The ‘Islamic State in Iraq and Syria’, or Da’esh, claimed territorial control and declared itself a state and Caliphate, but scholars disagree on the quality of these claims. Some argue that Da’esh really was a state, others reject this as propaganda of a non-state actor, and still others highlight that Da’esh challenged the international order as a whole. This article combines the notions of the ‘territory effect’ and ‘inter-territory’ to explain why the (self-)presentation of Da’esh appeared as a challenge to the (non-)state dichotomy of the modern international and its territorial underpinnings. While contesting the inter-territorial compartmentalisation of the state system, Da’esh projected a counter-territoriality beyond this system. The resulting horror vacui and collective campaign against Da’esh in turn shed light on an inter-territory effect of assuming and re-enacting contiguous state territories in a globally encompassing system of states, which thus locates and contains – but also enables – violence within states.