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Stanislas Dehaene (1999). The Number Sense: How the Mind Creates Mathematics.

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  1.  1
    Enculturation and Narrative Practices.Regina E. Fabry - forthcoming - Phenomenology and the Cognitive Sciences:1-27.
    Recent work on enculturation suggests that our cognitive capacities are significantly transformed in the course of the scaffolded acquisition of cognitive practices such as reading and writing. Phylogenetically, enculturation is the result of the co-evolution of human organisms and their socio-culturally structured cognitive niche. It is rendered possible by evolved cerebral and extra-cerebral bodily learning mechanisms that make human organisms apt to acquire culturally inherited cognitive practices. In addition, cultural learning allows for the intergenerational transmission of relevant knowledge and skills. (...)
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  2.  3
    Do Non‐Verbal Number Systems Shape Grammar? Numerical Cognition and Number Morphology Compared.Francesca Franzon, Chiara Zanini & Rosa Rugani - forthcoming - Mind and Language.
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  3.  8
    From Sensations to Concepts: A Proposal for Two Learning Processes.Peter Gärdenfors - forthcoming - Review of Philosophy and Psychology:1-24.
    This article presents two learning processes in order to explain how children at an early age can transform a complex sensory input to concepts and categories. The first process constructs the perceptual structures that emerge in children’s cognitive development by detecting invariants in the sensory input. The invariant structures involve a reduction in dimensionality of the sensory information. It is argued that this process generates the primary domains of space, objects and actions and that these domains can be represented as (...)
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  4.  1
    RECkoning with Representational Apriorism in Evolutionary Cognitive Archaeology.Duilio Garofoli - forthcoming - Phenomenology and the Cognitive Sciences:1-23.
    In evolutionary cognitive archaeology, the school of thought associated with the traditional framework has been deeply influenced by cognitivist intuitions, which have led to the formulation of mentalistic and disembodied cognitive explanations to address the emergence of artifacts within the archaeological record of ancient hominins. Recently, some approaches in this domain have further enforced this view, by arguing that artifacts are passive means to broadcast/perpetuate meanings that are thoroughly internal to the mind. These meanings are conveyed either in the form (...)
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  5.  18
    Learning to Represent Exact Numbers.Barbara W. Sarnecka - forthcoming - Synthese:1-18.
    This article focuses on how young children acquire concepts for exact, cardinal numbers. I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey. In this framework, the (...)
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  6. The Rational Role of Experience.David Bourget - 2018 - Inquiry : An Interdisciplinary Journal of Philosophy 61 (5-6):467-493.
    If there is content that we reason on, cognitive content, it is in the head and accessible to reasoning mechanisms. This paper discusses the phenomenal theory of cognitive content, according to which cognitive contents are the contents of phenomenal consciousness. I begin by distinguishing cognitive content from the closely associated notion of narrow content. I then argue, drawing on prior work, that the phenomenal theory can plausibly account for the cognitive contents of many relatively simple mental states. My main focus (...)
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  7. The Role of Consciousness in Grasping and Understanding.David Bourget - 2017 - Philosophy and Phenomenological Research 95 (2):285-318.
    One sometimes believes a proposition without grasping it. For example, a complete achromat might believe that ripe tomatoes are red without grasping this proposition. My aim in this paper is to shed light on the difference between merely believing a proposition and grasping it. I focus on two possible theories of grasping: the inferential theory, which explains grasping in terms of inferential role, and the phenomenal theory, which explains grasping in terms of phenomenal consciousness. I argue that the phenomenal theory (...)
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  8. The Faculty of Language Integrates the Two Core Systems of Number.Ken Hiraiwa - 2017 - Frontiers in Psychology 8.
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  9.  2
    Commentary: From ‘Sense of Number’ to ‘Sense of Magnitude’ – The Role of Continuous Magnitudes in Numerical Cognition.Luca Rinaldi & Luisa Girelli - 2017 - Frontiers in Psychology 8.
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  10. Darwinism in Metaethics: What If the Universal Acid Cannot Be Contained?Eleonora Severini & Fabio Sterpetti - 2017 - History and Philosophy of the Life Sciences 39 (3):1-25.
    The aim of this article is to explore the impact of Darwinism in metaethics and dispel some of the confusion surrounding it. While the prospects for a Darwinian metaethics appear to be improving, some underlying epistemological issues remain unclear. We will focus on the so-called Evolutionary Debunking Arguments (EDAs) which, when applied in metaethics, are defined as arguments that appeal to the evolutionary origins of moral beliefs so as to undermine their epistemic justification. The point is that an epistemic disanalogy (...)
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  11.  3
    Neurophilosophy of Number.Hourya Benis Sinaceur - 2017 - International Studies in the Philosophy of Science 31 (1):1-25.
    Neurosciences and cognitive sciences provide us with myriad empirical findings that shed light on hypothesised primitive numerical processes in the brain and in the mind. Yet, the hypotheses on which the experiments are based, and hence the results, depend strongly on sophisticated abstract models used to describe and explain neural data or cognitive representations that supposedly are the empirical roots of primary arithmetical activity. I will question the foundational role of such models. I will even cast doubt upon the search (...)
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  12.  2
    The Infinite Turn and Speculative Explanations in Cosmology.Reza Tavakol & Fabio Gironi - 2017 - Foundations of Science 22 (4):785-798.
    Infinity, in various guises, has been invoked recently in order to ‘explain’ a number of important questions regarding observable phenomena in science, and in particular in cosmology. Such explanations are by their nature speculative. Here we introduce the notions of relative infinity, closure, and economy of explanation and ask: to what extent explanations involving relative or real constructed infinities can be treated as reasonable?
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  13.  46
    Differential Calculus Based on the Double Contradiction.Kazuhiko Kotani - 2016 - Open Journal of Philosophy 6 (4):420-427.
    The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...)
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  14. Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children.Larissa Rauscher, Juliane Kohn, Tanja Käser, Verena Mayer, Karin Kucian, Ursina McCaskey, Günter Esser & Michael von Aster - 2016 - Frontiers in Psychology 7.
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  15.  1
    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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  16.  3
    Are Past and Future Symmetric in Mental Time Line?Xianfeng Ding, Ning Feng, Xiaorong Cheng, Huashan Liu & Zhao Fan - 2015 - Frontiers in Psychology 6.
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  17.  31
    On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry : An Interdisciplinary Journal of Philosophy 58 (1):57-79.
    This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics.
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  18. Multiple Object Individuation and Subitizing in Enumeration: A View From Electrophysiology.Veronica Mazza & Alfonso Caramazza - 2015 - Frontiers in Human Neuroscience 9.
  19.  4
    Parsing Heuristic and Forward Search in First‐Graders' Game‐Play Behavior.Luciano Paz, Andrea P. Goldin, Carlos Diuk & Mariano Sigman - 2015 - Cognitive Science 39 (5):944-971.
    Seventy-three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: a non-monotonic dependence of performance as a function of the distance between the beginning and the end-states of the problem, very high levels of performance when the first move was correct, and states in which accuracy of the first move was significantly below chance. These features are consistent with a non-Markov planning agent, with an inherently (...)
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  20.  6
    Link Between Cognitive Neuroscience and Education: The Case of Clinical Assessment of Developmental Dyscalculia.Orly Rubinsten - 2015 - Frontiers in Human Neuroscience 9.
  21.  10
    Processing of Numerical and Proportional Quantifiers.Sailee Shikhare, Stefan Heim, Elise Klein, Stefan Huber & Klaus Willmes - 2015 - Cognitive Science 39 (7):1504-1536.
    Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical or proportional quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning (...)
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  22. Why We Can't Say What Animals Think.Jacob Beck - 2013 - Philosophical Psychology 26 (4):520–546.
    Realists about animal cognition confront a puzzle. If animals have real, contentful cognitive states, why can’t anyone say precisely what the contents of those states are? I consider several possible resolutions to this puzzle that are open to realists, and argue that the best of these is likely to appeal to differences in the format of animal cognition and human language.
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  23.  65
    Conceptual Metaphors and Mathematical Practice: On Cognitive Studies of Historical Developments in Mathematics.Dirk Schlimm - 2013 - Topics in Cognitive Science 5 (2):283-298.
    This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of (...)
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  24.  54
    Fractions: The New Frontier for Theories of Numerical Development.Robert S. Siegler, Lisa K. Fazio, Drew H. Bailey & Xinlin Zhou - 2013 - Trends in Cognitive Sciences 17 (1):13-19.
  25.  42
    Iterating Semantic Automata.Shane Steinert-Threlkeld & I. I. I. Thomas F. Icard - 2013 - Linguistics and Philosophy 36 (2):151-173.
    The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic automata in (...)
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  26.  14
    Linguistic and Visual Cognition: Verifying Proportional and Superlative Most in Bulgarian and Polish. [REVIEW]Barbara Tomaszewicz - 2013 - Journal of Logic, Language and Information 22 (3):335-356.
    The verification of a sentence against a visual display in experimental conditions reveals a procedure that is driven solely by the properties of the linguistic input and not by the properties of the context (the set-up of the visual display) or extra-linguistic cognition (operations executed to obtain the truth value). This procedure, according to the Interface Transparency Thesis (ITT) (Lidz et al. in Nat Lang Semant 19(3):227–256, 2011), represents the meaning of an expression at the interface with the ‘conceptual-intentional’ system (...)
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  27. Mario Bunge’s Philosophy of Mathematics: An Appraisal.Jean-Pierre Marquis - 2012 - Science and Education 21 (10):1567-1594.
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  28.  40
    Cognitive Practices and Cognitive Character.Richard Menary - 2012 - Philosophical Explorations 15 (2):147 - 164.
    The argument of this paper is that we should think of the extension of cognitive abilities and cognitive character in integrationist terms. Cognitive abilities are extended by acquired practices of creating and manipulating information that is stored in a publicly accessible environment. I call these cognitive practices (2007). In contrast to Pritchard (2010) I argue that such processes are integrated into our cognitive characters rather than artefacts; such as notebooks. There are two routes to cognitive extension that I contrast in (...)
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  29.  34
    The Linguistic Subversion of Mental Representation.Whit Schonbein - 2012 - Minds and Machines 22 (3):235-262.
    Embedded and embodied approaches to cognition urge that (1) complicated internal representations may be avoided by letting features of the environment drive behavior, and (2) environmental structures can play an enabling role in cognition, allowing prior cognitive processes to solve novel tasks. Such approaches are thus in a natural position to oppose the ‘thesis of linguistic structuring’: The claim that the ability to use language results in a wholesale recapitulation of linguistic structure in onboard mental representation. Prominent examples of researchers (...)
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  30. Mentalism and Epistemic Transparency.Declan Smithies - 2012 - Australasian Journal of Philosophy 90 (4):723-741.
    Questions about the transparency of evidence are central to debates between factive and non-factive versions of mentalism about evidence. If all evidence is transparent, then factive mentalism is false, since no factive mental states are transparent. However, Timothy Williamson has argued that transparency is a myth and that no conditions are transparent except trivial ones. This paper responds by drawing a distinction between doxastic and epistemic notions of transparency. Williamson's argument may show that no conditions are doxastically transparent, but it (...)
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  31.  13
    Methodological Reflections on Typologies for Numerical Notations.Theodore Reed Widom & Dirk Schlimm - 2012 - Science in Context 25 (2):155-195.
    Past and present societies world-wide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. The present paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework to (...)
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  32.  34
    Idealization and External Symbolic Storage: The Epistemic and Technical Dimensions of Theoretic Cognition.Peter Woelert - 2012 - Phenomenology and the Cognitive Sciences 11 (3):335-366.
    This paper explores some of the constructive dimensions and specifics of human theoretic cognition, combining perspectives from (Husserlian) genetic phenomenology and distributed cognition approaches. I further consult recent psychological research concerning spatial and numerical cognition. The focus is on the nexus between the theoretic development of abstract, idealized geometrical and mathematical notions of space and the development and effective use of environmental cognitive support systems. In my discussion, I show that the evolution of the theoretic cognition of space apparently follows (...)
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  33. A New Look at the Problem of Rule-Following: A Generic Perspective.Kai-Yuan Cheng - 2011 - Philosophical Studies 155 (1):1 - 21.
    The purpose of this paper is to look at the problem of rule-following—notably discussed by Kripke (Wittgenstein on rules and private language, 1982) and Wittgenstein (Philosophical investigations, 1953)—from the perspective of the study of generics. Generics are sentences that express generalizations that tolerate exceptions. I first suggest that meaning ascriptions be viewed as habitual sentences, which are a sub-set of generics. I then seek a proper semantic analysis for habitually construed meaning sentences. The quantificational approach is rejected, due to its (...)
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  34.  25
    Generalized Quantifiers and Number Sense.Robin Clark - 2011 - Philosophy Compass 6 (9):611-621.
    Generalized quantifiers are functions from pairs of properties to truth-values; these functions can be used to interpret natural language quantifiers. The space of such functions is vast and a great deal of research has sought to find natural constraints on the functions that interpret determiners and create quantifiers. These constraints have demonstrated that quantifiers rest on number and number sense. In the first part of the paper, we turn to developing this argument. In the remainder, we report on work in (...)
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  35. Historical Objections Against the Number Line.Albrecht Heeffer - 2011 - Science & Education 20 (9):863-880.
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  36.  49
    Can Cognitive Neuroscience Ground a Science of Learning?Anthony E. Kelly - 2011 - Educational Philosophy and Theory 43 (1):17-23.
    In this article, I review recent findings in cognitive neuroscience in learning, particularly in the learning of mathematics and of reading. I argue that while cognitive neuroscience is in its infancy as a field, theories of learning will need to incorporate and account for this growing body of empirical data.
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  37.  41
    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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  38.  86
    Visualizing Thought.Barbara Tversky - 2011 - Topics in Cognitive Science 3 (3):499-535.
    Depictive expressions of thought predate written language by thousands of years. They have evolved in communities through a kind of informal user testing that has refined them. Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated. Like language, visual communications abstract and schematize; unlike language, they use properties of the page (e.g., proximity and place: center, horizontal/up–down, vertical/left–right) and the marks on it (e.g., (...)
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  39.  62
    On the Advantage (If Any) and Disadvantage of the Conceptual/Nonconceptual Distinction for Cognitive Science.Alessandro Dell’Anna & Marcello Frixione - 2010 - Minds and Machines 20 (1):29-45.
    In this article we question the utility of the distinction between conceptual and nonconceptual content in cognitive science, and in particular, in the empirical study of visual perception. First, we individuate some difficulties in characterizing the notion of “concept” itself both in the philosophy of mind and cognitive science. Then we stress the heterogeneous nature of the notion of nonconceptual content and outline the complex and ambiguous relations that exist between the conceptual/nonconceptual duality and other pairs of notions, such as (...)
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  40. The Linguistic Analogy: Motivations, Results, and Speculations.Susan Dwyer, Bryce Huebner & Marc D. Hauser - 2010 - Topics in Cognitive Science 2 (3):486-510.
    Inspired by the success of generative linguistics and transformational grammar, proponents of the linguistic analogy (LA) in moral psychology hypothesize that careful attention to folk-moral judgments is likely to reveal a small set of implicit rules and structures responsible for the ubiquitous and apparently unbounded capacity for making moral judgments. As a theoretical hypothesis, LA thus requires a rich description of the computational structures that underlie mature moral judgments, an account of the acquisition and development of these structures, and an (...)
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  41.  33
    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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  42.  18
    Beyond WEIRD: Towards a Broad-Based Behavioral Science.Joseph Henrich, Steven J. Heine & Ara Norenzayan - 2010 - Behavioral and Brain Sciences 33 (2-3):111-135.
    In our response to the 28 (largely positive) commentaries from an esteemed collection of researchers, we (1) consolidate additional evidence, extensions, and amplifications offered by our commentators; (2) emphasize the value of integrating experimental and ethnographic methods, and show how researchers using behavioral games have done precisely this; (3) present our concerns with arguments from several commentators that separate variable from or ; (4) address concerns that the patterns we highlight marking WEIRD people as psychological outliers arise from aspects of (...)
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  43.  56
    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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  44.  22
    Through Neural Stimulation to Behavior Manipulation: A Novel Method for Analyzing Dynamical Cognitive Models.Thomas Hope, Ivilin Stoianov & Marco Zorzi - 2010 - Cognitive Science 34 (3):406-433.
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  45.  54
    Indistinguishable From Magic: Computation is Cognitive Technology. [REVIEW]John Kadvany - 2010 - Minds and Machines 20 (1):119-143.
    This paper explains how mathematical computation can be constructed from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules, or arithmetical axioms, using only orally-based natural language capabilities, and motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Pāṇini’s invention, around the fifth century BCE, of a formal (...)
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  46.  11
    A Model of Knower‐Level Behavior in Number Concept Development.Michael D. Lee & Barbara W. Sarnecka - 2010 - Cognitive Science 34 (1):51-67.
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  47.  14
    Is Logic Necessary?Gregory McColm - 2010 - Logica Universalis 4 (2):241-254.
    “Logic” entails both a toolkit for dealing with situations requiring precision, and a prescription for a type of public reasoning. A sufficiently extended society facing a stream of genuinely novel opportunities and challenges will benefit from an ability to generate and encourage the use of such reasoning systems to deal with these opportunities and challenges. The study of “logic” is the result of using the toolkit on itself, which would appear to be a necessary and not unnatural step for a (...)
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  48.  29
    Numbers and Arithmetic: Neither Hardwired Nor Out There.Rafael Núñez - 2009 - Biological Theory 4 (1):68-83.
    What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...)
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  49.  87
    The Meaning of 'Most': Semantics, Numerosity and Psychology.Paul Pietroski, Jeffrey Lidz, Tim Hunter & Justin Halberda - 2009 - Mind and Language 24 (5):554-585.
    The meaning of 'most' can be described in many ways. We offer a framework for distinguishing semantic descriptions, interpreted as psychological hypotheses that go beyond claims about sentential truth conditions, and an experiment that tells against an attractive idea: 'most' is understood in terms of one-to-one correspondence. Adults evaluated 'Most of the dots are yellow', as true or false, on many trials in which yellow dots and blue dots were displayed for 200 ms. Displays manipulated the ease of using a (...)
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  50. Principles of Learning, Implications for Teaching: A Cognitive Neuroscience Perspective.Usha Goswami - 2008 - Journal of Philosophy of Education 42 (3-4):381-399.
    Cognitive neuroscience aims to improve our understanding of aspects of human learning and performance by combining data acquired with the new brain imaging technologies with data acquired in cognitive psychology paradigms. Both neuroscience and psychology use the philosophical assumptions underpinning the natural sciences, namely the scientific method, whereby hypotheses are proposed and tested using quantitative approaches. The relevance of 'brain science' for the classroom has proved controversial with some educators, perhaps because of distrust of the applicability of so-called 'medical models' (...)
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