What is this cognition that is supposed to be embodied?

Many cognitive scientists have recently championed the thesis that cognition is embodied. In principle, explicating this thesis should be relatively simple. There are, essentially, only two concepts involved: cognition and embodiment. After articulating what will here be meant by 'embodiment', this paper will draw attention to cases in which some advocates of embodied cognition apparently do not mean by 'cognition' what has typically been meant by 'cognition'. Some advocates apparently mean to use 'cognition' not as a term for one, among many, causes of behavior, but for what has more often been called "behavior." Some consequences for this proposal are considered.