New Arguments Against Carey's Bootstrapping Hypothesis

null, Eric Snyder (Ohio State University)

Major accounts of number concept possession, i.e. possession of concepts figuring in arithmetic thoughts such as 3 + 2 = 5, can be broadly grouped into two kinds: i) nativist accounts and ii) learning-based accounts. Of all of these, Susan Carey's learning-based account is arguably the most elaborate and influential. According to Carey, children acquire later number concepts via a kind of abductive process she calls bootstrapping. Specifically, in virtue of recognizing a certain structural similarity between count words and the sets they enumerate, children abductively infer a notion of successor, thus allowing them to generate a potentially infinite number of number concepts. Unfortunately, however, Carey's account faces serious empirical criticism. For example, it has been shown that children only possess the relevant notion of successor years after learning how to count. Consequently, many developmentalists have taken this as strong evidence in favor of nativism. However, I'll argue that both kinds of accounts are seriously flawed, in virtue of adopting an unobvious and unnecessary assumption: that in order to appreciate how count words represent cardinalities, young children must possess a notion of arithmetic successor. I'll argue that once we get clear about the actual content of the principles being assumed, we'll see that there was never any compelling reason for adopting this assumption. This opens the way for an entirely different, but utterly familiar, kind of learning-theoretic account.