I want to give a couple of examples of this idea. First consider some physical process that doesn’t have a limiting frequency but has a frequency that varies, always staying within some interval. This would be a process that is chancy, but fairly predictable. It might be that the best description of such a system is to just put bounds on its relative frequency. Such processes have been studied using IP models (Kumar and Fine 1985; Grize and Fine 1987; Fine 1988), and have been discussed as a potential source of imprecision in credence (Hájek and Smithson 2012). A certain kind of non-standard understanding of a quantum-mechanical event leads naturally to upper probability models (Suppes and Zanotti 1991; Hartmann and Suppes 2010). John Norton has discussed the limits of probability theory as a logic of induction, using an example which, he claims, admits no reasonable probabilistic attitude (Norton 2007, 2008a,b). One might hope that IP offers an inductive logic along the lines Norton sketches. Norton himself has expressed scepticism on this line (Norton 2007), although Benétreau-Dupin (2015) has defended IP as a candidate system for Norton’s project. Finally, particular views on vagueness might well prompt a rethinking of the formal structure of chance (Bradley 2016).