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  1. The Enculturated Move From Proto-Arithmetic to Arithmetic.Markus Pantsar - 2019 - Frontiers in Psychology 10.
    The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...)
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  • A Unified Theory of Psychophysical Laws in Auditory Intensity Perception.Fan-Gang Zeng - 2020 - Frontiers in Psychology 11.
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  • Sex Differences in Number Magnitude Processing Strategies Are Mediated by Spatial Navigation Strategies: Evidence From the Unit-Decade Compatibility Effect.Belinda Pletzer, TiAnni Harris & Andrea Scheuringer - 2019 - Frontiers in Psychology 10.
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  • Searching for the Critical P of Macphail’s Null Hypothesis: The Contribution of Numerical Abilities of Fish.Maria Elena Miletto Petrazzini, Alessandra Pecunioso, Marco Dadda & Christian Agrillo - 2020 - Frontiers in Psychology 11.
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  • Regular Distribution Inhibits Generic Numerosity Processing.Wei Liu, Yajun Zhao, Miao Wang & Zhijun Zhang - 2018 - Frontiers in Psychology 9.
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  • Magnitude Processing in Non-Symbolic Stimuli.Tali Leibovich & Avishai Henik - 2013 - Frontiers in Psychology 4.
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  • Are Past and Future Symmetric in Mental Time Line?Xianfeng Ding, Ning Feng, Xiaorong Cheng, Huashan Liu & Zhao Fan - 2015 - Frontiers in Psychology 6.
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  • Minds Without Language Represent Number Through Space: Origins of the Mental Number Line.Maria Dolores de Hevia, Luisa Girelli & Viola Macchi Cassia - 2012 - Frontiers in Psychology 3.
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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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  • Current Perspectives on Cognitive Diversity.Andrea Bender & Sieghard Beller - 2016 - Frontiers in Psychology 7.
  • The Developing Mental Number Line: Does Its Directionality Relate to 5- to 7-Year-Old Children’s Mathematical Abilities? [REVIEW]Lauren S. Aulet & Stella F. Lourenco - 2018 - Frontiers in Psychology 9.
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  • Effect of Presentation Format on Judgment of Long-Range Time Intervals.Camila Silveira Agostino, Yossi Zana, Fuat Balci & Peter M. E. Claessens - 2019 - Frontiers in Psychology 10.
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  • Ancestral Mental Number Lines: What Is the Evidence?Núñez Rafael & Fias Wim - 2017 - Cognitive Science 41 (8):2262-2266.
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  • A Mathematical Model of How People Solve Most Variants of the Number‐Line Task.Dale J. Cohen, Daryn Blanc‐Goldhammer & Philip T. Quinlan - 2018 - Cognitive Science 42 (8):2621-2647.
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  • Spontaneous Mapping of Number and Space in Adults and Young Children.Elizabeth S. Spelke Maria Dolores de Hevia - 2009 - Cognition 110 (2):198.
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  • Adaptation to Number Operates on Perceived Rather Than Physical Numerosity.M. Fornaciai, G. M. Cicchini & D. C. Burr - 2016 - Cognition 151:63-67.
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  • Linear Mapping of Numbers Onto Space Requires Attention.Giovanni Anobile, Guido Marco Cicchini & David C. Burr - 2012 - Cognition 122 (3):454-459.
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  • Processing of Numerical and Proportional Quantifiers.Sailee Shikhare, Stefan Heim, Elise Klein, Stefan Huber & Klaus Willmes - 2015 - Cognitive Science 39 (7):1504-1536.
    Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical or proportional quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning (...)
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  • Children's Understanding of the Natural Numbers’ Structure.Jennifer Asmuth, Emily M. Morson & Lance J. Rips - 2018 - Cognitive Science 42 (6):1945-1973.
    When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010; Siegler & Opfer, 2003). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011; Cantlon, Cordes, Libertus, & Brannon, (...)
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  • Estimating Large Numbers.David Landy, Noah Silbert & Aleah Goldin - 2013 - Cognitive Science 37 (5):775-799.
    Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about half (...)
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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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  • Developmental Trajectory of Number Acuity Reveals a Severe Impairment in Developmental Dyscalculia.Manuela Piazza, Andrea Facoetti, Anna Noemi Trussardi, Ilaria Berteletti, Stefano Conte, Daniela Lucangeli, Stanislas Dehaene & Marco Zorzi - 2010 - Cognition 116 (1):33-41.
  • Squeezing, Striking, and Vocalizing: Is Number Representation Fundamentally Spatial?Rafael Núñez, D. Doan & Anastasia Nikoulina - 2011 - Cognition 120 (2):225-235.
  • Parallel and Serial Processes in Number-to-Quantity Conversion.Dror Dotan & Stanislas Dehaene - 2020 - Cognition 204:104387.
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  • How Do We Convert a Number Into a Finger Trajectory?Dror Dotan & Stanislas Dehaene - 2013 - Cognition 129 (3):512-529.
  • Mental Magnitudes and Increments of Mental Magnitudes.Matthew Katz - 2013 - Review of Philosophy and Psychology 4 (4):675-703.
    There is at present a lively debate in cognitive psychology concerning the origin of natural number concepts. At the center of this debate is the system of mental magnitudes, an innately given cognitive mechanism that represents cardinality and that performs a variety of arithmetical operations. Most participants in the debate argue that this system cannot be the sole source of natural number concepts, because they take it to represent cardinality approximately while natural number concepts are precise. In this paper, I (...)
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  • In Search of a Theory: The Interpretative Challenge of Empirical Findings on Cultural Variance in Mindreading.Arkadiusz Gut & Robert Mirski - 2016 - Studies in Logic, Grammar and Rhetoric 48 (1):201-230.
    In this paper, we present a battery of empirical findings on the relationship between cultural context and theory of mind that show great variance in the onset and character of mindreading in different cultures; discuss problems that those findings cause for the largely-nativistic outlook on mindreading dominating in the literature; and point to an alternative framework that appears to better accommodate the evident cross-cultural variance in mindreading. We first outline the theoretical frameworks that dominate in mindreading research, then present the (...)
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  • Technology and Mathematics.Sven Ove Hansson - 2020 - Philosophy and Technology 33 (1):117-139.
    In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use of simple aide-mémoires for counting and arithmetic, via the use of mathematics in weaving, building and other trades, and the introduction of calculus to solve technological problems, to the modern use of computers to solve both technological and mathematical problems. Three important philosophical issues emerge from this historical résumé: (...)
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  • Right out of the box: how to situate metaphysics of science in relation to other metaphysical approaches.Alexandre Guay & Thomas Pradeu - 2020 - Synthese 197 (5):1847-1866.
    Several advocates of the lively field of “metaphysics of science” have recently argued that a naturalistic metaphysics should be based solely on current science, and that it should replace more traditional, intuition-based, forms of metaphysics. The aim of the present paper is to assess that claim by examining the relations between metaphysics of science and general metaphysics. We show that the current metaphysical battlefield is richer and more complex than a simple dichotomy between “metaphysics of science” and “traditional metaphysics”, and (...)
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  • Non-Symbolic Halving in an Amazonian Indigene Group.Koleen McCrink, Elizabeth Spelke, Stanislas Dehaene & Pierre Pica - 2013 - Developmental Science 16 (3):451-462.
    Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...)
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  • Brain Neural Activity Patterns Yielding Numbers Are Operators, Not Representations.Walter J. Freeman & Robert Kozma - 2009 - Behavioral and Brain Sciences 32 (3-4):336.
  • Concrete Magnitudes: From Numbers to Time.Christine Falter, Valdas Noreika, Julian Kiverstein & Bruno Mölder - 2009 - Behavioral and Brain Sciences 32 (3-4):335-336.
    Cohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).
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  • Philosophy of Mathematics for the Masses : Extending the Scope of the Philosophy of Mathematics.Stefan Buijsman - 2016 - Dissertation, Stockholm University
    One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...)
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  • Mitä Gödelin epätäydellisyysteoreemoista voidaan päätellä filosofiassa?Markus Pantsar - 2011 - Ajatus 68.
    Tutkin tässä artikkelissa Kurt Gödelin epätäydellisyysteoreemojen tulkintoja filosofiassa. Aihepiiri kattaa valtavan määrän eri tulkintoja tekoälystä fysiikkaan ja runouteen asti. Osoitan, että kriittisesti tarkasteltuna kaikki radikaalit epätäydellisyysteoreemojen sovellukset ovat virheellisiä.
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  • Numbers and Arithmetic: Neither Hardwired Nor Out There.Rafael Núñez - 2009 - Biological Theory 4 (1):68-83.
    What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...)
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  • Thinking Materially: Cognition as Extended and Enacted.Karenleigh A. Overmann - 2017 - Journal of Cognition and Culture 17 (3-4):354-373.
    Human cognition is extended and enacted. Drawing the boundaries of cognition to include the resources and attributes of the body and materiality allows an examination of how these components interact with the brain as a system, especially over cultural and evolutionary spans of time. Literacy and numeracy provide examples of multigenerational, incremental change in both psychological functioning and material forms. Though we think materiality, its central role in human cognition is often unappreciated, for reasons that include conceptual distribution over multiple (...)
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  • The Innateness Hypothesis and Mathematical Concepts.Helen3 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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  • The Language of Geometry : Fast Comprehension of Geometrical Primitives and Rules in Human Adults and Preschoolers.Pierre Pica & Mariano Sigman & Stanislas Dehaene With Marie Amalric, Liping Wang - 2017 - PLoS Biology 10.
    Article Authors Metrics Comments Media Coverage Abstract Author Summary Introduction Results Discussion Supporting information Acknowledgments Author Contributions References Reader Comments (0) Media Coverage (0) Figures Abstract During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to (...)
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  • Flexible Intuitions of Euclidean Geometry in an Amazonian Indigene Group.Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene - 2011 - Pnas 23.
    Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...)
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  • The Mapping of Numbers on Space : Evidence for a Logarithmic Intuition.Véronique Izard, Pierre Pica, Elizabeth Spelke & Stanislas Dehaene - 2008 - Médecine/Science 24 (12):1014-1016.
    Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l’espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan… Si les nombres complexes, comme l’utilisation de repères, sont apparus relativement récemment (vers le XVIIe siècle), la mesure des longueurs est en revanche un procédé très ancien, qui remonte au moins au 3e ou 4e millénaire av. J-C. Loin d’être fortuits, ces liens entre les nombres et l’espace (...)
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  • Theoretical Implications of the Study of Numbers and Numerals in Mundurucu.Pierre Pica & Alain Lecomte - 2008 - Philosophical Psychology 21 (4):507 – 522.
    Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...)
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  • Shape Beyond Recognition: Form-Derived Directionality and its Effects on Visual Attention and Motion Perception.Heida M. Sigurdardottir, Suzanne M. Michalak & David L. Sheinberg - 2014 - Journal of Experimental Psychology: General 143 (1):434-454.
  • Mapping Numerical Magnitudes Along the Right Lines: Differentiating Between Scale and Bias.Vyacheslav Karolis, Teresa Iuculano & Brian Butterworth - 2011 - Journal of Experimental Psychology: General 140 (4):693-706.
  • Core Multiplication in Childhood.Elizabeth S. Spelke - 2010 - Cognition 116 (2):204-216.
  • 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.
  • A Bayesian Perspective on Magnitude Estimation.Frederike H. Petzschner, Stefan Glasauer & Klaas E. Stephan - 2015 - Trends in Cognitive Sciences 19 (5):285-293.
  • The Mental Time Line: An Analogue of the Mental Number Line in the Mapping of Life Events.Shahar Arzy, Esther Adi-Japha & Olaf Blanke - 2009 - Consciousness and Cognition 18 (3):781-785.
    A crucial aspect of the human mind is the ability to project the self along the time line to past and future. It has been argued that such self-projection is essential to re-experience past experiences and predict future events. In-depth analysis of a novel paradigm investigating mental time shows that the speed of this “self-projection” in time depends logarithmically on the temporal-distance between an imagined “location” on the time line that participants were asked to imagine and the location of another (...)
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  • It All Adds Up …. Or Does It? Numbers, Mathematics and Purpose.Simon Conway Morris - 2016 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 58:117-122.
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  • Analog Representations and Their Users.Matthew Katz - 2016 - Synthese 193 (3):851-871.
    Characterizing different kinds of representation is of fundamental importance to cognitive science, and one traditional way of doing so is in terms of the analog–digital distinction. Indeed the distinction is often appealed to in ways both narrow and broad. In this paper I argue that the analog–digital distinction does not apply to representational schemes but only to representational systems, where a representational system is constituted by a representational scheme and its user, and that whether a representational system is analog or (...)
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