The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports (...) exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes. (shrink)

Why do people create extra representations to help them make sense of situations, diagrams, illustrations, instructions and problems? The obvious explanation— external representations save internal memory and com- putation—is only part of the story. I discuss seven ways external representations enhance cognitive power: they change the cost structure of the inferential landscape; they provide a structure that can serve as a shareable object of thought; they create persistent referents; they facilitate re- representation; they are often a more natural representation of (...) structure than mental representations; they facilitate the computation of more explicit encoding of information; they enable the construction of arbitrarily complex structure; and they lower the cost of controlling thought—they help coordinate thought. Jointly, these functions allow people to think more powerfully with external representations than without. They allow us to think the previously unthinkable. (shrink)

Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition (...) are the output of dedicated input analyzers, as with perceptual representations, but these core representations differ from perceptual representations in having more abstract contents and richer functional roles. Carey argues that the key to understanding cognitive development lies in recognizing conceptual discontinuities in which new representational systems emerge that have more expressive power than core cognition and are also incommensurate with core cognition and other earlier representational systems. Finally, Carey fleshes out Quinian bootstrapping, a learning mechanism that has been repeatedly sketched in the literature on the history and philosophy of science. She demonstrates that Quinian bootstrapping is a major mechanism in the construction of new representational resources over the course of childrens cognitive development. Carey shows how developmental cognitive science resolves aspects of long-standing philosophical debates about the existence, nature, content, and format of innate knowledge. She also shows that understanding the processes of conceptual development in children illuminates the historical process by which concepts are constructed, and transforms the way we think about philosophical problems about the nature of concepts and the relations between language and thought. (shrink)

What is the relation between the material, conventional symbol structures that we encounter in the spoken and written word, and human thought? A common assumption, that structures a wide variety of otherwise competing views, is that the way in which these material, conventional symbol-structures do their work is by being translated into some kind of content-matching inner code. One alternative to this view is the tempting but thoroughly elusive idea that we somehow think in some natural language (such as English). (...) In the present treatment I explore a third option, which I shall call the "complementarity" view of language. According to this third view the actual symbol structures of a given language add cognitive value by complementing (without being replicated by) the more basic modes of operation and representation endemic to the biological brain. The "cognitive bonus" that language brings is, on this model, not to be cashed out either via the ultimately mysterious notion of "thinking in a given natural language" or via some process of exhaustive translation into another inner code. Instead, we should try to think in terms of a kind of coordination dynamics in which the forms and structures of a language qua material symbol system play a key and irreducible role. Understanding language as a complementary cognitive resource is, I argue, an important part of the much larger project (sometimes glossed in terms of the "extended mind") of understanding human cognition as essentially and multiply hybrid: as involving a complex interplay between internal biological resources and external non-biological resources. (shrink)

Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the (...) brain capture bottom-up patterns of activation in sensory-motor areas. Later, in a top-down manner, association areas partially reactivate sensory-motor areas to implement perceptual symbols. The stor- age and reactivation of perceptual symbols operates at the level of perceptual components – not at the level of holistic perceptual expe- riences. Through the use of selective attention, schematic representations of perceptual components are extracted from experience and stored in memory (e.g., individual memories of green, purr, hot). As memories of the same component become organized around a com- mon frame, they implement a simulator that produces limitless simulations of the component (e.g., simulations of purr). Not only do such simulators develop for aspects of sensory experience, they also develop for aspects of proprioception (e.g., lift, run) and introspec- tion (e.g., compare, memory, happy, hungry). Once established, these simulators implement a basic conceptual system that represents types, supports categorization, and produces categorical inferences. These simulators further support productivity, propositions, and ab- stract concepts, thereby implementing a fully functional conceptual system. Productivity results from integrating simulators combinato- rially and recursively to produce complex simulations. Propositions result from binding simulators to perceived individuals to represent type-token relations. Abstract concepts are grounded in complex simulations of combined physical and introspective events. Thus, a per- ceptual theory of knowledge can implement a fully functional conceptual system while avoiding problems associated with amodal sym- bol systems. Implications for cognition, neuroscience, evolution, development, and artificial intelligence are explored. (shrink)

The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is. Although this has led previous researchers to argue for domain-specific constraints that are tied to different kinds/domains, an exciting possibility is that kinds/domains themselves can be (...) learned. General cognitive constraints, when combined with rich inputs, can establish domains, rather than these domains necessarily preexisting prior to learning. Knowledge is structured and richly differentiated, but its “skeleton” must not always be preestablished. Instead, the skeleton may be adapted to fit patterns of co-occurrence, task requirements, and goals. Finally, we argue that for models of development to demonstrate genuine cognitive novelty, it will be helpful for them to move beyond highly preprocessed and symbolic encodings that limit flexibility. We consider two physical models that learn to make tone discriminations. They are mechanistic models that preserve rich spatial, perceptual, dynamic, and concrete information, allowing them to form surprising new classes of hypotheses and encodings. (shrink)