S5 as the Logic of Metaphysical Modality: Two Arguments for and Two Arguments against

Abstract

Two arguments for S5 being the logic of metaphysical modality are favourably discussed: one from the logic of absolute necessity, one from Timothy Williamson. Two arguments against S5 being the logic of metaphysical modality are discussed and rebuffed: one from Nathan Salmon against S4, and thereby S5, being the logical of metaphysical modality; and one from Michael Dummett against the B principle for metaphysical modality. In the Appendix, some comments are offered on the logics of ‘true in virtue of the nature of’, and its relation to logical necessity. It is argued that the logic both of ‘true in virtue of the nature of x’ and of essentialist logical necessity is S5.