Chapter 2 considers legal uncertainty in the jus ad bellum as defined in the UN Charter and other sources of law. It describes paradigms, framing this law around ‘plain cases’ of lawful and unlawful force. Supervaluationism describes paradigms as determined not by one but several tests, overlapping but not co-extensive - cases may meet all or only some tests. Fuzzy logic refutes binary distinctions between lawful and unlawful force, arguing these are end-points of a continuum, separated by a ‘penumbra of uncertainty’. The chapter outlines ‘hard cases’ of force, different to cases the UN Charter most obviously prohibits: anticipatory self-defence, pre-emptive self-defence, self-defence against non-state actors, humanitarian intervention, use of force to prevent WMD proliferation. The chapter describes how interviewees and survey participants evaluated such justifications, the results displaying the vagueness already identified. The chapter identifies one possible explanation: lawyers align with different ‘interpretive cultures’, holding different opinions about valid legal tests and interpretive techniques. ‘Restrictivists’ prefer ‘formalist’ interpretation techniques, while ‘expansionists’ prefer ‘dynamist’ interpretation techniques.