Recently, some authors have begun to raise questions about thepotential unity of 4E (enactive, embedded, embodied, extended)cognition as a distinct research programme within cognitivescience. Two tensions, in particular, have been raised: (i) thatthe body-centric claims embodied cognition militate against thedistributed tendencies of extended cognition and (ii) that thebody/environment distinction emphasized by enactivism standsin tension with the world-spanning claims of extendedcognition. The goal of this paper is to resolve tensions (i) and(ii). The proposal is that a form of ‘wide computationalism’ canbe used to reconcile the two tensions and, in so doing, articulatea common theoretical core for 4E cognition.