Conference Paper: "Evaluating Ancient Numeracy: Social versus Developmental Perspectives on Ancient Mesopotamian Numeration" June 2005 Jean Piaget Society (Vancouver, British Columbia)
	The most ancient literate and proto-literate societies of Mesopotamia (Uruk and Proto-Elamite) used a wide variety of numerical notation systems whose sign-values cannot be interpreted absolutely. On this basis, Peter Damerow and others believe that archaic Mesopotamians lacked an abstract number concept, and thus define a universal historical stage of archaic numeration between pre-operative and abstract number concepts. Yet there are several reasons for doubting this theory. Evidence is drawn from the social and functional context of the systems, comparison with Sumerian numeral words, and comparative data from other ancient civilizations. Multiple numerical notation systems help users to work with metrological systems and help distinguish different categories of counted quantities. There is insufficient evidence to support a strong thesis that numeration systems are evidence of non-abstract numerical concepts. Social explanations of this phenomenon are at least as convincing as stage-based developmental ones.
Stephen Chrisomalis, Ph.D. Copyright 2004