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  1. 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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  • Microcognition: Philosophy, Cognitive Science, and Parallel Distributed Processing.Andy Clark - 1989 - MIT Press.
    Parallel distributed processing is transforming the field of cognitive science. Microcognition provides a clear, readable guide to this emerging paradigm from a cognitive philosopher's point of view. It explains and explores the biological basis of PDP, its psychological importance, and its philosophical relevance.
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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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  • Analog and analog.John Haugeland - 1981 - Philosophical Topics 12 (1):213-226.
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  • Analog and Analog.John Haugeland - 1981 - Philosophical Topics 12 (1):213-225.
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  • Microcognition: Philosophy, Cognitive Science, and Parallel Distributed Processing.Andy Clark - 1989 - Cambridge: MIT Press.
    Parallel distributed processing is transforming the field of cognitive science. Microcognition provides a clear, readable guide to this emerging paradigm from a cognitive philosopher's point of view. It explains and explores the biological basis of PDP, its psychological importance, and its philosophical relevance.
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  • Explaining systematicity.Kenneth Aizawa - 1997 - Mind and Language 12 (2):115-36.
    Despite the considerable attention that the systematicity argument has enjoyed, it is worthwhile examining the argument within the context of similar explanatory arguments from the history of science. This kind of analysis helps show that Connectionism, qua Connectionism, really does not have an explanation of systematicity. Second, and more surprisingly, one finds that the systematicity argument sets such a high explanatory standard that not even Classicism can explain the systematicity of thought.
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  • Explaining Systematicity.Kenneth Aizawa - 1997 - Mind and Language 12 (2):115-136.
    Despite the considerable attention that the systematicity argument has enjoyed, it is worthwhile examining the argument within the context of similar explanatory arguments from the history of science. This kind of analysis helps show that Connectionism, qua Connectionism, really does not have an explanation of systematicity. Second, and more surprisingly, one finds that the systematicity argument sets such a high explanatory standard that not even Classicism can explain the systematicity of thought.
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  • The Elm and the Expert: Mentalese and Its Semantics.Jerry A. Fodor - 1994 - MIT Press.
    This book is largely a reconsideration of the arguments that are supposed to ground this consensus.
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  • The Elm and the Expert: Mentalese and its Semantics.Jerry A. Fodor - 1995 - MIT Press.
    Written in a highly readable, irreverent style, The Elm and the Expert provides a lively discussion of semantic issues about mental representation, with special attention to issues raised by Frege's problem, Twin cases, and the putative indeterminacy of reference. Bound to be widely read and much discussed, The Elm and the Expert, written in Jerry Fodor's usual highly readable, irreverent style, provides a lively discussion of semantic issues about mental representation, with special attention to issues raised by Frege's problem, Twin (...)
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  • Large number discrimination in 6-month-old infants.Fei Xu & Elizabeth S. Spelke - 2000 - Cognition 74 (1):1-11.
    Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.
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  • Young Children Intuitively Divide Before They Recognize the Division Symbol.Emily Szkudlarek, Haobai Zhang, Nicholas K. DeWind & Elizabeth M. Brannon - 2022 - Frontiers in Human Neuroscience 16.
    Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic (...)
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  • The construction of large number representations in adults.Elizabeth Spelke & Hilary Barth - 2003 - Cognition 86 (3):201-221.
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  • Principles of object perception.Elizabeth S. Spelke - 1990 - Cognitive Science 14 (1):29--56.
    Research on human infants has begun to shed light on early-developing processes for segmenting perceptual arrays into objects. Infants appear to perceive objects by analyzing three-dimensional surface arrangements and motions. Their perception does not accord with a general tendency to maximize figural goodness or to attend to nonaccidental geometric relations in visual arrays. Object perception does accord with principles governing the motions of material bodies: Infants divide perceptual arrays into units that move as connected wholes, that move separately from one (...)
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  • Language and number: a bilingual training study.Elizabeth S. Spelke - 2001 - Cognition 78 (1):45-88.
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  • Core multiplication in childhood.Elizabeth S. Spelke - 2010 - Cognition 116 (2):204-216.
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  • On the proper treatment of connectionism.Paul Smolensky - 1988 - Behavioral and Brain Sciences 11 (1):1-23.
    A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...)
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  • Perceptual Pluralism.Jake Quilty-Dunn - 2019 - Noûs 54 (4):807-838.
    Perceptual systems respond to proximal stimuli by forming mental representations of distal stimuli. A central goal for the philosophy of perception is to characterize the representations delivered by perceptual systems. It may be that all perceptual representations are in some way proprietarily perceptual and differ from the representational format of thought (Dretske 1981; Carey 2009; Burge 2010; Block ms.). Or it may instead be that perception and cognition always trade in the same code (Prinz 2002; Pylyshyn 2003). This paper rejects (...)
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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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  • Recursive distributed representations.Jordan B. Pollack - 1990 - Artificial Intelligence 46 (1-2):77-105.
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  • Unwarranted philosophical assumptions in research on ANS.John Opfer, Richard Samuels, Stewart Shapiro & Eric Snyder - 2021 - Behavioral and Brain Sciences 44.
    Clarke and Beck import certain assumptions about the nature of numbers. Although these are widespread within research on number cognition, they are highly contentious among philosophers of mathematics. In this commentary, we isolate and critically evaluate one core assumption: the identity thesis.
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  • Icons, Magnitudes, and Their Parts.Corey J. Maley - 2023 - Critica 55 (163):129-154.
    Analog representations come in different types. One distinction is between those representations that have parts that are themselves representations and those that do not (i.e., those for which the Parts Principle is true and those for which it is not). I offer a unified account of analog representation, showing what all types have in common. This account clarifies when the Parts Principle applies and when it does not, thereby illuminating why the Parts Principle is less interesting than one might have (...)
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  • Analog and digital, continuous and discrete.Corey J. Maley - 2011 - Philosophical Studies 155 (1):117-131.
    Representation is central to contemporary theorizing about the mind/brain. But the nature of representation--both in the mind/brain and more generally--is a source of ongoing controversy. One way of categorizing representational types is to distinguish between the analog and the digital: the received view is that analog representations vary smoothly, while digital representations vary in a step-wise manner. I argue that this characterization is inadequate to account for the ways in which representation is used in cognitive science; in its place, I (...)
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  • Contents of the approximate number system.Jack C. Lyons - 2021 - Behavioral and Brain Sciences 44.
    Clarke and Beck argue that the approximate number system represents rational numbers, like 1/3 or 3.5. I think this claim is not supported by the evidence. Rather, I argue, ANS should be interpreted as representing natural numbers and ratios among them; and we should view the contents of these representations are genuinely approximate.
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  • Analog and digital.David K. Lewis - 1971 - Noûs 5 (3):321-327.
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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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  • Mental Structures.Kevin J. Lande - 2020 - Noûs (3):649-677.
    An ongoing philosophical discussion concerns how various types of mental states fall within broad representational genera—for example, whether perceptual states are “iconic” or “sentential,” “analog” or “digital,” and so on. Here, I examine the grounds for making much more specific claims about how mental states are structured from constituent parts. For example, the state I am in when I perceive the shape of a mountain ridge may have as constituent parts my representations of the shapes of each peak and saddle (...)
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  • What Is an Object File?E. J. Green & Jake Quilty-Dunn - 2021 - British Journal for the Philosophy of Science 72 (3):665-699.
    The notion of an object file figures prominently in recent work in philosophy and cognitive science. Object files play a role in theories of singular reference, object individuation, perceptual memory, and the development of cognitive capacities. However, the philosophical literature lacks a detailed, empirically informed theory of object files. In this paper, we articulate and defend the multiple-slots view, which specifies both the format and architecture of object files. We argue that object files represent in a non-iconic, propositional format that (...)
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  • What Do Object Files Pick Out?Edwin Green - 2018 - Philosophy of Science 85 (2):177-200.
    Many authors have posited an “object file” system, which underlies perceptual selection and tracking of objects. Several have proposed that this system internalizes principles specifying what counts as an object and relies on them during tracking. Here I consider a popular view on which the object file system is tuned to entities that satisfy principles of three-dimensionality, cohesion, and boundedness. I argue that the evidence gathered in support of this view is consistent with a more permissive view on which object (...)
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  • Beyond Resemblance.Gabriel Greenberg - 2013 - Philosophical Review 122 (2):215-287.
    What is it for a picture to depict a scene? The most orthodox philosophical theory of pictorial representation holds that depiction is grounded in resemblance. A picture represents a scene in virtue of being similar to that scene in certain ways. This essay presents evidence against this claim: curvilinear perspective is one common style of depiction in which successful pictorial representation depends as much on a picture's systematic differences with the scene depicted as on the similarities; it cannot be analyzed (...)
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  • Number estimation relies on a set of segmented objects.S. L. Franconeri, D. K. Bemis & G. A. Alvarez - 2009 - Cognition 113 (1):1-13.
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  • Connectionism and cognitive architecture: A critical analysis.Jerry A. Fodor & Zenon W. Pylyshyn - 1988 - Cognition 28 (1-2):3-71.
    This paper explores the difference between Connectionist proposals for cognitive a r c h i t e c t u r e a n d t h e s o r t s o f m o d e l s t hat have traditionally been assum e d i n c o g n i t i v e s c i e n c e . W e c l a i m t h a t t h (...)
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  • Connectionism and the problem of systematicity: Why Smolensky's solution doesn't work.Jerry Fodor & Brian P. McLaughlin - 1990 - Cognition 35 (2):183-205.
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  • Visual Reference and Iconic Content.Santiago Echeverri - 2017 - Philosophy of Science 84 (4):761-781.
    Evidence from cognitive science supports the claim that humans and other animals see the world as divided into objects. Although this claim is widely accepted, it remains unclear whether the mechanisms of visual reference have representational content or are directly instantiated in the functional architecture. I put forward a version of the former approach that construes object files as icons for objects. This view is consistent with the evidence that motivates the architectural account, can respond to the key arguments against (...)
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  • Knowledge and the flow of information.F. Dretske - 1989 - Trans/Form/Ação 12:133-139.
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  • The feature-binding problem is an ill-posed problem.Vincent Di Lollo - 2012 - Trends in Cognitive Sciences 16 (6):317-321.
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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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  • Colour Relations in Form.Will Davies - 2020 - Philosophy and Phenomenological Research 102 (3):574-594.
    The orthodox monadic determination thesis holds that we represent colour relations by virtue of representing colours. Against this orthodoxy, I argue that it is possible to represent colour relations without representing any colours. I present a model of iconic perceptual content that allows for such primitive relational colour representation, and provide four empirical arguments in its support. I close by surveying alternative views of the relationship between monadic and relational colour representation.
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  • The number sense represents (rational) numbers.Sam Clarke & Jacob Beck - 2021 - Behavioral and Brain Sciences 44:1-57.
    On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...)
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  • Mapping the Visual Icon.Sam Clarke - 2022 - Philosophical Quarterly 72 (3):552-577.
    It is often claimed that pre-attentive vision has an ‘iconic’ format. This is seen to explain pre-attentive vision's characteristically high processing capacity and to make sense of an overlap in the mechanisms of early vision and mental imagery. But what does the iconicity of pre-attentive vision amount to? This paper considers two prominent ways of characterising pre-attentive visual icons and argues that neither is adequate: one approach renders the claim ‘pre-attentive vision is iconic’ empirically false while the other obscures its (...)
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  • Cognitive penetration and informational encapsulation: Have we been failing the module?Sam Clarke - 2021 - Philosophical Studies 178 (8):2599-2620.
    Jerry Fodor deemed informational encapsulation ‘the essence’ of a system’s modularity and argued that human perceptual processing comprises modular systems, thus construed. Nowadays, his conclusion is widely challenged. Often, this is because experimental work is seen to somehow demonstrate the cognitive penetrability of perceptual processing, where this is assumed to conflict with the informational encapsulation of perceptual systems. Here, I deny the conflict, proposing that cognitive penetration need not have any straightforward bearing on the conjecture that perceptual processing is composed (...)
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  • Beyond the icon: Core cognition and the bounds of perception.Sam Clarke - 2022 - 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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  • Iconic Representation: Maps, Pictures, and Perception.Tyler Burge - 2018 - In Wuppuluri Shyam & Francisco Antonio Dorio (eds.), The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. Springer. pp. 79-100.
    Maps and realist pictures comprise prominent sub-classes of iconic representations. The most basic, most important sub-class is perception. Other types are drawings, photographs, musical notations, diagrams, bar graphs, abacuses, hieroglyphs, and color chits.
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  • The Generality Constraint and the Structure of Thought.Jacob Beck - 2012 - Mind 121 (483):563-600.
    According to the Generality Constraint, mental states with conceptual content must be capable of recombining in certain systematic ways. Drawing on empirical evidence from cognitive science, I argue that so-called analogue magnitude states violate this recombinability condition and thus have nonconceptual content. I further argue that this result has two significant consequences: it demonstrates that nonconceptual content seeps beyond perception and infiltrates cognition; and it shows that whether mental states have nonconceptual content is largely an empirical matter determined by the (...)
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  • Perception is Analog: The Argument from Weber's Law.Jacob Beck - 2019 - Journal of Philosophy 116 (6):319-349.
    In the 1980s, a number of philosophers argued that perception is analog. In the ensuing years, these arguments were forcefully criticized, leaving the thesis in doubt. This paper draws on Weber’s Law, a well-entrenched finding from psychophysics, to advance a new argument that perception is analog. This new argument is an adaptation of an argument that cognitive scientists have leveraged in support of the contention that primitive numerical representations are analog. But the argument here is extended to the representation of (...)
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  • Numbers, numerosities, and new directions.Jacob Beck & Sam Clarke - 2021 - Behavioral and Brain Sciences 44:1-20.
    In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.
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  • Contents and Vehicles in Analog Perception.Jacob Beck - 2023 - Crítica. Revista Hispanoamericana de Filosofía 55 (163):109–127.
    Building on Christopher Peacocke’s account of analog perceptual contentand my own account of analog perceptual vehicles, I defend three claims: that theperception of magnitudes often has analog contents; that the perception of magni-tudes often has analog vehicles; and that the first claim is true in virtue of the second—that is, the analog vehicles help to ground the analog contents.
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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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  • On representational content and format in core numerical cognition.Brian Ball - 2017 - Philosophical Psychology 30 (1-2):119-139.
    Carey has argued that there is a system of core numerical cognition – the analog magnitude system – in which cardinal numbers are explicitly represented in iconic format. While the existence of this system is beyond doubt, this paper aims to show that its representations cannot have the combination of features attributed to them by Carey. According to the argument from abstractness, the representation of the cardinal number of a collection of individuals as such requires the representation of individuals as (...)
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