Numerical Cognition

Edited by Oliver Marshall (The Graduate Center, CUNY, The Graduate Center, CUNY)
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  1. Ratio Dependence in Small Number Discrimination is Affected by the Experimental Procedure.Christian Agrillo, Laura Piffer, Angelo Bisazza & Brian Butterworth - 2015 - Frontiers in Psychology 6.
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  2. Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. [REVIEW]Jeremy Avigad - 2008 - Philosophia Mathematica 17 (1):95-108.
    Published in 1891, Edmund Husserl's first book, Philosophie der Arithmetik, aimed to ‘prepare the scientific foundations for a future construction of that discipline’. His goals should seem reasonable to contemporary philosophers of mathematics: "…through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. 1"But the ensuing strategy for grounding mathematical knowledge (...)
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  3. Non-Symbolic Arithmetic in Adults and Young Children.Hilary Barth, Kristen La Mont, Jennifer Lipton, Stanislas Dehaene, Nancy Kanwisher & Elizabeth Spelke - 2006 - Cognition 98 (3):199-222.
  4. Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
    Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to a (...)
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  5. Mathematical Cognition and its Cultural Dimension.Andrea Bender, Sieghard Beller, Marc Brysbaert, Stanislas Dehaene & Heike Wiese - 2009 - In N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society.
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  6. Representation of Numerical and Non-Numerical Order in Children.Ilaria Berteletti, Daniela Lucangeli & Marco Zorzi - 2012 - Cognition 124 (3):304-313.
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  7. Number Knows No Bounds.Elizabeth M. Brannon - 2003 - Trends in Cognitive Sciences 7 (7):279-281.
  8. The Development of Ordinal Numerical Knowledge in Infancy.Elizabeth M. Brannon - 2002 - Cognition 83 (3):223-240.
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  9. Number Bias for the Discrimination of Large Visual Sets in Infancy.Elizabeth M. Brannon, Sara Abbott & Donna J. Lutz - 2004 - Cognition 93 (2):B59-B68.
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  10. The Evolution and Ontogeny of Ordinal Numerical Ability.Elizabeth M. Brannon & Herbert S. Terrace - 2002 - In Marc Bekoff, Colin Allen & Gordon M. Burghardt (eds.), The Cognitive Animal: Empirical and Theoretical Perspectives on Animal Cognition. MIT Press. pp. 197--204.
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  11. Origins of Objectivity.Tyler Burge - 2010 - Oxford University Press.
    Tyler Burge presents an original study of the most primitive ways in which individuals represent the physical world. By reflecting on the science of perception and related psychological and biological sciences, he gives an account of constitutive conditions for perceiving the physical world, and thus aims to locate origins of representational mind.
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  12. Five Theses on De Re States and Attitudes.Tyler Burge - 2009 - In Joseph Almog & Paolo Leonardi (eds.), The Philosophy of David Kaplan. Oxford University Press. pp. 246--324.
    I shall propose five theses on de re states and attitudes. To be a de re state or attitude is to bear a peculiarly direct epistemic and representational relation to a particular referent in perception or thought. I will not dress this bare statement here. The fifth thesis tries to be less coarse. The first four explicate and restrict context- bound, singular, empirical representation, which constitutes a significant and central type of de re state or attitude.
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  13. Foundations of Mind.Tyler Burge - 2007 - Oxford University Press.
    Foundations of Mind collects the essays which established Tyler Burge as a leading philosopher of mind.
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  14. Everybody Counts but Not Everybody Understands Numbers: The Unrecognised Handicap of Dyscalculia.B. Butterworth - forthcoming - Proceedings of the British Academy.
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  15. Foundational Numerical Capacities and the Origins of Dyscalculia.Brian Butterworth - 2010 - Trends in Cognitive Sciences 14 (12):534-541.
  16. Verbal Counting and Spatial Strategies in Numerical Tasks: Evidence From Indigenous Australia.Brian Butterworth & Robert Reeve - 2008 - Philosophical Psychology 21 (4):443 – 457.
    In this study, we test whether children whose culture lacks CWs and counting practices use a spatial strategy to support enumeration tasks. Children from two indigenous communities in Australia whose native and only language (Warlpiri or Anindilyakwa) lacked CWs and were tested on classical number development tasks, and the results were compared with those of children reared in an English-speaking environment. We found that Warlpiri- and Anindilyakwa-speaking children performed equivalently to their English-speaking counterparts. However, in tasks in which they were (...)
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  17. Numerical Abstraction: It Ain't Broke.Jessica F. Cantlon, Sara Cordes, Melissa E. Libertus & Elizabeth M. Brannon - 2009 - Behavioral and Brain Sciences 32 (3-4):331-332.
    The dual-code proposal of number representation put forward by Cohen Kadosh & Walsh (CK&W) accounts for only a fraction of the many modes of numerical abstraction. Contrary to their proposal, robust data from human infants and nonhuman animals indicate that abstract numerical representations are psychologically primitive. Additionally, much of the behavioral and neural data cited to support CK&W's proposal is, in fact, neutral on the issue of numerical abstraction.
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  18. Beyond the Number Domain.Jessica F. Cantlon, Michael L. Platt & Elizabeth M. Brannon - 2009 - Trends in Cognitive Sciences 13 (2):83-91.
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  19. Précis of the Origin of Concepts.Susan Carey - 2011 - Behavioral and Brain Sciences 34 (3):113-124.
    A theory of conceptual development must specify the innate representational primitives, must characterize the ways in which the initial state differs from the adult state, and must characterize the processes through which one is transformed into the other. The Origin of Concepts (henceforth TOOC) defends three theses. With respect to the initial state, the innate stock of primitives is not limited to sensory, perceptual, or sensorimotor representations; rather, there are also innate conceptual representations. With respect to developmental change, conceptual development (...)
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  20. The Making of an Abstract Concept: Natural Number.Susan Carey - 2010 - In Denis Mareschal, Paul Quinn & Stephen E. G. Lea (eds.), The Making of Human Concepts. Oxford University Press. pp. 265.
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  21. Where Our Number Concepts Come From.Susan Carey - 2009 - Journal of Philosophy 106 (4):220-254.
  22. The Origin of Concepts.Susan Carey - 2009 - 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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  23. Math Schemata and the Origins of Number Representations.Susan Carey - 2008 - Behavioral and Brain Sciences 31 (6):645-646.
    The contrast Rips et al. draw between and approaches to understanding the origin of the capacity for representing natural number is a false dichotomy. Its plausibility depends upon the sketchiness of the authors' own proposal. At least some of the proposals they characterize as bottom-up are worked-out versions of the very top-down position they advocate. Finally, they deny that the structures that these putative bottom-up proposals consider to be sources of natural number are even precursors of concepts of natural number. (...)
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  24. The Representation of Number in Natural Language Syntax and in Language of Thought: A Case Study of the Evolution and Development of Representational Resources.Susan Carey - 2001 - In João Branquinho (ed.), The Foundations of Cognitive Science. Oxford: Clarendon Press. pp. 23--53.
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  25. Cognitive Foundations of Arithmetic: Evolution and Ontogenisis.Susan Carey - 2001 - Mind and Language 16 (1):37–55.
    Dehaene articulates a naturalistic approach to the cognitive foundations of mathematics. Further, he argues that the ‘number line’ system of representation is the evolutionary and ontogenetic foundation of numerical concepts. Here I endorse Dehaene’s naturalistic stance and also his characterization of analog magnitude number representations. Although analog magnitude representations are part of the evolutionary foundations of numerical concepts, I argue that they are unlikely to be part of the ontogenetic foundations of the capacity to represent natural number. Rather, the developmental (...)
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  26. Evolutionary and Ontogenetic Foundations of Arithmetic.Susan Carey - 2001 - Mind and Language 16 (1):37-55.
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  27. Temporal Order Judgment Reveals How Number Magnitude Affects Visuospatial Attention.Marco Casarotti, Marika Michielin, Marco Zorzi & Carlo Umiltà - 2007 - Cognition 102 (1):101-117.
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  28. Neuronal Models of Cognitive Functions Associated with the Prefrontal Cortex.J. -P. Pierre Changeux & S. Dehaene - 1992 - In Y. Christen & P. S. Churchland (eds.), Neurophilosophy and Alzheimer's Disease. Springer Verlag. pp. 60--79.
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  29. Toward a Multiroute Model of Number Processing: Impaired Number Transcoding with Preserved Calculation Skills.Lisa Cipolotti & Brian Butterworth - 1995 - Journal of Experimental Psychology: General 124 (4):375.
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  30. Numerical Cognition and Mathematical Realism.Helen De Cruz - 2016 - Philosophers' Imprint 16 (16).
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...)
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  31. The Innateness Hypothesis and Mathematical Concepts.Helen De Cruz & Johan De Smedt - 2010 - Topoi 29 (1):3-13.
    In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist (...)
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  32. Knowledge of Number and Knowledge of Language: Number as a Test Case for the Role of Language in Cognition.Helen De Cruz & Pierre Pica - 2008 - Philosophical Psychology 21 (4):437 – 441.
    The relationship between language and conceptual thought is an unresolved problem in both philosophy and psychology. It remains unclear whether linguistic structure plays a role in our cognitive processes. This special issue brings together cognitive scientists and philosophers to focus on the role of language in numerical cognition: because of their universality and variability across languages, number words can serve as a fruitful test case to investigate claims of linguistic relativism.
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  33. The Conceptual Basis of Numerical Abilities: One-to-One Correspondence Versus the Successor Relation.Lieven Decock - 2008 - Philosophical Psychology 21 (4):459 – 473.
    In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one (...)
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  34. Neo-Fregeanism Naturalized: The Role of One-to-One Correspondence in Numerical Cognition.Lieven Decock - 2008 - Behavioral and Brain Sciences 31 (6):648-649.
    Rips et al. argue that the construction of math schemas roughly similar to the Dedekind/Peano axioms may be necessary for arriving at arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume's principle. Frege arithmetic is arguably a more plausible start for a top-down approach in the psychological study of mathematical cognition than Peano arithmetic.
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  35. Cross-Linguistic Regularities in the Frequency of Number Words.S. Dehaene - 1992 - Cognition 43 (1):1-29.
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  36. Varieties of Numerical Abilities.S. Dehaene - 1992 - Cognition 44 (1-2):1-42.
  37. Long-Term Semantic Memory Versus Contextual Memory in Unconscious Number Processing.S. Dehaene, A. G. Greenwald, R. L. Abrams & L. Naccache - 2003 - Journal of Experimental Psychology 29 (2):235-247.
    Subjects classified visible 2-digit numbers as larger or smaller than 55. Target numbers were preceded by masked 2-digit primes that were either congruent (same relation to 55) or incongruent. Experiments 1 and 2 showed prime congruency effects for stimuli never included in the set of classified visible targets, indicating subliminal priming based on long-term semantic memory. Experiments 2 and 3 went further to demonstrate paradoxical unconscious priming effects resulting from task context. For example, after repeated practice classifying 73 as larger (...)
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  38. The Neural Basis of the Weber–Fechner Law: A Logarithmic Mental Number Line.Stanislas Dehaene - 2003 - Trends in Cognitive Sciences 7 (4):145-147.
  39. Author's Response: Is Number Sense a Patchwork?Stanislas Dehaene - 2001 - Mind and Language 16 (1):89–100.
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  40. Précis of the Number Sense.Stanislas Dehaene - 2001 - Mind and Language 16 (1):16–36.
    ‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...)
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  41. The Number Sense: How the Mind Creates Mathematics.Stanislas Dehaene - 1999 - British Journal of Educational Studies 47 (2):201-203.
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  42. The Mental Representation of Parity and Number Magnitude.Stanislas Dehaene, Serge Bossini & Pascal Giraux - 1993 - Journal of Experimental Psychology: General 122 (3):371.
  43. Space, Time and Number in the Brain.Stanislas Dehaene & Elizabeth Brannon (eds.) - 2011 - Oxford University Press.
    A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. * The ...
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  44. Space, Time, and Number: A Kantian Research Program.Stanislas Dehaene & Elizabeth M. Brannon - 2010 - Trends in Cognitive Sciences 14 (12):517-519.
  45. Response to Comment on "Log or Linear? Distinct Intuitions on the Number Scale in Western and Amazonian Indigene Cultures".Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke - 2009 - Science 323 (5910):38.
    The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.
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  46. The Case for a Notation-Independent Representation of Number.Stanislas Dehaene, Roi Cohen Kadosh & Vincent Walsh - 2009 - Behavioral and Brain Sciences 32 (3):333.
    Cohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.
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  47. Core Systems of Number.Stanislas Dehaene, Elizabeth Spelke & Lisa Feigenson - 2004 - Trends in Cognitive Sciences 8 (7):307-314.
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  48. Significant Inter-Test Reliability Across Approximate Number System Assessments.Nicholas K. DeWind & Elizabeth M. Brannon - 2016 - Frontiers in Psychology 7.
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  49. Rhesus Monkeys Map Number Onto Space.Caroline B. Drucker & Elizabeth M. Brannon - 2014 - Cognition 132 (1):57-67.
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  50. Beyond 'What' and 'How Many': Capacity, Complexity and Resolution of Infants' Object Representations.Jennifer M. Zosh & Feigenson & Lisa - 2009 - In Bruce M. Hood & Laurie R. Santos (eds.), The Origins of Object Knowledge. Oxford University Press.
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