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  1. 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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  • A Representational Account of Self-Knowledge.Albert Newen & Gottfried Vosgerau - 2007 - Erkenntnis 67 (2):337 - 353.
    Self-knowledge is knowledge of one’s own states (or processes) in an indexical mode of presentation. The philosophical debate is concentrating on mental states (or processes). If we characterize self-knowledge by natural language sentences, the most adequate utterance has a structure like “I know that I am in mental state M”. This common sense characterization has to be developed into an adequate description. In this investigation we will tackle two questions: (i) What precisely is the phenomenon referred to by “self-knowledge” and (...)
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  • Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. [REVIEW]Wojciech Krysztofiak - 2012 - Axiomathes 22 (4):433-456.
    The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...)
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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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  • Beyond Core Knowledge: Natural Geometry.Elizabeth Spelke, Sang Ah Lee & Véronique Izard - 2010 - Cognitive Science 34 (5):863-884.
    For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...)
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  • The Weirdest People in the World?Joseph Henrich, Steven J. Heine & Ara Norenzayan - 2010 - Behavioral and Brain Sciences 33 (2-3):61-83.
    Behavioral scientists routinely publish broad claims about human psychology and behavior in the world's top journals based on samples drawn entirely from Western, Educated, Industrialized, Rich, and Democratic (WEIRD) societies. Researchers assume that either there is little variation across human populations, or that these are as representative of the species as any other population. Are these assumptions justified? Here, our review of the comparative database from across the behavioral sciences suggests both that there is substantial variability in experimental results across (...)
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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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  • Where Our Number Concepts Come From.Susan Carey - 2009 - Journal of Philosophy 106 (4):220-254.
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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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  • Technology and Mathematics.Sven Ove Hansson - forthcoming - Philosophy and Technology.
    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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  • 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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  • Comparing Biological Motion in Two Distinct Human Societies.Pierre Pica, Stuart Jackson, Randolph Blake & Nikolaus Troje - 2011 - PLoS ONE 6 (12):e28391.
    Cross cultural studies have played a pivotal role in elucidating the extent to which behavioral and mental characteristics depend on specific environmental influences. Surprisingly, little field research has been carried out on a fundamentally important perceptual ability, namely the perception of biological motion. In this report, we present details of studies carried out with the help of volunteers from the Mundurucu indigene, a group of people native to Amazonian territories in Brazil. We employed standard biological motion perception tasks inspired by (...)
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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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  • Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers.Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene - 2008 - Philosophical Psychology 21 (4):491 – 505.
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...)
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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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  • The Enculturated Move From Proto-Arithmetic to Arithmetic.Markus Pantsar - 2019 - Frontiers in Psychology 10.
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  • Testimony and Children’s Acquisition of Number Concepts.Helen De Cruz - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. London, UK: pp. 172-186.
    An enduring puzzle in philosophy and developmental psychology is how young children acquire number concepts, in particular the concept of natural number. Most solutions to this problem conceptualize young learners as lone mathematicians who individually reconstruct the successor function and other sophisticated mathematical ideas. In this chapter, I argue for a crucial role of testimony in children’s acquisition of number concepts, both in the transfer of propositional knowledge (e.g., the cardinality concept), and in knowledge-how (e.g., the counting routine).
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  • Interface Transparency and the Psychosemantics of Most.Jeffrey Lidz, Paul Pietroski, Tim Hunter & Justin Halberda - 2011 - Natural Language Semantics 19 (3):227-256.
    This paper proposes an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence S is semantically associated with a canonical procedure for determining whether S is true; while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from a psycholinguistic experiment examining adult judgments (...)
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  • 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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  • Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
    What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral (...)
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  • Numerical Architecture.Eric Mandelbaum - 2013 - Topics in Cognitive Science 5 (1):367-386.
    The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, I review literature (...)
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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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  • Is Linguistic Determinism an Empirically Testable Hypothesis?Helen De Cruz - 2009 - Logique Et Analyse 52 (208):327-341.
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  • Representing Exact Number Visually Using Mental Abacus.Michael C. Frank & David Barner - 2012 - Journal of Experimental Psychology: General 141 (1):134-149.
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  • Memory for Multiple Visual Ensembles in Infancy.Jennifer M. Zosh, Justin Halberda & Lisa Feigenson - 2011 - Journal of Experimental Psychology: General 140 (2):141-158.
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  • Effects of Presentation Type and Visual Control in Numerosity Discrimination: Implications for Number Processing?Karolien Smets, Pieter Moors & Bert Reynvoet - 2016 - Frontiers in Psychology 7.
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  • The Approximate Number System Acuity Redefined: A Diffusion Model Approach.Joonkoo Park & Jeffrey J. Starns - 2015 - Frontiers in Psychology 6.
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  • Spatial Complexity of Character-Based Writing Systems and Arithmetic in Primary School: A Longitudinal Study.Maja Rodic, Tatiana Tikhomirova, Tatiana Kolienko, Sergey Malykh, Olga Bogdanova, Dina Y. Zueva, Elena I. Gynku, Sirui Wan, Xinlin Zhou & Yulia Kovas - 2015 - Frontiers in Psychology 6.
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  • Experimental Investigations of Ambiguity: The Case of Most.Hadas Kotek, Yasutada Sudo & Martin Hackl - 2015 - Natural Language Semantics 23 (2):119-156.
    In the study of natural language quantification, much recent attention has been devoted to the investigation of verification procedures associated with the proportional quantifier most. The aim of these studies is to go beyond the traditional characterization of the semantics of most, which is confined to explicating its truth-functional and presuppositional content as well as its combinatorial properties, as these aspects underdetermine the correct analysis of most. The present paper contributes to this effort by presenting new experimental evidence in support (...)
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  • Top-Down and Bottom-Up Philosophy of Mathematics.Carlo Cellucci - 2013 - Foundations of Science 18 (1):93-106.
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  • Spatial Arrangement and Set Size Influence the Coding of Non-Symbolic Quantities in the Intraparietal Sulcus.Johannes Bloechle, Julia F. Huber, Elise Klein, Julia Bahnmueller, Johannes Rennig, Korbinian Moeller & Stefan Huber - 2018 - Frontiers in Human Neuroscience 12.
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  • Improving Arithmetic Performance with Number Sense Training: An Investigation of Underlying Mechanism.Joonkoo Park & Elizabeth M. Brannon - 2014 - Cognition 133 (1):188-200.
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  • Brief Non-Symbolic, Approximate Number Practice Enhances Subsequent Exact Symbolic Arithmetic in Children.Daniel C. Hyde, Saeeda Khanum & Elizabeth S. Spelke - 2014 - Cognition 131 (1):92-107.
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  • The Role of Language in Mathematical Development: Evidence From Children with Specific Language Impairments.Chris Donlan, Richard Cowan, Elizabeth J. Newton & Delyth Lloyd - 2007 - Cognition 103 (1):23-33.
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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.
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  • Concept Innateness, Concept Continuity, and Bootstrapping.Susan Carey - 2011 - Behavioral and Brain Sciences 34 (3):152.
    The commentators raised issues relevant to all three important theses of The Origin of Concepts (henceforth TOOC). Some questioned the very existence of innate representational primitives, and others questioned my claims about their richness and whether they should be thought of as concepts. Some questioned the existence of conceptual discontinuity in the course of knowledge acquisition and others argued that discontinuity is much more common than was portrayed in TOOC. Some raised issues with my characterization of Quinian bootstrapping, and others (...)
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  • 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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  • WEIRD Languages Have Misled Us, Too.Asifa Majid & Stephen C. Levinson - 2010 - Behavioral and Brain Sciences 33 (2-3):103-103.
    The linguistic and cognitive sciences have severely underestimated the degree of linguistic diversity in the world. Part of the reason for this is that we have projected assumptions based on English and familiar languages onto the rest. We focus on some distortions this has introduced, especially in the study of semantics.
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  • Calibrating the Mental Number Line.Véronique Izard & Stanislas Dehaene - 2008 - Cognition 106 (3):1221-1247.
    Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...)
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  • Quantitative Standards for Absolute Linguistic Universals.Steven T. Piantadosi & Edward Gibson - 2014 - Cognitive Science 38 (4):736-756.
    Absolute linguistic universals are often justified by cross-linguistic analysis: If all observed languages exhibit a property, the property is taken to be a likely universal, perhaps specified in the cognitive or linguistic systems of language learners and users. In many cases, these patterns are then taken to motivate linguistic theory. Here, we show that cross-linguistic analysis will very rarely be able to statistically justify absolute, inviolable patterns in language. We formalize two statistical methods—frequentist and Bayesian—and show that in both it (...)
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  • Bootstrapping the Mind: Analogical Processes and Symbol Systems.Dedre Gentner - 2010 - Cognitive Science 34 (5):752-775.
    Human cognition is striking in its brilliance and its adaptability. How do we get that way? How do we move from the nearly helpless state of infants to the cognitive proficiency that characterizes adults? In this paper I argue, first, that analogical ability is the key factor in our prodigious capacity, and, second, that possession of a symbol system is crucial to the full expression of analogical ability.
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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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  • 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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  • Children’s Understanding of the Relationship Between Addition and Subtraction.Elizabeth Spelke & Camilla Gilmore - 2008 - Cognition 107 (3):932-945.
    In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields 12. Here, we investigate whether preschool children’s approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation (...)
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  • The Evolution of Foresight: What is Mental Time Travel, and is It Unique to Humans?Thomas Suddendorf & Michael C. Corballis - 2007 - Behavioral and Brain Sciences 30 (3):299-313.
    In a dynamic world, mechanisms allowing prediction of future situations can provide a selective advantage. We suggest that memory systems differ in the degree of flexibility they offer for anticipatory behavior and put forward a corresponding taxonomy of prospection. The adaptive advantage of any memory system can only lie in what it contributes for future survival. The most flexible is episodic memory, which we suggest is part of a more general faculty of mental time travel that allows us not only (...)
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  • The Universal Density of Measurement.Danny Fox & Martin Hackl - 2006 - Linguistics and Philosophy 29 (5):537 - 586.
    The notion of measurement plays a central role in human cognition. We measure people’s height, the weight of physical objects, the length of stretches of time, or the size of various collections of individuals. Measurements of height, weight, and the like are commonly thought of as mappings between objects and dense scales, while measurements of collections of individuals, as implemented for instance in counting, are assumed to involve discrete scales. It is also commonly assumed that natural language makes use of (...)
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  • Why Theories of Concepts Should Not Ignore the Problem of Acquisition.Susan Carey - 2015 - Disputatio 7 (41):113-163.
    Why Theories of Concepts Should Not Ignore the Problem of Acquisition.
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  • The Impact of Cultural Background on Structural Figure Perception: Cultural Biases in the Reproduction of the Rey-Osterrieth Complex Figure.Muriel Bossuroy, Bruno Falissard, Marie-Rose Moro & Philippe Wallon - 2014 - Journal of Cognition and Culture 14 (3-4):273-285.
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  • Current Perspectives on Cognitive Diversity.Andrea Bender & Sieghard Beller - 2016 - Frontiers in Psychology 7.
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  • Significant Inter-Test Reliability Across Approximate Number System Assessments.Nicholas K. DeWind & Elizabeth M. Brannon - 2016 - Frontiers in Psychology 7.
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