Related categories

2 found
Order:
  1. Analog Mental Representation.Jacob Beck - forthcoming - WIREs Cognitive Science.
    Over the past 50 years, philosophers and psychologists have perennially argued for the existence of analog mental representations of one type or another. This study critically reviews a number of these arguments as they pertain to three different types of mental representation: perceptual representations, imagery representations, and numerosity representations. Along the way, careful consideration is given to the meaning of “analog” presupposed by these arguments for analog mental representation, and to open avenues for future research.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  2. The Number Sense Represents (Rational) Numbers.Sam Clarke & Jacob Beck - forthcoming - Behavioral and Brain Sciences:1-32.
    On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system (ANS), 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 number, such as (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  3. 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 (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  4. What’s new: innovation and enculturation of arithmetical practices.Jean-Charles Pelland - 2020 - Synthese 197 (9):3797-3822.
    One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, (...)
    Remove from this list   Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  5. 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.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6. Introduction.Andrew Aberdein & Matthew Inglis - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. 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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  7. Learning the Natural Numbers as a Child.Stefan Buijsman - 2019 - Noûs 53 (1):3-22.
    How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  8. What Frege Asked Alex the Parrot: Inferentialism, Number Concepts, and Animal Cognition.Erik Nelson - 2019 - 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 (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  9. Concepts and How They Get That Way.Karenleigh 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, (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  10. The Material Origin of Numbers: Insights From the Archaeology of the Ancient Near East.Karenleigh 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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  11. 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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  12. 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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  13. 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).
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  14. 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.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  15. Numbers Through Numerals. The Constitutive Role of External Representations.Dirk Schlimm - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge: Approaches from Psychology and Cognitive Science. New York, NY, USA: pp. 195–217.
    Our epistemic access to mathematical objects, like numbers, is mediated through our external representations of them, like numerals. Nevertheless, the role of formal notations and, in particular, of the internal structure of these notations has not received much attention in philosophy of mathematics and cognitive science. While systems of number words and of numerals are often treated alike, I argue that they have crucial structural differences, and that one has to understand how the external representation works in order to form (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  16. 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.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  17. The Psychology and Philosophy of Natural Numbers.Oliver R. Marshall - 2017 - Philosophia Mathematica (1):nkx002.
    ABSTRACT I argue against both neuropsychological and cognitive accounts of our grasp of numbers. I show that despite the points of divergence between these two accounts, they face analogous problems. Both presuppose too much about what they purport to explain to be informative, and also characterize our grasp of numbers in a way that is absurd in the light of what we already know from the point of view of mathematical practice. Then I offer a positive methodological proposal about the (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  18. 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 (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  19. 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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  20. 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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  21. Significant Inter-Test Reliability Across Approximate Number System Assessments.Nicholas K. DeWind & Elizabeth M. Brannon - 2016 - Frontiers in Psychology 7.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  22. 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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  23. 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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  24. Ratio Dependence in Small Number Discrimination is Affected by the Experimental Procedure.Christian Agrillo, Laura Piffer, Angelo Bisazza & Brian Butterworth - 2015 - Frontiers in Psychology 6.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  25. 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 (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  26. 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 (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  27. Two Steps to Space for Numbers.Martin H. Fischer & Samuel Shaki - 2015 - Frontiers in Psychology 6.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  28. Commentary: A Pointer About Grasping Numbers.Martin H. Fischer, Elena Sixtus & Silke M. Göbel - 2015 - Frontiers in Psychology 6.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  29. Spatial Coding of Ordinal Information in Short- and Long-Term Memory.Vã©Ronique Ginsburg & Wim Gevers - 2015 - Frontiers in Human Neuroscience 9.
  30. Spatial Biases During Mental Arithmetic: Evidence From Eye Movements on a Blank Screen.Matthias Hartmann, Fred W. Mast & Martin H. Fischer - 2015 - Frontiers in Psychology 6.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  31. Identifying and Counting Objects: The Role of Sortal Concepts.Nick Leonard & Lance J. Rips - 2015 - Cognition 145:89-103.
    Sortal terms, such as table or horse, are count nouns (akin to a basic-level terms). According to some theories, the meaning of sortals provides conditions for telling objects apart (individuating objects, e.g., telling one table from a second) and for identifying objects over time (e.g., determining that a particular horse at one time is the same horse at another). A number of psychologists have proposed that sortal concepts likewise provide psychologically real conditions for individuating and identifying things. However, this paper (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  32. Language Influences Number Processing – A Quadrilingual Study.Korbinian Moeller, Samuel Shaki, Silke M. Göbel & Hans-Christoph Nuerk - 2015 - Cognition 136:150-155.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  33. How Space-Number Associations May Be Created in Preliterate Children: Six Distinct Mechanisms.Hans-Christoph Nuerk, Katarzyna Patro, Ulrike Cress, Ulrike Schild, Claudia K. Friedrich & Silke M. Göbel - 2015 - Frontiers in Psychology 6.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  34. 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. (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  35. Newborn Chicks Need No Number Tricks. Commentary: Number-Space Mapping in the Newborn Chick Resembles Humans' Mental Number Line.Samuel Shaki & Martin H. Fischer - 2015 - Frontiers in Human Neuroscience 9.
  36. Evidence Against Continuous Variables Driving Numerical Discrimination in Infancy.Ariel Starr & Elizabeth M. Brannon - 2015 - Frontiers in Psychology 6.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  37. Rhesus Monkeys Map Number Onto Space.Caroline B. Drucker & Elizabeth M. Brannon - 2014 - Cognition 132 (1):57-67.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  38. A Perceptual Account of Symbolic Reasoning.David Landy, Colin Allen & Carlos Zednik - 2014 - Frontiers in Psychology 5.
    People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
  39. 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 (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  40. 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 (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  41. Improving Arithmetic Performance with Number Sense Training: An Investigation of Underlying Mechanism.Joonkoo Park & Elizabeth M. Brannon - 2014 - Cognition 133 (1):188-200.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  42. Singing Numbers… in Cognitive Space — A Dual‐Task Study of the Link Between Pitch, Space, and Numbers.Martin H. Fischer, Marianna Riello, Bruno L. Giordano & Elena Rusconi - 2013 - Topics in Cognitive Science 5 (2):354-366.
    We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the spatial (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  43. 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 (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  44. 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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  45. 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. (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   22 citations  
  46. Can Statistical Learning Bootstrap the Integers?Lance J. Rips, Jennifer Asmuth & Amber Bloomfield - 2013 - Cognition 128 (3):320-330.
  47. Arithmetic of Infinity.Yaroslav D. Sergeyev - 2013 - E-book.
    This book presents a new type of arithmetic that allows one to execute arithmetical operations with infinite numbers in the same manner as we are used to do with finite ones. The problem of infinity is considered in a coherent way different from (but not contradicting to) the famous theory founded by Georg Cantor. Surprisingly, the introduced arithmetical operations result in being very simple and are obtained as immediate extensions of the usual addition, multiplication, and division of finite numbers to (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  48. Representation of Numerical and Non-Numerical Order in Children.Ilaria Berteletti, Daniela Lucangeli & Marco Zorzi - 2012 - Cognition 124 (3):304-313.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  49. Finger Counting and Numerical Cognition.Martin H. Fischer, Liane Kaufmann & Frank Domahs - 2012 - Frontiers in Psychology 3.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  50. Grey Parrot Number Acquisition: The Inference of Cardinal Value From Ordinal Position on the Numeral List.Irene M. Pepperberg & Susan Carey - 2012 - Cognition 125 (2):219-232.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   13 citations