Cities are perhaps the largest and most complex artefacts created by human activity. The characterisation of an object or system as an artefact assumes the existence of some form of intentionality behind its creation. Complexity science has been used to understand the formation of cities as products of self-organization and evolution, but it has paid little attention to the role of intentionality and design in the formation of cities. So in what sense are cities artefacts? Who is the design agent behind the creation of cities? Can societies be characterised as design agents? In this paper we unravel a view of design as a capacity that is derived from certain organisational principles, irrespective of whether these are realised in a brain, a cognitive system or a society. The essay brings together insights from design research, cognitive neuroscience and complexity to propose a theory of design intentionality that can be applied to cities.