The last ten years have seen an increasing interest, within cognitive science, in issues concerning the physical body, the local environment, and the complex interplay between neural systems and the wider world in which they function. --œPhysically embodied, environmentally embedded--� approaches thus loom large on the contemporary cognitive scientific scene. Yet many unanswered questions remain, and the shape of a genuinely embodied, embedded science of the mind is still unclear. I begin by sketching a few examples of the approach, and (...) then raise a variety of critical questions concerning its nature and scope. A distinction is drawn between two kinds of appeal to embodiment: 'simple' cases, in which bodily and environmental properties merely constrain accounts that retain the focus on inner organization and processing, and more radical appeals, in which attention to bodily and environmental features is meant to transform both the subject matter and the theoretical framework of cognitive science. (shrink)