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  1. The Nature of External Representations in Problem Solving.Jiajie Zhang - 1997 - Cognitive Science 21 (2):179-217.
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  • Idealization and External Symbolic Storage: The Epistemic and Technical Dimensions of Theoretic Cognition.Peter Woelert - 2012 - Phenomenology and the Cognitive Sciences 11 (3):335-366.
    This paper explores some of the constructive dimensions and specifics of human theoretic cognition, combining perspectives from (Husserlian) genetic phenomenology and distributed cognition approaches. I further consult recent psychological research concerning spatial and numerical cognition. The focus is on the nexus between the theoretic development of abstract, idealized geometrical and mathematical notions of space and the development and effective use of environmental cognitive support systems. In my discussion, I show that the evolution of the theoretic cognition of space apparently follows (...)
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  • Methodological Reflections on Typologies for Numerical Notations.Theodore Reed Widom & Dirk Schlimm - 2012 - Science in Context 25 (2):155-195.
    Past and present societies world-wide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. The present paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework to (...)
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  • Symbolic and Nonsymbolic Pathways of Number Processing.Tom Verguts & Wim Fias - 2008 - Philosophical Psychology 21 (4):539 – 554.
    Recent years have witnessed an enormous increase in behavioral and neuroimaging studies of numerical cognition. Particular interest has been devoted toward unraveling properties of the representational medium on which numbers are thought to be represented. We have argued that a correct inference concerning these properties requires distinguishing between different input modalities and different decision/output structures. To back up this claim, we have trained computational models with either symbolic or nonsymbolic input and with different task requirements, and showed that this allowed (...)
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  • From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
    Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...)
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  • How the Abstract Becomes Concrete: Irrational Numbers Are Understood Relative to Natural Numbers and Perfect Squares.Purav Patel & Sashank Varma - 2018 - Cognitive Science 42 (5):1642-1676.
  • Towards a Pluralist Theory of Singular Thought.Michele Palmira - 2018 - Synthese 195 (9):3947-3974.
    This paper investigates the question of how to correctly capture the scope of singular thinking. The first part of the paper identifies a scope problem for the dominant view of singular thought maintaining that, in order for a thinker to have a singular thought about an object o, the thinker has to bear a special epistemic relation to o. The scope problem has it is that this view cannot make sense of the singularity of our thoughts about objects to which (...)
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  • Don't Throw the Baby Out with the Math Water: Why Discounting the Developmental Foundations of Early Numeracy is Premature and Unnecessary.Kevin Muldoon, Charlie Lewis & Norman Freeman - 2008 - Behavioral and Brain Sciences 31 (6):663-664.
    We see no grounds for insisting that, because the concept natural number is abstract, its foundations must be innate. It is possible to specify domain general learning processes that feed into more abstract concepts of numerical infinity. By neglecting the messiness of children's slow acquisition of arithmetical concepts, Rips et al. present an idealized, unnecessarily insular, view of number development.
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  • Influences of Cognitive Control on Numerical Cognition—Adaptation by Binding for Implicit Learning.Korbinian Moeller, Elise Klein & Hans-Christoph Nuerk - 2013 - Topics in Cognitive Science 5 (2):335-353.
    Recently, an associative learning account of cognitive control has been suggested (Verguts & Notebaert, 2009). In this so-called adaptation by binding theory, Hebbian learning of stimulus–stimulus and stimulus–response associations is assumed to drive the adaptation of human behavior. In this study, we evaluated the validity of the adaptation-by-binding account for the case of implicit learning of regularities within a stimulus set (i.e., the frequency of specific unit digit combinations in a two-digit number magnitude comparison task) and their association with a (...)
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  • Numerical Ordering Ability Mediates the Relation Between Number-Sense and Arithmetic Competence.Ian M. Lyons & Sian L. Beilock - 2011 - Cognition 121 (2):256-261.
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  • Categories of Large Numbers in Line Estimation.David Landy, Arthur Charlesworth & Erin Ottmar - 2017 - Cognitive Science 41 (2):326-353.
    How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time (...)
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  • The Cost of Concreteness: The Effect of Nonessential Information on Analogical Transfer.Jennifer A. Kaminski, Vladimir M. Sloutsky & Andrew F. Heckler - 2013 - Journal of Experimental Psychology: Applied 19 (1):14.
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  • Numerals and Neural Reuse.Max Jones - 2020 - Synthese 197 (9):3657-3681.
    Menary OpenMIND, MIND Group, Frankfurt am Main, 2015) has argued that the development of our capacities for mathematical cognition can be explained in terms of enculturation. Our ancient systems for perceptually estimating numerical quantities are augmented and transformed by interacting with a culturally-enriched environment that provides scaffolds for the acquisition of cognitive practices, leading to the development of a discrete number system for representing number precisely. Numerals and the practices associated with numeral systems play a significant role in this process. (...)
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  • Material Representations in Mathematical Research Practice.Mikkel W. Johansen & Morten Misfeldt - 2020 - Synthese 197 (9):3721-3741.
    Mathematicians’ use of external representations, such as symbols and diagrams, constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical basis of the article consists of a qualitative interview study we conducted with active research mathematicians. In our analysis of the empirical material, we primarily used the empirically based frameworks provided by distributed cognition and (...)
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  • A Taxonomy of Cognitive Artifacts: Function, Information, and Categories.Richard Heersmink - 2013 - Review of Philosophy and Psychology 4 (3):465-481.
    The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. In this (...)
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  • Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology 12 (4):1-24.
    We present a model of how counting is learned based on the ability to perform a series of specific steps. The steps require conceptual knowledge of three components: numerosity as a property of collections; numerals; and one-to-one mappings between numerals and collections. We argue that establishing one-to-one mappings is the central feature of counting. In the literature, the so-called cardinality principle has been in focus when studying the development of counting. We submit that identifying the procedural ability to count with (...)
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  • Situated Counting.Peter Gärdenfors & Paula Quinon - 2021 - Review of Philosophy and Psychology 12 (4):721-744.
    We present a model of how counting is learned based on the ability to perform a series of specific steps. The steps require conceptual knowledge of three components: numerosity as a property of collections; numerals; and one-to-one mappings between numerals and collections. We argue that establishing one-to-one mappings is the central feature of counting. In the literature, the so-called cardinality principle has been in focus when studying the development of counting. We submit that identifying the procedural ability to count with (...)
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  • English and Chinese Children’s Performance on Numerical Tasks.Ann Dowker & Anthony M. Li - 2019 - Frontiers in Psychology 9.
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  • Mathematical Symbols as Epistemic Actions.Johan De Smedt & Helen De Cruz - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...)
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  • An Extended Mind Perspective on Natural Number Representation.Helen De Cruz - 2008 - Philosophical Psychology 21 (4):475 – 490.
    Experimental studies indicate that nonhuman animals and infants represent numerosities above three or four approximately and that their mental number line is logarithmic rather than linear. In contrast, human children from most cultures gradually acquire the capacity to denote exact cardinal values. To explain this difference, I take an extended mind perspective, arguing that the distinctly human ability to use external representations as a complement for internal cognitive operations enables us to represent natural numbers. Reviewing neuroscientific, developmental, and anthropological evidence, (...)
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  • Constraint, Cognition, and Written Numeration.Stephen Chrisomalis - 2013 - Pragmatics and Cognition 21 (3):552-572.
    The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the (...)
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  • Constraint, Cognition, and Written Numeration.Stephen Chrisomalis - 2013 - Pragmatics and Cognition 21 (3):552-572.
    The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the (...)
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  • “Free Rides” in Mathematics.Jessica Carter - 2021 - Synthese 199 (3-4):10475-10498.
    Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima, is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s framework as a tool to analyse the occurrence and properties of them. I consider (...)
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  • How numerals support new cognitive capacities.Stefan Buijsman - 2020 - Synthese 197 (9):3779-3796.
    Mathematical cognition has become an interesting case study for wider theories of cognition. Menary :1–20, 2015) argues that arithmetical cognition not only shows that internalist theories of cognition are wrong, but that it also shows that the Hypothesis of Extended Cognition is right. I examine this argument in more detail, to see if arithmetical cognition can support such conclusions. Specifically, I look at how the use of numerals extends our arithmetical abilities from quantity-related innate systems to systems that can deal (...)
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  • Variability in the Alignment of Number and Space Across Languages and Tasks.Andrea Bender, Annelie Rothe-Wulf & Sieghard Beller - 2018 - Frontiers in Psychology 9.
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  • The Role of Culture and Evolution for Human Cognition.Andrea Bender - 2020 - Topics in Cognitive Science 12 (4):1403-1420.
    Since the emergence of our species at least, natural selection based on genetic variation has been replaced by culture as the major driving force in human evolution. It has made us what we are today, by ratcheting up cultural innovations, promoting new cognitive skills, rewiring brain networks, and even shifting gene distributions. Adopting an evolutionary perspective can therefore be highly informative for cognitive science in several ways: It encourages us to ask grand questions about the origins and ramifications of our (...)
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  • The Power of 2: How an Apparently Irregular Numeration System Facilitates Mental Arithmetic.Andrea Bender & Sieghard Beller - 2017 - Cognitive Science 41 (1):158-187.
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  • The Cognitive Advantages of Counting Specifically: A Representational Analysis of Verbal Numeration Systems in Oceanic Languages.Andrea Bender, Dirk Schlimm & Sieghard Beller - 2015 - Topics in Cognitive Science 7 (4):552-569.
    The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences. These sequences constitute systems with distinct structural properties, the cross-linguistic variability of which has implications for number representation and processing. Such representational effects are scrutinized for two types of verbal numeration systems—general and object-specific ones—that were in parallel (...)
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  • Nature and Culture of Finger Counting: Diversity and Representational Effects of an Embodied Cognitive Tool.Andrea Bender & Sieghard Beller - 2012 - Cognition 124 (2):156-182.
  • Current Perspectives on Cognitive Diversity.Andrea Bender & Sieghard Beller - 2016 - Frontiers in Psychology 7.
  • Counting in Tongan: The Traditional Number Systems and Their Cognitive Implications.Andrea Bender & Sieghard Beller - 2007 - Journal of Cognition and Culture 7 (3-4):213-239.
    Is the application of more than one number system in a particular culture necessarily an indication of not having abstracted a general concept of number? Does this mean that specific number systems for certain objects are cognitively deficient? The opposite is the case with the traditional number systems in Tongan, where a consistent decimal system is supplemented by diverging systems for certain objects, in which 20 seems to play a special role. Based on an analysis of their linguistic, historical and (...)
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  • Anthropology in Cognitive Science.Andrea Bender, Edwin Hutchins & Douglas Medin - 2010 - Topics in Cognitive Science 2 (3):374-385.
    This paper reviews the uneven history of the relationship between Anthropology and Cognitive Science over the past 30 years, from its promising beginnings, followed by a period of disaffection, on up to the current context, which may lay the groundwork for reconsidering what Anthropology and (the rest of) Cognitive Science have to offer each other. We think that this history has important lessons to teach and has implications for contemporary efforts to restore Anthropology to its proper place within Cognitive Science. (...)
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  • Scientific Enquiry and Natural Kinds: From Planets to Mallards.P. Magnus - 2012 - Palgrave-Macmillan.
    Some scientific categories seem to correspond to genuine features of the world and are indispensable for successful science in some domain; in short, they are natural kinds. This book gives a general account of what it is to be a natural kind and puts the account to work illuminating numerous specific examples.
  • 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.
  • Interpreting Scientific and Engineering Practices: Integrating the Cognitive, Social, and Cultural Dimensions.N. J. Nersessian - 2005 - In M. Gorman, R. Tweney, D. Gooding & A. Kincannon (eds.), Scientific and Technological Thinking. Erlbaum. pp. 17--56.
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