Extreme and Non-Extreme Deontic Modals∗

We refer to operators like important, crucial, should and must as deontic necessity modals. Our goal in this paper is to contribute to the understanding of the differences ∗We thank Graham Katz and Elena Herburger for discussions which have shaped our understanding of the topic and Jessica Rett, Nate Charlow, and Stephen Finlay for comments on previous versions. Any errors are of course our responsibility, not theirs. We gratefully acknowledge the support of National Science Foundation grant BCS-1053038 to both authors, and support from the Mandel Scholion Interdisciplinary Research Center in the Humanities and Jewish Studies to the second author. This use of the term ‘necessity’ is common in linguistics but is more inclusive than is usual in philosophy. It reflects a theoretical assumption that the operators with weaker force (should, important) have the same