Download or read book Advances in Peircean Mathematics written by Fernando Zalamea and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-11-07 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores Peirce's non standard thoughts on a synthetic continuum, topological logics, existential graphs, and relational semiotics, offering full mathematical developments on these areas. More precisely, the following new advances are offered: (1) two extensions of Peirce's existential graphs, to intuitionistic logics (a new symbol for implication), and other non-classical logics (new actions on nonplanar surfaces); (2) a complete formalization of Peirce's continuum, capturing all Peirce's original demands (genericity, supermultitudeness, reflexivity, modality), thanks to an inverse ordinally iterated sheaf of real lines; (3) an array of subformalizations and proofs of Peirce's pragmaticist maxim, through methods in category theory, HoTT techniques, and modal logics. The book will be relevant to Peirce scholars, mathematicians, and philosophers alike, thanks to thorough assessments of Peirce's mathematical heritage, compact surveys of the literature, and new perspectives offered through formal and modern mathematizations of the topics studied.
Download or read book Advances in Peircean Mathematics written by Fernando Zalamea and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-11-07 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores Peirce's non standard thoughts on a synthetic continuum, topological logics, existential graphs, and relational semiotics, offering full mathematical developments on these areas. More precisely, the following new advances are offered: (1) two extensions of Peirce's existential graphs, to intuitionistic logics (a new symbol for implication), and other non-classical logics (new actions on nonplanar surfaces); (2) a complete formalization of Peirce's continuum, capturing all Peirce's original demands (genericity, supermultitudeness, reflexivity, modality), thanks to an inverse ordinally iterated sheaf of real lines; (3) an array of subformalizations and proofs of Peirce's pragmaticist maxim, through methods in category theory, HoTT techniques, and modal logics. The book will be relevant to Peirce scholars, mathematicians, and philosophers alike, thanks to thorough assessments of Peirce's mathematical heritage, compact surveys of the literature, and new perspectives offered through formal and modern mathematizations of the topics studied.
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.
Download or read book Peirce and Husserl Mutual Insights on Logic Mathematics and Cognition written by Mohammad Shafiei and published by Springer Nature. This book was released on 2019-10-05 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to provide the elements for a systematic exploration of certain fundamental notions of Peirce and Husserl in respect with foundations of science by means of drawing a parallelism between their works. Tackling a largely understudied comparison between these two contemporary philosophers, the authors highlight the significant similarities in some of their fundamental ideas. This volume consists of eleven chapters under four parts. The first part concerns methodologies and main principles of the two philosophers. An introductory chapter outlines central historical and systematical themes arising out of the recent scholarship on Peirce and Husserl. The second part is on logic, its Chapters dedicated to the topics from Peirce’s Existential Graphs and the philosophy of notation to Husserl’s notions of pure logic and transcendental logic. The third part includes contributions on philosophy of mathematics. Chapters in the final part deal with the theory of cognition, consciousness and intentionality. The closing chapter provides an extended glossary of central terms of Peirce’s theory of phaneroscopy, explaining them from the viewpoint of the theory of cognition.
Download or read book Studies in the Logic of Charles Sanders Peirce written by Nathan Houser and published by Indiana University Press. This book was released on 1997-07-22 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents an important contribution to Peirce's work in mathematics and formal logic. An internationally recognized group of scholars explores and extends understandings of Peirce's most advanced work. The stimulating depth and originality of Peirce's thought and the continuing relevance of his ideas are brought out by this major book.
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.
Download or read book Reasoning and the Logic of Things written by Charles Sanders Peirce and published by Harvard University Press. This book was released on 1992 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles Sanders Peirce (1839-1914) was an American philosopher, physicist, mathematician and founder of pragmatism. This book provides readers with philosopher's only known, complete account of his own work. It comprises a series of lectures given in Cambridge, Massachusetts in 1898.
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.
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.
Download or read book Equations from God written by Daniel J. Cohen and published by JHU Press. This book was released on 2007-04-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This illuminating history explores the complex relationship between mathematics, religious belief, and Victorian culture. Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece. In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.
Download or read book Arguing with Numbers written by James Wynn and published by Penn State Press. This book was released on 2021-05-14 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: As discrete fields of inquiry, rhetoric and mathematics have long been considered antithetical to each other. That is, if mathematics explains or describes the phenomena it studies with certainty, persuasion is not needed. This volume calls into question the view that mathematics is free of rhetoric. Through nine studies of the intersections between these two disciplines, Arguing with Numbers shows that mathematics is in fact deeply rhetorical. Using rhetoric as a lens to analyze mathematically based arguments in public policy, political and economic theory, and even literature, the essays in this volume reveal how mathematics influences the values and beliefs with which we assess the world and make decisions and how our worldviews influence the kinds of mathematical instruments we construct and accept. In addition, contributors examine how concepts of rhetoric—such as analogy and visuality—have been employed in mathematical and scientific reasoning, including in the theorems of mathematical physicists and the geometrical diagramming of natural scientists. Challenging academic orthodoxy, these scholars reject a math-equals-truth reduction in favor of a more constructivist theory of mathematics as dynamic, evolving, and powerfully persuasive. By bringing these disparate lines of inquiry into conversation with one another, Arguing with Numbers provides inspiration to students, established scholars, and anyone inside or outside rhetorical studies who might be interested in exploring the intersections between the two disciplines. In addition to the editors, the contributors to this volume are Catherine Chaput, Crystal Broch Colombini, Nathan Crick, Michael Dreher, Jeanne Fahnestock, Andrew C. Jones, Joseph Little, and Edward Schiappa.
Download or read book Hayek in Mind written by Leslie Marsh and published by Emerald Group Publishing. This book was released on 2011-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together for the first time state-of-the-art contributions from neuroscientists and philosophers of mind as well as economists and social theorists, all critically engaging in many aspects of Hayek's philosophical psychology.
Download or read book A Knowledge Representation Practionary written by Michael K. Bergman and published by Springer. This book was released on 2018-12-12 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This major work on knowledge representation is based on the writings of Charles S. Peirce, a logician, scientist, and philosopher of the first rank at the beginning of the 20th century. This book follows Peirce's practical guidelines and universal categories in a structured approach to knowledge representation that captures differences in events, entities, relations, attributes, types, and concepts. Besides the ability to capture meaning and context, the Peircean approach is also well-suited to machine learning and knowledge-based artificial intelligence. Peirce is a founder of pragmatism, the uniquely American philosophy. Knowledge representation is shorthand for how to represent human symbolic information and knowledge to computers to solve complex questions. KR applications range from semantic technologies and knowledge management and machine learning to information integration, data interoperability, and natural language understanding. Knowledge representation is an essential foundation for knowledge-based AI. This book is structured into five parts. The first and last parts are bookends that first set the context and background and conclude with practical applications. The three main parts that are the meat of the approach first address the terminologies and grammar of knowledge representation, then building blocks for KR systems, and then design, build, test, and best practices in putting a system together. Throughout, the book refers to and leverages the open source KBpedia knowledge graph and its public knowledge bases, including Wikipedia and Wikidata. KBpedia is a ready baseline for users to bridge from and expand for their own domain needs and applications. It is built from the ground up to reflect Peircean principles. This book is one of timeless, practical guidelines for how to think about KR and to design knowledge management (KM) systems. The book is grounded bedrock for enterprise information and knowledge managers who are contemplating a new knowledge initiative. This book is an essential addition to theory and practice for KR and semantic technology and AI researchers and practitioners, who will benefit from Peirce's profound understanding of meaning and context.
Download or read book The Oxford Handbook of Charles S Peirce written by Cornelis De Waal and published by Oxford University Press. This book was released on 2024 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Oxford Handbook of Charles S. Peirce brings together 35 essays on the American philosopher and polymath Charles Sanders Peirce (1839-1914) with the aim of showing how his work is still relevant today. The volume takes its cues from Peirce's work in phenomenology and normative philosophy-where the latter includes, besides aesthetics and ethics, also logic. Within the domain of logic, attention is given to his work in formal logic as well as his work in graphical or diagrammatic logic. Ample attention is given also to Peirce's pragmatism and his metaphysics. The volume further includes biographical papers as well as papers on abduction, semiotics, linguistics, physics, biology, religion, history, science, and education"--
Download or read book A History in Sum written by Steve Nadis and published by Harvard University Press. This book was released on 2013-11-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
Download or read book Dictionary Of Modern American Philosophers written by John R. Shook and published by Bloomsbury Publishing. This book was released on 2005-05-15 with total page 2759 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dictionary of Modern American Philosophers includes both academic and non-academic philosophers, and a large number of female and minority thinkers whose work has been neglected. It includes those intellectuals involved in the development of psychology, pedagogy, sociology, anthropology, education, theology, political science, and several other fields, before these disciplines came to be considered distinct from philosophy in the late nineteenth century. Each entry contains a short biography of the writer, an exposition and analysis of his or her doctrines and ideas, a bibliography of writings, and suggestions for further reading. While all the major post-Civil War philosophers are present, the most valuable feature of this dictionary is its coverage of a huge range of less well-known writers, including hundreds of presently obscure thinkers. In many cases, the Dictionary of Modern American Philosophers offers the first scholarly treatment of the life and work of certain writers. This book will be an indispensable reference work for scholars working on almost any aspect of modern American thought.
Download or read book Charles S Peirce s Philosophy of Signs written by Gerard Deledalle and published by Indiana University Press. This book was released on 2001-03-22 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Note: Picture of Peirce available] Charles S. Peirce's Philosophy of Signs Essays in Comparative Semiotics Gérard Deledalle Peirce's semiotics and metaphysics compared to the thought of other leading philosophers. "This is essential reading for anyone who wants to find common ground between the best of American semiotics and better-known European theories. Deledalle has done more than anyone else to introduce Peirce to European audiences, and now he sends Peirce home with some new flare." -- Nathan Houser, Director, Peirce Edition Project Charles S. Peirce's Philosophy of Signs examines Peirce's philosophy and semiotic thought from a European perspective, comparing the American's unique views with a wide variety of work by thinkers from the ancients to moderns. Parts I and II deal with the philosophical paradigms which are at the root of Peirce's new theory of signs, pragmatic and social. The main concepts analyzed are those of "sign" and "semiosis" and their respective trichotomies; formally in the case of "sign," in time in the case of semiosis. Part III is devoted to comparing Peirce's theory of semiotics as a form of logic to the work of other philosophers, including Bertrand Russell, Wittgenstein, Frege, Philodemus, Lady Welby, Saussure, Morris, Jakobson, and Marshall McLuhan. Part IV compares Peirce's "scientific metaphysics" with European metaphysics. Gérard Deledalle holds the Doctorate in Philosophy from the Sorbonne. A research scholar at Columbia University and Attaché at the Centre National de la Recherche Scientifique, Paris, he has also been Professor of Philosophy and Head of the Philosophy Department of the universities of Tunis, Perpignan, and Libreville. In 1990 he received the Herbert W. Schneider Award "for distinguished contributions to the understanding and development of American philosophy. In 2001, he was appointed vice-president of the Charles S. Peirce Society. Contents Introduction -- Peirce Compared: Directions for Use Part I -- Semeiotic as Philosophy Peirce's New Philosophical Paradigms Peirce's Philosophy of Semeiotic Peirce's First Pragmatic Papers (1877-1878) The Postscriptum of 1893 Part II -- Semeiotic as Semiotics Sign: Semiosis and Representamen -- Semiosis and Time Sign: The Concept and Its Use -- Reading as Translation Part III -- Comparative Semiotics Semiotics and Logic: A Reply to Jerzy Pelc Semeiotic and Greek Logic: Peirce and Philodemus Semeiotic and Significs: Peirce and Lady Welby Semeiotic and Semiology: Peirce and Saussure Semeiotic and Semiotics: Peirce and Morris Semeiotic and Linguistics: Peirce and Jakobson Semeiotic and Communication: Peirce and McLuhan Semeiotic and Epistemology: Peirce, Frege, and Wittgenstein Part IV -- Comparative Metaphysics Gnoseology -- Perceiving and Knowing: Peirce, Wittgenstein, and Gestalttheorie Ontology -- Transcendentals "of" or "without" Being: Peirce versus Aristotle and Thomas Aquinas Cosmology -- Chaos and Chance within Order and Continuity: Peirce between Plato and Darwin Theology -- The Reality of God: Peirce's Triune God and the Church's Trinity Conclusion -- Peirce: A Lateral View
