Notes on Stratified Semantics

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature (see, e.g. Mares, Studia Logica 51(1), 1-20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71(1), 163-187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are (Fine, Journal of Philosophical Logic 17(1), 27-59, 1988; Mares, Studia Logica 51(1), 1-20, 1992), both of which are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a user friendly' presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic.