The Origin of Concepts (Carey Reference Carey2009; henceforth Origin) is among the most interesting works in cognitive psychology to appear in decades. It takes central theoretical issues head on – for example, how people acquire notions of number and matter. And to a very impressive degree, Carey has turned ideas about these issues into workable experiments, often with intriguing results. Although we disagree with specific conclusions, her arguments are arresting ones, worth the time to stop and sift. The book's main point is that people learn concepts that are genuinely novel, concepts that can't be spelled out in the vocabulary of their earlier knowledge. The paradox of the book, however, is that the more carefully Carey explains the steps that take children's preexisting concepts to their later ones, the less convincing her case for conceptual discontinuity. In earlier articles, one of us examined Carey's theory of how children acquire concepts of the natural numbers (Rips et al. Reference Rips, Asmuth and Bloomfield2006; Reference Rips, Bloomfield and Asmuth2008). In this commentary, we take a more general look at the thesis that later concepts can be incommensurable with earlier ones.
1. Puzzle 1: Computation and translation
According to Origin, children shift from earlier to later concepts by learning the latter in terms of the former. Some mental process transforms one into the other, even when the later concepts are new ones, not expressible in terms of the old. In this discontinuous case, Carey calls the process Quinian bootstrapping, and it occupies a central focus of the book. Bootstrapping must meet the following requirements: (a) produce new concepts that can't be translated in terms of earlier ones, but (b) do so in a computationally feasible way. Moreover, previously understood concepts must be the input to bootstrapping: Carey rules out the possibility that children could simply introduce an entirely new set of mental tokens, relate them systematically to each other, and thereby provide these tokens with meanings of their own (p. 419). Although “placeholder” tokens – ones that have no antecedent meaning – play an important role in bootstrapping, (c) bootstrapping requires old, already meaningful concepts to ground the placeholders in the final system.
The puzzle is why requirement (b) and (c) don't collectively defeat requirement (a). If bootstrapping takes already understood concepts and combines them computationally to produce new concepts, doesn't that mean that the old and new concepts are intertranslatable by the same computable function? The key process in bootstrapping is a complex nondeductive inference, such as analogy, for which cognitive science has struggled to provide an adequate account. But troubles in formulating the bootstrap's inductive step don't show that the process is computationally impossible, and Carey proposes a computational approach to these inferences. If bootstrapping is computationally possible, though, why can't we use this process to achieve a translation between conceptual systems, contrary to (a)?
One way out of this dilemma is to reject requirement (b) and contend that bootstrapping is not computed, but something children do, for example, as a matter of brute maturation. However, this move would imply that cognitive development is unable to illuminate these interesting cases of concept acquisition. We favor giving up requirement (a), the claim for developmentally incommensurable systems.
2. Puzzle 2: Coordinating dual factor semantics
Not every change in inter-concept relations produces a change in meaning. Learning a new fact about daisies – for example, whether they cause hay fever – doesn't change the meaning of “daisy.” Otherwise, we would never be able to change our mind about the same concept, as every change would produce a novel concept (see the critique of Carey in Fodor Reference Fodor1994). This forces Carey to distinguish changes in beliefs that don't alter a concept's meaning from more sweeping changes of belief that do (e.g., in bootstrapping). It's to Carey's credit that she sees the difficulty of separating these, as discussions of this problem are rare in psychology.
To account for the stability of concepts over incidental changes in belief, many semantic theories anchor the meaning of concepts through causal relations to their external referents (e.g., the relation between actual daisies and the mental representation DAISY). These causal relations then remain constant even when a person's beliefs about the concepts change. Origin accepts the idea that these external relations are part of what confers a concept's meaning, but adds that its meaning also depends on its conceptual role, that is – on the inferential relations it bears to other concepts.
This dual theory of meaning, however, creates difficulties when conceptual change occurs. Bootstrapping obviously produces radical changes to the inter-concept relations. But in many cases (e.g., concepts of matter), it must also produce new external connections, as otherwise the new system of concepts would remain tethered to the wrong referents (or to none). The second puzzle about bootstrapping is how it manages to do this.
Carey is attracted to theories by Laurence and Margolis (Reference Laurence and Margolis2002) and Macnamara (Reference Macnamara1986) in which a concept's internal content mediates its external content. Mental structures – visual gestalts in Macnamara or sustaining mechanisms in Laurence and Margolis – focus the external causal relations on the designated concept. These causal relations then stick to the concept through future change in beliefs. In Origin, however, no boundary separates the mental structure that determines reference from other mental representations. The focusing mechanisms are themselves inferentially connected to the rest of the conceptual system. Therefore, without further constraints on how and when the focusing process occurs, the theory threatens to collapse the two-part semantics to one internal part, thus failing to separate change in meaning from mere change in belief. Carey is forthright in acknowledging not having a fully worked-out semantic theory (p. 523), but we doubt the puzzle can be solved within her framework.
3. Coda
Origin should be on the reading list of all cognitive psychologists, as it combines striking theories with imaginative experiments. It raises new questions that will generate experiments and insights for years. The two questions we raise here concern whether its bold empirical claims mesh with theoretical requirements. We've offered two examples of this clash in the present commentary.
The Origin of Concepts (Carey Reference Carey2009; henceforth Origin) is among the most interesting works in cognitive psychology to appear in decades. It takes central theoretical issues head on – for example, how people acquire notions of number and matter. And to a very impressive degree, Carey has turned ideas about these issues into workable experiments, often with intriguing results. Although we disagree with specific conclusions, her arguments are arresting ones, worth the time to stop and sift. The book's main point is that people learn concepts that are genuinely novel, concepts that can't be spelled out in the vocabulary of their earlier knowledge. The paradox of the book, however, is that the more carefully Carey explains the steps that take children's preexisting concepts to their later ones, the less convincing her case for conceptual discontinuity. In earlier articles, one of us examined Carey's theory of how children acquire concepts of the natural numbers (Rips et al. Reference Rips, Asmuth and Bloomfield2006; Reference Rips, Bloomfield and Asmuth2008). In this commentary, we take a more general look at the thesis that later concepts can be incommensurable with earlier ones.
1. Puzzle 1: Computation and translation
According to Origin, children shift from earlier to later concepts by learning the latter in terms of the former. Some mental process transforms one into the other, even when the later concepts are new ones, not expressible in terms of the old. In this discontinuous case, Carey calls the process Quinian bootstrapping, and it occupies a central focus of the book. Bootstrapping must meet the following requirements: (a) produce new concepts that can't be translated in terms of earlier ones, but (b) do so in a computationally feasible way. Moreover, previously understood concepts must be the input to bootstrapping: Carey rules out the possibility that children could simply introduce an entirely new set of mental tokens, relate them systematically to each other, and thereby provide these tokens with meanings of their own (p. 419). Although “placeholder” tokens – ones that have no antecedent meaning – play an important role in bootstrapping, (c) bootstrapping requires old, already meaningful concepts to ground the placeholders in the final system.
The puzzle is why requirement (b) and (c) don't collectively defeat requirement (a). If bootstrapping takes already understood concepts and combines them computationally to produce new concepts, doesn't that mean that the old and new concepts are intertranslatable by the same computable function? The key process in bootstrapping is a complex nondeductive inference, such as analogy, for which cognitive science has struggled to provide an adequate account. But troubles in formulating the bootstrap's inductive step don't show that the process is computationally impossible, and Carey proposes a computational approach to these inferences. If bootstrapping is computationally possible, though, why can't we use this process to achieve a translation between conceptual systems, contrary to (a)?
One way out of this dilemma is to reject requirement (b) and contend that bootstrapping is not computed, but something children do, for example, as a matter of brute maturation. However, this move would imply that cognitive development is unable to illuminate these interesting cases of concept acquisition. We favor giving up requirement (a), the claim for developmentally incommensurable systems.
2. Puzzle 2: Coordinating dual factor semantics
Not every change in inter-concept relations produces a change in meaning. Learning a new fact about daisies – for example, whether they cause hay fever – doesn't change the meaning of “daisy.” Otherwise, we would never be able to change our mind about the same concept, as every change would produce a novel concept (see the critique of Carey in Fodor Reference Fodor1994). This forces Carey to distinguish changes in beliefs that don't alter a concept's meaning from more sweeping changes of belief that do (e.g., in bootstrapping). It's to Carey's credit that she sees the difficulty of separating these, as discussions of this problem are rare in psychology.
To account for the stability of concepts over incidental changes in belief, many semantic theories anchor the meaning of concepts through causal relations to their external referents (e.g., the relation between actual daisies and the mental representation DAISY). These causal relations then remain constant even when a person's beliefs about the concepts change. Origin accepts the idea that these external relations are part of what confers a concept's meaning, but adds that its meaning also depends on its conceptual role, that is – on the inferential relations it bears to other concepts.
This dual theory of meaning, however, creates difficulties when conceptual change occurs. Bootstrapping obviously produces radical changes to the inter-concept relations. But in many cases (e.g., concepts of matter), it must also produce new external connections, as otherwise the new system of concepts would remain tethered to the wrong referents (or to none). The second puzzle about bootstrapping is how it manages to do this.
Carey is attracted to theories by Laurence and Margolis (Reference Laurence and Margolis2002) and Macnamara (Reference Macnamara1986) in which a concept's internal content mediates its external content. Mental structures – visual gestalts in Macnamara or sustaining mechanisms in Laurence and Margolis – focus the external causal relations on the designated concept. These causal relations then stick to the concept through future change in beliefs. In Origin, however, no boundary separates the mental structure that determines reference from other mental representations. The focusing mechanisms are themselves inferentially connected to the rest of the conceptual system. Therefore, without further constraints on how and when the focusing process occurs, the theory threatens to collapse the two-part semantics to one internal part, thus failing to separate change in meaning from mere change in belief. Carey is forthright in acknowledging not having a fully worked-out semantic theory (p. 523), but we doubt the puzzle can be solved within her framework.
3. Coda
Origin should be on the reading list of all cognitive psychologists, as it combines striking theories with imaginative experiments. It raises new questions that will generate experiments and insights for years. The two questions we raise here concern whether its bold empirical claims mesh with theoretical requirements. We've offered two examples of this clash in the present commentary.