Abstract:
I will argue that cognitive science now has the tools to address
the age-old problem of accounting for the human conceptual
repertoire. Such an account includes both descriptive and
explanatory components. Descriptively, we must specifying the
initial representational repertoire, conceptual system 1, specify the
repertoire at a later point in development, conceptual system 2, and
characterize the developmental difference. Explanatorily, we must
characterize the learning mechanism that underlies the change. I
illustrate by offering an account of the human capacity to represent
natural number. I provide evidence for three innate and
evolutionarily ancient representational systems with numerical content,
showing how each falls short of having the capacity to represent
positive integers. I characterize the first representational
system young children (3-year-olds) create that expresses at least a
finite subset of the positive integers. And I characterize the
bootstrapping process that underlies the child's achievement. I
will also touch on new data bearing on the construction, in history, of
the integers.