Embodiment has recently enjoyed renewed consideration as a means to amplify the faculties of smart machines. Proponents of embodiment seem to imply that optimizing for movement in physical space promotes something more than the acquisition of niche capabilities for solving problems in physical space. However, there is nothing in principle which should so distinguish the problem of action selection in physical space from the problem of action selection in more abstract spaces, like that of language. Rather, what makes embodiment persuasive as a means toward higher intelligence is that it promises to capture, but does not actually realize, contingent facts about certain bodies (living intelligence) and the patterns of activity associated with them. These include an active resistance to annihilation and revisable constraints on the processes that make the world intelligible. To be theoretically or practically useful beyond the creation of niche tools, we argue that "embodiment" cannot be the trivial fact of a body, nor its movement through space, but the perpetual negotiation of the function, design, and integrity of that body$\unicode{x2013}$that is, to participate in what it means to $\textit{constitute}$ a given body. It follows that computer programs which are strictly incapable of traversing physical space might, under the right conditions, be more embodied than a walking, talking robot.