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Radicalizing numerical cognition

Synthese 198 (Suppl 1):529-545 (2020)

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  1. An extended mind perspective on natural number representation.Helen De Cruz - 2008 - Philosophical Psychology 21 (4):475 – 490.
    Experimental studies indicate that nonhuman animals and infants represent numerosities above three or four approximately and that their mental number line is logarithmic rather than linear. In contrast, human children from most cultures gradually acquire the capacity to denote exact cardinal values. To explain this difference, I take an extended mind perspective, arguing that the distinctly human ability to use external representations as a complement for internal cognitive operations enables us to represent natural numbers. Reviewing neuroscientific, developmental, and anthropological evidence, (...)
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  • Mathematical Cognition: A Case of Enculturation.Richard Menary - 2015 - Open Mind.
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  • Cognition.Gary Hatfield - 2014 - In Lawrence A. Shapiro (ed.), The Routledge Handbook of Embodied Cognition. New York: Routledge. pp. 361–73.
    What is cognition? What makes a process cognitive? These questions have been answered differently by various investigators and theoretical traditions. Even so, there are some commonalities, allowing us to specify a few contrasting answers to these questions. The main commonalities involve the notion that cognition is information processing that explains intelligent behavior. The differences concern whether early perceptual processes are cognitive, whether representations are needed to explain cognition, what makes something a representation, and whether cognitive processes are limited to the (...)
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  • 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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  • 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: Routledge. 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 (...)
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  • Evolving Enactivism: Basic Minds Meet Content.Daniel D. Hutto & Erik Myin - 2017 - Cambridge, MA, USA: MIT Press. Edited by Erik Myin.
    An extended argument that cognitive phenomena—perceiving, imagining, remembering—can be best explained in terms of an interface between contentless and content-involving forms of cognition. -/- Evolving Enactivism argues that cognitive phenomena—perceiving, imagining, remembering—can be best explained in terms of an interface between contentless and content-involving forms of cognition. Building on their earlier book Radicalizing Enactivism, which proposes that there can be forms of cognition without content, Daniel Hutto and Erik Myin demonstrate the unique explanatory advantages of recognizing that only some forms (...)
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  • Doing Without Representing?Andy Clark - 1994 - University of Sussex, School of Cognitive and Computing Sciences.
    Connectionism and classicism, it appears, have at least this much in common: both place some notion of internal representation at the heart of a scientific study of mind. In recent years, however, a much more radical view has gained increasing popularily. This view calls into question the commitment to internal representation itself. more strikingly still, this new wave of anti-representationalism is rooted not in 'armchair' theorizing but in practical attempts to model and understand intelligent, adaptive behaviour. In this paper we (...)
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  • The Representational Theory of Mind: An Introduction.Kim Sterelny - 1994 - Philosophical Quarterly 44 (175):252-254.
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  • Arguing about representation.Mark Rowlands - 2017 - Synthese 194 (11):4215-4232.
    The question of whether cognition requires representations has engendered heated discussion during the last two decades. I shall argue that the question is, in all likelihood, a spurious one. There may or may not be a fact of the matter concerning whether a given item qualifies as a representation. However, even if there is, attempts to establish whether cognition requires representation have neither practical nor theoretical utility.
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  • Bayesian Sensorimotor Psychology.Michael Rescorla - 2016 - Mind and Language 31 (1):3-36.
    Sensorimotor psychology studies the mental processes that control goal-directed bodily motion. Recently, sensorimotor psychologists have provided empirically successful Bayesian models of motor control. These models describe how the motor system uses sensory input to select motor commands that promote goals set by high-level cognition. I highlight the impressive explanatory benefits offered by Bayesian models of motor control. I argue that our current best models assign explanatory centrality to a robust notion of mental representation. I deploy my analysis to defend intentional (...)
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  • Do connectionist representations earn their explanatory keep?William Ramsey - 1997 - Mind and Language 12 (1):34-66.
    In this paper I assess the explanatory role of internal representations in connectionist models of cognition. Focusing on both the internal‘hidden’units and the connection weights between units, I argue that the standard reasons for viewing these components as representations are inadequate to bestow an explanatorily useful notion of representation. Hence, nothing would be lost from connectionist accounts of cognitive processes if we were to stop viewing the weights and hidden units as internal representations.
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  • Do Connectionist Representations Earn Their Explanatory Keep?William Ramsey - 1997 - Mind and Language 12 (1):34-66.
    In this paper I assess the explanatory role of internal representations in connectionist models of cognition. Focusing on both the internal‘hidden’units and the connection weights between units, I argue that the standard reasons for viewing these components as representations are inadequate to bestow an explanatorily useful notion of representation. Hence, nothing would be lost from connectionist accounts of cognitive processes if we were to stop viewing the weights and hidden units as internal representations.
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  • Concepts and how they get that way.Karenleigh A. 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, (...)
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  • The ontology of concepts: Abstract objects or mental representations?Eric Margolis & Stephen Laurence - 2007 - Noûs 41 (4):561-593.
    What is a concept? Philosophers have given many different answers to this question, reflecting a wide variety of approaches to the study of mind and language. Nonetheless, at the most general level, there are two dominant frameworks in contemporary philosophy. One proposes that concepts are mental representations, while the other proposes that they are abstract objects. This paper looks at the differences between these two approaches, the prospects for combining them, and the issues that are involved in the dispute. We (...)
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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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  • 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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  • The Natural Origins of Content.Daniel D. Hutto & Glenda Satne - 2015 - Philosophia 43 (3):521-536.
    We review the current state of play in the game of naturalizing content and analyse reasons why each of the main proposals, when taken in isolation, is unsatisfactory. Our diagnosis is that if there is to be progress two fundamental changes are necessary. First, the point of the game needs to be reconceived in terms of explaining the natural origins of content. Second, the pivotal assumption that intentionality is always and everywhere contentful must be abandoned. Reviving and updating Haugeland’s baseball (...)
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  • Psychosemantics: The Problem of Meaning in the Philosophy of Mind.Jerry A. Fodor - 1987 - MIT Press. Edited by Margaret A. Boden.
    Preface 1 Introduction: The Persistence of the Attitudes 2 Individualism and Supervenience 3 Meaning Holism 4 Meaning and the World Order Epilogue Creation Myth Appendix Why There Still Has to be a Language of Thought Notes References Author Index.
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  • Explaining Behavior: Reasons in a World of Causes.Fred Dretske - 1988 - MIT Press.
    In this lucid portrayal of human behavior, Fred Dretske provides an original account of the way reasons function in the causal explanation of behavior.
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  • Radicalizing Enactivism: Basic Minds Without Content.Daniel D. Hutto & Erik Myin - 2013 - Cambridge, MA: MIT Press.
    In this book, Daniel Hutto and Erik Myin promote the cause of a radically enactive, embodied approach to cognition that holds that some kinds of minds -- basic minds -- are neither best explained by processes involving the manipulation of ...
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  • Radical Embodied Cognitive Science.Anthony Chemero - 2009 - Bradford.
    While philosophers of mind have been arguing over the status of mental representations in cognitive science, cognitive scientists have been quietly engaged in studying perception, action, and cognition without explaining them in terms of mental representation. In this book, Anthony Chemero describes this nonrepresentational approach, puts it in historical and conceptual context, and applies it to traditional problems in the philosophy of mind. Radical embodied cognitive science is a direct descendant of the American naturalist psychology of William James and John (...)
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  • Representation Reconsidered.William M. Ramsey - 2007 - Cambridge University Press.
    Cognitive representation is the single most important explanatory notion in the sciences of the mind and has served as the cornerstone for the so-called 'cognitive revolution'. This book critically examines the ways in which philosophers and cognitive scientists appeal to representations in their theories, and argues that there is considerable confusion about the nature of representational states. This has led to an excessive over-application of the notion - especially in many of the fresher theories in computational neuroscience. Representation Reconsidered shows (...)
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  • Naturalizing the Mind.Fred Dretske - 1995 - MIT Press.
    In this provocative book, Fred Dretske argues that to achieve an understanding of the mind it is not enough to understand the biological machinery by means of...
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  • Mental Representation.David Pitt - 2020 - Stanford Encyclopedia of Philosophy.
    The notion of a "mental representation" is, arguably, in the first instance a theoretical construct of cognitive science. As such, it is a basic concept of the Computational Theory of Mind, according to which cognitive states and processes are constituted by the occurrence, transformation and storage (in the mind/brain) of information-bearing structures (representations) of one kind or another.
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  • Constructing a concept of number.Karenleigh Overmann - 2018 - Journal of Numerical Cognition 2 (4):464–493.
    Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like (...)
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  • Updating the “abstract–concrete” distinction in Ancient Near Eastern numbers.Karenleigh Overmann - 2018 - Cuneiform Digital Library Journal 1:1–22.
    The characterization of early token-based accounting using a concrete concept of number, later numerical notations an abstract one, has become well entrenched in the literature. After reviewing its history and assumptions, this article challenges the abstract–concrete distinction, presenting an alternative view of change in Ancient Near Eastern number concepts, wherein numbers are abstract from their inception and materially bound when most elaborated. The alternative draws on the chronological sequence of material counting technologies used in the Ancient Near East—fingers, tallies, tokens, (...)
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  • Naturalizing the Mind.Fred Dretske - 1997 - Noûs 31 (4):528-537.
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  • Naturalizing the Mind.Fred Dretske - 1995 - Philosophy 72 (279):150-154.
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  • The Number Sense: How the Mind Creates Mathematics.Stanislas Dehaene - 1999 - British Journal of Educational Studies 47 (2):201-203.
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