paves the way for a partial reconciliation between these two divided camps.