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The Small Number System

Philosophy of Science 87 (1):113-134 (2020)

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  1. How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts.Eric Margolis & Stephen Laurence - 2008 - Cognition 106 (2):924-939.
    Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that clearly (...)
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  • The origin of concepts.Susan Carey - 2009 - New York: Oxford University Press.
    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 (...)
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  • One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles.Mathieu Le Corre & Susan Carey - 2007 - Cognition 105 (2):395-438.
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  • Large number discrimination in 6-month-old infants.Fei Xu & Elizabeth S. Spelke - 2000 - Cognition 74 (1):1-11.
    Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.
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  • Languages Treat 1‐4 Specially.James R. Hurford - 2002 - Mind and Language 16 (1):69-75.
    This commentary is in two sections. The first presents some specifically linguistic evidence regarding Dehaene’s statement that, in animals and prelinguistic humans, only very small numbers (up to about 3) can be represented accurately 1. The second section contains some more general reflections on Dehaene’s work.
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  • (1 other version)Indexing and the object concept:” what” and” where” in infancy.Alan M. Leslie, Fei Xu, Patrice D. Tremoulet & Brian J. Scholl - 1998 - Trends in Cognitive Sciences 2 (1):10-18.
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  • A memory span of one? Object identification in 6.5-month-old infants.Zsuzsa Káldy & Alan M. Leslie - 2005 - Cognition 97 (2):153-177.
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  • (1 other version)Indexing and the object concept: developing `what' and `where' systems.Alan M. Leslie, Fei Xu, Patrice D. Tremoulet & Brian J. Scholl - 1998 - Trends in Cognitive Sciences 2 (1):10-18.
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  • Addition and subtraction by human infants. 358 (6389), 749-750. Xu, F., & Spelke, ES (2000). Large number discrimination in 6-month-old infants. [REVIEW]Karen Wynn - 1992 - Cognition 74 (1).
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  • What makes us Smart? Core knowledge and natural language.Elizabeth S. Spelke - 2003 - In Dedre Gentner & Susan Goldin-Meadow (eds.), Language in Mind: Advances in the Study of Language and Thought. MIT Press. pp. 277--311.
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  • Languages treat 1-4 specially.James R. Hurford - 2001 - Mind and Language 16 (1):69–75.
    This commentary is in two sections. The first presents some specifically linguistic evidence regarding Dehaene’s statement that, in animals and prelinguistic humans, only very small numbers can be represented accurately 1. The second section contains some more general reflections on Dehaene’s work.
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  • Baby arithmetic: one object plus one tone.Tessei Kobayashi, Kazuo Hiraki, Ryoko Mugitani & Toshikazu Hasegawa - 2004 - Cognition 91 (2):B23-B34.
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