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46 found
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  1. On Radical Enactivist Accounts of Arithmetical Cognition.Markus Pantsar - 2022 - Ergo: An Open Access Journal of Philosophy 9.
    Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...)
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  2. From Maximal Intersubjectivity to Objectivity: An Argument from the Development of Arithmetical Cognition.Markus Pantsar - 2022 - Topoi 42 (1):271-281.
    One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...)
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  3. Numbers, numerosities, and new directions.Jacob Beck & Sam Clarke - 2021 - Behavioral and Brain Sciences 44:1-20.
    In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.
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  4. The number sense represents (rational) numbers.Sam Clarke & Jacob Beck - 2021 - Behavioral and Brain Sciences 44:1-57.
    On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...)
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  5. Finger-counting and numerical structure.Karenleigh A. Overmann - 2021 - Frontiers in Psychology 2021 (12):723492.
    Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of (...)
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  6. (1 other version)Numerical Origins: The Critical Questions.Karenleigh A. Overmann - 2021 - Journal of Cognition and Culture 21 (5):449-468.
    Four perspectives on numerical origins are examined. The nativist model sees numbers as an aspect of numerosity, the biologically endowed ability to appreciate quantity that humans share with other species. The linguistic model sees numbers as a function of language. The embodied model sees numbers as conceptual metaphors informed by physical experience and expressed in language. Finally, the extended model sees numbers as conceptual outcomes of a cognitive system that includes material forms as constitutive components. If numerical origins are to (...)
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  7. (1 other version)Numerical origins: The critical questions.Karenleigh Anne Overmann - 2021 - Journal of Cognition and Culture 5 (21):449-468.
    Four perspectives on numerical origins are examined. The nativist model sees numbers as an aspect of numerosity, the biologically endowed ability to appreciate quantity that humans share with other species. The linguistic model sees numbers as a function of language. The embodied model sees numbers as conceptual metaphors informed by physical experience and expressed in language. Finally, the extended model sees numbers as conceptual outcomes of a cognitive system that includes material forms as constitutive components. If numerical origins are to (...)
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  8. A new look at old numbers, and what it reveals about numeration.Karenleigh Anne Overmann - 2021 - Journal of Near Eastern Studies 2 (80):291-321.
    In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. Similarities between (...)
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  9. Bootstrapping of integer concepts: the stronger deviant-interpretation challenge.Markus Pantsar - 2021 - Synthese 199 (3-4):5791-5814.
    Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...)
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  10. Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
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  11. The Small Number System.Eric Margolis - 2020 - Philosophy of Science 87 (1):113-134.
    I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific (...)
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  12. What Frege asked Alex the Parrot: Inferentialism, Number Concepts, and Animal Cognition.Erik Nelson - 2020 - Philosophical Psychology 33 (2):206-227.
    While there has been significant philosophical debate on whether nonlinguistic animals can possess conceptual capabilities, less time has been devoted to considering 'talking' animals, such as parrots. When they are discussed, their capabilities are often downplayed as mere mimicry. The most explicit philosophical example of this can be seen in Brandom's frequent comparisons of parrots and thermostats. Brandom argues that because parrots (like thermostats) cannot grasp the implicit inferential connections between concepts, their vocal articulations do not actually have any conceptual (...)
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  13. The curious idea that Māori once counted by elevens, and the insights it still holds for cross-cultural numerical research.Karenleigh Anne Overmann - 2020 - Journal of the Polynesian Society 1 (129):59-84.
    The idea the New Zealand Māori once counted by elevens has been viewed as a cultural misunderstanding originating with a mid-nineteenth-century dictionary of their language. Yet this “remarkable singularity” had an earlier, Continental origin, the details of which have been lost over a century of transmission in the literature. The affair is traced to a pair of scientific explorers, René-Primevère Lesson and Jules Poret de Blosseville, as reconstructed through their publications on the 1822–1825 circumnavigational voyage of the Coquille, a French (...)
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  14. Fermat’s Last Theorem Proved by Induction (and Accompanied by a Philosophical Comment).Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (8):1-8.
    A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite (...)
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  15. Aritmética e conhecimento simbólico: notas sobre o Tractatus Logico-Philosophicus e o ensino de filosofia da matemática.Gisele Dalva Secco - 2020 - Perspectiva Filosófica 47 (2):120-149.
    Departing from and closing with reflections on issues regarding teaching practices of philosophy of mathematics, I propose a comparison between the main features of the Leibnizian notion of symbolic knowledge and some passages from the Tractatus on arithmetic. I argue that this reading allows (i) to shed a new light on the specificities of the Tractarian definition of number, compared to those of Frege and Russell; (ii) to highlight the understanding of the nature of mathematical knowledge as symbolic or formal (...)
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  16. Introduction.Andrew Aberdein & Matthew Inglis - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 1-13.
    There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such (...)
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  17. Mathematical Cognition: Brain and Cognitive Research and Its Implications for Education.Qi Dong, Hong-Chuan Zhang & Xin-lin Zhou - 2019 - Journal of Human Cognition 3 (1):25-40.
    Mathematical cognition is one of the most important cognitive functions of human beings. The latest brain and cognitive research have shown that mathematical cognition is a system with multiple components and subsystems. It has phylogenetic root, also is related to ontogenetic development and learning, relying on a large-scale cerebral network including parietal, frontal and temporal regions. Especially, the parietal cortex plays an important role during mathematical cognitive processes. This indicates that language and visuospatial functions are both key to mathematical cognition. (...)
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  18. Concepts and how they get that way.Karenleigh A. Overmann - 2019 - Phenomenology and the Cognitive Sciences 18 (1):153-168.
    Drawing on the material culture of the Ancient Near East as interpreted through Material Engagement Theory, the journey of how material number becomes a conceptual number is traced to address questions of how a particular material form might generate a concept and how concepts might ultimately encompass multiple material forms so that they include but are irreducible to all of them together. Material forms incorporated into the cognitive system affect the content and structure of concepts through their agency and affordances, (...)
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  19. The material origin of numbers: Insights from the archaeology of the Ancient Near East.Karenleigh Anne Overmann - 2019 - Piscataway, NJ 08854, USA: Gorgias Press.
    What are numbers, and where do they come from? A novel answer to these timeless questions is proposed by cognitive archaeologist Karenleigh A. Overmann, based on her groundbreaking study of material devices used for counting in the Ancient Near East—fingers, tallies, tokens, and numerical notations—as interpreted through the latest neuropsychological insights into human numeracy and literacy. The result, a unique synthesis of interdisciplinary data, outlines how number concepts would have been realized in a pristine original condition to develop into one (...)
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  20. 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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  21. The cultural challenge in mathematical cognition.Andrea Bender, Dirk Schlimm, Stephen Crisomalis, Fiona M. Jordan, Karenleigh A. Overmann & Geoffrey B. Saxe - 2018 - Journal of Numerical Cognition 2 (4):448–463.
    In their recent paper on “Challenges in mathematical cognition”, Alcock and colleagues (Alcock et al. [2016]. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41) defined a research agenda through 26 specific research questions. An important dimension of mathematical cognition almost completely absent from their discussion is the cultural constitution of mathematical cognition. Spanning work from a broad range of disciplines – including anthropology, archaeology, cognitive science, history of science, linguistics, philosophy, and psychology – we (...)
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  22. Testimony and Children’s Acquisition of Number Concepts.Helen De Cruz - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge: Approaches From Psychology and Cognitive Science. New York: Routledge. 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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  23. Updating the “abstract–concrete” distinction in Ancient Near Eastern numbers.Karenleigh Overmann - 2018 - Cuneiform Digital Library Journal 1:1–22.
    The characterization of early token-based accounting using a concrete concept of number, later numerical notations an abstract one, has become well entrenched in the literature. After reviewing its history and assumptions, this article challenges the abstract–concrete distinction, presenting an alternative view of change in Ancient Near Eastern number concepts, wherein numbers are abstract from their inception and materially bound when most elaborated. The alternative draws on the chronological sequence of material counting technologies used in the Ancient Near East—fingers, tallies, tokens, (...)
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  24. Constructing a concept of number.Karenleigh Overmann - 2018 - Journal of Numerical Cognition 2 (4):464–493.
    Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like (...)
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  25. Early numerical cognition and mathematical processes.Markus Pantsar - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):285-304.
    In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.
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  26. Infants, animals, and the origins of number.Eric Margolis - 2017 - Behavioral and Brain Sciences 40.
    Where do human numerical abilities come from? This article is a commentary on Leibovich et al.’s “From 'sense of number' to 'sense of magnitude' —The role of continuous magnitudes in numerical cognition”. Leibovich et al. argue against nativist views of numerical development by noting limitations in newborns’ vision and limitations regarding newborns’ ability to individuate objects. I argue that these considerations do not undermine competing nativist views and that Leibovich et al.'s model itself presupposes that infant learners have numerical representations.
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  27. 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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  28. Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.
    In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...)
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  29. Numerical cognition and mathematical realism.Helen De Cruz - 2016 - Philosophers' Imprint 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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  30. The difficulty of prime factorization is a consequence of the positional numeral system.Yaroslav Sergeyev - 2016 - International Journal of Unconventional Computing 12 (5-6):453–463.
    The importance of the prime factorization problem is very well known (e.g., many security protocols are based on the impossibility of a fast factorization of integers on traditional computers). It is necessary from a number k to establish two primes a and b giving k = a · b. Usually, k is written in a positional numeral system. However, there exists a variety of numeral systems that can be used to represent numbers. Is it true that the prime factorization is (...)
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  31. The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.
    The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA and (...)
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  32. In search of $$\aleph _{0}$$ ℵ 0 : how infinity can be created.Markus Pantsar - 2015 - Synthese 192 (8):2489-2511.
    In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
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  33. The Olympic medals ranks, lexicographic ordering and numerical infinities.Yaroslav Sergeyev - 2015 - The Mathematical Intelligencer 37 (2):4-8.
    Several ways used to rank countries with respect to medals won during Olympic Games are discussed. In particular, it is shown that the unofficial rank used by the Olympic Committee is the only rank that does not allow one to use a numerical counter for ranking – this rank uses the lexicographic ordering to rank countries: one gold medal is more precious than any number of silver medals and one silver medal is more precious than any number of bronze medals. (...)
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  34. Book review: Cultural Development of Mathematical Ideas, written by Geoffrey B. Saxe. [REVIEW]Karenleigh A. Overmann - 2014 - Journal of Cognition and Culture 14 (3-4):331-333.
    A review of Geoffrey B. Saxe, Cultural Development of Mathematical Ideas. Saxe offers a comprehensive treatment of social and linguistic change in the number systems used for economic exchange in the Oksapmin community of Papua New Guinea. By taking the cognition-is-social approach, Saxe positions himself within emerging perspectives that view cognition as enacted, situated, and extended. The approach is somewhat risky in that sociality surely does not exhaust cognition. Brains, bodies, and materiality also contribute to cognition—causally at least, and possibly (...)
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  35. An empirically feasible approach to the epistemology of arithmetic.Markus Pantsar - 2014 - Synthese 191 (17):4201-4229.
    Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical (...)
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  36. 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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  37. 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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  38. Education Enhances the Acuity of the Nonverbal Approximate Number System.Manuela Piazza, Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene - 2013 - Psychological Science 24 (4):p.
    All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...)
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  39. The prehistory of number concept.Karenleigh A. Overmann, Thomas Wynn & Frederick L. Coolidge - 2011 - Behavioral and Brain Sciences 34 (3):142-144.
    Carey leaves unaddressed an important evolutionary puzzle: In the absence of a numeral list, how could a concept of natural number ever have arisen in the first place? Here we suggest that the initial development of natural number must have bootstrapped on a material culture scaffold of some sort, and illustrate how this might have occurred using strings of beads.
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  40. The Encoding of Spatial Information During Small-Set Enumeration.Harry Haladjian, Manish Singh, Zenon Pylyshyn & Randy Gallistel - 2010 - In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Cognitive Science Society.
    Using a novel enumeration task, we examined the encoding of spatial information during subitizing. Observers were shown masked presentations of randomly-placed discs on a screen and were required to mark the perceived locations of these discs on a subsequent blank screen. This provided a measure of recall for object locations and an indirect measure of display numerosity. Observers were tested on three stimulus durations and eight numerosities. Enumeration performance was high for displays containing up to six discs—a higher subitizing range (...)
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  41. 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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  42. 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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  43. Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures.Pierre Pica, Stanislas Dehaene, Elizabeth Spelke & Véronique Izard - 2008 - Science 320 (5880):1217-1220.
    The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...)
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  44. A new applied approach for executing computations with infinite and infinitesimal quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.
    A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The (...)
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  45. Number and natural language.Stephen Laurence & Eric Margolis - 2005 - In Peter Carruthers, Stephen Laurence & Stephen Stich (eds.), The Innate Mind: Structure and Contents. New York, US: Oxford University Press on Demand. pp. 1--216.
    One of the most important abilities we have as humans is the ability to think about number. In this chapter, we examine the question of whether there is an essential connection between language and number. We provide a careful examination of two prominent theories according to which concepts of the positive integers are dependent on language. The first of these claims that language creates the positive integers on the basis of an innate capacity to represent real numbers. The second claims (...)
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  46. Exact and Approximate Arithmetic in an Amazonian Indigene Group.Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene - 2004 - Science 306 (5695):499-503.
    Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...)
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