Many studies have demonstrated that the sensory and motor systems are activated during conceptual processing. Such results have been interpreted as indicating that concepts, and important aspects of cognition more broadly, are embodied. That conclusion does not follow from the empirical evidence. The reason why is that the empirical evidence can equally be accommodated by a 'disembodied' view of conceptual representation that makes explicit assumptions about spreading activation between the conceptual and sensory and motor systems. At the same time, the strong form of the embodied cognition hypothesis is at variance with currently available neuropsychological evidence. We suggest a middle ground between the embodied and disembodied cognition hypotheses--grounding by interaction. This hypothesis combines the view that concepts are, at some level, 'abstract' and 'symbolic', with the idea that sensory and motor information may 'instantiate' online conceptual processing.