Necessarily Maybe: Quantifiers, Modality and Vagueness

Abstract

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 17.1 is a discussion of various possible sources of vague modality. Section 17.2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Sect. 17.3, the framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams.