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  1. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Jenz Høyrup - 2005 - Studia Logica 80 (1):143-147.
  • Mechanization of Reasoning in a Historical Perspective.Witold Marciszewski & Roman Murawski (eds.) - 1995 - Brill | Rodopi.
    This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of (...)
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  • Philosophy and Geometry: Theoretical and Historical Issues.L. Magnani - 2001 - Springer Verlag.
    The book also ties together the concerns of philosophers of science and cognitive science researchers, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are covered from a novel combination of both historical and contemporary perspectives."--Jacket.
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  • Core Knowledge.Elizabeth S. Spelke - 2000 - American Psychologist 55 (11):1233-1243.
    Complex cognitive skills such as reading and calculation and complex cognitive achievements such as formal science and mathematics may depend on a set of building block systems that emerge early in human ontogeny and phylogeny. These core knowledge systems show characteristic limits of domain and task specificity: Each serves to represent a particular class of entities for a particular set of purposes. By combining representations from these systems, however human cognition may achieve extraordinary flexibility. Studies of cognition in human infants (...)
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  • A Perceptual Account of Symbolic Reasoning.David Landy, Colin Allen & Carlos Zednik - 2014 - Frontiers in Psychology 5.
    People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often (...)
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  • Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry.Nathaniel Miller - 2007 - Center for the Study of Language and Inf.
    Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In _Euclid and His Twentieth-Century Rivals_, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer (...)
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  • Abductive Cognition: The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning.Lorenzo Magnani - 2009 - Springer Verlag.
    Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...)
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  • Boundaries of the Mind: The Individual in the Fragile Sciences - Cognition.Robert A. Wilson - 2004 - Cambridge University Press.
    Where does the mind begin and end? Most philosophers and cognitive scientists take the view that the mind is bounded by the skull or skin of the individual. Robert Wilson, in this provocative and challenging 2004 book, provides the foundations for the view that the mind extends beyond the boundary of the individual. The approach adopted offers a unique blend of traditional philosophical analysis, cognitive science, and the history of psychology and the human sciences. The companion volume, Genes and the (...)
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  • Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1981 - Dover Publications.
    A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions — rather than strictly historical and mathematical issues — and features several helpful appendixes.
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  • The Visual Brain in Action.A. David Milner & Melvyn A. Goodale - 1995 - Oxford University Press.
    Although the mechanics of how the eye works are well understood, debate still exists as to how the complex machinery of the brain interprets neural impulses...
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  • Cognitive Pluralism.Steven Horst - 2016 - MIT Press.
    This book introduces an account of cognitive architecture, Cognitive Pluralism, on which the basic units of understanding are models of particular content domains. Having many mental models is a good adaptive strategy for cognition, but models can be incompatible with one another, leading to paradoxes and inconsistencies of belief, and it may not be possible to integrate the understanding supplied by multiple models into a comprehensive and self-consistent "super model". The book applies the theory to explaining intuitive reasoning and cognitive (...)
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  • The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
    An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.
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  • Diagrams as Tools for Scientific Reasoning.Adele Abrahamsen & William Bechtel - 2015 - Review of Philosophy and Psychology 6 (1):117-131.
    We contend that diagrams are tools not only for communication but also for supporting the reasoning of biologists. In the mechanistic research that is characteristic of biology, diagrams delineate the phenomenon to be explained, display explanatory relations, and show the organized parts and operations of the mechanism proposed as responsible for the phenomenon. Both phenomenon diagrams and explanatory relations diagrams, employing graphs or other formats, facilitate applying visual processing to the detection of relevant patterns. Mechanism diagrams guide reasoning about how (...)
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  • Beyond Core Knowledge: Natural Geometry.Elizabeth Spelke, Sang Ah Lee & Véronique Izard - 2010 - Cognitive Science 34 (5):863-884.
    For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...)
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  • The Modularity of Mind.Robert Cummins & Jerry Fodor - 1983 - Philosophical Review 94 (1):101.
  • Science and Core Knowledge.Susan Carey & Elizabeth Spelke - 1996 - Philosophy of Science 63 (4):515 - 533.
    While endorsing Gopnik's proposal that studies of the emergence and modification of scientific theories and studies of cognitive development in children are mutually illuminating, we offer a different picture of the beginning points of cognitive development from Gopnik's picture of "theories all the way down." Human infants are endowed with several distinct core systems of knowledge which are theory-like in some, but not all, important ways. The existence of these core systems of knowledge has implications for the joint research program (...)
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  • Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Michael Boylan - 1983 - Philosophy of Science 50 (4):665-668.
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  • Core Knowledge of Geometry in an Amazonian Indigene Group.Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke - 2006 - Science 311 (5759)::381-4.
    Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.
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  • Mathematical Cognition: A Case of Enculturation.Richard Menary - 2015 - Open Mind.
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  • ¿“Natural” y “Euclidiana”? Reflexiones Sobre la Geometría Práctica y Sus Raíces Cognitivas.Jose Ferreiros & Manuel Garcia - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):325-344.
    We discuss critically some recent theses about geometric cognition, namely claims of universality made by Dehaene et al., and the idea of a “natural geometry” employed by Spelke et al. We offer arguments for the need to distinguish visuo-spatial cognition from basic geometric knowledge, furthermore we claim that the latter cannot be identified with Euclidean geometry. The main aim of the paper is to advance toward a characterization of basic, practical geometry – which in our view requires a combination of (...)
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  • A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices.Yehuda Rav - 2007 - Philosophia Mathematica 15 (3):291-320.
    In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents genuine (...)
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  • Formalism.Michael Detlefsen - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 236--317.
    A comprehensive historical overview of formalist ideas in the philosophy of mathematics.
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  • Menaechmus Versus the Platonists: Two Theories of Science in the Early Academy.Alan C. Bowen - 1983 - Ancient Philosophy 3 (1):12-29.
  • An Essay on the Psychology of Invention in the Mathematical Field. [REVIEW]E. N. & Jacques Hadamard - 1945 - Journal of Philosophy 42 (12):333.
  • The Four-Color Problem and its Philosophical Significance.Thomas Tymoczko - 1979 - Journal of Philosophy 76 (2):57-83.
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  • The Twofold Role of Diagrams in Euclid’s Plane Geometry.Marco Panza - 2012 - Synthese 186 (1):55-102.
    Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...)
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  • Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
    Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...)
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  • Peirce’s Notion of Diagram Experiment: Corrollarial and Theorematical Experiments With Diagrams.Frederik Stjernfelt - 2011 - In David Wagner, Wolfram Pichler, Elisabeth Nemeth & Richard Heinrich (eds.), Publications of the Austrian Ludwig Wittgenstein Society - N.S. 17. De Gruyter. pp. 305-340.
  • Telling More Than We Can Know: Verbal Reports on Mental Processes.Richard E. Nisbett & Timothy D. Wilson~ - 1977 - Psychological Review 84 (3):231-59.
    Reviews evidence which suggests that there may be little or no direct introspective access to higher order cognitive processes. Ss are sometimes unaware of the existence of a stimulus that importantly influenced a response, unaware of the existence of the response, and unaware that the stimulus has affected the response. It is proposed that when people attempt to report on their cognitive processes, that is, on the processes mediating the effects of a stimulus on a response, they do not do (...)
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  • Beyond the Doubting of a Shadow.Roger Penrose - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2:89-129.
  • The Computer Revolution in Philosophy: Philosophy, Science and Models of Mind.Stephen P. Stich - 1981 - Philosophical Review 90 (2):300.
  • Core Knowledge.Elizabeth S. Spelke & Katherine D. Kinzler - 2007 - Developmental Science 10 (1):89-96.
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  • Commentary: The Poverty of Embodied Cognition.Kinga Wołoszyn & Mateusz Hohol - 2017 - Frontiers in Psychology 8.
  • A Purely Geometric Module in the Rat's Spatial Representation.Ken Cheng - 1986 - Cognition 23 (2):149-178.
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  • Modularity and Development: The Case of Spatial Reorientation.Linda Hermer & Elizabeth Spelke - 1996 - Cognition 61 (3):195-232.
  • Children's Use of Geometry and Landmarks to Reorient in an Open Space.Stéphane Gouteux & Elizabeth S. Spelke - 2001 - Cognition 81 (2):119-148.
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  • Thinking in Groups.Todd M. Gureckis & Robert L. Goldstone - 2006 - Pragmatics and Cognition 14 (2):293-311.
    Is cognition an exclusive property of the individual or can groups have a mind of their own? We explore this question from the perspective of complex adaptive systems. One of the principal insights from this line of work is that rules that govern behavior at one level of analysis can cause qualitatively different behavior at higher levels. We review a number of behavioral studies from our lab that demonstrate how groups of people interacting in real-time can self-organize into adaptive, problem-solving (...)
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  • The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
    This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...)
     
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  • Diagrammatic Reasoning: Abstraction, Interaction, and Insight.Kristian Tylén, Riccardo Fusaroli, Johanne Stege Bjørndahl, Joanna Raczaszek-Leonardi, Svend Østergaard & Frederik Stjernfelt - 2014 - Pragmatics and Cognition 22 (2):264-283.
    Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. The active involvement and manipulation of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds (...)
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  • “What” and “Where” in Spatial Language and Spatial Cognition.Barbara Landau & Ray Jackendoff - 1993 - Behavioral and Brain Sciences 16 (2):217-238.
    Fundamental to spatial knowledge in all species are the representations underlying object recognition, object search, and navigation through space. But what sets humans apart from other species is our ability to express spatial experience through language. This target article explores the language ofobjectsandplaces, asking what geometric properties are preserved in the representations underlying object nouns and spatial prepositions in English. Evidence from these two aspects of language suggests there are significant differences in the geometric richness with which objects and places (...)
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  • The Computer Revolution in Philosophy: Philosophy, Science and Models of Mind.Aaron Sloman - 1978 - British Journal for the Philosophy of Science 30 (3):302-304.
  • Thinking in Groups.Todd M. Gureckis & Robert L. Goldstone - 2006 - Pragmatics and Cognition 14 (2):293-311.
    Is cognition an exclusive property of the individual or can groups have a mind of their own? We explore this question from the perspective of complex adaptive systems. One of the principal insights from this line of work is that rules that govern behavior at one level of analysis can cause qualitatively different behavior at higher levels . We review a number of behavioral studies from our lab that demonstrate how groups of people interacting in real-time can self-organize into adaptive, (...)
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  • Computational Models of Collective Behavior.Robert L. Goldstone & Marco A. Janssen - 2005 - Trends in Cognitive Sciences 9 (9):424-430.
  • The Surveyability of Mathematical Proof: A Historical Perspective.O. Bradley Bassler - 2006 - Synthese 148 (1):99-133.
    This paper rejoins the debate surrounding Thomas Tymockzko's paper on the surveyability of proof, first published in the "Journal of Philosophy", and makes the claim that by attending to certain broad features of modern conceptions of proof we may understand ways in which the debate surrounding the surveyability of proof has heretofore remained unduly circumscribed. Motivated by these historical reflections. I suggest a distinction between local and global surveyability which I believe has the promise to open up significant new advances (...)
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  • A Formal System for Euclid’s Elements.Jeremy Avigad, Edward Dean & John Mumma - 2009 - Review of Symbolic Logic 2 (4):700--768.
    We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.
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  • Human Spatial Representation: Insights From Animals.Ranxiao Frances Wang & Elizabeth S. Spelke - 2002 - Trends in Cognitive Sciences 6 (9):376-382.
  • Core Systems of Number.Stanislas Dehaene, Elizabeth Spelke & Lisa Feigenson - 2004 - Trends in Cognitive Sciences 8 (7):307-314.
  • Developmental Neuroimaging of the Human Ventral Visual Cortex.John Gabrieli Kalanit Grill-Spector, Golijeh Golarai - 2008 - Trends in Cognitive Sciences 12 (4):152.
  • Language, Embodiment, and the Cognitive Niche.Andy Clark - 2006 - Trends in Cognitive Sciences 10 (8):370-374.
    Embodied agents use bodily actions and environmental interventions to make the world a better place to think in. Where does language fit into this emerging picture of the embodied, ecologically efficient agent? One useful way to approach this question is to consider language itself as a cognition-enhancing animal-built structure. To take this perspective is to view language as a kind of self-constructed cognitive niche: a persisting though never stationary material scaffolding whose critical role in promoting thought and reason remains surprisingly (...)
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  • The Child's Conception of Geometry.Jean Piaget, Barbel Inhelder, Alina Szeminska & E. A. Lunzer - 1960 - British Journal of Educational Studies 9 (1):84-85.