The emphasis placed on behavioural regularities in archaeologically grounded explanatory arguments has not led to a commensurate success in formulating such explanations. It is argued that the lack of success stems from using an inappropriate analytical level along with an undue emphasis on universal laws. Instead, emphasis should be on embedding structuring principles into a representational system amenable to mathematical reasoning as a means to uncover the properties entailed by these structuring principles. An example based on demographic properties of the !Kung San is used to illustrate the argument.