Space Number And Geometry From Helmholtz To Cassirer

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Space, Number, and Geometry from Helmholtz to Cassirer

Author : Francesca Biagioli
Publisher : Springer
ISBN 13 : 3319317792
Total Pages : 258 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Space, Number, and Geometry from Helmholtz to Cassirer by : Francesca Biagioli

Download or read book Space, Number, and Geometry from Helmholtz to Cassirer written by Francesca Biagioli and published by Springer. This book was released on 2016-08-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

Cassirer

Author : Samantha Matherne
Publisher : Taylor & Francis
ISBN 13 : 135104883X
Total Pages : 222 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Cassirer by : Samantha Matherne

Download or read book Cassirer written by Samantha Matherne and published by Taylor & Francis. This book was released on 2021-04-25 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ernst Cassirer (1874–1945) occupies a unique place in 20th-century philosophy. His view that human beings are not rational but symbolic animals and his famous dispute with Martin Heidegger at Davos in 1929 are compelling alternatives to the deadlock between 'analytic' and 'continental' approaches to philosophy. An astonishing polymath, Cassirer's work pays equal attention to mathematics and natural science but also art, language, myth, religion, technology, and history. However, until now the importance of his work has largely been overlooked. In this outstanding introduction Samantha Matherne examines and assesses the full span of Cassirer’s work. Beginning with an overview of his life and works she covers the following important topics: Cassirer’s neo-Kantian background Philosophy of mathematics and natural science, including Cassirer’s first systematic work, Substance and Function, and subsequent works, like Einstein’s Theory of Relativity The problem of culture and the ground-breaking The Philosophy of Symbolic Forms Cassirer’s ethical and political thought and his diagnosis of fascism in The Myth of the State Cassirer’s influence and legacy. Including chapter summaries, suggestions for further reading, and a glossary of terms, this is an ideal introduction to Cassirer’s thought for anyone coming to his work for the first time. It is essential reading for students in philosophy as well as related disciplines such as intellectual history, art history, politics, and literature.

Cassirer in Contexts

Author : Andrzej Karalus
Publisher : Felix Meiner Verlag
ISBN 13 : 3787343741
Total Pages : 213 pages
Book Rating : 4.7/5 (873 download)

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Book Synopsis Cassirer in Contexts by : Andrzej Karalus

Download or read book Cassirer in Contexts written by Andrzej Karalus and published by Felix Meiner Verlag. This book was released on 2023-12-11 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Der Band »Cassirer in Contexts« ist Bestandteil des wiederauflebenden Interesses an den philosophischen Errungenschaften Ernst Cassirers. Die hier versammelten Aufsätze wurden von Forscherinnen und Forschern aus verschiedenen akademischen Disziplinen verfasst, was sich in der Reichhaltigkeit der behandelten Themen widerspiegelt. Der Sammelband enthält Zusammenfassungen und kritische Diskussionen mehrerer für Cassirers Philosophie wichtiger Konzepte – etwa die Bedeutung des Symbolischen oder des Mythos – sowie Erörterungen hinsichtlich des Einflusses von Cassirers Denken auf die Entwicklung bestimmter philosophischer Teildisziplinen, besonders der Sprachphilosophie und Philosophie der Mathematik. Des Weiteren dient der Band als Beleg für die Aktualität von Cassirers Denken, als Beweis dafür, dass dieses nach wie vor eine Quelle theoretischer und philosophischer Inspiration ist und sein Erklärungspotenzial in einer Vielzahl von Kontexten genutzt werden kann

Weyl and the Problem of Space

Author : Julien Bernard
Publisher : Springer Nature
ISBN 13 : 3030115275
Total Pages : 433 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Weyl and the Problem of Space by : Julien Bernard

Download or read book Weyl and the Problem of Space written by Julien Bernard and published by Springer Nature. This book was released on 2019-10-09 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.

The Prehistory of Mathematical Structuralism

Author : Erich H. Reck
Publisher : Oxford University Press
ISBN 13 : 0190641223
Total Pages : 469 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis The Prehistory of Mathematical Structuralism by : Erich H. Reck

Download or read book The Prehistory of Mathematical Structuralism written by Erich H. Reck and published by Oxford University Press. This book was released on 2020 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

Foundations of Geometric Cognition

Author : Mateusz Hohol
Publisher : Routledge
ISBN 13 : 042950859X
Total Pages : 188 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Foundations of Geometric Cognition by : Mateusz Hohol

Download or read book Foundations of Geometric Cognition written by Mateusz Hohol and published by Routledge. This book was released on 2019-09-12 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.

Philosophers and Einstein's Relativity

Author : Chiara Russo Krauss
Publisher : Springer Nature
ISBN 13 : 3031364988
Total Pages : 207 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Philosophers and Einstein's Relativity by : Chiara Russo Krauss

Download or read book Philosophers and Einstein's Relativity written by Chiara Russo Krauss and published by Springer Nature. This book was released on 2023-09-30 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an up-to-date insight into the early philosophical debate on Einsteinian relativity. The essays explore the reception and interpretation of Einstein’s ideas by some of the most important philosophical schools of the time, such as logical positivism (Reichenbach), neo-Kantianism (Cassirer, Natorp), critical realism (Sellars), and radical empiricism (Mach). The book is aimed at physicists and historians of science researching the epistemological implications of the theory of relativity, as well as to scholars in philosophy interested in understanding how leading philosophical figures of the early twentieth century reacted to the relativistic revolution.

Lumen Naturae

Author : Matilde Marcolli
Publisher : MIT Press
ISBN 13 : 0262358328
Total Pages : 390 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Lumen Naturae by : Matilde Marcolli

Download or read book Lumen Naturae written by Matilde Marcolli and published by MIT Press. This book was released on 2020-05-26 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.

Rediscovering Léon Brunschvicg’s Critical Idealism

Author : Pietro Terzi
Publisher : Bloomsbury Publishing
ISBN 13 : 1350171689
Total Pages : 352 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Rediscovering Léon Brunschvicg’s Critical Idealism by : Pietro Terzi

Download or read book Rediscovering Léon Brunschvicg’s Critical Idealism written by Pietro Terzi and published by Bloomsbury Publishing. This book was released on 2022-01-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Léon Brunschvicg's contribution to philosophical thought in fin-de-siècle France receives full explication in the first English-language study on his work. Arguing that Brunschvicg is crucial to understanding the philosophical schools which took root in 20th-century France, Pietro Terzi locates Brunschvicg alongside his contemporary Henri Bergson, as well as the range of thinkers he taught and influenced, including Lévinas, Merleau-Ponty, de Beauvoir, and Sartre. Brunschvicg's deep engagement with debates concerning spiritualism and rationalism, neo-Kantian philosophy, and the role of mathematics in philosophy made him the perfect supervisor for a whole host of nascent philosophical ideas which were forming in the work of his students. Terzi outlines Brunchvicg's defence of neo-Kantian judgement, historical analysis and the inextricability of the natural and humanist sciences to any rigorous system of philosophy, with wide-ranging implications for contemporary scholarship.

Non-diophantine Arithmetics In Mathematics, Physics And Psychology

Author : Mark Burgin
Publisher : World Scientific
ISBN 13 : 9811214328
Total Pages : 960 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Non-diophantine Arithmetics In Mathematics, Physics And Psychology by : Mark Burgin

Download or read book Non-diophantine Arithmetics In Mathematics, Physics And Psychology written by Mark Burgin and published by World Scientific. This book was released on 2020-11-04 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.

New Perspectives on Neo-Kantianism and the Sciences

Author : Helmut Pulte
Publisher : Taylor & Francis
ISBN 13 : 1040090869
Total Pages : 400 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis New Perspectives on Neo-Kantianism and the Sciences by : Helmut Pulte

Download or read book New Perspectives on Neo-Kantianism and the Sciences written by Helmut Pulte and published by Taylor & Francis. This book was released on 2024-07-05 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers the exchange between the Neo-Kantian tradition in German philosophy and the sciences from the last third of the nineteenth century to the Great war and partly beyond. During this period, various scientific disciplines underwent modernisation processes characterised by an increasing empirical inclination and a decline in the influence of metaphysics, the pluralisation of theories, and the historical and pragmatic revitalisation of scientific claims against philosophy. The various contributions look at the ways in which a certain ‘Kantian orthodoxy’ was influenced by these new developments and whether (and how) itself had some impact on the development of the sciences. The volume is not limited to the 'exact sciences' of mathematics and physics, which are particularly important for the Kantian tradition, but also takes into account less recognised disciplines such as biology, chemistry, technology and psychology. It is complemented by contributions that contrast Neo-Kantianism with other 'scientific philosophies' of the period in question.

Eranos Yearbook 74 - The Age of Immediacy at the Test of Meaning

Author : Eranos Foundation
Publisher : Daimon
ISBN 13 : 3856309993
Total Pages : 551 pages
Book Rating : 4.8/5 (563 download)

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Book Synopsis Eranos Yearbook 74 - The Age of Immediacy at the Test of Meaning by : Eranos Foundation

Download or read book Eranos Yearbook 74 - The Age of Immediacy at the Test of Meaning written by Eranos Foundation and published by Daimon. This book was released on with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 74th volume of the Eranos Yearbooks, The Age of Immediacy at the Test of Meaning, presents to the public the work of the last two years of activities at the Eranos Foundation (2017–2018). The book gathers the lectures presented at the occasion of the 2017 Eranos Conference, Where is the World Going? The Uncertain Future, between Traditional Knowledge and Scientific Thought, the 2018 Eranos Conference, Space for Thinking and Thinking about Space. Reflections on the Relations between the Soul and Places at the Time of the Anthropocene, the 2017 Eranos-Jung Lectures, Who is Afraid of Interiority? A Journey through Literature, Philosophy, and Psychology, the 2018 Eranos-Jung Lectures, Who is Stealing our Time? The Age of Immediacy at the Test of Meaning, and the 2018 Eranos School seminar, The Mechanisms of Heresy: Old and New Forms of Exclusion and Repression. The volume includes essays by Valery Afanassiev, Stephen Aizenstat, Arnaldo Benini, Paul Bishop, Roberto Casati, Adriano Fabris, Franco Ferrari, Giuseppe O. Longo, Jaap Mansfeld, Panos Mantziaras, Grazia Shōgen Marchianò, Massimo Mori, Guy Pelletier, Antonio Prete, Francesca Rigotti, René Roux, Silvano Tagliagambe, Yannis Tsiomis, Amelia Valtolina, Matteo Vegetti, Antonio Vitolo, Samaneh Yasaei, and Chiara Zamboni.

The Best Writing on Mathematics 2019

Author : Mircea Pitici
Publisher : Princeton University Press
ISBN 13 : 0691198357
Total Pages : 288 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Best Writing on Mathematics 2019 by : Mircea Pitici

Download or read book The Best Writing on Mathematics 2019 written by Mircea Pitici and published by Princeton University Press. This book was released on 2019-11-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective

Author : Mark Burgin
Publisher : World Scientific
ISBN 13 : 9811236852
Total Pages : 370 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective by : Mark Burgin

Download or read book Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective written by Mark Burgin and published by World Scientific. This book was released on 2022-04-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.

Multiplicity and Ontology in Deleuze and Badiou

Author : Becky Vartabedian
Publisher : Springer
ISBN 13 : 3319768379
Total Pages : 198 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Multiplicity and Ontology in Deleuze and Badiou by : Becky Vartabedian

Download or read book Multiplicity and Ontology in Deleuze and Badiou written by Becky Vartabedian and published by Springer. This book was released on 2018-03-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book approaches work by Gilles Deleuze and Alain Badiou through their shared commitment to multiplicity, a novel approach to addressing one of the oldest philosophical questions: is being one or many? Becky Vartabedian examines major statements of multiplicity by Deleuze and Badiou to assess the structure of multiplicity as ontological ground or foundation, and the procedures these accounts prescribe for understanding one in relation to multiplicity. Written in a clear, engaging style, Vartabedian introduces readers to Deleuze and Badiou’s key ontological commitments to the mathematical resources underpinning their accounts of multiplicity and one, and situates these as a conversation unfolding amid political and intellectual transformations.

Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle

Author : Paola Cantù
Publisher : Springer Nature
ISBN 13 : 3031421906
Total Pages : 333 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle by : Paola Cantù

Download or read book Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle written by Paola Cantù and published by Springer Nature. This book was released on 2024-01-23 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a collection of chapters on the development of scientific philosophy and symbolic logic in the early twentieth century. The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in the sciences. The scholarship contained provides a rich historical and philosophical understanding of these groups and research areas. Specifically, the contributions focus on a detailed investigation of the relation between structuralism and modern mathematics. In addition, this book provides a closer understanding of the relation between symbolic logic and previous traditions such as syllogistics. This volume also informs the reader on the relation between logic, the history and didactics in the Peano School. This edition appeals to students and researchers working in the history of philosophy and of logic, philosophy of science, as well as to researchers on the Vienna Circle and the Peano School.

Plato's Ghost

Author : Jeremy Gray
Publisher : Princeton University Press
ISBN 13 : 1400829046
Total Pages : 528 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Plato's Ghost by : Jeremy Gray

Download or read book Plato's Ghost written by Jeremy Gray and published by Princeton University Press. This book was released on 2008-09-02 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.