Work on grounding has made a start towards an understanding of where simple perceptual categories come from. But human concepts are made up of more than the simple categories of these models; concepts have internal structure. Within the visual/spatial domain, it is necessary to go beyond an account of how \square" and \above" are grounded to an account of how \here is a square above a circle which is to the left of a triangle" is grounded. Conceptual/linguistic structure is not just arbitrary patterning which falls out once the object and relation categories have been identi ed. Rather, it re ects fundamental aspects of the perception of objects and relations. Thus there is a need to ground the structure as well as the categories which make up concepts. Grounding and Structure Since Harnad's important paper on the need to ground symbols in perception or action (Harnad, 1990), there have been various attempts to train systems to categorize visual inputs in terms of noun or noun-like categories or simple oneor two-place relations (Dor ner, 1990; Nenov, 1991; Regier, 1992). While the progress made by these researchers should not be minimized, grounded categories by themselves are only the beginning. One of the hallmarks of human concepts is their structure. On the traditional view, symbols combine to form an e ectively unlimited set of possible symbol structures, which are interpretable In Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (1993), 149{152