Modality: The Three-layered Scalar Square

This paper analyses the semantic and pragmatic relations between the notions of possibility and necessity and of their negations. In so doing it reconciles insights stemming from Aristotle and partially different ones expounded by Hintikka, Horn, and Lobner on the basic quadripartite, tripartite, and scalar nature of the field of modality. From Aristotle and his commentators it maintains the Aristotelian square and the view that possibility has two senses, from Lobner the duality square, from Hintikka the tripartite division of the field of modality with one sense of possibility extending over the other sense and over necessity, and from Horn the Gricean scalar analysis of the relation between the two possible senses. This paper further illustrates the basic geometry of modality notions with lexicalization patterns