Possibility and necessity are gradable notions: There might be only an ever so slight possibility that global warming will stay below the 2°C mark, whereas there is a good possibility that this will not happen. We should, or rather, must reduce our carbon footprint significantly. While the discussion of gradable modality already features in Moore (1900) and Russell (1903), and, more prominently, in Lewis (1970) and Kratzer (1981), it has only recently been the focus of a more sustained research effort in linguistics (Villalta 2008; Yalcin 2010; Lassiter 2011, 2017; Rubinstein 2012, 2014; Pasternak 2016; Portner & Rubinstein 2016), which centers around the following two questions, which we will also explore in this course unit: First, are all modal expressions gradable, and second, what is the linguistic representation of this gradability, and how does it compositionally interact with other linguistic material? We recommend that participants have some background in formal semantics, or take the introduction in week 1. If you’re unsure if this class is for you, feel free to reach out directly to the instructor.