Bootstrapping & the origin of concepts

By Susan Carey. 2004

beings create scienti1⁄2c theories, mathematics, literature, moral systems, and complex technology. And only humans have the capacity to acquire such culturally constructed knowledge in the normal course of immersion in the adult world. There are many reasons for the differences between the minds of humans and other animals. We have bigger brains, and hence more powerful information processors; sometimes differences in the power of a processor can create what look like qualitative differences in kind. And of course human beings also have language–the main medium for the cultural transmission of acquired knowledge. Comparative studies of humans and other primates suggest that we differ from them as well in our substantive cognitive abilities– for example, our capacity for causal analysis and our capacity to reason about the mental states of others. Each of these factors doubtless contributes to our prodigious ability to learn. But in my view another factor is even more important: our uniquely human ability to ‘bootstrap.’ Many psychologists, historians, and philosophers of science have appealed to the metaphor of bootstrapping in order to explain learning of a particularly dif1⁄2cult sort– those cases in which the endpoint of the process transcends in some qualitative way the starting point. The choice of metaphor may seem puzzling–it is selfevidently impossible to pull oneself up by one’s own bootstrap. After all, the process I describe below is not impossible, but I keep the term because of its historical credentials and because it seeks to explain cases of learning that many have argued are impossible. Sometimes learning requires the creation of new representational resources that are more powerful than those present at the outset. Early in the cultural history of mathematics, for instance, the concept of the number included only positive integers: with subsequent development the concept came to encompass zero, rational numbers (fractions), negative numbers, irrational numbers like pi, and so on.

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Citations in the corpus

Asymmetries in the Acquisition of Numbers and Quantifiers (2006, background): “This has prompted intense experimentation and theorizing about child semantics for quantification and its expression (see Carey, 2004; Cordes & Gelman, in press; Gelman, 1993; Gelman & Butterworth, 2004; Mitchie, 1984; Mix, Huttenlocher, & Levine 2002; Sarnecka & Gelman, 2003; Wynn, 1990, 1992, for…”
Naturally Biased? In Search for Reaction Time Evidence for a Natural Number Bias in Adults. (2012, background): “In contrast, the development of the natural number concept is mediated from early on by cultural representational tools [e.g., language (Carey, 2004)] and practices such as finger counting (Andres, Di Luca, & Pesenti, 2008) as well as counting songs, rhymes, and cardboard games.”
How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation (2010, background): “On the contrary, the development of the natural number concept is mediated from early on by cultural representational tools, language being probably the most prominent ( Carey, 2004 ), and also practices such as finger counting (Andres, Di Luca, & Pesenti, 2008).”
Psychological universals: what are they and how can we know? (2005, background): “Undoubtedly, numerical reasoning is rooted in human biology in that infants seem to be naturally endowed with a primitive number sense with an analog representational system of quantity (Dehaene, 1997), natural language quantifiers, and object representation (Carey, 2004).”
Acquisition of English Number Marking: The Singular-Plural Distinction (2006, background): “Our confidence in the results of these studies is bolstered by convergent data from a totally different paradigm (Wood, Kouider, & Carey, 2004), in which famil- iar objects and nouns were used.”
Bootstrapping the Mind: Analogical Processes and Symbol Systems (2010, background): “The learning is at first slow and piecemeal—even after binding two to sets of cardinality two, weeks or months may ensue before the child realizes that three refers to a set with three items (Carey, 2004; Mix, 2002; Mix et al., 2005).”
One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. (2007, unknown): “…the counting principles from enriched parallel individuation Several authors have proposed that the counting principles could be constructed from enriched parallel individuation and the memorized verbal count list by a bootstrapping process (Carey, 2004; Hurford, 1987, Klahr and Wallace, 1976).”
Cattell–Horn–Carroll cognitive‐achievement relations: What we have learned from the past 20 years of research (2010, background): “…& Primerano, 2005; Flanagan et al., 2006; Floyd, Evans, & McGrew, 2003; Fuchs et al., 2006; McGrew, 2008; Swanson & Jerman, 2006) especially as Gc relates to the development of number concepts (e.g., Carey, 2004; Gelman & Butterworth, 2005) and the retrieval of math facts (Chong & Siegel, 2008).”