It is widely believed that the mind can be studied in isolation from the details of its physical embodiment and environmental surroundings. This is a form of residual Cartesianism which cognitive science can ill afford. Arguments are presented to show that cognitive powers should not be treated in isolation from the motor and object manipulation skills conferred upon us by our physical bodies. A new model is needed in which inner computational processes are seen to co-operate with external (physical and social) structures to produce the phenomena of natural cognition. The scope of investigations required by such a model is examined, and suggestions made concerning its practical implications for workers in the field.