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  1. Why do numbers exist? A psychologist constructivist account.Markus Pantsar - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...)
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  • The link between transitive reasoning and mathematics achievement in preadolescence: the role of relational processing and deductive reasoning.Terry Tin-Yau Wong & Kinga Morsanyi - 2023 - Thinking and Reasoning 29 (4):531-558.
    The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...
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  • Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
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  • Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense.Ilona Friso-van den Bos, Evelyn H. Kroesbergen & Johannes E. H. Van Luit - 2018 - Frontiers in Psychology 9.
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  • Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners.Belde Mutaf Yıldız, Delphine Sasanguie, Bert De Smedt & Bert Reynvoet - 2018 - Frontiers in Psychology 9.
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  • 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 (...)
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  • Sculpting the space of actions. Explaining human action by integrating intentions and mechanisms.Machiel Keestra - 2014 - Dissertation, University of Amsterdam
    How can we explain the intentional nature of an expert’s actions, performed without immediate and conscious control, relying instead on automatic cognitive processes? How can we account for the differences and similarities with a novice’s performance of the same actions? Can a naturalist explanation of intentional expert action be in line with a philosophical concept of intentional action? Answering these and related questions in a positive sense, this dissertation develops a three-step argument. Part I considers different methods of explanations in (...)
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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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  • Mobile Learning: Essays on Philosophy, Psychology and Education.Kristóf Nyíri (ed.) - 2003 - Passagen Verlag.
    The changing conditions for the accumulation and transmission of knowledge in the age of multimedia networks make it inevitable that old philosophical problems become formulated in a new light. Above all, the problem of the unity of knowledge is once again a topical issue. The situation-dependent acquisition of knowledge that is made possible by mobile learning transcends the boundaries of traditional disciplines, linking the domains of text, diagram, and picture. Database integration and multimedia search become central problems in the epistemology (...)
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  • Extended cognition and fixed properties: steps to a third-wave version of extended cognition. [REVIEW]Michael David Kirchhoff - 2012 - Phenomenology and the Cognitive Sciences 11 (2):287-308.
    This paper explores several paths a distinctive third wave of extended cognition might take. In so doing, I address a couple of shortcomings of first- and second-wave extended cognition associated with a tendency to conceive of the properties of internal and external processes as fixed and non-interchangeable. First, in the domain of cognitive transformation, I argue that a problematic tendency of the complementarity model is that it presupposes that socio-cultural resources augment but do not significantly transform the brain’s representational capacities (...)
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  • Is There a Place for Epistemic Virtues in Theory Choice?Milena Ivanova - 2014 - In Abrol Fairweather & Owen Flanagan (eds.), Virtue Epistemology Naturalized: Bridges between Virtue Epistemology and Philosophy of Science. Cham: Synthese Library. pp. 207-226.
    This paper challenges the appeal to theory virtues in theory choice as well as the appeal to the intellectual and moral virtues of an agent as determining unique choices between empirically equivalent theories. After arguing that theoretical virtues do not determine the choice of one theory at the expense of another theory, I argue that nor does the appeal to intellectual and moral virtues single out one agent, who defends a particular theory, and exclude another agent defending an alternative theory. (...)
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  • The Psychology and Philosophy of Natural Numbers†.Oliver R. Marshall - 2018 - Philosophia Mathematica 26 (1):40-58.
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  • A “sense of magnitude” requires a new alternative for learning numerical symbols.Delphine Sasanguie & Bert Reynvoet - 2017 - Behavioral and Brain Sciences 40.
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  • Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. [REVIEW]Wojciech Krysztofiak - 2012 - Axiomathes 22 (4):433-456.
    The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...)
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  • The Relationship Between Non-symbolic and Symbolic Numerosity Representations in Elementary School: The Role of Intelligence.Tatiana Tikhomirova, Yulia Kuzmina, Irina Lysenkova & Sergey Malykh - 2019 - Frontiers in Psychology 10.
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  • The Use of Local and Global Ordering Strategies in Number Line Estimation in Early Childhood.Jaccoline E. Van ’T. Noordende, M. J. M. Volman, Paul P. M. Leseman, Korbinian Moeller, Tanja Dackermann & Evelyn H. Kroesbergen - 2018 - Frontiers in Psychology 9.
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  • Spatial Arrangement and Set Size Influence the Coding of Non-symbolic Quantities in the Intraparietal Sulcus.Johannes Bloechle, Julia F. Huber, Elise Klein, Julia Bahnmueller, Johannes Rennig, Korbinian Moeller & Stefan Huber - 2018 - Frontiers in Human Neuroscience 12.
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  • 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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  • 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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  • 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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  • Representational Structures of Arithmetical Thinking: Part I.Wojciech Krysztofiak - 2016 - Axiomathes 26 (1):1-40.
    In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a (...)
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  • Probing the Relationship Between Home Numeracy and Children's Mathematical Skills: A Systematic Review.Belde Mutaf-Yıldız, Delphine Sasanguie, Bert De Smedt & Bert Reynvoet - 2020 - Frontiers in Psychology 11.
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  • The influence of math anxiety on symbolic and non-symbolic magnitude processing.Julia F. Dietrich, Stefan Huber, Korbinian Moeller & Elise Klein - 2015 - Frontiers in Psychology 6.
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  • Is thirty-two three tens and two ones? The embedded structure of cardinal numbers.Diego Guerrero, Jihyun Hwang, Brynn Boutin, Tom Roeper & Joonkoo Park - 2020 - Cognition 203 (C):104331.
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  • Developmental Changes in ANS Precision Across Grades 1–9: Different Patterns of Accuracy and Reaction Time.Sergey Malykh, Yulia Kuzmina & Tatiana Tikhomirova - 2021 - Frontiers in Psychology 12.
    The main aim of this study was to analyze the patterns of changes in Approximate Number Sense precision from grade 1 to grade 9 in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1–5, and the second cohort was assessed at grades 5–9. ANS precision was assessed by accuracy and reaction time in a non-symbolic comparison test. The patterns of (...)
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  • Comparing Data Sets: Implicit Summaries of the Statistical Properties of Number Sets.Bradley J. Morris & Amy M. Masnick - 2015 - Cognitive Science 39 (1):156-170.
    Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of means, coefficient of variation, and number of observations, by measuring eye fixations, accuracy, and confidence when assessing differences between number sets. Results indicated that participants implicitly create and (...)
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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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  • Numerical estrangement and integration between symbolic and non-symbolic numerical information: Task-dependence and its link to math abilities in adults.Xueying Ren, Ruizhe Liu, Marc N. Coutanche, Julie A. Fiez & Melissa E. Libertus - 2022 - Cognition 224 (C):105067.
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  • Hearing and music in unilateral spatial neglect neuro-rehabilitation.Alma Guilbert, Sylvain Clement & Christine Moroni - 2014 - Frontiers in Psychology 5.
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