Children acquire complex concepts like DOG earlier than simple concepts like BROWN, even though our best neuroscientific theories suggest that learning the former is harder than learning the latter and, thus, should take more time (Werning 2010). This is the Complex- First Paradox. We present a novel solution to the Complex-First Paradox. Our solution builds on a generalization of Xu and Tenenbaum’s (2007) Bayesian model of word learning. By focusing on a rational theory of concept learning, we show that it (...) is easier to infer the meaning of complex concepts than that of simple concepts. (shrink)

Susan Carey's account of Quinean bootstrapping has been heavily criticized. While it purports to explain how important new concepts are learned, many commentators complain that it is unclear just what bootstrapping is supposed to be or how it is supposed to work. Others allege that bootstrapping falls prey to the circularity challenge: it cannot explain how new concepts are learned without presupposing that learners already have those very concepts. Drawing on discussions of concept learning from the philosophical literature, this article (...) develops a detailed interpretation of bootstrapping that can answer the circularity challenge. The key to this interpretation is the recognition of computational constraints, both internal and external to the mind, which can endow empty symbols with new conceptual roles and thus new contents. (shrink)

In her recent (2009) book, The Origins of Concepts, Susan Carey argues that what she calls ‘Quinean Bootstrapping’ and processes of analogy in children show that the expressive power of a mind can be increased in ways that refute Jerry Fodor's (1975, 2008) ‘Mad Dog’ view that all concepts are innate. I argue that it is doubtful any evidence about the manifestation of concepts in children will bear upon the logico-semantic issues of expressive power. Analogy and bootstrapping may be ways (...) to bring about the former, but only by presupposing the very expressive powers Carey is claiming they explain. Analogies must be understood, and bootstrapping involves confirmation of hypotheses already expressible; otherwise they can't select among an infinitude of hypotheses compatible with the finite data the child has encountered, a fact rendered vivid by Goodman's ‘grue’ paradox and Chomsky's poverty of stimulus argument. The problems have special application to minds, since there is no reason to expect a child's concepts to be ‘projectible’ or to correspond to mind-independent natural kinds. I conclude with an ecumenical view that concepts are reasonably regarded as both innate and often learned, and that what is learned can in fact increase what really concerns Carey, the functioning psychological expressive power of the child, even if it leaves untouched what concerns Fodor, the semantic expressive power. Less ecumenically: maybe Fodor (2008) miscast the debate, and the real issue that bothers people concerns not nativism, but an issue on which Carey and Fodor surprisingly agree, his conceptual Atomism, or the view that all mono-morphemic concepts are primitive and unanalyzable. The issue deserves further discussion independently of Mad-doggery. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

The Origin of Concepts sets out an impressive defense of the view that children construct entirely new systems of concepts. We offer here two questions about this theory. First, why doesn't the bootstrapping process provide a pattern for translating between the old and new systems, contradicting their claimed incommensurability? Second, can the bootstrapping process properly distinguish meaning change from belief change?

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...) collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

Why Theories of Concepts Should Not Ignore the Problem of Acquisition.

Human cognition is striking in its brilliance and its adaptability. How do we get that way? How do we move from the nearly helpless state of infants to the cognitive proficiency that characterizes adults? In this paper I argue, first, that analogical ability is the key factor in our prodigious capacity, and, second, that possession of a symbol system is crucial to the full expression of analogical ability.