Diagrams Visual Imagination And Continuity In Peirce S Philosophy Of Mathematics
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Diagrams Visual Imagination And Continuity In Peirce S Philosophy Of Mathematics
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Author : Vitaly Kiryushchenko
language : en
Publisher: Springer Nature
Release Date : 2023-05-12
Diagrams Visual Imagination And Continuity In Peirce S Philosophy Of Mathematics written by Vitaly Kiryushchenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Mathematics categories.
This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.
Visual Reasoning With Diagrams
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Author : Amirouche Moktefi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-08
Visual Reasoning With Diagrams written by Amirouche Moktefi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-08 with Mathematics categories.
Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning.
Interdisciplinary Perspectives On Math Cognition
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Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2019-09-14
Interdisciplinary Perspectives On Math Cognition written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-14 with Mathematics categories.
This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Peirce On Perception And Reasoning
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Author : Kathleen A. Hull
language : en
Publisher: Taylor & Francis
Release Date : 2017-03-27
Peirce On Perception And Reasoning written by Kathleen A. Hull and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-27 with Education categories.
In this book, scholars examine the nature and significance of Peirce’s work on perception, iconicity, and diagrammatic thinking. Abjuring any strict dichotomy between presentational and representational mental activity, Peirce’s theories transform the Aristotelian, Humean, and Kantian paradigms that continue to hold sway today and forge a new path for understanding the centrality of visual thinking in science, education, art, and communication. This book is a key resource for scholars interested in Perice’s philosophy and its relation to contemporary issues in mathematics, philosophy of mind, philosophy of perception, semiotics, logic, visual thinking, and cognitive science.
Diagrammatic Representation And Reasoning
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Author : Michael Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Diagrammatic Representation And Reasoning written by Michael Anderson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.
The rise in computing and multimedia technology has spawned an increasing interest in the role of diagrams and sketches, not only for the purpose of conveying information but also for creative thinking and problem-solving. This book attempts to characterise the nature of "a science of diagrams" in a wide-ranging, multidisciplinary study that contains accounts of the most recent research results in computer science and psychology. Key topics include: cognitive aspects, formal aspects, and applications. It is a well-written and indispensable survey for researchers and students in the fields of cognitive science, artificial intelligence, human-computer interaction, and graphics and visualisation.
Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Oxford University Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Language Arts & Disciplines categories.
Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
Pragmatism As A Principle And Method Of Right Thinking
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Author : Charles Sanders Peirce
language : en
Publisher: SUNY Press
Release Date : 1997-01-01
Pragmatism As A Principle And Method Of Right Thinking written by Charles Sanders Peirce and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Philosophy categories.
This is a study edition of Charles Sanders Peirce's manuscripts for lectures on pragmatism given in spring 1903 at Harvard University. Excerpts from these writings have been published elsewhere but in abbreviated form. Turrisi has edited the manuscripts for publication and has written a series of notes that illuminate the historical, scientific, and philosophical contexts of Peirce's references in the lectures. She has also written a Preface that describes the manner in which the lectures came to be given, including an account of Peirce's life and career pertinent to understanding the philosopher himself. Turrisi's introduction interprets Peirce's brand of pragmatism within his system of logic and philosophy of science as well as within general philosophical principles.
Diagrammatic Immanence
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Author : Rocco Gangle
language : en
Publisher: Edinburgh University Press
Release Date : 2016-08-18
Diagrammatic Immanence written by Rocco Gangle and has been published by Edinburgh University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-18 with Philosophy categories.
A renewal of immanent metaphysics through diagrammatic methods and the tools of category theorySpinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuzes philosophy of difference in conjunction with the formal operations of category theory. Category theory reveals deep structural connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work. Gangle introduces the methods of category theory from a philosophical and diagrammatic perspective, allowing philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.
Realizing Reason
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Author : Danielle Macbeth
language : en
Publisher:
Release Date : 2014-03
Realizing Reason written by Danielle Macbeth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03 with Mathematics categories.
Danielle Macbeth offers a new account of mathematical practice as a mode of inquiry into objective truth, and argues that understanding the nature of mathematical practice provides us with the resources to develop a radically new conception of ourselves and our capacity for knowledge of objective truth.
The Rule Of Reason
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Author : Jacqueline Brunning
language : en
Publisher: University of Toronto Press
Release Date : 1997-01-01
The Rule Of Reason written by Jacqueline Brunning and has been published by University of Toronto Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Philosophy categories.
While Peirce scholarship has advanced considerably since its earliest days, many controversies of interpretation persist, and several of the more obscure aspects of his work remain poorly understood.