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  1. Does the number sense represent number?Sam Clarke & Jacob Beck - 2020 - In Blair Armstrong, Stephanie Denison, Michael Mack & Yang Xu (eds.), Proceedings of the 42nd Meeting of the Cognitive Science Society.
    On a now orthodox view, humans and many other animals are endowed with a “number sense”, or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques, with critics maintaining either that numerical content is absent altogether, or else that some primitive analog of number (‘numerosity’) is represented as opposed to number itself. We distinguish three arguments for these claims – the arguments from congruency, confounds, and imprecision – and show that none succeed. (...)
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  • Cognition, Meaning and Action: Lodz-Lund Studies in Cognitive Science.Piotr Łukowski, Aleksander Gemel & Bartosz Żukowski (eds.) - 2015 - Kraków, Polska: Lodz University Press & Jagiellonian University Press.
    The book is addressed to all readers interested in cognitive science, and especially in research combining a logical analysis with psychological, linguistic and neurobiological approaches. The publication is the result of a collaboration between the Department of Cognitive Science at University of Lodz and the Department of Cognitive Science at Lund University. It is intended to provide a comprehensive presentation of the key research issues undertaken in both Departments, including considerations on meaning, natural language and reasoning, linguistic as well as (...)
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  • Beyond the icon: Core cognition and the bounds of perception.Sam Clarke - 2020 - Mind and Language 37 (1):94-113.
    This paper refines a controversial proposal: that core systems belong to a perceptual kind, marked out by the format of its representational outputs. Following Susan Carey, this proposal has been understood in terms of core representations having an iconic format, like certain paradigmatically perceptual outputs. I argue that they don’t, but suggest that the proposal may be better formulated in terms of a broader analogue format type. Formulated in this way, the proposal accommodates the existence of genuine icons in perception, (...)
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  • Absence perception and the philosophy of zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
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  • Philosophy of Mathematics for the Masses : Extending the scope of the philosophy of mathematics.Stefan Buijsman - 2016 - Dissertation, Stockholm University
    One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...)
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  • Small-range numerical representations of linguistic sounds in 9- to 10-month-old infants.Silvia Benavides-Varela & Natalia Reoyo-Serrano - 2021 - Cognition 213 (C):104637.
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  • 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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  • Analogue Magnitudes, the Generality Constraint, and Nonconceptual Thought.Jacob Beck - 2014 - Mind 123 (492):1155-1165.
    I reply to comments by David Miguel Gray and Grant Gillett concerning my paper, ‘The Generality Constraint and the Structure of Thought’.
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  • Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
    Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to a (...)
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  • Non-symbolic arithmetic in adults and young children.Hilary Barth, Kristen La Mont, Jennifer Lipton, Stanislas Dehaene, Nancy Kanwisher & Elizabeth Spelke - 2006 - Cognition 98 (3):199-222.
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  • Judgments of discrete and continuous quantity: An illusory Stroop effect.Hilary C. Barth - 2008 - Cognition 109 (2):251-266.
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  • Evidence for a non-linguistic distinction between singular and plural sets in rhesus monkeys.David Barner, Justin Wood, Marc Hauser & Susan Carey - 2008 - Cognition 107 (2):603-622.
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  • Do mental magnitudes form part of the foundation for natural number concepts? Don't count them out yet.Hilary Barth - 2008 - Behavioral and Brain Sciences 31 (6):644-645.
    The current consensus among most researchers is that natural number is not built solely upon a foundation of mental magnitudes. On their way to the conclusion that magnitudes do not form any part of that foundation, Rips et al. pass rather quickly by theories suggesting that mental magnitudes might play some role. These theories deserve a closer look.
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  • Language and the development of spatial reasoning.Anna Shusterman & E. S. Spelke - 2005 - In Peter Carruthers, Stephen Laurence & Stephen P. Stich (eds.), The Innate Mind: Structure and Contents. New York, US: Oxford University Press on Demand. pp. 89--106.
    This chapter argues that human and animal minds indeed depend on a collection of domain-specific, task-specific, and encapsulated cognitive systems: on a set of cognitive ‘modules’ in Fodor's sense. It also argues that human and animal minds are endowed with domain-general, central systems that orchestrate the information delivered by core knowledge systems. The chapter begins by reviewing the literature on spatial reorientation in animals and in young children, arguing that spatial reorientation bears the hallmarks of core knowledge and of modularity. (...)
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  • How do people apprehend large numerosities?Catherine Sophian & Yun Chu - 2008 - Cognition 107 (2):460-478.
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  • Infants chunk object arrays into sets of individuals.Lisa Feigenson & Justin Halberda - 2004 - Cognition 91 (2):173-190.
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  • The cognitive and neural correlates of “tactile consciousness”: A multisensory perspective.Alberto Gallace & Charles Spence - 2008 - Consciousness and Cognition 17 (1):370-407.
    People’s awareness of tactile stimuli has been investigated in far less detail than their awareness of stimuli in other sensory modalities. In an attempt to fill this gap, we provide an overview of studies that are pertinent to the topic of tactile consciousness. We discuss the results of research that has investigated phenomena such as “change blindness”, phantom limb sensations, and numerosity judgments in tactile perception, together with the results obtained from the study of patients affected by deficits that can (...)
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  • Enumeration takes time: Accuracy improves even after stimuli disappear.Yanfei Yu & Kristy vanMarle - 2022 - Cognition 225 (C):105147.
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  • Numerosity discrimination in infants: Evidence for two systems of representations.Fei Xu - 2003 - Cognition 89 (1):B15-B25.
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  • Chronometric studies of numerical cognition in five-month-old infants.Justin N. Wood & Elizabeth S. Spelke - 2005 - Cognition 97 (1):23-39.
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  • The role of ANS acuity and numeracy for the calibration and the coherence of subjective probability judgments.Anders Winman, Peter Juslin, Marcus Lindskog, Håkan Nilsson & Neda Kerimi - 2014 - Frontiers in Psychology 5:97227.
    The purpose of the study was to investigate how numeracy and acuity of the approximate number system (ANS) relate to the calibration and coherence of probability judgments. Based on the literature on number cognition, a first hypothesis was that those with lower numeracy would maintain a less linear use of the probability scale, contributing to overconfidence and nonlinear calibration curves. A second hypothesis was that also poorer acuity of the ANS would be associated with overconfidence and non-linearity. A third hypothesis, (...)
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  • Symbolic and nonsymbolic number comparison in children with and without dyscalculia.Christophe Mussolin, Sandrine Mejias & Marie-Pascale Noël - 2010 - Cognition 115 (1):10-25.
    Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The performance of 10- and 11-year-old children with DD characterised by a weakness in arithmetic facts retrieval and age-matched control children was compared on various number comparison tasks. Participants were asked to compare a (...)
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  • Lexicalisation and the Origin of the Human Mind.Thomas J. Hughes & J. T. M. Miller - 2014 - Biosemiotics 7 (1):11-27.
    This paper will discuss the origin of the human mind, and the qualitative discontinuity between human and animal cognition. We locate the source of this discontinuity within the language faculty, and thus take the origin of the mind to depend on the origin of the language faculty. We will look at one such proposal put forward by Hauser et al. (Science 298:1569-1579, 2002), which takes the evolution of a Merge trait (recursion) to solely explain the differences between human and animal (...)
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  • An association between understanding cardinality and analog magnitude representations in preschoolers.Jennifer B. Wagner & Susan C. Johnson - 2011 - Cognition 119 (1):10-22.
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  • Infants’ auditory enumeration: Evidence for analog magnitudes in the small number range.Kristy vanMarle & Karen Wynn - 2009 - Cognition 111 (3):302-316.
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  • Numerical Architecture.Eric Mandelbaum - 2013 - Topics in Cognitive Science 5 (1):367-386.
    The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, I review literature (...)
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  • Beyond perceptual symbols: A call for representational pluralism.Guy Dove - 2009 - Cognition 110 (3):412-431.
    Recent evidence from cognitive neuroscience suggests that certain cognitive processes employ perceptual representations. Inspired by this evidence, a few researchers have proposed that cognition is inherently perceptual. They have developed an innovative theoretical approach that rests on the notion of perceptual simulation and marshaled several general arguments supporting the centrality of perceptual representations to concepts. In this article, I identify a number of weaknesses in these arguments and defend a multiple semantic code approach that posits both perceptual and non-perceptual representations.
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  • Core systems of number.Stanislas Dehaene, Elizabeth Spelke & Lisa Feigenson - 2004 - Trends in Cognitive Sciences 8 (7):307-314.
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  • Processing of Numerical and Proportional Quantifiers.Sailee Shikhare, Stefan Heim, Elise Klein, Stefan Huber & Klaus Willmes - 2015 - Cognitive Science 39 (7):1504-1536.
    Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical or proportional quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning (...)
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  • Quantity discrimination in 9 ungulate species: Individuals take item number and size into account to discriminate quantities.Alina Schaffer, Alvaro L. Caicoya, Anja Widdig, Ruben Holland & Federica Amici - 2025 - Cognition 254 (C):105979.
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  • The Management of Visual Attention in Graphic Displays.Ronald A. Rensink - 2011 - In Human Attention in Digital Environments. Cambridge University Press. pp. 63-92.
    This chapter presents an overview of several recent developments in vision science, and outlines some of their implications for the management of visual attention in graphic displays. These include ways of sending attention to the right item at the right time, techniques to improve attentional efficiency, and possibilities for offloading some of the processing typically done by attention onto nonattentional mechanisms. In addition it is argued that such techniques not only allow more effective use to be made of visual attention, (...)
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  • 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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  • From numerical concepts to concepts of number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
    Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...)
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  • Rational Number Representation by the Approximate Number System.Chuyan Qu, Sam Clarke, Francesca Luzzi & Elizabeth Brannon - 2024 - Cognition 250 (105839):1-13.
    The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...)
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  • Towards a Darwinian approach to mathematics.Helen De Cruz - 2006 - Foundations of Science 11 (1-2):157-196.
    In the past decades, recent paradigm shifts in ethology, psychology, and the social sciences have given rise to various new disciplines like cognitive ethology and evolutionary psychology. These disciplines use concepts and theories of evolutionary biology to understand and explain the design, function and origin of the brain. I shall argue that there are several good reasons why this approach could also apply to human mathematical abilities. I will review evidence from various disciplines (cognitive ethology, cognitive psychology, cognitive archaeology and (...)
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  • Number and natural language.Stephen Laurence & Eric Margolis - 2005 - In Peter Carruthers, Stephen Laurence & Stephen P. 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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  • Knowledge before belief.Jonathan Phillips, Wesley Buckwalter, Fiery Cushman, Ori Friedman, Alia Martin, John Turri, Laurie Santos & Joshua Knobe - 2021 - Behavioral and Brain Sciences 44:e140.
    Research on the capacity to understand others' minds has tended to focus on representations ofbeliefs,which are widely taken to be among the most central and basic theory of mind representations. Representations ofknowledge, by contrast, have received comparatively little attention and have often been understood as depending on prior representations of belief. After all, how could one represent someone as knowing something if one does not even represent them as believing it? Drawing on a wide range of methods across cognitive science, (...)
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  • 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.
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  • Don't throw the baby out with the math water: Why discounting the developmental foundations of early numeracy is premature and unnecessary.Kevin Muldoon, Charlie Lewis & Norman Freeman - 2008 - Behavioral and Brain Sciences 31 (6):663-664.
    We see no grounds for insisting that, because the concept natural number is abstract, its foundations must be innate. It is possible to specify domain general learning processes that feed into more abstract concepts of numerical infinity. By neglecting the messiness of children's slow acquisition of arithmetical concepts, Rips et al. present an idealized, unnecessarily insular, view of number development.
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  • Two dogmas of neo-empiricism.Edouard Machery - 2006 - Philosophy Compass 1 (4):398–412.
    This article critically examines the contemporary resurgence of empiricism (or “neo-empiricism”) in philosophy, psychology, neuropsychology, and artificial intelligence. This resurgence is an important and positive development. It is the first time that this centuries-old empiricist approach to cognition is precisely formulated in the context of cognitive science and neuroscience. Moreover, neo-empiricists have made several findings that challenge amodal theories of concepts and higher cognition. It is argued, however, that the theoretical foundations of and the empirical evidence for neo-empiricism are not (...)
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  • Concept empiricism: A methodological critique.Edouard Machery - 2006 - Cognition 104 (1):19-46.
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  • Preschool children master the logic of number word meanings.Jennifer S. Lipton & Elizabeth S. Spelke - 2006 - Cognition 98 (3):57-66.
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  • From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition.Tali Leibovich, Naama Katzin, Maayan Harel & Avishai Henik - 2017 - Behavioral and Brain Sciences 40.
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  • Why the verbal counting principles are constructed out of representations of small sets of individuals: A reply to Gallistel.Mathieu Le Corre & Susan Carey - 2008 - Cognition 107 (2):650-662.
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  • One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles.Mathieu Le Corre & Susan Carey - 2007 - Cognition 105 (2):395-438.
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  • (1 other version)Monkeys match and tally quantities across senses.Elizabeth M. Brannon Kerry E. Jordan, Evan L. MacLean - 2008 - Cognition 108 (3):617.
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  • (1 other version)Monkeys match and tally quantities across senses.Kerry E. Jordan, Evan L. MacLean & Elizabeth M. Brannon - 2008 - Cognition 108 (3):617-625.
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  • Calibrating the mental number line.Véronique Izard & Stanislas Dehaene - 2008 - Cognition 106 (3):1221-1247.
    Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...)
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  • Re-affirming experience, presence, and the world: setting the RECord straight in reply to Noë.Daniel D. Hutto & Erik Myin - 2021 - Phenomenology and the Cognitive Sciences 20 (5):971-989.
    This paper responds to Alva Noë’s general critique of Radical Enactivism. In particular, it responds to his claim that Radical Enactivism denies experience, presence and the world. We clarify Radical Enactivism’s actual arguments and positive commitments in this regard. Finally, we assess how Radical Enactvism stands up in comparison with Noë’s own version of Sensorimotor Knowledge Enactivism.
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  • Children's understanding of number is similar to adults' and rats': numerical estimation by 5–7-year-olds.Gavin Huntley-Fenner - 2001 - Cognition 78 (3):27-40.
    Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the (...)
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