Optimising the 4E revolution in cognitive science arguably requires the rejection of two guiding commitments made by orthodox thinking in the field, namely that the material realisers of cognitive states and processes are located entirely inside the head, and that intelligent thought and action are to be explained in terms of the building and manipulation of content-bearing representations. In other words, the full-strength 4E revolution would be secured only by a position that delivered externalism plus antirepresentationalism. I argue that one (...) view in 4E space—extended functionalism—is appropriately poised to deliver externalism but not antirepresentationalism. By contrast, in the case of a competing 4E view—radical enactivism—even if that view can deliver antirepresentationalism, its pivotal notion of extensiveness falls short of establishing externalism. These conclusions are justified via an examination of, and by responding critically to, certain key arguments offered in support of their view by the radical enactivists. (shrink)