One, Two, Three, Four, Nothing More: An Investigation of the Conceptual Sources of the Verbal Counting Principles

The culturally widespread verbal count list (“one, two, three...”), deployed in accord with what Gelman & Gallistel (1978) call the “counting principles,” represents the positive integers1. The counting principles provide an account of how the count list encodes the successor function; i.e. if a numeral “n” refers to cardinal value n and “p” immediately follows “n” in the count list then “p” refers to n + 1 (see Gelman & Gallistel, 1978, for the classic analysis of the successor function in terms of counting principles). Ever since the publication of Gelman & Gallistel’s (1978) seminal investigation of knowledge of counting in childhood, the question of the sources of the verbal counting principles has been a central concern to developmental psychologists. Following Spelke, Breilinger, Macomber, & Jacobsen (1992; see also Carey & Spelke, 1996) we take the view that evolutionarily ancient, innate “core knowledge” systems provide the cognitive primitives that support learning in childhood. Thus, on our view, determining what core systems support the acquisition of the counting principles is a key aspect of the investigation of their sources.