Abstract: Over the past few decades, number cognition researchers have paid extensive attention to how children acquire tacit knowledge of the numerical notion of successor. Though different proposals exist, one common suggestion, often associated with Chomsky, is that such knowledge may be explained in terms of our linguistic – specifically, morphosyntactic – capacities (Chomsky, 1988). In particular, many number cognition researchers maintain what we call the Knowledge Thesis:
(KT) Knowledge of successor is due to knowledge of natural language morphosyntax.
The basic idea appears to be that if one aims to explain knowledge of successor in terms of known cognitive resources, natural language morphosyntax is an especially plausible candidate since it, like the successor function, is recursive.
This talk has a pair of aims. First, we critically assess two very influential versions of KT, which differ with respect to which morphosyntactic principles they deem most relevant. The first, Merge Model, traces knowledge of successor to a general syntactic principle known as Merge. The second, Complex Cardinal Model, traces knowledge of successor to morphosyntactic principles specifically responsible for generating count words – words, such as ‘one’, ‘two’, ‘three’.., that are used in counting and answering ‘how many’-questions. We argue that neither model, at least in present form, provides an adequate explanation for how knowledge of successor is acquired. Specifically, while the Merge Model faces insurmountable theoretical challenges, often associated with Benacerraf (1965)’s Identification Problem, the Complex Cardinal Model requires the adoption of certain empirically untenable assumptions.
A second, related aim of this paper is to articulate an apparent implication of the Complex Cardinal Model for the development of quotidian number cognition. Specifically: though it fails to explain how children acquire the notion of successor as defined within modern mathematics, it would, if correct, suggest that children, and perhaps even most adults, possess a potentialist conception of successor.