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Diagrams Visual Imagination And Continuity In Peirces Philosophy Of Mathematics
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Book Synopsis Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics by : Vitaly Kiryushchenko
Download or read book Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics written by Vitaly Kiryushchenko and published by Springer Nature. This book was released on 2023-05-12 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Peirce on Perception and Reasoning by : Kathleen A. Hull
Download or read book Peirce on Perception and Reasoning written by Kathleen A. Hull and published by Routledge. This book was released on 2017-03-27 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The founder of both American pragmatism and semiotics, Charles Sanders Peirce (1839–1914) is widely regarded as an enormously important and pioneering theorist. In this book, scholars from around the world 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, in so doing, forge a new path for understanding the centrality of visual thinking in science, education, art, and communication. The essays in this collection cover a wide range of issues related to Peirce’s theories, including the perception of generality; the legacy of ideas being copies of impressions; imagination and its contribution to knowledge; logical graphs, diagrams, and the question of whether their iconicity distinguishes them from other sorts of symbolic notation; how images and diagrams contribute to scientific discovery and make it possible to perceive formal relations; and the importance and danger of using diagrams to convey scientific ideas. 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.
Book Synopsis Peirce's Logic of Continuity by : Fernando Zalamea
Download or read book Peirce's Logic of Continuity written by Fernando Zalamea and published by . This book was released on 2012 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peirce's logic of continuity is explored from a double perspective: (i) Peirce's original understanding of the continuum, alternative to Cantor's analytical Real line, (ii) Peirce's original construction of a topological logic -- the existential graphs -- alternative to the algebraic presentation of propositional and first-order calculi. Peirce's general architectonics, oriented to back-and-forth hierarchical crossings between the global and the local, is reflected with great care both in the continuum and the existential graphs.
Book Synopsis The Continuity of Peirce's Thought by : Kelly A. Parker
Download or read book The Continuity of Peirce's Thought written by Kelly A. Parker and published by Vanderbilt University Press. This book was released on 1998 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Continuity of Peirce's Thought, Kelly Parker shows how the principle of continuity functions in phenomenology and semeiotic, the two most novel and important of Peirce's philosophical sciences, which mediate between mathematics and metaphysics. Parker argues that Peirce's concept of continuity is the central organizing theme of the entire Peircean philosophical corpus. He explains how Peirce's unique conception of the mathematical continuum shapes the broad sweep of his thought, extending from mathematics to metaphysics and in religion. This new book should appeal to all who seek a fuller, unified understanding of the career and overarching contributions of Peirce, one of the key figures in the American philosophical tradition.
Book Synopsis Visual Reasoning with Diagrams by : Amirouche Moktefi
Download or read book Visual Reasoning with Diagrams written by Amirouche Moktefi and published by Springer Science & Business Media. This book was released on 2013-07-08 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Iconic Logic of Peirce's Graphs by : Sun-Joo Shin
Download or read book The Iconic Logic of Peirce's Graphs written by Sun-Joo Shin and published by MIT Press. This book was released on 2002 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: A case study of multimodal systems and a new interpretation of Charles S. Peirce's theory of reasoning and signs based on an analysis of his system of Existential Graphs. At the dawn of modern logic, Charles S. Peirce invented two types of logical systems, one symbolic and the other graphical. In this book Sun-Joo Shin explores the philosophical roots of the birth of Peirce's Existential Graphs in his theory of representation and logical notation. Shin demonstrates that Peirce is the first philosopher to lay a solid philosophical foundation for multimodal representation systems. Shin analyzes Peirce's well-known, but much-criticized nonsymbolic representation system. She presents a new approach to his graphical system based on her discovery of its unique nature and on a reconstruction of Peirce's theory of representation. By seeking to understand graphical systems on their own terms, she uncovers the reasons why graphical systems, and Existential Graphs in particular, have been underappreciated among logicians. Drawing on perspectives from the philosophy of mind, cognitive science, logic, and computer science, Shin provides evidence for a genuinely interdisciplinary project on multimodal reasoning.
Book Synopsis History and Applications by : Charles S. Peirce
Download or read book History and Applications written by Charles S. Peirce and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-12-16 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: In three comprehensive volumes, Logic of the Future presents a full panorama of Charles S. Peirce’s most important late writings. Among the most influential American thinkers, Peirce took his existential graphs to be a significant contribution to human thought. The manuscripts from 1895–1913, with many of them being published here for the first time, testify to the richness and open-endedness of his theory of logic and its applications. They also invite us to reconsider our ordinary conceptions of reasoning as well as the conventional stories concerning the evolution of modern logic. This first volume of Logic of the Future is on the historical development, theory and application of Peirce’s graphical method and diagrammatic reasoning. It also illustrates the abundant further developments and applications Peirce envisaged existential graphs to have on the analysis of mathematics, language, meaning and mind.
Book Synopsis The Existential Graphs of Charles S. Peirce by : Don D. Roberts
Download or read book The Existential Graphs of Charles S. Peirce written by Don D. Roberts and published by Walter de Gruyter. This book was released on 2009-10 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peirce's contemporaries had the advantage of some popular lectures on the graphs (the Lowell Lectures of 1903, principally), but his graphical publications were few and not easy to understand, as he admitted himself.
Book Synopsis Interdisciplinary Perspectives on Math Cognition by : Marcel Danesi
Download or read book Interdisciplinary Perspectives on Math Cognition written by Marcel Danesi and published by Springer Nature. This book was released on 2019-09-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Philosophy of Mathematics by : Charles S. Peirce
Download or read book Philosophy of Mathematics written by Charles S. Peirce and published by Indiana University Press. This book was released on 2010-08-19 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.
Book Synopsis Peirce on Perception and Reasoning by : Kathleen A. Hull
Download or read book Peirce on Perception and Reasoning written by Kathleen A. Hull and published by Taylor & Francis. This book was released on 2017-03-27 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce by : Carolyn Eisele
Download or read book Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce written by Carolyn Eisele and published by Studies in Philosophy. This book was released on 1979 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce".
Book Synopsis Peircean Imagination by : Kathleen A. Hull
Download or read book Peircean Imagination written by Kathleen A. Hull and published by . This book was released on 1996 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diagrammatology by : Frederik Stjernfelt
Download or read book Diagrammatology written by Frederik Stjernfelt and published by Springer Science & Business Media. This book was released on 2007-06-20 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diagrammatology investigates the role of diagrams for thought and knowledge. Based on the general doctrine of diagrams in Charles Peirce's mature work, Diagrammatology claims diagrams to constitute a centerpiece of epistemology. This book reflects Peirce's work on the issue in Husserl's contemporaneous doctrine of categorical intuition and charts the many unnoticed similarities between Peircean semiotics and early Husserlian phenomenology.
Book Synopsis Visual Thinking in Mathematics by : Marcus Giaquinto
Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto and published by Oxford University Press. This book was released on 2007-07-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pragmatism as a Principle and Method of Right Thinking by : Charles Sanders Peirce
Download or read book Pragmatism as a Principle and Method of Right Thinking written by Charles Sanders Peirce and published by SUNY Press. This book was released on 1997-01-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Synthetic Philosophy of Contemporary Mathematics by : Fernando Zalamea
Download or read book Synthetic Philosophy of Contemporary Mathematics written by Fernando Zalamea and published by National Geographic Books. This book was released on 2012-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
