Recently, Michael Wheeler (2017) has argued that despite its sometimes revolutionary rhetoric, the so called 4E (embodied-embedded-enacted-extended) cognitive movement, even in the guise of ‘radical’ enactivism (REC), cannot achieve a full revolution in cognitive science. A full revolution would require the rejection of two essential tenets of traditional cognitive science, namely internalism and representationalism. Whilst REC might secure antirepresentationalism, it cannot do the same, so Wheeler argues, with externalism. In this paper, expanding on Wheeler’s analysis (2017), we argue that what compromises REC’s externalism is the persistence of cognitively relevant asymmetries between its purported cognitive systems and the environment. Complementarily, we argue that an antirepresentationalist ancestor of enactivism, the autopoietic theory of cognition, is able to deliver and secure externalism, thus offering the explosive combination (i.e., antirepresentationalism plus externalism) that Wheeler claims us needed for a revolution in cognitive science.