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  1. Mathematical intuition and the cognitive roots of mathematical concepts.Giuseppe Longo & Arnaud Viarouge - 2010 - Topoi 29 (1):15-27.
    The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the foundational analysis (...)
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  • Number Nativism.Sam Clarke - forthcoming - Philosophy and Phenomenological Research.
    Number Nativism is the view that humans innately represent precise natural numbers. Despite a long and venerable history, it is often considered hopelessly out of touch with the empirical record. I argue that this is a mistake. After clarifying Number Nativism and distancing it from related conjectures, I distinguish three arguments which have been seen to refute the view. I argue that, while popular, two of these arguments miss the mark, and fail to place pressure on Number Nativism. Meanwhile, a (...)
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  • The dark and bright side of the numbers: how emotions influence mental number line accuracy and bias.Saied Sabaghypour, Farhad Farkhondeh Tale Navi, Elena Kulkova, Parnian Abaduz, Negin Zirak & Mohammad Ali Nazari - 2024 - Cognition and Emotion 38 (5):661-674.
    The traditional view of cognition as detached from emotions is recently being questioned. This study aimed to investigate the influence of emotional valence on the accuracy and bias in the representation of numbers on the mental number line (MNL). The study included 164 participants who were randomly assigned into two groups with induced positive and negative emotional valence using matched arousal film clips. Participants performed a computerised number-to-position (CNP) task to estimate the position of numbers on a horizontal line. The (...)
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  • Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition.César Frederico Dos Santos - 2022 - Philosophical Psychology 35 (8):1152-1180.
    In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...)
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  • The mental representation of universal quantifiers.Tyler Knowlton, Paul Pietroski, Justin Halberda & Jeffrey Lidz - 2022 - Linguistics and Philosophy 45 (4):911-941.
    A sentence like every circle is blue might be understood in terms of individuals and their properties or in terms of a relation between groups. Relatedly, theorists can specify the contents of universally quantified sentences in first-order or second-order terms. We offer new evidence that this logical first-order vs. second-order distinction corresponds to a psychologically robust individual vs. group distinction that has behavioral repercussions. Participants were shown displays of dots and asked to evaluate sentences with each, every, or all combined (...)
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  • Epistemic Limitations and Precise Estimates in Analog Magnitude Representation.Justin Halberda - 2016 - In A. Baron & D. Barner (eds.), Core Knowledge and Conceptual Change. Oxford University Press. pp. 167-186.
    This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS having noisy (...)
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  • Dealing with Big Numbers: Representation and Understanding of Magnitudes Outside of Human Experience.Resnick Ilyse, S. Newcombe Nora & F. Shipley Thomas - 2017 - Cognitive Science 41 (4):1020-1041.
    Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception. This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events (...)
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  • Perception and Cognition Are Largely Independent, but Still Affect Each Other in Systematic Ways: Arguments from Evolution and the Consciousness-Attention Dissociation.Carlos Montemayor & Harry Haroutioun Haladjian - 2017 - Frontiers in Psychology 8:1-15.
    The main thesis of this paper is that two prevailing theories about cognitive penetration are too extreme, namely, the view that cognitive penetration is pervasive and the view that there is a sharp and fundamental distinction between cognition and perception, which precludes any type of cognitive penetration. These opposite views have clear merits and empirical support. To eliminate this puzzling situation, we present an alternative theoretical approach that incorporates the merits of these views into a broader and more nuanced explanatory (...)
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  • Comparing apples and pears in studies on magnitude estimations.Mirjam Ebersbach, Koen Luwel & Lieven Verschaffel - 2013 - Frontiers in Psychology 4.
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  • Children’s mappings between number words and the approximate number system.Darko Odic, Mathieu Le Corre & Justin Halberda - 2015 - Cognition 138 (C):102-121.
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  • 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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  • 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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  • The nature of anchor-biased estimates and its application to the wisdom of crowds.Hidehito Honda, Rina Kagawa & Masaru Shirasuna - 2024 - Cognition 246 (C):105758.
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  • Sequential Presentation Protects Working Memory From Catastrophic Interference.Ansgar D. Endress & Szilárd Szabó - 2020 - Cognitive Science 44 (5):e12828.
    Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (...)
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  • The mechanism of non-numerical anchoring heuristic based on magnitude priming: is it just the basic anchoring effect in disguise?Jakub Traczyk & Pawel Tomczak - 2017 - Polish Psychological Bulletin 48 (3):401-410.
    The anchoring heuristic refers to phenomena when an arbitrary number affects subsequent numerical estimations. Oppenheimer, LeBoeuf and Brewer showed that it is not necessary for the anchor to be a numerical value, yet current models describing the anchoring heuristic do not fully account for the mechanism of non-numerical anchoring. However, this effect shows similarity to the basic anchoring effect - obtained without the comparative question and based on the availability of the given number in working memory. In this study, we (...)
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  • A hand full of numbers: a role for offloading in arithmetics learning?Annelise Júlio Annelise - 2011 - Frontiers in Psychology 2.
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  • Estimation abilities of large numerosities in Kindergartners.Sandrine Mejias & Christine Schiltz - 2013 - Frontiers in Psychology 4.
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  • Concrete magnitudes: From numbers to time.Christine Falter, Valdas Noreika, Julian Kiverstein & Bruno Mölder - 2009 - Behavioral and Brain Sciences 32 (3-4):335-336.
    Cohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).
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  • The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters.Iro Xenidou-Dervou, Camilla Gilmore, Menno van der Schoot & Ernest C. D. M. van Lieshout - 2015 - Frontiers in Psychology 6.
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  • Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study.Maja Rodic, Tatiana Tikhomirova, Tatiana Kolienko, Sergey Malykh, Olga Bogdanova, Dina Y. Zueva, Elena I. Gynku, Sirui Wan, Xinlin Zhou & Yulia Kovas - 2015 - Frontiers in Psychology 6.
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  • Does learning to count involve a semantic induction?Kathryn Davidson, Kortney Eng & David Barner - 2012 - Cognition 123 (1):162-173.
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  • Radicalizing numerical cognition.Karim Zahidi - 2020 - Synthese 198 (Suppl 1):529-545.
    In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities, there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I (...)
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  • Do analog number representations underlie the meanings of young children’s verbal numerals?Susan Carey, Anna Shusterman, Paul Haward & Rebecca Distefano - 2017 - Cognition 168 (C):243-255.
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  • Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children.Daniel C. Hyde, Saeeda Khanum & Elizabeth S. Spelke - 2014 - Cognition 131 (1):92-107.
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  • Working Memory in Nonsymbolic Approximate Arithmetic Processing: A Dual‐Task Study With Preschoolers.Iro Xenidou‐Dervou, Ernest C. D. M. Lieshout & Menno Schoot - 2014 - Cognitive Science 38 (1):101-127.
    Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an important predictor of children's math development and achievement. The aim of our study was to uncover the specific role of WM in nonsymbolic approximate math. For this purpose, we conducted a (...)
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  • The knowledge of the preceding number reveals a mature understanding of the number sequence.Francesco Sella & Daniela Lucangeli - 2020 - Cognition 194 (C):104104.
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  • Nonsymbolic approximate arithmetic in children: Abstract addition prior to instruction.(Manuscript under review.Hilary Barth, Lacey Beckmann & Elizabeth S. Spelke - 2008 - Developmental Psychology 44 (5).
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  • Probing the mental representation of quantifiers.Sandro Pezzelle, Raffaella Bernardi & Manuela Piazza - 2018 - Cognition 181 (C):117-126.
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  • Children’s Non-symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability.Yanjun Li, Meng Zhang, Yinghe Chen, Zhijun Deng, Xiaoshuang Zhu & Shijia Yan - 2018 - Frontiers in Psychology 9.
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  • Free versus anchored numerical estimation: A unified approach.John E. Opfer, Clarissa A. Thompson & Dan Kim - 2016 - Cognition 149 (C):11-17.
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  • Numerical representation in the parietal lobes: Abstract or not abstract?Roi Kadosh & Vincent Walsh - 2009 - Behavioral and Brain Sciences 32 (3-4):313-328.
    The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological (...)
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  • Categories of Large Numbers in Line Estimation.David Landy, Arthur Charlesworth & Erin Ottmar - 2017 - Cognitive Science 41 (2):326-353.
    How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time (...)
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  • An undeniable interplay: Both numerosity and visual features affect estimation of non-symbolic stimuli.I. Abalo-Rodríguez, D. De Marco & S. Cutini - 2022 - Cognition 222 (C):104944.
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  • The Developmental Trajectory of the Operational Momentum Effect.Pedro Pinheiro-Chagas, Daniele Didino, Vitor G. Haase, Guilherme Wood & André Knops - 2018 - Frontiers in Psychology 9.
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  • Knowing your heart and your mind: The relationships between metamemory and interoception.Elizabeth F. Chua & Eliza Bliss-Moreau - 2016 - Consciousness and Cognition 45:146-158.
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  • Non-abstract numerical representations in the IPS: further support, challenges, and clarifications.Roi Cohen Kadosh & Vincent Walsh - 2009 - Behavioral and Brain Sciences 32 (3-4):356-373.
    The commentators have raised many pertinent points that allow us to refine and clarify our view. We classify our response comments into seven sections: automaticity; developmental and educational questions; priming; multiple representations or multiple access(?); terminology; methodological advances; and simulated cognition and numerical cognition. We conclude that the default numerical representations are not abstract.
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  • Increasing entropy reduces perceived numerosity throughout the lifespan.Chuyan Qu, Nicholas K. DeWind & Elizabeth M. Brannon - 2022 - Cognition 225 (C):105096.
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  • Why try saving the ANS? An alternative proposal.Titia Gebuis, Roi Cohen Kadosh & Wim Gevers - 2017 - Behavioral and Brain Sciences 40.
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  • Brain neural activity patterns yielding numbers are operators, not representations.Walter J. Freeman & Robert Kozma - 2009 - Behavioral and Brain Sciences 32 (3-4):336.
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  • The importance of being relevant: modulation of magnitude representations.Tali Leibovich, Liana Diesendruck, Orly Rubinsten & Avishai Henik - 2013 - Frontiers in Psychology 4.
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  • Task Constraints Affect Mapping From Approximate Number System Estimates to Symbolic Numbers.Dana L. Chesney & Percival G. Matthews - 2018 - Frontiers in Psychology 9.
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